A lllQb 3^5=134

PUBLICATIONS

L

NBSIR 81-2235

1 980 Annua? Report: Technical

Contributions to the Development

of Incipient Fault Detection/

Location Instrumentation

W. E. Anderson and J. D. Ramboz

Electrosystems Division

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

Janua'y 1 981

issued March 1 981

c- 100

. U56

81-2235

1981

i c. 2 .

red Ov: :e of Electric Energy Systems

artntmer.t of Energy

NBSIR 81-2235

• * •

national bueeau

07 STANDABBS

UfitAHT

APR 1 5 1981

nt>i oct - (jVc

1980 ANNUAL REPORT: TECHNICAL

CONTRIBUTIONS TO THE DEVELOPMENT

OF INCIPIENT FAULT DETECTION/

Ouoo

LOCATION INSTRUMENTATION

W. E. Anderson and J. D. Ramboz

Electrosystems Division

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

January 1981

Issued March 1 381

Sponsored by:

Office of Electric Energy Systems

Department of Energy

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director
•
TABLE OF CONTENTS

Summary i Abstract i i i

I. Introduction 1

II. Technical Progress 3

11. 1 Measurement System 3

11. 2 Experimental Results 7

11. 3 Software Development 39

III. Conclusion 46

IV. References 47

Append ixA 49

Append ixB 59

AppendixC 68

Append ixD 76

Appendix E 84

1

Summary

The objective of this NBS program is to identify and, insofar as practical,

remove technical barriers to the development of instrumentation for use in

detecting and locating incipient faults in underground power transmission

systems.

Underground transmission of electrical energy has economic a"d environmental

advantages compared to overhead transmission. A major concern, however, is

reliability. Failures are more costly to locate and repair.

The Department of Energy has a program to develop instrumentation for

the detection and location of incipient faults (the condition within a cable

n which insulation degradation is occurring at a significantly higher than

normal rate which, if not corrected, will cause the cable to fail prematurely)

If this program is successful, cables about to fail can be repaired during

scheduled outages minimizing perturbation to the transmission system.

Three contracts were awarded by DoE to develop such instrumentation.

Besides monitoring the technical progress under these contracts, NBS has

provided technical support where needed. Technical barriers include lack

of knowledge of (1) the physical, chemical, and electromagnetic behavior of

cable insulation immediately preceding breakdown; (2) the manner in which

characteristic information concerning this behavior is propagated through the

power system; and (3) appropriate methods of coupling detection systems to

operating transmission cables.

A measurement system has been developed at MBS to enable studies of

the rf properties of cables, and of the spectral content of discharges at

incipient fault sites, and to perform time and frequency domain refl ectometry

and other related measurements.
Preliminary measurements were aimed at determining the sensitivity of

cable sounding techniques (frequency or time domain) in detecting impedance

changes in the cable. Changes of the order of a few parts per million (ppm) were

detectable in some cases. A sharp needle was inserted into the cable dielectric

and voltage applied. After several breakdowns the resulting breakdown channels

were not detectable. The high frequency signals necessary to interact with

small damage sites were apparently not reaching the breakdown region. Substantia'

effort was applied to improving the coupling between the TDR (Time Domain

Reflectometry) unit and the cable under test. While this improved matters,

the intrinsic attenuation in the dielectric was shown to rule out sounding

approaches in the cable selected for these measurements. Such techniques

might still be useful in other types of cables and for fault location in general.

Future measurements will characterize the rf properties of underground

transmission cables. Extensive software has been developed to permit these

measurements in the time domain and analysis in the frequency domain.
Abstract

Technical barriers exist in the development of instrumentation to detect

and locate incipient faults in underground transmission cables. Knowledge

is required of the physical, chemical, and electromagnetic properties of cables

which precede breakdown, of the manner in which characteristic rf signals

propagate in cables, and of appropriate methods of coupling detection systems

to operating transmission cables. A measurement program has been initiated

that will provide data on the rf properties of cables and on the characteristics

of some forms of incipient faults. Preliminary measurements demonstrate the

limitations of frequency- and time-domain-reflectometry techniques

in the detection of incipient faults. Software is presented which permits

the Fourier transform of step-like waveforms.

I. Introduction

The objective of this NBS program is to identify and, insofar as

practical, remove technical barriers to the development of instrumentation

for use in detecting and locating incipient faults in underground power

transmission systems.

In many situations underground power transmission cables have economic

(and environmental) advantages over overhead transmission lines resulting

in an increase in underground installations. Underground transmission does

have a major disadvantage in the area of reliability. Faults can be extremely

difficult to locate accurately and repair with the results that either long

unscheduled outages or extensive redundant cables are necessary.

To alleviate this problem, the Department of Energy has a program area

entitled "Research and 'Development of Fault Detection/Location Techniques

and/or Equipment for Underground Power Transmission Cable Systems." The

output of this program is expected to be instrumentation and techniques for the

detection and location of incipient faults in different types of underground

cables; viz. pipe-type (high or medium pressure oil or gas impregnated),

extruded solid dielectric, compressed gas, and possibly cryogenic. An

"incipient fault" is defined to be the condition within a cable system in

which local insulation degradation is occurring at a significantly higher

than normal rate which, if not corrected, will cause the cable system to

fail prematurely. A reliable incipient fault detector/locator would allow

the defective area to be repaired during a scheduled outage, minimizing the

perturbation to the transmission system.
- 2

-

The Department of Energy in the summer of 1978 awarded contracts

to Purdue University, SRI International, and Westinghouse Corporation to

develop (or determine the feasibility of) instrumentation for the detection/

location of incipient faults. The School of Electrical Engineering, Purdue

University proposed to develop instrumentation that would correlate, using

variable time delay, the noise signal received at both ends of the cable

emanating from partial discharges at incipient fault sites. The Remote

Measurements Laboratory of SRI International proposed instrumentation

based on swept-frequency reflectometry. A two-frequency mixing (resulting

from the nonlinear incipient fault region) approach was proposed by the

Electromagnetics Sciences Laboratory of SRI International. The Chemical

Sciences Division of the Westinghouse R&D Center proposed to do a feasibility

study on the use of acoustic waveguides for sensing incipient faults. As

their work evolved this also included acousto-optic techniques using fiber optics.

The MBS contribution to this program, besides monitoring the technical

progress of the three contractors for DoE, was to provide technical support

to the research, development, and testing of incipient fault detection/location

instrumentation. In general, the MBS research program was directed towards

providing knowledge of the physical, chemical, and electromagnetic behavior

which immediately precede breakdown of cables, of the manner in which

characteristic information concerning these events is propagated through

the power system, and of appropriate methods of coupling detection systems to

operating transmission cables.
-3-

II. Technical Progress

II. 1 Measurement System

During this year a measurement system has been developed at NBS to

enable studies of the rf properties of cables and of the spectral content of

discharges at incipient fault sites, to perform time- and frequency-domain

reflectometry and to conduct other related measurements. Time-domainreflectometry (TDR) measurements were performed on cables with induced

defects to determine the sensitivity of TDR techniques for incipient fault

detection. Software was developed that will permit the determination of

the velocity and attenuation of rf signals in cables as a function of

frequency (or equivalently the transfer function) in the time domain.

Figure 1 shows a block diagram of the measurement system for generating

signals, capturing signals, and providing signal analysis capabilities in

both the time and frequency domains J The heart of the system is the

Tektronix^ 4051 intelligent terminal with its peripherals. The intelligent

terminal is connected to both the RS-232 and general purpose interface bus

(GPIB). This provided direct communication between other system components

shown. Also through the modem the terminal can communicate with other

intelligent sources such as the NBS Univac^ 1108 computer or with a

minicomputer at relatively high data transfer rates. The terminal outputs

can go to the Univac^ 1108, via the RS-232 bus, the printer via the RS-232

bus, the plotter via the GPIB bus, or to a hard copy unit. Directly attached

to this system is the floppy disc file manager system capable of storing

approximately 1900 kilobytes of information for direct access. Both data

files and programs can be accessed rapidly. The ROM (read-only-memory)
- 4 -

fU 4-

o

u

a

CJ

Sr3o

INCIPIENT

FAULT

PROGRAM

EQUIPMENT
-5-

expander provides eight slots for specially designed and programmed "ROM

packs" for editing, matrix functions, binary conversions and loading, special

signal processing routines, etc. This adds a quick utility to the system

without using memory overhead or requiring additional programming time.

Having 32 kilobytes of memory, the 4051 system possesses substantial "stand

alone" analysis and processing power. Large jobs are more efficiently

managed by batch processing by the Univac^ 1108 or other large system. A

Tektronix^ 4054 intelligent terminal is also available which is an order

of magnitude faster than the 4051.

The Norland^ 2001 A digital oscilloscope is a digitizing oscilloscope with

sample times as short as 2 ps/point for a 10-bit word to 1 ys/point for an

8-bit word. It can digitize simultaneously up to 4 input channels each of

1024 points, 2 simultaneous channels of 2048 points each, or 1 large continuous

array of 4096 points. It has signal processing intelligence that can do,

among other things, FFT (fast Fourier transform) and correlations with single

keystroke commands. Programs and data can be stored and retrieved from its

floppy disc system. It currently communicates with the remaining system

over the RS-232 bus but can be adapted to use the GPIB structure through an

interface.

The Tektronix^ 7704A oscilloscope coupled with the Tektronix 1 P7001

Prograrroner forms a versatile digital processing oscilloscope (DP0) which

can accept spectrum analyzer plug-ins, time-domain reflectometer plug-ins

as well as numerous Tektronix^ series 7000 plug-ins. Using on-hand spectrum

analyzers, capability exists for spectral analysis over a frequency range
- 6 -

from 20 Hz to 1.8 GHz. Because the DPO is interfaced onto the GPIB structure,

the digitized output from any of the plug-ins can be "captured" and processed

by the intelligent terminal. The digitized waveform consist of 512 10-bit

words. A high-speed-average option is included which permits up to 4096

different waveform samples to be averaged before transmission to the

intelligent terminal. In principle these 4096 waveforms could be transmitted

sequentially to the terminal which could do the averaging, but because the

transfer time is relatively long, the latter method is not normally

practical

The Tektronix^ 7912AD is a very high speed state-of-the-art digitizer

capable of digitizing rates up to 1 GHz. Fast transients can be sampled

every nanosecond for an array of 512 points and with a resolution of 9-bits.

Using a special direct access plug-in, rise-times as fast as 350 ps can be

digitized. Data can be output over the GPIB to the intelligent terminal.

The time-domain reflectometry equipment consists of the Tektronix^ 7S12

plug-in and associated sampling, pulse generator, and trigger recognizer heads.

Used for TDR, the 7S12 can measure reflection coefficients, p, from

-3 -'3 2 x 10 /division to 500 x 10 "/division. (When p = ±1 , there is total

reflection, when p

= 0, there is no reflection). Used as a general-purpose

sampler, repetitive waveforms up to 18 GHz can be displayed. This TDR/sampler

can be used as a plug-in in the DPO permitting digitizing and transmitting

of waveforms to the intelligent terminal.

Three spectrum analyzers are available. Two of them (Tektronix^ 7L5 and

7L13) can be used in the DPO. The 7L5 has a frequency range of 20 Hz to
-7-

5 MHz and the 7L13 has a 1 kHz to 1.8 GHz range. A third spectrum analyzer

(Tektronix^ 5L4N) is available for low frequency measurements (20 Hz to 100 kHz).

Besides the above-described instrumentation the measurement system

consists of various pulse generators, counters, and sweep-frequency oscillators

most of which can communicate with the intelligent terminal over the GPIB.

II .2 Experimental Results

Time-domain-reflectometry measurements were made on cable samples

containing known defects in order to determine the limitations of TDR methods

for incipient fault detection. The TDR unit was used as a plug-in in the

digital processing oscilloscope permitting communication with the intelligent

terminal. Software (see Appendix A) was written to process this data. The

software permits automatic acquisition of waveforms, high-speed averaging,

proper scaling, plotting, and filtering. Portions of the waveforms can

even be enlarged for more detailed plots.

A series of TDR measurements was performed on a short length of distribution

cable. The cable studied was a 6.2 m long, 2 cm diameter, 15-kV, extrudedpolyethelene distribution cable with semiconducting screen layers. The cable

had three skid wires helically wound around the outer surface of the dielectric.

Preliminary measurements indicated that the cable could not be treated as a

coaxial cable with the skid wires serving as the return conductor. The

calculated characteristic impedance of a coaxial cable, of the same dimensions

is about 40 ohms. The measured impedance varied between 50 and 75 ohms. The

reduced capacitance. between the skid wires (as opposed to a solid coaxial

sheath) and the center conductor results in a higher characteristic impedance,

Zg, since

Z Q

= kTTC . ( 1 )
- 8

-

Another indication of the non-coaxial cable behavior was the unstable

TDR results obtained on measurements of the coiled cable. The skid

wires did not provide adequate shielding between adjacent loops of

the cable. In order to overcome these problems an improved outer conductor

was needed and a copper braid sheath was used. With the improved coaxial -like

behavior, the characteristic impedance was measured to be about 37 ohms --

near the predicted value of 40 ohms.

In a TDR measurement a pulse with a fast risetime is sent down a cable

and is reflected back by variations in the cable impedance. The output of

a TDR measurement is the reflection coefficient, p. A positive reflection

referenced from the peak of the incident pulse indicates the impedance is

greater than the TDR output impedance. The reflection coefficient varies

from -1 to 1.. The reflection coefficient is related to the load impedance

(R^) by the equation

r

l = Z 0

(l + p)/(l - p) . (2)

This relation with Z

Q

equal to 50 ohms is used in the following discussion

in order to permit the approximate calculation of the impedance along the

cable length from the TDR response.

Figure 2 shows the measured impedance (average over 50 runs) along

the entire cable length. The response over the first 17 ns shows an impedance

of 50 ohms. This represents the impedance of the connector and RG-58/U cable

from the TDR output to the distribution cable input. The response from about

17 ns to 80 ns shows the impedance of the distribution cable. Since the cable
UINE

IMPEDANCE,

FULL

LENGTH

CI5

kV

CABLED

SWHO '30NV03dWI

FIGURE

2.

TDR

resDonse

of

full

cable

length.
- 10 -

was unterminated, the impedance rapidly increases at the cable end. The

times shown are times for the signal to reach a point and return. Therefore,

the time for the TDR signal to propagate the length of the cable is actually

about 31.5 ns. Assuming a dielectric constant of 2.26, the length of the

cable can be calculated to be (3 x 10® m/s)(31.5 x 10 ^s)//2.26 or 6.3 meters,

close to the actual length of 6.2 meters.

The circled region of Fig. 2 is the point of interest for the following

discussion. It represents a small segment of the cable located about 1.9 meters

from the input end of the cable. Figure 3 shows the impedance (average over

200 runs) of a 0.5 m length (2.5 ns) of the cable centered about this

point. The impedance is seen to vary by about 0.1 ohm along this distance.

A mass of 120 grams (1.2 newton force) had been placed on the cable at

this location. Figure 4 shows the measured impedance (average over 200

runs) with and without this force applied (lower and upper trace, respectively).

Apparently application of the force produces a net decrease in the separation

of the outer and inner conductors, a localized capacitance increase, and a

consequent (Eq. 1) localized decrease in impedance.

The difference between the two traces is shown in Fig. 5. The difference

has been scaled by a factor of 10 to show the sensitivity available. The

circled region in Fig. 5 has been further amplified (Fig. 6) in order to

demonstrate the ultimate meaningful sensitivity of this particular set of

measurements. The impedance variation over this 10 cm length is seen to be

about 3 x 10~ 3

ohm. Impedance variations less than 2 x 10"^ ohm (5 ppm) can

be resolved. With increased sampling frequency and improved experimental

techniques an ultimate TDR resolution of 1 ppm or better in such impedance

measurements may be expected.
IMPEDANCE,

EXPANDED

SCALE

<0.2

OHMS

F.S.)

- 11 -

SWHO "3CNVC3dWI

Figure

3.

TDR

response

of

0.5

m

length

cable

segment.
37,75

T T T T T

CO o LO

CO co U) lO rco CO CO co SWHO "30NVa3dWI

FIGURE

4

TOR

response

with

and

without

external

force

(lower

and

upper

trace).
IMPEDANCE,

DIFFERENCE

CO.

02

OHM

SPAN}

C\J <o OJ 00

CO — — Q <s

• GO CO G? GO

• • • • Q CO CO GO

SWHO '33NVC3dWI

Figure

5.

Impedance

difference

from

Fig.
IMPEDANCE

DIFFERENCE

C0.004

OHM

SPAN)

-14-

10

Q

CM

"f

<s

CO

o

Q

CO

CM

a

Q

00

S’

C3

00

CD

(O

<s

<1c

iLl z: o

CM

S>

<S

GJ

SWHO '33NV<J3dUr

FIGURE

6.

TDR

response

of

10

cm

segment

showing

ultimate

resolution.
-15-

This series of measurements suggests that if the dielectric constant

changes by a part per million over a few millimeters length, the TDR technique

should resolve it.

The cable dielectric was purposely altered in order to see if such

changes were indeed detectable. A hole was drilled through the cable sheath

and dielectric to the center conductor. The resulting hole was 2.3 mm in

diameter and 4.6 mm deep. The TDR response of the cable with the empty

hole was obtained and then the hole was filled with either isopropyl alcohol

(2-propanol) or water. Figures 7 and 8 show the impedance change resulting

from filling the hole with water and alcohol respectively. In Fig. 9

the TDR response of a portion of the cable with the empty hole (upper-trace)

alcohol-filled hole (middl e- trace) , and water-filled hole is shown. The

length of cable shown in' Figs. 7-9 is (5 x 10'^s)(3 x 10

8

m/s)//2. 26 or

3

about 1 meter. The volume of the dielectric in this cable is about 240 cm

per meter of length. The volume of the hole drilled through the dielectric

3

is about 0.020 cm . The resulting defect represents a change in the dielectric

volume in a length of 1 meter of 80 ppm. The dielectric properties of the

hole are a function of the fluid it contains. Water has a static dielectric

constant of about 80 and 2-propanol, 18. This is consistent with the trend

shown in Fig. 9. One difficulty with this experiment is that the purity of

the liquids is questionable within this hole drilled in the dielectric.

Particularly of concern is the resistivity of the fluid under these conditions.

This series of measurements seems to imply that TDR techniques would

be effective in detecting at least one type of incipient fault. In extruded
<uo

c:5

roCM

fOcnc

<+- ra2

-Q CL

ra •a •*-> <u3 -M

ra •«- u 2

a> u

C7! • r— c 1-

H3 +J sz U

u CJ

1 OJ CJ u 'r* c •a

ra T3 O)

aj r— cljd £ rau

c:

rjo
0,089

DIA

2-PROPANOL

a

lREE

17-

FIGURE

8.

Impedance

change

caused

by

filling

cable

dielectric

with

alcohol.
EXPANDED

LINE

IMPEDANCE

18 -

FIGURE

9.

TDR

response

of

air-filled

(upper

trace),

alcohol

-fi 1

led

(middle

trace),

and

water-filled

(lower

trace)

2.3

mm

diameter

hole

in

cable

dielectric.
-19-

polyethylene cables partial discharge activity promotes the growth of hollow

channels in the dielectric. These channels branch out forming a tree-like

structure. Cables in service for several years have been found to contain

3

many of these "trees". If these "trees" extend from the inner to outer

conductor, breakdown does occur. The inner walls of the "trees" are

conductive^ suggesting from the above experiment that TDR techniaues could

detect them.

There is a further difficulty with this series of measurements. It

appears in Fig. 9 that the length of the disturbed area is 2 nanoseconds

or about 0.4 meter long. The actual hole diameter is only 2.3 mm. The water and

alcohol either must be diffusing a considerable distance outside the

constraints of the hole, probably along the stranded wires that constitute

the inner conductor, or the high-frequency components of the TDR signal are

being attenuated so much that spatial resolution is hampered.

Further experiments were next initiated to determine if "trees" or

localized sites damaged by partial discharges would be discernible by

time-domain reflectometry techniques. Measurements were performed on the

same cable described above. A fine steel sewing needle 1.3 mm in diameter

was carefully inserted into the dielectric of the cable to within about one

millimeter of the center conductor. (The outer semiconducting layer was

previously removed from the vicinity of the needle site). Negative pulses

having a duration of 500 ps were applied between the needle and the center

conductor. At first, 10 pulses of 500 volts amplitude were applied and the

TDR response obtained. Then the voltage was increased in 500 volt increments

and more data were obtained. The maximum voltage applied (the limit of the

power supply) was 2500 volts. The field at the tip of the needle under these
- 20 -

conditions is estimated to be of order 500 kV/mm. That is certainly high

enough to cause damage to the dielectric. However, after applying these

impulses even at the maximum voltage level, no change was seen in the TDR

response.

While the voltage levels appeared to be high enough to cause some

damage, the lack of change in the TDR response suggested that the dielectric

v/as not being signif icantly altered. In order to test that hypothesis, dc

voltage was applied to the needle. At 7 kV a breakdown was observed. The

TDR response showed no change. After an additional 10 breakdowns another

TDR response was taken. The results are shown in Fig. 10. The portion of

cable over which the impedence is being measured is (3 x 10^ cm/s) x

(2 x 10" s/2)//2. 26 or about 20 centimeters long. The reflection coefficient

is negative because of the cable's impedance of 37 ohms compared to the

output impedance of the TDR unit of 50 ohms. The data shown in Fig. 10

are the average of 512 runs. Any change in the TDR response is lost in the

noise.

The result was initially surprising. Previous work had shown this

technique to be quite sensitive. We assumed that the partially conducting

surfaces of the breakdown channels or "trees" would be readily discernible using

TDR. To further test the system, a hole 1.5 mm in diameter was drilled in

the cable dielectric to the center conductor. The hole was then filled

with graphite (pencil lead). The results are shown in Fig. 11. The TDR

technique can readily detect the change in impedance. The graphite effectively

is forming a resistive shunt between the outer and inner conductors. This is

similar to the case of a "tree" extending across the dielectric.
- 21 -

FIGURE 1

TDR RKPONSC Or CABLE DCfORS DR CAK DOWN

a.ae+aca t .ae-aeo 2 .ae-ee©

TIMECSEC5

ArTCR l I BREAKDOWNS

a. ae-^eaa i . ae-aaa

T2MCCSEC3

2 . ae-aeo

OirrTRENCE

a.aE-t-aaa i.ae-aea s.oe-aaa

TINE CSEC3

. Change in TOR response of cable resulting from 11 breakdowns at

7 kV dc. Breakdown channel is estimated. to be 1 mm long and is

undetectable in the noise.
- 22 -

FIGURE

TDR RESPONSE Or CABLE WITH DRIL.i_ED MOLE

TIMECSEC3

HOLE rXl_i_ED WITH GRAPHITE

o.aEtaQa t . ee-aaa a.aE-eaa

TXNECSECO

DlffERENCE

o.aE+eaa I .os-aaa 2,oE-oaa

TINE CSEC5

11. Change in TDR response of cable resulting from filling a drilled

hole in the cable with graphite. The hole is 1.5 mm in diameter

and 4 mm deep.
-23-

The negative results shown in Fig. 10 prompted a study to determine

whether they arise from a fundamental limitation of the TDR or sweptfrequency approach. In order for a reflection (or interaction) to occur

from a region of inhomogeniety within a dielectric, the minimum size of

that region must be the same order of magnitude as the wavelength of the

incident signal (e.g., an electromagnetic signal with a minimum wavelength

component of one meter would have little interaction with a defect one

millimeter in length).

In the case of our TDR measurements, the incident pulse has a risetime

of less than 30 picoseconds implying a maximum frequency component of the

order of 30 GHz or a wavelength in the dielectric of about 6 mm. The estimated

length of the breakdown channel in Fig. 10 is 1 mm. Assuming the high

frequency components actually get to the damage site, detection should indeed be

possible.

In order to determine if the higher frequency components were being

severely attenuated making detection of small sites impossible, further

measurements were made. Figure 12 shows the TDR response of a shorted RG-58/U

cable and the power cable shorted at the damage site previously studied. Whereas

the effect of the short in the RG-58/U cable is evident over a time interval

of the order of 100 ps (length of 1 cm), the effect of the short in the power

cable extends over 2 ns (20 cm in length). The difficulty in resolving the

location of the short in the power cable demonstrates that high frequency

attenuation is occurring. Without these high frequency components, resolution

of small damage sites is impossible.

Two solutions to this problem have been considered: (1) better impedance

matching to increase the high frequency content within the power cable; and
REFLECTION

COEFFICIENT

REFLECTION

COEFFICIENT

-24-

TDR RESPONSE OF SHORTED RG 58 CABLE

a.aE^eaa i.aE-oia 2.0E-013

TIMECSECO

TDR RESPONSE OF SHORTED POWER CABLE

0.0E+003 2.5E-00O 5.0E-00O

TIHECSEC3 '

FIGURE 12. TDR response of RG-58/U cable and power terminated by zero impedance.
-25-

(2) after careful measurements, compensation for the attenuation in software.

As seen in Fig. 12 and discussed above, there is a serious attenuation of the

high frequency components of the step input. A large fraction of this "loss'1

may be the result of the impedance mismatch between the 50 ohm TDR system

and the 37 ohm high voltage cable. Additionally at or near the connection

to the cable other mismatches are evident from the reflections present in

that region. These results suggested the need for an impedance matching

device to improve coupling of the high frequency components into the high

voltage cable.

Impedance transforming baluns were considered, but the idea discarded

since pulse risetimes of 25 ns or shorter are being considered. An investigation

into other impedance matching schemes led to the use of tapered sections

of coaxial transmission tines to achieve an impedance transformation. A

design having minimal reflections over a wide bandwidth employing a gradual

exponential taper was examined. A linear conical tapered line was also

investigated. Although the exponential taper is theoretically better, the

difference is so little so as to make the difficult exponential taper not

5 worth the extra machine time and costs. This is especially true if the taper

is long and gradual in comparison to the wavelength of the lowest frequency of

interest. The tapered section will act as a high pass filter so long as the

phase constant does not contain an imaginary term. At lower frequencies the

phase constant is complex and the signal is attenuated. Practically,

impedance changes of 2 to 1 can be made if the tapered section is one wavelength

long or longer. A good impedance match will result for higher frequencies.
-26-

Figure 13 shows details of the tapered line. The outer conductor

of the line is made from a thick-walled section of brass tubing

which clamps over the braided shield of the high voltage cable.

In the right end of the "tube", a machined adaptor is inserted. This

couples to a General Radio^ type 874-BP58A flanged panel connector. This

type of connector is known to have a constant 50-ohm impedance throughout

its length and to provide for a good electrical connection with low series

and shunt losses. The stepped portion of the center conductor shov/n in

Fig. 13 fits inside the adaptor. The dimensions have been selected to

maintain a 50-ohm characteristic impedance throughout its entire length.

The susceptances at each "step" should be low enough even at the highest

frequencies to provide a constant 50-ohm match in this region of the line.

The center conductor of the line is tapered. The tapered length is

30.18 cm which is one wavelength at a frequency of 993 MHz. It would be

desirable to have a longer line so the lower cutoff frequency would be less,

but this becomes mechanically difficult and cumbersome.

The left end of the tapered center conductor fits directly over the

center conductor of the high voltage cable. Because of possible end effects

of the tapered section and the abrupt discontinuity of the Dolyethylene

dielectric at the end of the cable, impedance mismatch reflections can be

expected. The influence of these remaining reflections has been experimentally

determined.
50-OHM

COAXIAL

CONNECTOR

-

-27-

OVER

OUTSIDE

OF

CABLE
-28-

The performance of the transition section is shown in Figs. 14 to 17.

Figure 14 shows the TDR response at the end of the 50-ohm coaxial cable and at

the beginning of the 37-ohm distribution cable without the transition section.

The output of the TDR analyzer was adapted to BNC-type coaxial connectors.

A one meter length of RG-58/U cable was connected to a GR^ type 874 BNC-to-GR

adaptor. The six outer strands of the distribution cable center conductor

were removed leaving only one strand at the center. The female portion of

the BNC-to-GR adaptor was placed over the single remaining center strand of

the cable's inner conductor. The braided sheath of the cable was then dressed

over the adaptor and the whole assemblage taped into place. Using this

arrangement, two major impedance mismatches occurred. The first was due

to the short length of small diameter single-strand center conductor. This

length was about 9 mm and caused the impedance to increase to about 90 ohms,

the first major peak in Fig. 14. The second mismatch is due to the lower

characteristic impedance of the distribution cable. (The small variations

of impedance seen in the 37-ohm portion of the cable are caused principally

by the unevenness of the braided sheath).

Figure 15 shows a cross-sectional view of the 50-ohm end of the

transition. (The GR874BP connector is not shown on the left end). The

steps of the center conductor were designed to coincide with the steps of

the outer conductor. However, an error on the design drawing of 0.2 cm shifted

the two larger diameters on the right towards the left end resulting in a

lack of coincidence between the inner and outer conductors. This was discovered

after the piece was fabricated and assembled and the TDR response obtained.
-29-

gure 14. TDR response of RG-58/U cable connection onto 37-ohm distribution

cable.
Oin*- • o iz. tu 7- 3 9. O CO o V- — CV o o

O)

s_

13cn

50-ohm

end

of

the

transition

section

as

per

first

design

speci f

ications.
ocn :z

h- 1* O O

tij _u >1 OJ Q J— a o

nr:

Figure

16.

50

ohm

end

of

the

transition

section

per

second

design.
-32-

The TDR response is keyed to the stepped center conductor as shown

in Fig. 15. (Vertical sensitivity is about 5 ohms per division). Several

problems were evident upon examination of this response. First the impedance

variations were greater than expected and second, the impedance of the

fourth step was lower than design specifications. From the latter, a

second drawing error was discovered: the inside diameter of the outer

conductor was too small by 0.09 cm.

It was obvious that even though the steps in diameter were each only

0.12 cm, a 3-to 5-ohm impedance change occurred at each step. Because

the impedance decreased in the vicinity of each step, this indicated that

the shunt susceptance at the steps was too great. In order to compensate

for and to reduce this susceptance, each of the steps of the center conductor

piece was shifted to the "right by an amount equal to D/8 where D is the

inside diameter of the outer conductor. Also the inside diameter of the last

step of the outer conductor was increased by 0.09 cm to increase the impedance

in that region of the transition section. The TDR response in Fig. 16 shows

a significant improvement over that of Fig. 15. The impedance does not vary

by more than two ohms.

Figure 17 shows the TDR response for the entire length of the tapered

transition section. At the left is the 50-ohm TDR system impedance; in the

center is the tapered line; and on the right is the 37-ohm high voltage

distribution cable. As can be seen at the right end of the tapered section,

impedance variatiations are apparent. These are caused by the end effects of

the tapered line attaching to the distribution cable center conductor and
Figure 17. TDR response of tapered line transition section.
-34-

imperfections in the shield geometry at and near the beginning of the

distribution cable.

Comparing Figs. 14 and 17 we see that the transition section has

fulfilled its intended purpose -- a smooth impedance transition from the

50-ohm output impedance of the TDR analyzer to the 37-ohm characteristic

impedance of the cable. The next step was to determine if this transition

section permitted significantly more high frequency signal to enter the

cable and, if so, would this enable resolution of incipient faults or

would attenuation within the cable still be a problem.

With the transition section in place the outer and inner conductors

were shorted together at a distance of 61 cm from the cable end (and the

TDR analyzer). The TDR display was averaged 512 times and sent to the

intelligent terminal for 'display. The results are shown in Fig. 18. The

ordinate has not been normalized as on the previous figures (i.e., a

constant has not been added to the reflection coefficient in order to

force it to be zero for the power cable's characteristic impedance of 37 ohms)

The important parameter, reflection coefficient variation, is not affected.

The upper graph is from Fig. 12 and is taken without benefit of the transition

section. The lower graph demonstrates the effect of the transition section.

For the sake of simplicity we will define the decay time as the time it takes

the signal to decrease from 7/8 to 1/8 of the difference of the average

maximum and minimum values. The decay time, thus defined, is 1750 ps without

and 800 ps with the transition section. This means the additional high

frequency components entering the cable with the transition section have

permitted better spatial resolution of the short. The 800 ps decay time

corresponds to a length of 8 cm which is much longer than the shorted hole's
REFLECTION

COEFFICIENT

REFLECTION

COEFFICIENT

- 35 -

0.0E+000 2.5E-000 S.0E-00S

TIME CSECONDSD

SHORTED POWER CABLE., LENGTH 61cm

TIME < SECONDS

!

' figure 18 . jqr response of power cable terminated by zero impedance with and

! without transition section.
-36-

diameter (0.13 cm). Sufficient high frequency content, therefore, is

still not available to resolve this region adequately.

The second factor affecting high frequency propagation is the attenuation

in the cable itself. Figure 19 shows results, taken as before, with the short

located at two different distances from the TDR analyzer. The figure indicates

that the greater the distance of propagation in the cable the greater the

decay time of the TDR response. A short located at 4 cm from the cable end

has a decay time of 340 ps while a short located at 163 cm has a decay time

of 1050 ps. From above we found that a short 61 cm from the cable end has

a decay time of 800 ps. At 4 cm the decay time corresponds to a spatial

resolution of 3.4 cm and at 163 cm to 10.5 cm. These results are troubling

in that they imply that the intrinsic high frequency attenuation in this

type of cable makes the detection at large distances of small-size damage

sites very difficult, if not impossible.

Figure 20 shows this quite clearly. In the previous measurements, we

had not been able to detect a hole drilled through the dielectric 1.3 mm in

diameter. We again attempted this with holes drilled 4 cm from the cable

end and 61 cm from the cable end. At 61 cm the response with the hole

(light trace) and without (heavy trace) are nearly the same, any differences

not being repeatable. At 4 cm, there is a definite difference between the

two traces. New minima and maxima have been introduced with the drilling of

the hole. From these data, it is inferred that, at distances greater than

a few centimeters, the high frequency attenuation has caused this information

to be lost.
REFLECTION

COEFFICIENT

REFLECTION

COEFFICIENT

I -37-

SHORTED POWER CABLE, LENGTH 4cm

TIMECSECONDS3

SHORTED POWER CABLE, LENGTH 163cm

TIHECSECONDSD

.

j Figure 19. TDR response of power caDle terminated by zt>'n impedance; the

location of short is 4 cm and 163 cm from cable end; measurements

made using transition section.
REFLECTION

COEFFICIENT

REFLECTION

COEFFICIENT

TDR RESPONSE OF CABLE AT Aem

TIME CSECCNDSD

TDR RESPONSE OF CABLE AT 61cm

0.0080

0.0000

-0.0080

0 . 0E+000 S . 0E-0 1

TIME CSEC0NDS3

1 . 0E-003

TOP response of power cable (using transition

(lighter) and without (darker) a hole drilled

dielectric. Distance of 1.3 mm diameter hole

is 4 cm (upper) and 61 cm (lower).

section) with

through

from cable end

Figure 20.
-39-

The results indicate that incipient fault detection schemes based on

high frequency sounding may not be practical for plastic-insulated cables

although it is possible that such techniques may be of value for compressed-gas

(spacer failure), superconducting, and other cable types. It is also possible

that our results obtained on a 15 kV extruded polyethylene distribution cable

may not fully apply to higher voltage transmission cables of similar design.

High frequency sounding could still be useful for fault location and, if a

sufficiently large damage site is available, incipient fault location.

1 1. 3 Software Development

In addition to the software presented in Appendix A which was developed

for data transfer between the digital processing oscilloscope and the

intelligent terminal, other software needed to be developed. Experiments

in the coming year will be initiated with the objective of determining the

signal velocity and attenuation in cables at rf frequencies. Initial

measurements will be in the time-domain. Step-like voltage waveforms

will be applied to the cable and the output waveform digitized and

transmitted to the smart terminal. A Fourier transform will then

yield the transfer function in the frequency domain. Problems arise,

however, because instead of a Fourier transform of continuous data we

have a Fourier transform of discretely sampled data or a discrete Fourier

transform (DFT). A DFT of an impulse-like waveform (a waveform which ends

at the same amplitude it begins) is straightforward and a fast algorithm

exists for its solution (FFT).^ Step-like waveforms, however, will produce

a serious truncation error'

7 if they are treated by conventional DFT (and FFT)

techniques.

We have found two different (but related) methods to overcome this problem.

8 The first is the sin x/x expansion presented by Samulon.
-40-

The measured curve is sampled at time intervals, x, such that:

x<l/2f

c . ( 3 )

where f is the highest frequency component present. This restraint is

7 9

necessary to avoid "aliasing" problems ’

. Using a sin x/x expansion the

given time function, F(t), can be expressed

00 A sin f (t-nx)2ir

F(t) = A

'-- f it-nx)2, (4) n=o c

where A

n is the amplitude of the nth sampled point. The Fourier transform

of the nth term of Eq. (4) is given by

.<-> -I

^

A sin[2rrf (t-nx)] e'^^dt

2 Trf c

( t-nx

(5)

or

~ 2tt ?

c J

A^ r sin[2Trf (t-nx)] {cos wt - j sin cot} dt

t-nx

( 6 )

Subsituting t' for t-nx and using

ex /

sin mx cos nx dx

= it for m>n>o (7)
-41-

We obtain

4> n (w) -

2 f

c

( 8 )

or

c (9)

Software based or. Eq. (9) has been written and is incorporated in

Appendix B. However, this is not the most useful form of the sin x/x expansion.

If A

n does not equal zero for some n greater than an arbitrary m, Eq. (9) does

not converge and cannot be used. If A

n does not converge and the summation is

arbitrarily terminated at some point, ripples will occur obscuring the results.

A modified form of Eq. (9) can be used which does not have such limitations.

Let B

n = An

- A

n

_.j and replace the sequence {A

Q

, A-j , A^ ...} by {A

Q

, A-j e~

T//<5

,

. . }. The value of 5 can be made arbitrarily large so as not to affect

our transient unless i is very large or in the frequency domain oo is very small.

Using the relation

n

( 10 )

Eq. (9) becomes
- 42 -

$(u)) En=o

n

( E m=o

B ) e “J nwT “ nT / 5 m' (ID

If we let ne = jnoox + nx/6, we obtain

2f $(uj)

c

00 n E ( E B m

)e'

m

n=o m=o

( 12 )

or equivalently

oo

00 2f Ha) = ( E e‘ ne

) ( E B e'

mE

) n=o m=o( 13 )

~ - n c The series Ee is absolutely convergent if

^ 1 0

-jnarr - naj/5 . ( 14 )

converges. But

e

-jnu)T - nx/6 , = g

-nx/6

( 15 )

and (14) is seen to be a geometric progression, convergent for e~

T/ <1

Using the formula for the sum of an infinite geometric progression:

COE e n=o

= 1/0 - e" e

) ( 16 )
-43-

o r

l e" ne

= 1/(1 - e

‘ T/ 5

e'J “T

) . (17) n=o

The factor e~

T//(5 can be made arbitrarily close to unity yielding

E e" ne

= 1/(1 - e"

ja3T

) . (18) n=o

From Eq. (13), we obtain

. oo Urn) = [l/(2f (1 - e'J “T

)] 2 B

n e'0 TM1

. (19) n=o

Appendix C contains the software utilizing Eg. (19). This program is nood for

waveforms of arbitrary shape and can always be used assuming t £l/2f and that,

for n greater than some m, B

n approaches some constant (not necessarily zero).

The only difficulty with Eg. (19) is that the processing can take several seconds

per frequency point making it impractical for some experiments.

The second method used a modified FFT. As mentioned above a conventional

FFT yields incorrect results due to truncation error. A modified FFT has

recently been presented^ which overcomes this problem.

From Eq. (19) and the definition of B

n we obtain

tU) * [l/(2f

c O - e'jVr

))] z (A - A )e'

jn“ . (20) n=o

We assume the waveform becomes a constant at T = Nr (i.e., A.. = A.

^ for i>N).

It is further assumed that A

Q

is equal to zero (i.e., the dc offset of the

waveform is zero. A . is defined to be zero. Substitutinq v

-I r for v
-44-

(v = co/2n) such that

v = kv = ic(l/T) = k/Nt, k = 1,2, N - 1 < o

Eq. (20) becomes

<±> K

[t/( 1 - e-jK2¥/N )]V (A - a )e

-jm<*T/N

n=o

n n

( 21 )

( 22 )

In Eq. (22), t has been set equal to l/2f satisfying the sampling theorem.

In order to be consistent with FFT conventional formalism the factor x will

be removed from Eq. (22). Separating the sum into two parts, we obtain

= 1/(1 - e~

Jl<2Tr/N

) {V A„ejnK2,T/N

- V A

n

_ ie

-

J

' nK2,r/N

} . (23) n=o n=o

Defining S ,

S

K

Z A e

- jnK2,r/H

, (24)

to be the FFT acting on the data set {

n

} , Eq. (23) becomes

$ - i/(i . e -jx2VN

} {s . N ’ 1 A e-jn<2ir/N

}

, (25)

k k n-1

or

i, = (1 - e-j^^1 )- 1 (S < ' K

e

~ j k2tt/N

N-2

Z 9=0 V

- j J?,k2tt/N

}

(26)
-45-

This is equivalent to

= O - e

and, since * 1,

4- = S + Am ,/(l - e k k N-r

-jk2tt/N

) k = 1 ,

. . . , M - 1 . (28)

This is a very important result in that it permits considerable saving

in computational time. Using an FFT read-only-memory pack our intelligent

terminal can compute for 256 frequency points, in under a minute compared

to over an hour if Eq. (19) were used. Appendix D contains the software

utilizing Eq. (28). Appendix E contains the results of using the sin x/x

approach Eq. (19) and the modified FFT approach Eq. (28) on the same data. The

results are identical.

Both approaches are sensitive to dc offset. Assuming the zero

frequency result is not of interest the waveform should be shifted so as

to make the amplitude zero at time equal to zero. Equivalently, using Eq. (19),

B q can be set to zero in software or using the modified FFT approach replacing

Eq. (28) by

( 29 )
-46-

If the software is modified in such a way both methods are insensitive, as

they should be, to dc offset.

The software development will be invaluable in future measurements.

The sin x/x approach has the advantage of allowing the user to choose the

points to be calculated. The modified FFT approach is considerably faster.

III. Conclusion

A measurement program has been initiated at NBS that will contribute

to the development, testing, and utilization of incipient fault detection/

location instrumentation. The measurement system, centered on an intelligent

terminal, permits the digitizing of transient and continuous waveforms and

subsequent processing.

The system was initially configured in such a way as to permit time-domain

reflectometry studies on -a 15 kV distribution cable. The results were

significant in that they showed that TDR techniques would have very limited

use for detection of incipient faults. The difficulty is that the high

frequency attenuation in the extruded polyethylene insulated distribution cable

prevents the spatial resolution of the anticipated incipient faults.

Measurements in the future will determine the rf properties of high

voltage transmission cables. These results will be important in the design

of incipient-fault intrumentation . These measurements will be made in the

time domain requiring mathematical transformation to the desired frequency

domain. Extensive software has been written and tested using two different

methods
-47-

IV. References

1. Certain commercial equipment, instruments, or materials are identified

in this report in order to adequately specify the experimental procedure.

In no case does such identification imply recommendation or endorsement

by the National Bureau of Standards, nor does it imply that the material

or equipment identified is necessarily the best available for the purpose.

2. The Tektronix General Purpose Interface Bus (GPIB) is compatible with

the Hewlett Packard HP-IB and both are compatible with the IEEE-488-1975

interface specifications.

3. T. P. Lanctoe, J. H. Lawson, W. L. McVey, "Investigation of Insulation

Deterioration in 15' kV and 22 kV Polyethylene Cables Removed from

Service - III," IEEE Power Engineering Society Summer Meeting, Los Angeles, CA,

pp. 759-763 (1978).

4. E. F. Kelley and R. E. Hebner, "The Electric Field Distribution

Associated with Prebreakdown Phenomena in Nitrobenzene," Journal

of Applied Physics (submitted).

5. H. H. Skilling, "Electric Transmission Lines," First Edition,

McGraw-Hill, pp. 353-355 (1951).

6. J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation

of complex Fourier series," Math. Comput. , Vol . 19, pp. 297-301 (1965).
-48-

7. E. Oran Briqham, The Fast Fourier Transform, Englewood Cliffs, NO:

Prentice Hall (1974)

8. H. A. Samulon, "Spectrum Analysis of Transient Response Curves,"

Proc. of I.R.E., Vol . 39, pp. 175-186 (1951).

9. C. Shannon, "Communications in the presence of noise," Proc. I.R.E.

Vol. 37, pp. 10-22 (1949).

10.

J. Waldmeyer, "Fast Fourier transform for step-like functions: the

synethesis of three apparently different methods," IEEE Trans. Inst

Meas. Vol. IM-29, No. 1, pp. 36-39 (1980).
APPENDIX A

This software permits the collection of data from the digital processing

oscilloscope DPO. The data can first be averaged up to 4096 times by the

DPO. The data are plotted on the terminal screen. Portions may be expanded.

The data can be filtered (adjacent points averaged). The data can be

output to a plotter for quality graphics.
1

INXT 2

P5=8 3

GO

TO

9994

4

REM

PROGRAM

“DOE/DPO/UERS

I0N3

U

9-30-80

5

REM

DATA

COLLECT

€

SET

NOKEY

Ci ® X

® <L

£LX

o lu

•*r OLU

r>« <xi

UJ

/'

oX

UJ

to

ON

X

0

CL

1 UJ LU

L3 u

<X <2 <2

-J o C£ QC ON

<r LU UJ UJ <r J—

x C3 x> o o M X <2 <2 -J L3 <2 o Cl

~4 Ou Cs ON

QC X LU UJ *-« OC O UJ UJ UJ o o

QC CL Cl U>

H- tz ® H UJ COON CD ON Q ON ®

GDO>QLU>CSDO>rOH*> ® >© >^on:

Ch-JUJCDH-UJ®-JUJy")h~UJ®X UJ®XUJ®UJLU<5)-ULU

LUO *~>Q UJO JO O v-hQ O'Q (—» O 0C«:20U.20^20Q.2 QXsoxxo«:SOhX H H- H* H* H* (««* **$ Xh Ih Xh XH X H* x H X! OUJUJOUiWQWUJOUJUJOUJ UJ Q UJ UJ & UJ l ^UQSONOS'LU Q UJ UJ fN S>uc*®JL

VJ3® © fU NMMM "•;? UN N CO vNJ N ^
- 51 -

VOro

(VI ro

coOJ

•s CM

k

CD

CM

©

VO

VO

in

CM

m a © VS a © s a vH © CM >— GO © © «v © © s s a © CM •» a o Hk «•. *. © *4 *«. a a a a a CM a © ~ t a a

<_) <*• C- n© •> C»* <o O© -J© -JO A 2 *—» ro ~ ® m» ^-l-J M H-ro OQ. 20 X LU Q. M* 'f-J roxo

o CO 20 0(0 4* * rox Ll 2 CJ «oco*s

* o 2 a a <0 •»h a LLUili. u. * CM • » 0>

h— m • H ••••• A

o>®ro rororo rorom*

-J UJ «-* GL —» © (ft; <1* CM ©© © CO

o-ztin h »-• ^ 'w

ZLUO • HHHIOhHh J aazoz HZZ3 I ZZZCC 3 hHQiXHHCLZHHi^H

KITH- ao

UJUJUIOO-U. aatoo

utzizz ii act 2 ii u zclo.hxq.&.hdi;

I ©

'W* fS- 4-ro ©MO

©

It O DU

min-©

x it ro JZ

-jOb.

Q. <—

© • • • • x o

vororotro® a u. ©

in

n

o •• a 2© »* \ © ZD OHHACQOITliahiZvh HZDIiDH I DZDHZ

Ml O. <0 Ul«n|- 3 h

S£SSs3S«S.S£SSI&e

CD CD CD (9 CD ^0 CD CD CD CD CD CD CD CD CD CD CD ^ roM-invoNwav

<MCMCVJ<MCM<MCMI

mvorwco © CMfO m VO Pw © CTi © -m jvj | I©©©©©©©©

i -m cm p 't in vo n ©

irmronhmr«m390

PRINT

03

:

4W

INPUT

03

:

416

K=UA

L<S*>
-52-

C£

s CO

G£ CO

LU

CO QC

CO Q_

Ui

esc: •» a. *— - x

L3M

Li- C£

Ui

_J *-

<r © x

o 3 IX © v-4 O ex v»

«K DC <2 CO

DC

H* <2 ** UJ ¥ X os 3 o 3 LU

S 1 2 2u UJ ws <2 es X

CO X Q.H O lx -J CL H*

8 ** C ro © <1 CL es X X 4* 1 CD -J UJ -50 ® \ \

CO E V CD CL ~5 1! CM #*s X CM As CO V 3 CM a DC a Del V % © © 9 N 'w' UJ CD X 3 A 3 B UJ UJ UI +*M X **< Vrf' CO UI CO > 44 CM CO oc DC H- H* fr— 1 lO H* in H*

o CO o H © *<?• <x S-H 3 O UJ # X X UJ 3 X Q o UJ *4 X t2» W 3

CL II a. X CD1 ***4I 1 DC 10 3 CO HE II !»-) JC >M 11 UI LL II O

11 <* n H II II II II II II II II II Q UiO^ ex © a Q£ © U» ’X 11 H II II X fr- X X UJIO © 03 lx £3» N H» O L3 eas Cl a. X 0. Ol. *x o UJ a O o N N

CD ee CD CD ©1 CM CO CO CD CM ro \n © 8 CD © © ® vis a uo N © ®in © ®

CM ro ^r in COtt CO CO CO CTj CO CTi CTi •*•4 QhC9 <M ro *r io m U"> N w Q3 ©

-7t vf

1 '*? V 4j» *#* 10 wF* 03 03 o5 © © Co © fa © 03 © CO ©

916

A^WCDi

915

B=M<D1

>

917

Zl^Z

H1H

512

928

FOR

TO

Z1

930

HIM

I4<

!
-53-

UJ

fSJ

in

CD

W

in

cvj

in

in

GO

GO

\ CQ^

~<X

ill I •‘CO ^

CD *30 0

ID *>4 » — CD \ \ 00

•s. © /N \ © inujuj^ —©cm i i <x — OO I »© X Nrf* ^ ©

CD *‘UJ CO OO ^ lL

N

M in CM D CMOicom -s •‘O V o CD © •M *H-<X<X®UIH 2 ® /N © © h- © HUJ •••«•«•«

VO © CM DC CM DC — OLDL3LDO X cr» <2> V-* CM O 03 II OlOMKlO) n <X —• II 2 >-4 X O 0.0 Q.OID —

Z O — II ©DC CM h-rv3KUJ3Oa.C;D0D0DUJ

hCD X

H UJ

fflZ

coin

yf

ON ON

<£© /*S H* ZD ID ro — UJ OUJZ HHH^Qli

II II CM LUO<XCQNCjQC — XUDh- II O II hO*I*-*«HXXXOO — — II O II II II II II || OvUOUUUUDUCLD3hiZ*I*XCU. CCCQHUUJOCICONiOLuUZUO; ® — CMn*IQ®r'0''frin®®®® ©®®®®— —

— ojn ,£in - ®®®®®®®®®®®©

CM CM CM CM N CM CM CM CM CM CM CM

worw — cMr^mvais-®

^^inu^inintninin

cr»cr,cMTnT»OScriCri^^

;

2860

DRAM

eG:X*I/5l.2,C<I>

2070

HEX T

I

2080

HOME

0G:X*D/51.2,A

2690

PRINT

0GS-JJ

HUM*

i
- 54 -

w

CD

1 X <x “a V

XJ CO s— w CQ ^*s —“a CD <i m s 32 1 -H- i -ax <£ LO <X

33“» 'w* »-« XXI CO © CO -a LaJ CD » © ' XT~S <r © <r 033 H i «

~a>~< in ogeuin

:D~a \ \ —

»~»33 © »*s ©

eg 1U • X© » CM \ 33 ”3 © + ^ © tf5 \ y~v }-• XI i <r<x i m © /•v CON <x “a*-* cawvacn © % LU — 4* -a «« «S « « 9, « t • ©

+ CD 0X0^ a c /*\ a © 1 O —O') >w* “0SU.C3UJ OUJOUJO i sn

til \. O E O 33”^r0 i ^ i 'tf i ^r If) m • * 9 • w XIX uj xi ego » O « O 1 © • © r ms xzo UlJ •«1U. V QvCivG * © <4

UJ * LiJ = US 330 1 a 33 X CO 1 CO i CO 1 © $#• X = <rx3« XI a <r X3UJ © O 33UJ CD s © * CD s 1 X 1 ~:n XI ~3ico © ^ 5*3~aui re <x <x <x BS •s ucy rau 33L3 eg 33'-' ^ CO ^3X3”lh» ** U-HOH13 O o o X \ 33X X3X \ -auj eg cn i*iu. 33 y*> xnxuox **

>—« /% Ti>—

23 m/n-IZ <1^10^*^ fc—« a~i S—t -fH *“< in ro » ro

CO UJ ~Hif) “1C0LU”3>-*X-^^X]“^ 1! V CO . CO «co ©a

ZD + ”SZD<2~33 + “53H*UJCQi*3UJ 33^© 3©X® © »o «**> % Os •.a O * s x~o*3“a uco t 1 1 ® © a

0 • V 0 0 0 0 O •« •» '»/* a • » a <— » 5*333“* i UJ » a UJ * a UJ * 9 CO 1 »

h- 1 »

i U-.UJL3 » « L3 L3 • • U3 U3 © idCsi ~3<S: » « UJ • » U »« LD rO » » W3 » * L3 -> » U3

f+> 13 C& Qj O Qj ®J LJ QJ QJ i * a a UJ®U3C&U3®CgU?i&i'*’‘*»Ji&) 1.3 ^

QU QJ <2J —*1x1 5/5© © © <§J H Qy ©

h- H* t— H- H— h* }~ li H® H* H* £0 h* H~ ® 1— X H~ H* xwxxiuxxujxxu3Lyx:xx<£yjxuJ3:uiX!"-iyx yj x ui x *— ^ m I> w h !*n v-4 fy ^ tv < aoaaoaaoQ5aLoaQt:Q£:u.oQ5ac!;o&:oQQ:oo^o^

a.aca.a.2:a.CLKa.a.^x:a.cLCL0Hi;a.z;eL3;cLUCQuu.s:Q.i:ai

©®®®®®CD®®©in®®®CDin®®®®®©tn®CUin®®®® ®—«cwfo^ ,ny3N©cftCPi©^cgMi^‘^n®N©ff'tO^®®cs*"«cyro ,it‘ <\JC^CVJOifWC^fvjCJCNJ<NJC4CsjCJ<N3<VJW<VJfVIC4CV|i\l\NiNfvJf^C^Csl04CV|vN

235B

PRINT

0G;

~H#0,

2360

IF

^0.5^>1

THEN

2380

2370

NEXT

H

2375

HOH£

06:

2388

IF

P5*i

THEN

2540
- 55 -

CVICM x

\ X L&i /N M

®<T o

+ H

GDffl U. VV Li.

•a LU a O

LULU —

03

1 ! > X OO XX M

VV/ ISO QC

COCO 33»—

LU mm XI- -« H*

<r<x HO + ® m -J ®

-N--W- xlu <viro •k •—

ion COOOOSJ \ in 04 U. ® ®

<7N XJli. ® a /% 04 \ •• ®n • • • •XLU •• C** ^ /M 't U. ®®IOXttlO Ul XX LU^3Q.a o ^ X

I 1 0J • » CVI .J LU + *2 X «* 00 XLU

LULU ID O O* *~XlO u '-'LUX®

% # •• r^rwrw|x.ro«-« iuh- «xv mH* •• a ..CO Ul l-XI-'*

®..(J u un o XI- ®

^^d/OU® ® 04* X COLO®—*® ® 04 a cn*-« «n X®® H— —

® II »-» ®

Q£ hhhhOHHX II O l-HO hhW II *nq

LUX LUUJ XXXXHXShUUH-LUX ZhZZhUI H n a s si

ouiooaaaa i^xza.a.o. 0. mCL I! L3 ^mQCmXhm X ' 0. <X oasx^u.aooixoacijuttcttoaosxitu.u.oii U Ql »-< CL h« a. U X CL Ul CL X Ol a. U X Ou *-t ® «-! *-« UO)

in®®iovo®tn®®®®anio®®®®®®in®

QOCT<®®®--i-«<-< 04 ®—•P4 C\IC\irO*<finLON 03 a5 <7> nn^^^^^^^uoinuouiininininuoiniomo

<VJO^CVICVjrvj<VICV4<VJCVJ<\IOJC\4C4CslCVJ?VJCv4CVIc0cviCVl?Vl

® in n ® 10 ®

'-’t -* -»« 04 04 M ®®m®®®304 0

IF

8/2* I

MT

(S/2)

THEM

3050

3845

GO

TO

3090

3058

8*8*1

3088

IF

8*>Z-D

THEM

3280

-57-

&co

Ul

K3

<r

QL

Hi

z>

cm <r e~ X 4* t-

= tsj 0. xH«4v4 s u r> EEC <*• z o «- — CO *

/nWs s H <2> As

M. U. 0. Z AS

(Ms CD Cx • Ul v \ \ z t KJL3H > CQ LkJ 1— *-* OZ* ——<X • LU CL *

JM _ s a at 4* mm* Z 04 \ r» oc z • — L3 X as Srf* f*’ ® A c** UJ Z <x z X -<03> jj CD *—

z * + AS Elld <x a zo H* ro l\i as >-* vai liiiut- CJC0 4* LU DC A A | L3UJ« -J-J<x ^ - •% » CO as Z ® 04 CM^* o*x OH*«fflHHO 0^« M* z •• •« H-rM \ \ - K04 tt -j-TiPoinu.u.ao>z« + • t rororoco HN(/) •> ON® V^* As

v« © s OZ^vQ, '*'T<h ® & s** m H-I O w«* 0X0

f- H- QCCL «0(MU_ * -j hhtt It w* I 2f-l-Ohh<llHhUJ^ LUI-HH® H- HH-K04 04ZXC0C0 »-« tt w22H ZZ» OiaUHZQWZIDD Z 3Z3 + + 4 •—1 2> Z> VO VjO A 4» » »-•*-< It 0. II II H>-*UJ<XO*-'«-«CLII*-«»-«a.>-»tLCiNtt It It II ^QCO:OOCaC4*X¥H**Z£l.UJ-jaCOCZV$ It OCZOCZ H It VO CD CO U*> It « Ovv ra.Q.UQ.a.UHCLflLLu30Qi;ua.CLMDca.Ha.MAN0N5QidNu.30

®®®®®-«<M®<\J'<fCOtn®®rO!r>®in®®~«CMrO*tnVpNCO®tf?COO»®®lrt

tn^is-oo®®®»Hr-'r'r,'^, tf?^S5^PNNaatcriCM^2!2)2>2joS®CDCD®'^cvic4 ©©a®®®®®®®®®®® ®®®®®®®®®®®®'*4 *>4*">'*a4^l*«l**,*4 v*M'*wiowinHu^inKin
- 58 -

(M®4V

X

e

OJ

CQ

s

s sC—

-J-J

/% v.

*-• Ch

t>» /N | fM

A

CM

^4

in

X

A

CM

*-4 in

in X CJ a i a X LU o A CM o

CM CJ CO CO X a-* © H* **

TJ- B 3 CO £ ro V W Nw1 N fM ® CT) * l CM CJ CJ r- \ ® CM

ro n ro CO x \ + -H O ®

c& Q* © CO CO V a «- X © X X A ** CM m • + V V LD V © n <*N II -I <2 <*% CM X

© a H H- H 1 CO LU CO **) % © X X © l « © & X

h- i i X X X <r a CO a H H* V i- \y N 3 © © X a (35 fSJ HS-J >—

>*»4 cu x- CL II Ol X II a « Cfe£ © CD X ® a U n CO it X ©

uu ii H ii II QC Qi X ii il <4 ll 11 rv. ii ii O (I II UJ 1! ii II il ii © UJ N it X a 3 N © a. a. P“>t X X H- X X h- <£ a u. <£ © X UJ X U. a X U5 ££ LL © o

<35 in 'J3 N CO © ® O ® ® ® ® © in « ® © © © © ® M m © m © © n VO

ro n ro ro n 4* in M3 N CO Ch © rH ro 4* in M3 (S. Ch Ch CM & 9-* *«< »-4 v*< CM fM CM CM <M CM ?u CM CM CM VM CM ro ro

IT) m in in in m in in in m in in \n in in n in in m n m m in m bn m

9997

U*0

9998

ON

SRQ

THEN

250

9999

SET

KEY

IB0&&

GO

TO

9998
APPENDIX B

This software, using the sin x/x approach described in the text, Eq.

can be used for a discrete Fourier transform of time-doinain results.

( 9 ),

It is

essential that the last digitized point of the waveform equal zero or

truncation errors will result.
REN

PROGRAM

"

0DOE/DPO/ARR

AYDFT/ANM

INF

"

9-30-60

POLL

N,

M;

DELETE

U,W

REN

DPO

DATA

COLLECT

- 60 -

i

I

1

XUJ

UJ -J

HI CD M > t J— UJ LU CD 03

ZD ZZ X

o *—

HH X

CL H* h— o • Vs X X y~* 03

J— o o • v> >- Uu CL QC CD * <x H- t—

UJ CL o x a ID -J ©

QC _J 03 X m -J * » S \ © a. — a © © © ©

-J O I— o* x 2 a o UJ © © *—

• Vs © X UJ X CD UJ QC © * 2 S K- CO x uj k- ZD *—* Cxi X K- © <1 CO X o t— h- ©O © JOD

o 3 CC _J >—

CL UJ UJ tZ3 h- ro OK ©

C3 ZD h- © X LU -J -J 03 X 03 X

o CO a x L3 X *-»« ©03 O a a a O. © CO © O CD * © © © u. © u. © ©CL » « CO KTM

Ca 3— CD CDCC © X cox©>© © © fO PS fO

CD CD © CD V— CD © LU ro © © © UJ in LU© cr> « © in ©© ©

CD h- ro oc ^OCJhnK- ro k- oc co a. Cl CD 'w' II v-* o ro cc _J U- t- CL © © ©H-h-X*-* r** H- K» -J © OlOQOZOQOCOH OhOUD^S t- XXX

CD Cl o h~ h- K* h- © h~ hOO)HMXCiX V»H h~ f— 2Z X 2C X X X II X ©C©CL*-<QUJ©©© n LU OLJOLJOLU ououjoujcgouoa.uiiiiaii ©©© O UJ O CC lX DC LD © ID QC X © L3 © L3 © X L3 © L3

1-3 C£ L3 © v\i co © © © © in

f*0 © N. ©**< af* UDCOiTi'!f, m©a3©<\)rO©©©©'^\)rOrf*'*

CO 03 O') -H o-t OJ OJ 0>J oj oj cu ^ nr in in m •H •H vN v»«4
- 61 -

X

• • UJ

UJT

o

u.o

X

<r

2:

O'*

~T* ot—

*—

o

X

3 s in O

CM D>

ffl m A »< oh eg *s s X «-« WMVTf 1—

V Vs lS) CO

r B S A SB /*N vH 4* »•«, v-*og^ »>n> UJ

c** X C** «-* *>H— X ixiwn H*

CD -J-J X +*ro-j_j Vs Vs Vs^

CL xo ro . xo « 1 « ro 3 3 CM -X CL O OCO<*~* 1 CMOCO* ©x a 1 CM vs v. v^ eg uj UJ

t 3 * 0 </5 1> /“s v S « CO /*n » s* —

. . UL H 4.10

» 1 ll^I TV «. U

H* roro

• ••••• rororox© ® \ roro

• TM mtf ^ y f ro to to e® \

yk y\ ^ TTM M<lrth UJ *m

C*> © CM <2/ d* 01* v* h dj C#J <3L> w CO 'w v-* © XX QC-* * <X —• UJ _J *=> _J s*’ U '-' -H ® « 1 30 II “—inH- V« L“ “ I- <X tO LU CO —< * U0 fO ® ® O CL CM H> 1— XX 1 ZZDIiJD DHZ2 DDOWOX^®UJ M3^UO©-J-JO)3XUJXX*

*-• Q. 3 *-< »—« CL _J II I! X'-M-'O. II a. II CL II X II X CJ II II II II-J-IXUI L3>-*CL

ax 11 a a x uj 11 11 a a x ^ 11 v* 11 *-« 11 cMox<Mn 3-tn<xo:*-*~u.®CL'x OLM3Q.CL*HQ3r^3Q.fi.MXrH-EXh-XIUJ3^DDOU3^»-‘a.iL«

©®®®®®in®®®®®®®®®®®®-«(Mmn®v’M’**tO®VsQ®'t‘mU>>^Cev

in <0 n © © ® ® ^ eg ro in md n. co © ® <-« cm cm eg cm cm ro n n r*:* in in in 10 uo in -« ^ ^ (\j oj c\j cm cm eg cvi CM cm cm cvj ro ro n ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro
QLO

5QCO

o * UJ • QCd

*—

1 i

, i CO K*

LUO

OUJ

CO UJ

CO

o

UJ

* H- 2:0

OUJ

•-•x

Y— Ui

CO

CO

ox 2 * XX CL O

z> x 0 0 —

0 *-* >—« X X

O MHf- X

= \ V— 1—* —

OCO

x 0 ©CO CO MO

»-«x 000 oca. OxOL OHO.

\ X x 1

W - 1— X UJ X *-»v 3 X U. U- clo

: UJ U. UJ UJ *—* *—

i> oc UJXX CO CL

^ Ok X _J UJ

x = 0 OUJ cD UJ

UJ OCLX X

2 •

UJ 0 KUK UJ X

L3 —r 0 IM X

••X >—

ac CL DC X CL

u*-« X Cl. UJU-O O

Xf- X 1— >—1 u_ OIL

V-I |— 0 X X X

\— LjJ CL u. *—• \ s \

1— CO *—

ON J CL CL & UJ X X 0. v v UJn

<X CO • u. CO Cvj © X

o5 CO —

UJ © © CTt <T» X ©

CD - UJ X X \ O X U) ©

«• CO UJ CO X ©XXO rr « ©CO \ X DC QC »X X * Cl CL X 3 Q CD s CL X X in UJ UJ X X X X e X > > xxxxx ~rxx

= OUJ CD XUJ H- \ <r *-UJ UJ **XX 1U UJ

o_ x ©0 « so: © oc » CL CL L*) * ® CL

CO \ 1— © .*•>-< UJ > © (X © XI XS » © XIX

CvJ © H~ ^ X X X © © Ti- xi JNyi XCL

Ci « C7i CO © b a cl CO » ro a 1 1 i >4) S 3 s 3 in 11 u XQC U 11 1 ) OJ CO X X J— X cl© cox in in © X X X X M* V* O l— X V—1 UJWXUD* XXX X UJ DZ^in^yinDUiimuoi-^Liiii

UJ 1 ' XCO II mhhQHIIIJOIh I) || || II II 0)Thhmm 11 x* *~* »** *~« © © x u. 0 0 ^ 0: cl cl z uj uj © a cl oj cvj ro x u~> 0 0 ct oc ac o ll Ll 0 co 0 cl cl oc ncxiMiuccc.cKU'jaaa.LjQ.XDDDDUza.ia.a.HMOxxa.a.a.

®®im-®^OJ*'r©©©©©(\IU")©©CVJTl"CD©©©©CV|Tf©®v\jTr©v\J'Tr©©

' 0 r- r- © © co © co © © vr © © © ~h cm cm oj cm cvj ro rt in in in u> n n cr* cr> cn ©

roronrororoforofo^''ttfcovficovj)vjocD^ovjov^vavovjflivj5 vj5 ujvfiv*vj&vfiiVJv^NN
-63-

= Ck

T

• ©

I- o Ul 8 M —

• H“ X a

»—

© © CM a O UJ > 3C

CL. © a a »•* H o a X H- n 3

L3 *—» © o Cl a *—

X * \

CL 30

ST \ »-»X

ZD 3 > Ck CL

ST \ © \ •—

tu

DC M

<r © © a v*

z CL h- •O

CL ©

ui © i—

x« X X

f- ~P © a •• O L3

CL *—

2C ••X O X © Uh

Ll 3 © Ih © 1 M|-

V O 311-

Ll h- a © 3IJ-0D

N. • «* 31© 31©

CM ® * UJ 3IX 31© • © U>© ~J3 31 31 OD

4*P^|S- 31© 3<d 3I©X

x O “J© 3»3 ”10^©

CL ~xx © 31 \ 3»©0D 3 MD©© X m 31 31©

1— >xx 31 CL 3»> 31

LlI h~ o ID 31 UJ 31© 3a© k

0L ® © A/\l- X Dh 3»0C 3* X CL »Xt a ® in© 1 31

31 CL © 3a>-©

CM CLLl® xxio~ © 31 LU

^ 31© 31-3

c —

CL » * ID- vvXw X » > © a a ro a a a ID LlI ll II CM 1— »— II w —

sy 1 CM in

f— \-Vt¥KD~* I2h2 \ f— P— 1— —* >• H> P- ® CM in© HHh ziuzcioi-in WH 4* h- to LUI2D> + UI IIN^UIMDUI XXX II CD II II OCWX II Imho. || 3Tmm |l II || II © X '-**—' *—* aOOLLO^D !l ID © O II UJ^OQ^QdZM II O 0C 0C CM 13 ^ ID O O CL CL <L

I o.rQ.MHUxwxxu.(nz«sa.£LN>*asii{L»»»Duiiiii.ii.

j ®©®®CM-«r®CM <<r©®©®®CM*«f©®©®CM'<r®®CM*-©®®®®® ojojn^^^L0cocacarw©<Tl ®®®^s\iiv)'<rM,,<rJnMDM5©uiis.o?c*®^

r* pw pw r>. r* r* p* n r*. r* p*. is. is. co © © © © © ® © co © © © © © co © <o cr>

915

X2=8

928

END

999

REH

ARRAY

SQUASH

SUBRGUTME
- 64 -

o-CO

a

• •

LU

1ZO2

•> o

04 <x

ro UJ X

•s CL • CD LU

r* 4 US >— CD LU CC © -J DC

a Cl CL

•tr 3 |

2 <r

•w UJ O - 04 2 LU O o “1 t~» _J UJ

US *— >—» U X

~~IQL CD 2 ZD U. 2 CO

-no <Z *--« o —4 X

~J\- h- CLUJ X ® “30 CL 2 CL <1 QJ TT -*<r lu O L3 a; LU co *> 1U. H- CL Zf- CL ® ”1 CO (—4 -r-4 *—« —t CM ^

—»3Z L3 Cs QC UJ 2 ». •> 3^ *. lO 04 2 <X LU r> _J OJ ^ >D

>—-i LU h- WK •—* ~s»- in O CL2 H* X Ll ® •> *» x

-mo <x LU •A 0K CLIXX - - ~1Z) o ^ LU LU a — H-3LU QL ~ 04 LO IQ~

) cc CL «». X A «i I • CL <2« * OU)

3LU <T> as C3 CC a ~oj nnc XX *> ”30: CT) z> <x CA —« ^ UJ h- ~a a^nroK <X *"< H

* = <X \0 || *~« 2 -~1 00 Cl B « U. U0 ®y <24 a 0X2 CL UJ OJ ^ »-« + II GJ <Z <E ItLJv -J» • 30 hHhhH^ OC4 A H H* H- h" H3Hhh X Oi

22Z>UJU0 © G>OJf~>~ LU IIDDLJ ZD 2 2 JJ03 m^clj ii z ii a ii ax ii OEUhhQ. 2 JSICLHDSJJiLiJ

QCQC2UJCri*-«OJOOJ^lJul‘r-4XliJ®Os:QCX»“'UJ*~*XXQt:XUJ<C<I»-*^

Q_Q_^CiOc2iC3U-CH®-2H-LUQc:a.CL0->-HU.C!Cl^^CuL]CiCOO3Z>'

I

®^OJ'*UOCOCDin®®©®iN®CDUO®CD©®04'<J'VD®C»®CCCBi®CS>UO

® © © © ® © ® © © © © © cd © in m in uo uo uo uo in uo uo uo uo ® cd © © co

*“* *-i *H H WHHWH *"4 H H 9H v*S «“1 H M vH V\1 OsJ 04 04 04

'iI

*1

2846

CALL

"DISP"

*

2858

AXIS

(Q2-i>/10,Ul

2655

HOHE

2856

PRIHT
- 65 -

* a N d X LU •* •»* h”

a a © a a -J A »•> • • • 3 ©~ /*N O V © N N J X ©X X © X o UJ © a DC ©2 -T* UJ

-r-» —* tH • • CD ©

\ >-* Nrf* /*N 73

N •a LL>- > X _J X

••O u X *—

LU

a X za T HLU LU X »- ©3 3 *—

CD © •—

CJ a V h- a LU LU X •a > DC DC 3 y X UlL LL o f-N O u 2 M CL LU

LUX y 1— 3 O 30 O 3 v^* > •a C3 *-* »—

_J O CJ LU

LU J— 1— O »s X CD

DC© © cn >-s LU ©

U 1 _J LU DC 3 X 3 3 DC Nrf’ Q>* CL

coo O & LU a _j • DC -H «a cn © © CJ A lx. X « >-o CJ LU DC O LU

_j DC 'w- a *—

CD

©O' DC lx. ro © 3

LU X LU LU CM •» -*© —

ZCi ©3 CL Ci © A -J t *—« •> O a. LU ro DC DC 3 2

*-CJ X-J 3 DC • «K C_) CM3 - 3 ro —

X X • -J©© eoq: X LU CM LU O') rotu ©M3X

•a » •-•X ©X LU CM X /A LUn« *“• CL 4* Xh ro h- CD ® f“ o ro «a ri

xh- - — © © © © ro 2 X « % % ~Ll_ X «L XOC © X DC ©DC ©CM a Nw' KhX % VD

CM O «. X /*s LU ©LULU ©LU ® U. X DC > LU L3 LU CJ CM

C3 > LU *-«LU f— © H- ®\Uv •> CD LU X LU •a »Z k x l-XX ©H-X ©X ®AXh /A CD r- DC CM

MI-LU!If)® LUCTi® LUCMOIOH-X *4 © LL ro UJ hh« CM u.^©« U. *-t a U. -*L_ >—

2 a H Li* ©

3 LU LU Hv * * 1 * N

OQQh b— h- 0} \ H’ — h-intnH*l— CTih-H-CMOWV*^ X — — h* h“

ci ujujjzia^zzDu.LLi 3 u. 23 Lu.aa+ t x o^zzz GZEJU Jhm II II 1—4 1—I cl. II HQ. II t-»D. II DC X DC *-* X »-i *-»>-*©

z»-«Luuj©©acoc*H-<acQcxinii.acx<yiocxcMtiim.ii*-*itai:LJXocacDcit

UJ3Qc:CiQ_OQ-11.3U.Q-CL*-^U.»-'Q-'—'U.CL'-tLL.QL'-tH-MXCiCt'a.iXOCl.CLCL-J

®~<©iM©<M <»riD©-«CMrO’'rin'sOM-U303 ©*HCMTMn®LOr'-COON®®®®in©tn

M3 tfN © © ^ ^ ^ ^ <M OJ CM CM CM CM CM © CO CO Oi <£ CT> CD CT\ © © © © © ~* CM M* L*> ID CD ©©©©©©©©©©©©©©©©© © © © © © ® ^4 <*«4 >»i cm cm ro ro ro ro ro ro ro ro ro ro ro ro ro n ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro to ro

P9

s

Pl* 2

tT

1
66-

Ju! O

t*

-v in

BH I ** +

Hr

QC % t*. _J O h-

'w- Ol O

Ok oc -J

«s LU 0.

7\ ^ _J UJ Z -*• CD »—« S-^ f\l O

CM cdq_ u_ '“» 0_ >-* —

U_ Q. ** CO h-

-W- '“'V f\J -r-» /*N ** <x\n

a. C/W _J H Z> CO

LlJ 4 | \ \ Z ^ «*

1

i 2: aO\2IC?< s uj m m

CO Z ^ v\J '-r VN ». CTl •S V^- V «- X -J CD CT> CD h~ CD *< ON X Ol-v ® Oi CD a CD <104 If) U_ CO >-* + <x z ® • % La CD »-* 3010 OJ-H'W CO Z CO ua CD U. * 1 -J O CJ -H 4— K"i h~ GD UJ cvj L3 CD O m - #**s "S.

I

O -H ^ CO 0.0 CD X *S US o> 04 «J «H O >-t I-a2 ^ \ <M U3 z w H* v

in X 'W /-. Q£ CD-H \ ro UJ \ Hh'H U*>0 O

lo- a co cd ”0 —• CL) “0 L3 0s: » *> 04 »>

ll HO l Z CO-^CNJ U_~) 2UJ03 CO »'* II »-« *•*< n X II 1! X> —• II II II H- II h- H- H-OCU2 0.0 K-4 + + H- + /-n ^ X “3 X > X 12 21 Ci UJ CO UJ r£H- a®®Q:2:XC02DX^-J-J-J^ X^O.*-*Q*-«»--;eLJXLD»-«:>C£<EX Oil H O ^ ^ II IILUII'wwvwaU.UJC^OQCX^UJUJ^^OCXOOOiiUJ ilwdlx>wdz jxa,aa.^za,ua,Uii.cs^22!i^iLOZ

®f^^©®aD®®t»CD©aD®CDCDCDiN^, vxJODCDO©U'*)®®CDCOCSC»®

r^rwh.oocri®inLorwCO<ri®*-«<vjPO*r'«f, '*, ’trinvoNi»i»ch®«-u'vm'*tf>

^^^^^ojojOsiojo>jcvj(v)ror)nrororoMnr,5PMr*)N^ ,t',,t'^ ,^',t

n n n n n n n ro n n ro ro n n ro n n ro n ro h ro n ro ^ n ro ro ro ro

3466

HOME

3479

END

4800

REH

BEGIH

OF

MAGNITUDE

PLOT

4605

PAGE
- 67 -

—«o

*-*Q- =~QlO

2U. O

•-•00

t-H- •vt <X • ft OX

o*-* • • _J_J X

UJ

*— lii H

<X o —

ZD *—

= h- a:

i »« X a ro_j % UJ Ed UJ H* —

cq UJ

= <z -J

o CL

CO x a h- X

•-»® UJ o

X X UJ o lii H-»_J

zd a UJ»“—

ID JZ xxu. X

<E <X *—• o •—

3 h-qcuj —

X IO x a. *—

Eh VO ® OO <1 CL —'ZDX - -h clxh* 3

•-•X ID \ —» <>—• «M LlJ Vf L3I-QC 3 UJ

roxx ®33 X •—* UJ •k —1

x <r h- c\j - - »-» 4*

»X HtfOO h— 3 X X u. CD

x a: -3-* o *-« UJ •k •s •uiuj^in >n ^ QelUJ* H-3 UJ ft = ~T Q, •*. « • » • CL UJ XhZ •> <X« roro<x X

<E UJrOJ--* 1 X X ujH-ni ror>»- —

It > 3d _J -k(M * a.* u. & ® • K O 3 • It (H*H <x u.

f— — H» a. O HH hhhh — H* H* JZZDZQCnU 31— UJ UJ ZZ3CZZZ -1 j«MQ.uzM3a<ixrDur <iao:ZHHXooauoz<iu

aa.Q.^z>3<iz:ijLCiZXUja-c^

•—• i—• Q.

QCQCX

q- a.

CD X

h cl

X»— ••-•O—J*^f— Cs

*-« CL CL QL X <2 CL UJ X

a. Q- a. a. uj o a. oc uj

<Vjn®®®®®®®®®®®®**®U*)®in®in®tn®®®Cr\

® ® ® ® ® ® ® ® ® ® — »* ffi ® ® ® ® ® ® ® ® ® ® ® ®

’fTTirT'fWW’f^V^O'vO^vO'vOVOVjDVjsva^iJ.inScri
- 68 -

APPENDIX C

This software using a modified sin x/x approach, Eq. (19), results in a

discrete Fourier transform of time-domain data. The final point of

the digitized waveform need not equal zero but the waveform is required to

approach some constant value.
- 69 -

lj

!

i

CD

<T © I CD CM

I (M © I ro©

I ©XO

CD

= a: a ZUi UJ

mo -J \ x o

h-<e > a u_ UJ UJ o ©

o>- X X

>-CD —

X a <E h- *— o N. atz 3 3 L—

©

OCO O o H> ««( <r i-» > QC 0c o a \ © <X H- UJ

occ a o u o -J ©

QlLU a -j x X -J * 03 i— <x a. *-• oca ca<x<x \ o o - CJ» a a a LULU UJ O UJ <x *—

19^ ««c OCJ -J <r x uj o uj CSC © a a a a QZ -1 H- © X UJ (- 3 QC X H- H

(Si UJ o <X <X © X O H- <xo ® 303© a OC CJ o 3 <r *-> -j *-» uj UJ oh- © Oh'IQ.

UJ o 3 h- a. x -i -J © X©XO

EU.

<T 1 • <rLb

O © CS 3 L3 »-M H4

1m

® O 4^0 i i i i 2

O >® ®QC®XCOX® ©

Uh» w

© ®oro-< wwrmr'S

(30 ML «hO © ®<x®j— ® ®ujrD sLumui ® ©a ® m — O* OlOkl © ©

o cd ai-nQt.HOfvjHnHrohi'Q.^a. to w n OCX ~ o**oroa j u. *- u. « <x ®H-H-X^H H-H-)-*-V- 0.0X3 0. -J ©OO.OOOOOOOHOHOUI3XX H22I23 (-000.0 (- 1— (•*(- H- HJUJ H- H-X X X X X X X <x oocac^o zejji X UJOUJOUJOUJOUJOUJOUJ o cl Ul4.au. SS!£'g££ ujLuoujujoiuottuaaJttUttUttu&ott u

OC 0C CL O OC U QC L3 OjrOU5N®^*lf>©©®® CVJ ro ©CVj'T©®®©©^^®© ®©®®*HvNrD^ ,9

,,,tuDvS

Irt tri ^•4 ** ««4 iN
UJ

x

Ul

o

ll

o

X

©X

O') z

o

CM

in3

a

z

o

o

m CD /N CM rs s c rH t~4 *»« X h-

»«s /A OK VS 3 CO

3 s A s a A ’H ** /~S CM UJ

f** v4 z A C- 3* H- z X JC X ro H

-J _j X ** ro -J -J «KS *?\ •»* »» VS 3 2 3

X o OK ro « X CJ • 1 a ro 3 2 CM QC 4K CJ CO *-# 1 CVJ CJ CO sV CO Z a 1 CM IK CM UJ a © B X CO 3 A V © m B CO /A a sv C s/ a a m 3 r— © s* 4* 4- & STS 3 in Z X ns z © \

ro ro ro Z CO © \ ro ro ro CO oo x © \ © V— UJ CM

CM cu ou <U> V & Qb © w CO V./ a o-M © sc X © a © »-• UJ -J H 3 -J w U3 •w* © h a 2 © a MD

in b- h- <1 i~ i~ r— <r CO UJ <0 -W m ro ® © © CL H H*

i z X ZD UJ 3 3 w- X X X 3 o 03 © X v-4 UJ vo i~» in © -J © 2 UJ Z 3 UJ-J Ul 3 •—4 —

CL -J II II 3 V—

-M X It 0. II CL II X s o n ii it ii -J Z Ul L3 © >-9-J 3C

ii ct: CL X IjJ **4 II *“» II oc QC X JSM Ii 4ft I! v*± II z vM ro S’ in © © *»» *-» © © 2 ®© 3 © 0. o 3X3 2 CL © X z H- X X 1— z u3 3 b 3 h U w 2 30.© t—

©O ©2

© © © © in ©® © © © O © © cO © © © v«i ro m © CJ t UD © M5 © O’tQN © ®© rw CO Ch © © *n cm ro lO CD N. 03 ©I © w* CM CM CM (M ro ro 0^ in uouJ WO m ©j>N cS

i—

*—< H CM Cvj CM CVJ CVJ CM CM CM CM CM CM ro ro ro roro ro ro rO ro roro ro ro fOroro ro jo row w
- 71 -

3

Hi , T 3 « Mk

3 6' 3M VO 3

o M

* \ CM • • 30 ro Ck

•-•X «3 ®

CkQC CO Ui 3 \ 0

• His Ui

MM ® Ui H

3 M* VL m Ui —3 M- -J

Ti Mk OL o CL X* CM • h X

MM M Ui o

3 •• UJ 3 mM XUJ O

L3 x HI mm -J

• •X h- T.« <T» UJh-*-» L9 u«-» 3 "1QC ® X 3 U. X ZH O HIO MO MM MH* CL Hth- a. H-QCUi a

j-U CD HICJ Ui A 3 CL ®

i-cn 3 Hi® H* o> OLD® Ui

Ui CO HIU_ cn ® QCXK QC

<Z </) . HI 1 mm m* «s <n X HIX CM VJOQC *« 3 UJ

» UJX CO HO •m a X®Ui 3 •* • • if) UI <r Hi*-« in w MM UJ H- •k «M MM

• ®CO 3 Hil— X OQCX X U. O ffl a HIO o 1 ® Ui *. *» X s • in HI3 i— A UiUJs MM K3U OTIUH

HlS Ch^N

*M aa.*» X A « % • « Ow ®0« XOC > ® a ®* MCMroro® ® HkM UJ ® HIQCC^3® <T\ •H ® UIH-Hi ®H-«M-3 a « ® \ a 'wCTi II m* 3^0> CL* * iL in®«in3

<r>cn® « a UJCVW XCC-h + ii a® ® U.UW

Ui X® II -fa CM /S -H hhhh H XV“ H

fflHHhh a ujxxxuiin <ph aCMHI- Ui XZOOUi 33X 3« XXX 3 x cl -j it x ii -• n at n ax n cxjx~~a.x.JXCLCL~

CO II whnQHCi ODOC4^Ui^X«UJ^Oc:3Cv-44J»-»XXQe o 4* ac. cl gc 2 uj uj x a. a. >-< o o a a 3 ® u. a 3 x h- Ui cl qc a. cl u. & o*+ *-*

LD®CLCLCLUJ5C0C ©M*CM^tn®®inCO®®®®®<M

§ ®®®®® »-*-« *« cm ro * in to 1 ®o®®®®®®®®®®®®< «-«c\j* ® ®®

coo coTi®m

fo ro po ro •* «*

® CTi i

*• ov

®®®®CJ^^D©©
- 72 -

NX

QD /"v CD N

CD X

CD X

CD

CD X

•A

NXX

•4fc 9

°l M X • • \ 'w- M A

»-« S->* N

Ll>- X

>* X

* X O

UJ X X

CD 3 UJ *-« -* cs 3 V

UJ GJ

>C£ UJ X OL GC o X U *~4 UJ© h- A 3 UJ © 3 >- CSI— LU -J <r U) <X H* o

oc C£_l <r CD

QC U.3 -j LU

<X C_> 3 QC

CD-J O

© «-H <X _J • Ui COO <x C3 X >- o LU

CD —J H* 0C

<L <XCD 0C LL 3 CD LU XUS Ui

Of rr ©X <xx CL ©

CD o Cl LU

\s vA Q OH x~s 3 *—I -» (\J v~A f-A cvj -3 3 ro *-* 3 - -X - 3 EC£Q XLU CvJUJ CD n

<\J •*-« ~£D •» *»> »>Qcl Hi ®x LU CVJ > zi^n © ^ Q- ¥*> XH HO H- A ©

<X *•• »-X •*“• 3 X ~H- H- <2 © © © n

Qi *~"S 3 •> K ^ \ i** XQ£ ©XGC ©cs: ©OJ

CK ~ «*0JU")* ^ 0J ~© ^ Ul CO UJ lu ©UJ QU.X

<x * a G3 Cf> 0. GJ> UJ "* UJ H* ©xw ©H» © \ Ul

xz * cn i • ~X X HXX ©H>*X ©X ©^x <X *—t ">—t }•—!—’« (\J ~t4**»t4H«UJin© Ul CN © UJ <\| ©

o XX 0COC3CD 13 HHCSCUa a U, <3 R U. ^ a U^lL

_J©* B XO« ^ 3> X UJ UJ a M v +* H 1 a. ii OCl II I*- OHCfi h- H- \ H“ h* H- Ch W- H» 0J 0\ \** 3 /-\ .j -j a x -j co '-nu x ouj © It X-'.-J-JXUJ-J*-' ZUJUV<1<IWM<IX UiDaDU03^0<S

^SwQIJ'X O C* X « UJ LU DS&UJlQfit

UJ-ZS^3:ZSU,LkS3U.ZpLLU.lX

L3 *« || ^ h || Q* M h* CL It s<*' CSCSQtlQC^aCQSXinU-aCXONOiXCvJHU. o.o^o.u-CkCL^kw^CL^u-a.^u-ca:'^

G9®*HLD®®®tn©®C\JinU5®*-«®’*H®Cv4 ,<f©iHCv4i

h-®®®^ojnro^!fiintntn©<Ti®®^*»^»MCvjCvj in®®©®©®®®®®®©®®®®®®®®®® ^cNjcucM<\jojcucvjcwcvjcu^j^J^&^nr)nn^nr:;y

<9*WVj0’'t®C0®-«<N*i CUCU<NJ©©©c£©^Ch' ®©®®®©©©®©'
•31

aN>

*o

Ul

<x * —J A

- 1 CJ >-»> -J x

<xO Ui

DC

Ul

CD CD

T3

-J

-J Z »—« u

3 h-K

CD ® AN

1- * AN

^ w*. CD JQ M S * Ck 0 u CO x

Qu Ui z m. r> Ck 1 • >• •>

* 3 * 1 CJ Ui * * 4 Z CO \n *

Ul <x X A QC %•* 3 Z 'A -1 O h

C5* Q. \ '-»• QC 0

Ul* * ANAS O DC

QC* MD3 Ui CL

(J.Z » X* an O Ui A AS * VO -1 Ui z

3 »-« O 33 Sa' N 0 3 —I- 3 CM **

U. *^CL *«» k-4 CM ^<1 h- U. ON ON *<D AN -k © h ® 4—1 *-» a. cl t#HA * OC 3 QC 3 Z a. ** vaIT)na*_J * 3

AN —O CJ UJ AS AN \ XX'a * Z

z QC * -J®® I- ON ^ '-A \ X * Ui

Ul V a cox cdon 1 1 CM VA AN vk *k h* T O U-OPOs ON zz f ZJO AA^hV© ® »- — •k 0 3 - ro ON OS V V ® * ® <X A z > • u. ON NANA CM CM 4 OCX® LSI ©

/> QC h- *-»Z • M3 z O CO z \ \ CM*'- © VO LSI ® lL

QC V UJ CJ Ui O CM O Ui o~ ")3fHh® CM LSI ® O V CL CDUJZUJ » -*»-x ouco **CDQ-L3® •v Ul ® »— •k CDJ-tt CM h- H- h- * * ONON'-'\,j'*— CM L3 z 2 A <Z U. ro *w AN AN O.D.DC®* N 3 LSI \ M DC > *UJ« <u CMU-*-« ~*xz WQI00O3 ® • 3 L9 A V *3 * II u. II 'W^-Z ®ZCD^CM 3 Z ui V —« JC~< h- *>-< H* H* h- zoo ^Qh || 0 Oh* H* h- DC ©

QC + 1 Z COZZ Ql 3 4 + H4UWAAA2H2 >Z Z3 »-• »-t •—

cd M oc ®®oc©3x.j w ti -j«j j^x^CL^tD^i-x

u- « *—• ii qcluzqcqcdc u onou. ti u on 11 u u u*>vo '-*>-• wocujacoocxaeujm

•-« DC O DC CL DC © CL CL CL -J CL li. *-• CD 3 Ll CD 3 X -J 30 X X &. © Cl 2 CL UCl Ui CL QC 5

©vOfS.C00N®®®®ir)®lfi®*'«<M ,'r®©®®®in'O®®®®®<N'<r'O®®®©

—* —* i « *h ^ cm cm cm cm cj 3 3 3 ro 3 ro 3 3 3 3 3
• 74-

a a“Ja hH j *— Q_

* CLO

X Li, O*-« CD

H* H* Mt

<X *-« * oi

o -» « • -j-j X

UJ

H-UJ H-

<X O h~ O »—

s j— QC3 a fD-J UJ

I&. UJ H*

•~3e ca UJ

a <2: —

o Cl

CDX * t~ X

h* UJ o O 2C ZUJ o

-J UJ

CL Z>0 UJ H- *— o JZ ZDli X

uj <x <r wO *•-» o o H- CL UJ H*

m 3 X ID 3 Cl >—

LD 1— 3"v- VO ® O L3 ’X QC M<H ^ X *> OCXH- X

tnto xv~< x in \ -«

m.y)- L3 Ul OH- CL 3 UJ

CD * <xn X X 033 Z»~<UJ *> -J

CvJJO 3CX <£i~ OJ *> *" v— GC H* «•-* k~« —i yf H-2X X u. • I -J LlX C£ -3— -J >-* UJ •k ID ** r\ /% o - uj uj m «. \ «*s CLUJ* V-XUJ

C\l _J hOw IhSCJ JahOw 2 Cl * *> * 5 » » Cl

•s w H- ^ IXHZ ~ <£» roN<r

H* »-« ina a v-t<z UirOH-^ 1 X X UJH*“3 r>r*>Ha m »CM » OX a 8 30C J v,<\! *. CL a » U, a 03 CD *~t H v— — UJ* <r u. 0.0 i~« CO H* J— H* CL O v— hhHH Hhh

30UJV5LU 3H-UJ UJ JZZS^CiOnj XH-UJ UJ ZZSOZZZ ujzuM3a<3:xxciui:jwHa,uj3:HDQs:<s:x.i:auSHHQ.iHHwa)

^»-«<rxooa:ujox<cujccaa:3:^^xaoo5:wo3:<je:uicjt:oc3:^at:Qccs;S z>3o.<cxu.oxxujCLacja.a.>**o-a:<i3Cu.CiS3:uja.Sska.^Uua-tnxuS

in®®®®CD®®CDCD®*HC\jr,0©®®®®aD®©®®©®’'H®in®lpCDU’>®^

COC^©-^Ojn^^Vj5N©®^’-»OvjrVflpV3NCOasi©^C4CD©^^$Jv\inrO^^

m n n n m n n n w m ^ vf ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ w Q) ^ w 'SQi
<Ti ®

VOCQ

*> «s O I CMCT>CDCS)®^CDCD © LU •‘OMO©©—•© © —< 2C

<7* «h cvi po n•*• <a in vo •- <*

H-m

LUtiiUiUiUJUiUJUJUJUia X

H* h* fr— I— b" h" H* H* QH

Lai UJ UJ UJ LU UJ UJ UUJ UJ «4 X ID

UJUJUJUJUIUJUJUJUJUJCCaUJ oaoooa o a o <2 o cl tt

©-^cxjro^tnvaN®^©®® ®CD©®QCDO®9CDCD^rO

^4 H «* ^4 im4 «H © ® © CTl ^VDV0^V0<^VOV£VOViD?iO^?iCPli

33

END
-76-

APPENDIX D

This software performs a fast Fourier transform of time

technique is a modified' Eq. (28) Cool ey-Tukey technique

transform waveforms that do not have the same beginning

The waveform must begin at an amplitude of zero.

domain data. The

that can successful ly

and ending values.
- 77 -

I ®

CD

I CDro

I <n <9

CD

I CM

= CM

h- I Ll. Ch

<ro

OC CD

CZ.CC

<ZUi >

\ O ® oz 0C

o_<r QC D K <X \ > O

Lliffl Ui O O -J ® z Ui OZ -J h- CO ; UJ h-

<5,0 o <x ® CO Z O

3 M o o 3 ® H -J

CO a» 3 »- a. ucc <x o CO as 3

<ZUi H Q- ® CO® o ® • acoro z® O >® ® QC ® Z

o ~ ~o® ® ® ® H-® ® UJ

o<r

ohid oj-rooc^acuh-ro an •> o^ofoa -j u. O.U.2UJQ. -J <10 0-00 HOOCLO

JUi rrjj UJUJOUJ

aoca.o

*« T

I CM CM

O

-J

Q_

HiO3

UJ ® <x®

CO 2 ®

n cd ni-t

u. ooo

h“ h“

Ui

-J

UJ O

UJ z >

Ui UJ z *-« o

z 31 1-4 H*

•—» »-h — 3 z

h- f- 3 O o

3 3 O QC 1-4 O O DC h

OC 0c U o

UJ *y UJ

L3 UJ z *-4 -J Z z *-4 H*

1-4 *-4 H- H o®

o >—OC o«

<x *—

OC z <*> Ui DC z «* «*

DC z hL HH* 3 * ®o ®

UJ UJ 3 CL v oh* ro

-J -J a. H-3 CO

*—* z 3 » ®0» ’v

u.® u. ® ' ® o *® ®cl »»niCD ® CD

^ll*5 unnuj®o®o %*®

a. ^ a. ® 55 n to * n

<1 ' wmUJ HOHOOOO OlilDZZ ZhOO)wH

®oro^

Ch«

* ** OJhhlH

H*

OCX

2 UJ O LUO

UJOUIOOCCJOCU

ittUlZU

cvi ro vo tnOLU

L3 0C SoSoSq£clOCLU&.&.OIl

?3 S ?5 !Q ?3 &

o UJ o _

uc*u>ocuoeu5 c*l325 u

OD®<Mn<JONO^CM

^•inirtln^ln'S^LD

28SSS21

®CM”TCO®®® ®®®®^£3 l^
8

• • Ul

z

UJ

z

o

u.o

X

<xX

CO

tc

CD

CO

z

o

CD

cq <r <r

= 83

JOOhZ CO

s E

<"* I> CD

<XCL XQX 8 2

CQ

z•U

3 0

c*- „J_J zoU CO

z a roro

C£> at; ZZ—< *-H aoc

CLCL

rororo

Q; Q; &> CM

»-( H* h- UO 2 Z X I mhQ.3

qcqcz h CL Q.HI

roro

Qj QJ

ZZ>—< —!

CC QC

O.O.

CO©'*'-

» 3 m roxco

il; \a

UJ-J hH<I

ouj ©

0 J I! ZUI -*

>-< O ©

CM

CQ

asX as

** ro ro 3

I CM vx CD

4- -*-« © \

«»-* *»* W©

*H W

© H

H|| 2

II v« II ZZ>Z

xo

CJ CO

a a roro

cy ©

ZZH *-« occ*

cl cl

^^^inccr^ocfi©©"-<<Mro^uoco

AS •rs AS AS

*-« ** 1“ z * »“» ** >4

8 1 a ro

A* CO X Cl i CO A 3 fK £ s*> ¥f IS n <** ro CO V* CO s cs © CO s^* a <H

-J \A L3 'w' **

H" <x © LU CO H

© © o CO o X

CL 11 CL II Cl n Z 11 II

<9RA) t»H X X H 2 X

© m © © ® N

CM ft ro CMro

CM

©

CM •* WHlt *s Ws v*» (M *») •«. JEXXrO

». • •> 3^ 23CM -

*. •>»—< CM

* U0© ZX VS *—> <E v-t H* XX C£ © a a 30

in ro ® © o cl

UJ

2£Cj II n W 11 -J-JXUJ

Q©©©©uu 30

o

2

o

o

a

6£

Ui

H*X

Ui

a

UJ z

o *-« ©SC

ClU

'©unaD^^rv

i^nbhnF)
8

”3

x

Mk

8 Mk 3 8 Mfc M m o C-* * \ (VJ •• 30 ro a

*-«X «k ®

OQC VO Li \ 0£

¥l» • k

•m 00 LI

m v-4 •k CD —3

Mb «k O

X* CM * H

Mk •k LJ

3 LJ 3 Ml ZLI

L3 Z m •-•-J

• •Z H Ln-«-» UM 3 moc <r> Z3L. Zh O mo ® M O

*H f— QC mn HOC Li

-Li ffl mo a. 3 CL

hco 3 m© lj OO®

<* Li CO mL. h 0CXH

<Z CO . m co *-« «d CO T* mz UOQC “•

s LIZ CO mo cm Z®LI 3 • • CO Li <1 m*-« —

m Li H •>

- ©to mi- in ©OCX H 3D Ct CO Of mo ® Li *

m, *k z« CO m3 o ^ LI LI **

b CD OmLUH mo i- -« 0C 0. X *-s CL+* ©U« ZQC >» mixi a ®« ~C\|

CO \ CD Li <1 mocoMxio ^ ^ LIHm z~« ®H4*H3 Ct • © \ a u h3hj\ Cl • « L w

<r o —

<7iC0 © * • ct LlICM ^ II QIC ® LUiw'

in Li z« hhhh^D aicg^s H hhhh HZ H flQhh-hh CC LJZZ3Liin ® QI04HH LI ZS3CUI

3LU.JC0LJ3* XXX 3 Z CL -J II Z II 0S II 0 X 11 OUXhniIZJX

Q.L9 || whhQHZ OQCQCZLIO^^OJOOJ^LJ—

X® LJOCOCX^W^ x®®xoo4*attocx LI Li za.a.MQaoaiu.QiDZhUio.ttd.a.Hu.oci

Hi]LO<xzu<za.a.cLUJtttt ® — <\J 2 inoo®in®®®®<\j CD®tn®CD®©Cv|'* ©©©in®-*TM*®®® CD 0^ ®®®®®®*-**-«<Mfo^rtnin

mcopwrw oo oo oo oo tj) ® n n-f?i®®®®®®©®®®®®® ©ininuDUDiiDuSinin

rororon ronrofor»w*
- 80 -

a

•NX

X

CD®

CD

CD

CD

CD

\

aCO

>

o

aa

UJ

H*©

-JX

CJ

-J

<xo

UJ

CQ

Lx. «-«

CO

h-X*-» o

Qs *y

• UJ >

UJ /% 3

1— > O ©X

UJ © UJ OUi

-J tt QC 'w' O

a. GC u. OCB X <r ~LU-*4

o © ^QLM o o *—

©Ll*4

UJ © O X

u X > * O X 07 _J u. ••.*-=» M © <r OJh

Ck 3 © UJ X *-v \ © © a CtX © ©©-J

UJ CO •S DOS a: <«4 <33 Oh X v »»>0 M M OJ 'H *H •>3 3 X* -.J 3 UJ 3 - -X » 3 QCO X ~ ©

» _J CM •*-* »CD »• ~QL /-sixo M M > zz^ro ® a. X CO Q X Lu © ^ ^SC H* © a X

cl 3 3 XU. •s X •w' H- *-» h-XLU oc m •> (\J U0 8 A *"U. a /A, >UJU3

• • • Cl a S * OMDO.-^ > UJ ~*Ui *>© U3 ro ro <z XX - CO 1 •sX X H* X *** /*S cq

nroh U* <Z ^ "*** 5~» >**i CM X »-» >-«*M**H + ©<£

tl> Cfc * /•NO xx gl o a co u hH<£ CMa CMOa ** *-»«J®» « X O a <w-0 LU UJ a 'W \ ^ H

V— H* H* ^ Ol ii o a. ii f- h*gq KU\U ©XH>*$ 33X 3 ^.-J-jqx^jcoz-sujx UJ UI-JXX^X £> X

Q.Q.WO II X Z tt X CO UJ ^ <X © - hi cl uj 3 a 3 cj u

XUJ.J^^X^Ci-jXLJ.J^*--* II ^ II X'-iXCD

•“.^aX^ODCXUJLU^CCIK^^fitCO^CSiUJ II x^cj<c^xa.ujcscsSQ0 <3)a»3Lii,ei»ociCLca:x

VjDCDCD©®-«<^®eDC0m©CDiMingDCS!®^®<M^-'sD^iM^NC7>©w

-< *4 «h cm cm rvj <m <\j 04 cm cm cm cm cm cm cm ro n ro ro ro m n n ro m ro ro ro

3112

P

3= 0

3113

D=8

3115

F9*F1*2/D9

3120

CALL

*FFT*,U

3130

CALL

"DHL£AU

,

SU,X,Y
-Pi3

/A. •M « H- V mO

JO J

*“«CL

111 /A MS

a: A * oco

CO <H XU.

T5 1 o vs X M©

z \s b-hLU u ©«-• »- ON OZ

h- a. OM

© JJ

3 ©

m O Si l-UI 3 <_) A © «©

La * X 3

LU CM v in h- © I © a>M

as CM as

• i ro-i

LU V A + £0.

CO \ X «r © AS A V © x /AM Q_ t-

£L <M lX- as o ©X

3 1 ** /A h- *-«©

XCM^A SC © o z

3 WA V -J Ui

iii * \ X x T a. 3© © (T|AV as o JZ z> Q.CMX a© M © ©©

ta©

CM

\A

CM

v4*\ TAA

•-•xx Wvv

+*>->-

as + \a

CM CM X » ro

s ••coin ••in^<c

• M)©\/MWX-*

C5 CM ZCMZ'-'^

LU W *Of *1X0.

QC ©CMH-^CM'A'^ \

u_ \ ro xroxa© s m||>(\|vQ)vOCD

a. mx >co*h f-*KX U h H I! It CM X AlAAA MM ft aa^iaOvQCvvv

o. a. a. a. ll xa. >- z a.

A

CMVX

NA

Xv

©©

©

©

*4

\

ON

U.

«*•

/A. ©• • U5

CM U ^ •

-W©

CM

It A

X

v©

I X

CM

PO©

at

L3

L3U

La

La

x>-x>-x

©to

DM5

z

UJtOM*

H* •> »

i- ©in

©CM'S* H | U. as as otn©

CM©

z*-< h- CM

UJ3

LUO 3

©0.0 3©

© 3

HXH0.HQruj2 aujflccoszuNN

Q. X CL U 0. ki C* 3 3

©

/A A

CM O ^

v|-v

(O© © as as CM a

©CM « h.

LU©UJ 31

L3*-*D0C©; axootf! q.©kll©:

in

M5

ZhC 6*5 L3 asM Ixl as ©r>xx © ZZ©K cm

cM^tn^ooinoooooocM^fvjssinooocp©©©

rororon’»rininM3r^©criffl»H iM

, '^fM> in©coo>®aHCMpo^tn

n n ro ro ro n ro n n n ro r*> ro ro H ho W to to po to po to Hi to to

U.X 3 O «UUIt»

» IH3CM ZXHZ * m© WMh

L3X» * 30C

IU« O

© HLhO.

UJ © JZZ33 X © L5 X 0. Ul IOZ©©©OCOCZ^

:ZLi0ulXO4ia.M^

aNCMPO©©®

a<a<Cvif
- 82 -

UJ

QC2 8

' UJ

UJ 1—

CD UJ

-J O CL

* H~ X

UJ o

ZLU

*~*_J

o

Ul V— -* UJ IDU. x wO M

h-CCUl H*

CD © Q- >-H ou<r CSC \ K2H 3

TT ^ H »~4 3 3 UHK © UJ

«* «*. Z*-<UJ •5 _J ro© H C£ H* v-A V-4 3 —« co H-ZXX X U

~\ o UJ •> 05 A/N A Q£ Ul a H-3U4 QWCVJOw IQ.** « » »• Cu <M

*> | % J— w <1 » roro <r *4 (VJC02C X ujH-~a nroh- «** 1 £> *-C\J *. a. a a u. ® <&J a n u © u. Ul

o *-> h- H* H- H» HHH- H*

OCOUJ 2H-UJ Ul ZIDD2X2 UJ

UD

OiCD ©® CT> in ©® cn ^cjro

UIUJUIUI Hhhh

UJ UJ UJ UJ z^^acxsrQusMMdZMHwQjj j jj ^xooaujozaiuaazt-'aaiotfxujujuiuiuj

aC4XXU.OZXUJCLCKQ.a.»-4U.CLCLOLUJCaaO£lA

CD ^

'i-* CD

5*1 ®

crx ©

•5 © © © v-» U UJ US UJ UJ

UJUi

-J-l

UJUJ

oo

UJUJUJ Jjj

UJUJUJ

aUJ

x*— UJh- X©*-0

*-cc ©

OL3

ocz

*—

OH

x *-«

*-« e*; H-X

*—

dco 3 ©v-4 OCb ©*

OHX X ** UJC£

Sou

®®©®®®®®®^© in ® i/)® u*)© m ©^ csuy)’^ inu) N © iT\©©

«<f ^^*^^^^^ U3

v5 U5 US 'sfiUD ® U>®'2 ^l ^ U5 V0 V£j ^ VS ^ v^ iv0 |S1 N 78

15

PRINT

"UNIT?®

7616

INPUT

2

7017

CALL

*UH1T")2

7020

PRINT

"DISC

FILE

NAMECcg#

DPO/WAUEi>

7030

INPUT

E$
® *U.

® -00 4* ®b O CD

mu. - at (Via 4* S — *<1 UiX

lii — >-<4*

h- CD

LULU > Z

H- UJiXi b-QC 4ZHW JZ3

a: a. r* -i z <x a uj OOZOUJOGLtt

ID®®®®®®®

n^-tn^rwcc^r) ® ® ® CD ® ® CP ®

rwrwfwNNChCTjfft

9999

END
- 84 -

APPENDIX E

Five different sets of data are included. The first two show the results

of using the software contained in Appendices B and C on the same data.

The results are identical because the waveform ends at zero amplitude.

The other three sets of data illustrate the performance of the different

software approaches, Appendices B, C, and D, to the rising step (starting

at zero, ending above zero). Only the software contained in Appendices C

and D handle the data correctly.
- 85 -

The following three pages demonstrate the results of applying the software

contained in Appendix B to a step with endpoint equal to zero.

The first page shows the waveform as acquired from the DPO and a reduced

form of the waveform which includes only every fourth data point. The

sin x/x software yields the frequency spectrum of the reduced waveform

on the second page and a plot of this spectrum is on the third page.

This software correctly transforms waveforms of this type.
- 86 -

M-

<>• r> M- z> *—

LD

•— o

c> \ CM \ o ro tnx «. QC M?

CTt *—

i in •s LU • CD

G> G> • CM .. U CM

CTi • •X

-rf L3 •—

• «K « • X t— Cei

<T. —« tO

cm h- LU h“ • •Z t— CO O

ro <x LU <1

CO . LU

CO

CD Ci LU

X -v CO 2 CO LU 8 ! O <X CO *—< >— u CO t— cj « a O H- LU k- X ( CO x a a —' LU *-• LU LU ro t— t— X- Ctc
- 87 -

i;

li

ONUorsoo oo rs CD —• is CD yf yf ON CD ro —

Srf* <j< —* is- in ro is ro ® 00 ON ® CD 3 CD is- ro SI CM U0 ^ ON yf CD 03 ro -m-iscd ® IS. CM CD *4 ON

UJ

n. oo ld ro ro h- CM CM 03 CM IS. uo yf CM ON CO CD

is ro on in rs ro -• CD M“U0<r> IN. ® ® ® ^4 yt ON

QL rs on cm cd ® rs cr> uors. cm ro M* CD UO ro CD

CD

®-*® CM—«(SCM tH ON ro ^ ^ CD CM yt is. ® ^-4 lO CD 00 CM CM CM ON is 03 U0 CD CM ® CD —4 rs. rs CM

73 ON (S U0 ON —• ® ® CD ® ro 03 CD CM yt CD 3 ® CD IS

•fc CM ro IS- IS- UD —• -« UO CD ro ro M" uo CM M- uo CD CD ® X CMCD-* • • . - UJ • • * CD Tf CD VO CD is co on on ON ® ® ® ® ® v-4 H fS» ^ ^-4 ^

*4 ^ CM CM CM CM CM CM

1—

<r ® I l 1 1 1 l 1 1 i r i i 1 1 1 1 ‘ 1 1

CD

CD

CD cm ^ is. ro o- 00 m- CM M- M3 Tf CD CM CM UO

*0 ® oo ro cd on ro uo o- uo CO uo ONinrs uo UO IS- CD CO CD M3 ro vD®ro®M-uo-«uo ro ® CD ON M3 CD uo ^4 ^4 00 CD ®

M‘®ro—*rsrs-«oN on cm ro uo CD uo CD ON CM ON

• • .. o uo cd is ro ro ® oo CD IS. CD CD ON ro UO ®CM ® ON

/A. /v UJ on —® uo ® uo cm on uo CM ro —' cd ® CD CM ® ro UO yt N n y- UJ moMiors-incoinm ro CD ro m- cd ® CD UO —

ON CM ® X X® X UJ roro-*0N03CM0N0N 00 ro ON M- —

UO CM UO ro —

CD <X> X EIOJ 3 tT UO CM CD 00 00 rf 00 CM couoro uo IS. CD 03 CM ro ON

N — 3 •s M- —• ® UO ON CM IS VD CD CD VO U0 —

CD CM CM CM UO CD CD X 2! X o UJ ODCMfO • • • • - UO ro jr -» M % « 1 CO • • • ® U0 U0 ® CM TT 03 ON IS IS ® CD CM ®ro • • \y <X <x CDrois-r-nonovocD uo rororo r3 CM CM ^*4 ^4 is uo ® NO X rocDoo i i i i i i i i i i i r l i I 1 1 CD >-x CL

CM o UEUi

ro -r X CD

UJ UJ X CDCDCDCDCD333 <D ® CD 3 —

^4

CO 3 3—<3 ^ ^4 —« —« ® ^-4 4 ^4

h-l a (3^3 1 1 1 1 1 1 1 1 1 i 1 1 -« 1 i 1 I I 1 1 UJ UJ *-* UJUIUJUJUJUJUJUJ UJ UJ UJUJ 1 3 3 3 3 3 3 3

> a; axz ^ U0 CM CD is. CM CD ro M" CD IS. CM 3 CM UO UO IN- CM CM 03 Ou. Ll O 9 2 8 1 5 5 1 3 CM CM ® CDr3 ro UO CM 00 ro CO ON

TJ* • CO CM —• CM -« -« M3 CM "4 ® rOCDCD ® 03 IS. UO ® 03 ®

UJ X Ihl

UJ <d <X) is oo 'O' —* —• oo 03 CM oo —« r3 CM ® CM ON CM yf IS

ID o O 3 X O 00 ro ON CM CD CM CD CD 00 03 CD ON CD CM o- ro ON ON CO ro a 1—

M JH 3 CM—«U3—«roil000CD Is- 03 on® ro CO r3 ® UO ® **4 r*> LlI — H- O O H* rOCMU0VDM-®CM^ UO CD ® ON® 3 <x> rs. CD CD •^4 cl <L a: co a. M (Dvooo—•--'Trrs.r^ CD CM ro ® ® n n ’*-4 ® IS. ® ^-1 3 _J 3 UJ T~ yt *-* —< —« |S. IS. ^ Tf ro —^ ® ® ON on 03 is. IS rN 3 300 UJ

CO O o o a 00 00 CD CM —^ »h —4 M 3 3 « X X

® c/><x<rc3uj — >UUUJD • • _j cl a

® <10: 0:33

ro X 33 CL

• • 2 C 3 CLOL

ro <x OQ.UJ

-"•••X_J 3 Qc:®

• 3 CM ® o X 3 3 CO

00 X —

X X 3 3

i o X r— »— 3 O

K- CJ <x CJ X QL CL CL 1— • o H- 3 3 3 3 a ® ® ®

1 CO 3 r— r- H- CO 3 UO ® uo ®

^4 3 X X X X CL mmt ro yr M3 ro >— r- 3 3 3 <Z 3

®®®®®®®®®®®®®®

® ® in 05 in cd in ® uo ® uo ® uo ® uo ®

UO ® ® CM ro UO M3 CO ON <-• CM 'S* UO IS CO ®

fw 1X1 ^ ^ h vh CM 00 CM CM CM vM ro
THE

MAXIMUM

UALUE

IS

9.

403280294E10

AT

LOCATION

- 88 -
- 89 -

The following three pages demonstrate the results of applying the software

contained in Appendix C to a step with endpoint equal to zero.

The first page shows the waveform as acquired from the DPO and a waveform

showing the difference between every fourth data point. The modified

sin x/x software yields the frequency spectrum of the reduced waveform

on the second page and a plot of this spectrum is on the third page.

This software correctly transforms waveforms of this type.
- 90 -

i

.. t. --1 ——— Mc-Tf

CD

z>

V—

CM

*-* o ro o \

\ o CD

V) X H

C£

cr» CO

1 UO

UJ

CD CD

• CM

CM •• rs UJ

CM • « z

4 UJ *—

% *s • • z t— ck: o

Tt h- UJ h-

• • z h- CO CJ

ro ca UJ <X

«-"4 • « CO • LU

• CO

CD O UJ z Z

CO Z CO LU o

1 O <E CO —4

h- CJ m H*

O • o

O t- UJ t— 3

1 CO z oc Cj

»—• Ll) —I UJ UJ ro h— u- z> Ct
-91

V

is o* © © © © CM © © 44 © ©CM 4* © yf ©*-« -«• is- 4* ro IS ro ® © © © © CM © rs ro X (MU’) o- © 4* © © ro <•4 4- IS © ®|S © © ^4 ©

UJ

IS.® in ro ro IS CM CM 4* © CM rs 4* in y? © © © © rsro © in IS ro ^4 © ^p4 4- in © IS® © ® yt ©

Q£ is.^r © CM © © IS © 4- uo IS CM TOO* © in 4“ ro ©

©

® © CM rs CM 4-4 © ro © 4 ©CM »4 4* is ® *4

tnoo © CM CM CM © is © in © CM ®© •H is IS ©

TJ CMS. m © —

® © © ® ro © © CM 4- © © © © IS cm ro rs. IS- © <•4 in ® ro TO 4- in cm 4- in © © ©

21 CM CO ^4

UJ • • • © 4* © © © is © © © ©© © ® © ©

H- —<ro is. —* *•4 4-4 ^4 44 —

44 CM CM CM© © © —

<X

© i i I 1 1 i l 1 1 l 1 i 1 1 1 i 1 i l

©© ro t © ^4 ro in © © cm ro © IS O" ro © ID© © to is © ro uo ro in © in © in is ©in rs © IS in © ^r4 © CO ©ro © M- in in to © © © © ©uo ^4 *4 ©© © ro rr ©ro rs IS ^4 ©^4 © CM ro uo ©m© ©©© • « Ck mco IS. ^4 ro ro © © © IS © © ©ro u*> © ©© © >*v • « UJ © •

m © in CM © in CM ro © ®© CM © ro in 4-

N /s UJ in ©in rs. in © in in ro © ro 4- © ©©in <i4 © © © I N © <L Ul ro ro -4 © © CM © © © ro © 4“ t4 in cm in ro —

©QD

SI X in_j o in cm © © © 4- O’ © CM © UO ro in is © © © ro © N X4*4 3 •s m* 4rvi in © CM IS © © © © in --» ©CM CM CM uo © © XT O Ul CD cciro in ro X X • • CO % • • © in m © CM 4* © © IS IS ©© © ©ro • • V Mr\ <X <r © rOISIS in in © © UO 4“ ro ro ro TO CM CM ^4 ^4 IS in © NO X ro CO© i i i i 1 1 i i i i i i 1 i l 1 i © D- X Q.

CVI O > X UJ

ro ~T‘ o CD

UJ X X © ©© © © © © © © © © © 1-1-4 44 ^4 ^4 ^4

OD 3 UJ M_J «*«4 ^4 rH ^4 4*4 4 44 © ^4 44 ^4 ^p-4 ^4 ^4 i—

¥-4 C5 3 3 i 1 ( l l i I i 1 1 l l l t l l 1 l l UJ C3 Ul UJ LD Ul UJ Ul Ul Ul © LD LD © i LD Ul UJ ID ID © ©

y- QC UJ XX o- in cm © is CM © ro 4* © IS CM Ul cm in in rs © © ©

oU_ QC o © CM© <»4 in in ro CM CM ® © ro rotn CM © ro © © X U_ MCO CM i—

CM *4 «-4 © sr CM 4-4 © ro © © ©© IS uo ©© ©

LU O K »— UJ © OS I''- © iH © © CM © »4 ro CM© © © © 4* rs 3UJ C t T o CD ro© CM © CM © © © © © © © CM 4" ro ©© © ro CJ»— UJ_J t—

3 CM co ro U") © © IS © © ® ro co ro © in © i ro UJ <X H- o o H- ro cm in © sj- © CM ^4 in © © © ® ©© IS © ro ©

QC-J <X CO Q_ i—© CO© —

4“ is is © CM ro © © nn44 ©IS ® 4

U. 3 _1 UJ -<r ^4 IS rs 4* 4- 4 ro 44 © © © © © IS IS ro O 3 QC 0- UJ

tn _J O O © © © CO M- CM — ©

t4 ^4 4-4 •M 44 —

©©© © © ©

-» <r _j .2 © coo<xaui

O' y- OLD ZD

•• _J»- C£GJ

<rc/)a:u_ui

O' XLDLD OC

• •Z<13 1DL.

IOCD QQ-Ul ..x_J3Q£®

• ZD -<©

©Cl ©XI o

»-o 0

O h1 in —r UJ

ro hXID ID CO M XZUJU. XHKQO

<X

XQCQCOiHLDUJLDUJ

LD H- H- f— CO XXXX

H* UJ UJ UJ <E

03

UJ

OL

U.

®®®®®®®®®®®®®®

® © ffl ® ® ® U*) ® U”) ® in ® U*) ® O') ® m ® lf> ®

m©in©in®®©rom©©©~«©’4*inrs©®

*• IO 4

1 © is © •* *h -h -«* --i —* *** © © © © © CM TO
THE

MAXIMUM

UALUE

IS

9.

403280294E-10

AT

LOCATION

- 92 -
- 93 -

The following ten pages show the results of applying the software contained

in Appendix B to a step-like waveform with endpoint not equal to zero.

The waveform, as acquired from the DPO, is on the first page. The

transformed spectra is tabulated on the next eight pages and plotted

on the last page.

From theoretical considerations in the text and results shown next in

this appendix, this software is clearly not applicable to waveforms of this

type.
0- > > T

CD

aa ' \ \ CM w o ro X v Q CL CD .

— 1 ID -

Ll! • CD S Q ' T

CNJ •• -> O CM

— • Z

K) CD ' • > — z h- CL CD —1 h- O

K) h- Ld 1—

-- Z 1— CO

U

ID <- Ld < — .. CO • Ll

CO s a UJ z Z

CD Z CD LxJ o 1 o < LO 1- u CD y- u CJ o t- Ld H- 3 1 to X CL a — Ld ~ Ld Ld ro i- 1- > CL
II

-55-

— 'too — 0)oo ro3ininr^3CDinin — ro ro — b* 3 cm n a) 3 in ro in cd 3 3 3 n cm cm 3 ro x — id — q a) o) co CD ro oo co no Q oo co -QOOOO-SCD^^-lf)N^iOQCJ)N(jO

id cocorv'(Md)roDQ-<T^rcoiso(\ir^Qr^- —

cl — r- — b* co co cm ro s id b* b* co — o) 3 cd — ro o) oo ro co io od id cd - ooojqsm - ro b- O) 3

CD CD ID T IO K) — CM 00 3 NO ID CO CM CM fO CO 00 b^ IO

"O — M- CO CM 3 CO 00 CM fO CM — 00 3 CM IO b* CO S fO ro ro in 3 ro 3 r^- 3 3 ro cd b* cm 3 ro co ro 3

LlI 3 fO D b'- CD Q — N N) ’T lO in CJ3 NN 00 00 O) CD

b- — CM CM CM CM CM CM CM CM CM CM CM CM CM CM

b- 3 I I I I I I I I I l I l I l I I l I | <

s

(3

<3

(3 CO T CM CO K> O) 00 — 00 CM ID "T CO b- <- 00 — co 3 CM (M -

3 in CD s 00 CM bv in ro in — s- 3 in ro b- 00

ID 3 b* co 3 00 CD 00 b- — ro b- in ro in 3 CO s- CM CO O)

a ro IO b' 00 fO CM 00 "T 00 in CM CM CO b' 00 00 b*

.. .. Id 00 O) ro CM CO M" ID co s 3 ro 3 00 CO 3 ro ro

h- ro 00 ID CM CM 00 — ro ro CO — co CO O) CM ro — b' co N N < o ro 00 — CO CD IO 3 D O) ro CM co ID ro CD — CO CM 3

N X X 3 _l Ld CM 3 3 3 CD if) CD CO K) 3 b' ro in <• CM — ro in ID X x x 3 o a ro CO 3 1^ IO to K) CD ID in CM 00 3 ro ro CM 'T x D u * CM 00 CM ro O) CO T — 00 3 D — O) CM CM in 00

z z Ld CM

3 M - < •CO r* • CO 00 00 r- b* bv CO CO co in in ID ro "T ro ro ro CM

(3 w N— u < co CD 00 00 00 00 00 CO 00 CO co 00 00 00 00 00 00 00 oo CD

<3 N X i 00 1 i 1 i 1 1 1 1 i 1 i • i 1 i i i l 00 > > I Ld CL

CM O O H CD

Ld 3 Z 3

CO 3 3 — 3

>—1 O a ~ —

Ld 3 ^

> cl CL Z

CJ Ll_ 3 O CO

z — bLd z ZbZ 3

3 o 0 3 — O

O *

1 — 30 3

Ld r- b- O 0- bCL < < CO b—

Ll _j 1 3 > z

3 3 CL O o

LO CJ O Z <

—

3 3 • 3 X

b- 3 < <03

in > O CJ 3 O

CL 3

CD < CL CL 3 CL ro z Id 3 3

.. z < CL a

in < o 3 3 CO _ - x 3 CD CL if)

• 3 — CM

s ax 3 3 CO

00 Z — X X 3 3

l O X b- b- a o

h- u <

u cl 01 CL bO b- 3 3 3 3 o

1 CO Ld b- b- b- CO 3

Ld X z Z Z CL ro t— b- 3 3 3 < 3

S3 3 S3 •— •

•

•—

1 3

1 3

1 3

1 3i 3

i 3

i 3

1 31 31 3

i 3

i 3

1 3

i 3 i1 3 1 1

1 3

CM in CD CD in bv M" CM ro CM — CM CM ID 3 CD 3 3 M" i b' ro — (M O) b- 00 3 CD ro in CM SI b- ro — CM CM b- 3

ro CM CD 3 in CD CM •'T ''T D ro in T ro — ro 3 3

S3 ro CM 00 CM co CD ro CO 3 CD b* M- CM in b' D Q

CM in 0) CD in 'r 3 
 CD 3 CD 3 CD 3 CM Q S3 •< CM ro 3 CM — 3 S3 CD CO CM in in <s Q — S3 CD M- 3 — ro T

'T CD 3 CM 3 S3 00 in CM 3 ro ro b- M* CD in CD CM — 3

— in 3 CM b- M- ro CD CD CM s b- 3 3 CM b- TT in M" — in — in in in b* —

CD ro s in ro CM Q O) 3 b' CD

ID _ — 00 co in M- ro ro ro CM CM CM CM CM — —

ID CM CM fO fO "T

Q S Q S s <a S) S 3

S3 S SJ S3 S3 S3 <3 3

in S in S D S in 3

3 b- b* 3 3 CD 3 — 10

500

1

.

59

1

948

1

67E1

I

-82.

1659365175

-30.

1

366706129

1

1000

1

. 5

1

07027

ME1

-82.4782992032

-30.5916688853

1

1500

1

. 4

779200

16E-1

l

-80.9256223103

-30.

7822304

533

12000

1

.

38

1

455295E1

-80.989939681

1

-31

.3685123659

12500

1

.

334392581

E-1

1

-80.7428608879

-31

.6695767012
-96-

T CO in in CD CO CM NO in CD M" CD CD CO CM CD NO in NO CD CD NO in CO M" CO CO , CM CD

CO NO CD "T CD "T N- CM NO 3 3 *r CD

CO CD CO — CO -

NO CM CD S —

— CO "T CO CM CO CO CD CO

M" ao NO CM .

CO in NO N' 3 CO CD CO CD 3 — N* CM T CM T in •

CO CD in CD N- N- S CD xr T NO NO _ *— — CO NO CD M" N- CD 3 S 3 CD CD CM NO

NO CD NO NO in M" N» CD «— CO CD Cv NO CO 'T NO 00 r- N" in CD CD CO CD in — CO NO CD 00 CD CM 3 S3 N- CM CD — CM Cm 3 CM CO NO 00 NO

0) NO CO 00 CD N* in NO — M" CO CD 00 — CO NO CD — in NO -

M- CO in CO in in s N' CO in CD in Q

in ,

in CD NO 3 CD in s 3 CD M" TT in in

3 3 3 M" CD CO 3 CD V M" NO CM NO M" CM CM N' NO

00 in in CD CD s — r- 00 CO N- CM si CD CD N- CD M" CD M" 3 3 CO CD CD in in 3 , Nv NO in

r" in TT CO CM CD TT CD — NO M" CD NO N- N- CD — M* CD N* CD CM in CM CM CM N' CO CD NO NO in M- m- V 3 CNJ in 3 3 M" in — — CO SI CM NO CO CD CM NO CO 3 CD "=r CO N- — NO in CO in CO

CM CM CM NO NO NO NO T TT in in in in m CO CD CO CD CO N' CO fX Ns N- N* CO CD 00 00 CO CO CD CD

NO

» NO

1 NOi NO1 NO

1 NO1 NO1 NO

1 NO

1 NO

1 NO

1 NO

i NO

) NO

1 roi NO

1 NO

1 NO

1 NO

1 NO

1 NO

I NO

1 NO

I NO

1 NO

1 NO

1 NO1 NO

1 NO1 NO

1 NO1 NO

i NO

1 NO

1 NO1

in N' *— CM M- in — in CD CD — CO CO M- NO in — M" CM CD CM 03 M- NO NO N- N' 03 CD CO NO CO CD CD in

N» NO N- 00 — CM CO — in CO ^r CD in N- •

CO 3 in CD in •— 00 in in CO CD NO CO NO 3 N- 3

(\ S in M" S) CD — 00 3 NO CD CM CO m CM 03 CD N' 03 13 CD M- M- NT N- CO CO — — NO CD CD in

CO CD CO CO s r- in CD NO N' CD CD CD m CD T CO CO Q CM M- (3 NO V CM in 3 N- CO CO CO

m CM 00 in M" 3 CO NO 03 S) NO in CO 3 in CO in CO TT M" CD

in — 'T CO CO r- CM in CD rr in CO NO r- s in NO in CD m CO P" CM s CO CO NO 03 — 03

3 CM -

CO NO CO CD _ T NO CD

N' M- CD s CM (M r— V CD M- CO NO CD 03 in CO •

•— CM s CO NO 03

NO in in 03 CO in N- in CD 3 CM 3 CD NO s N» CM in NO 3 N* CO CO N- 3 (3 CM CM NO N- NO 03 M" 3 N- CD CM NO NO CO CO

CD NO 3 00 S3 CD CO M" — CD 3 00 03 CO CO in — CD in — NO in N' CD XT ’'T M- LO CD 3 in TT N- CD

CM O) CO m CM M- NO CD '

NO M* '

M" CO CD CD in r- CD •

CD CD M- — 3 CO NO 3 •M- CO CO

CD 3 CO s 3 N- CO CD' CO N' CD in CO in NO CO CM M- CM CM NO CM CM (M CM 3 3 3 CD CD N- CD

CO h' 00 CO N' N* N* N* N- O' N' r- N' N' r- N' N' N' N' N' r- N' N' N* CO CO CO CO

I I I I I I I ! I I I I I I I I I I I I I I I I I I I I I I I I I I |

— — — — — — CM — (M

CM

CM CM CM CM CM CM CM CM CM CM

(2 12

CM

CM

CM CM CM CM CM CM CM CM CM

*— — • — *— CM — —

1 LlI

1 UJ

1 UJ1 UJ1 UJ

1 UJ1 UJ

1 LlI

I UJ

I Id 1

1 LU

1 Ld

1 Ld1 Ld1 LdI U1 Ld1 U

1 Ld

1 Ld i i

1 Ld 1I Ld

1 u1 UJ1 UJ

1 u

1 UJ

1 UJ 1

1 31 3

CM — N* CM CO CD N* NO M- CO Ll) in M" CO CO NO N- in M" CM Ld Ld CO Ld CO CO in CM N' 3 — 3 3 NO

NO NO CD r* 00 — — M- CD — NO CM CM U3 N- CM N- CO NO in N- LO — NO 3 NO NO M" 3 CM in —

CO "M" — CD CD CO N* N- N- NO — in •

CD NO 3 in CM NO CO CO S CO CM •

— — NO 3 3 N' NO

r- NO

CM CD CM 3 CD r* N* CM CO M- CM in in M" CO CO m Nv CD NO NO — NO N' in in 3 3 CM in 3 NO — CD 3 CO — in in CO CM CM CD 03 N* «— 03 — in in — — CO CM 3 M" Nv CO in NO 3 3 in N- 3 N- NO 3 NO — CM S CD N>» (M N' — CM CO CD NO N» CD — — r- in CO CO V CM CM N' 03 3 rv 3 — 3 3 3 T

NO CO CO — 3 in *- CO NO CM NO 'T 3 CD in CO in CD 3 CO in N- in 03 CO 3 M" 3 3 3 r- 3 in

I s* ’T 3 NO CD N- CO 3 00 CO CD in — — CD 3 CO M" 3 CD s CO rv — 3 — in in CM 3 N' CM CM CM — — 3 3 CD 3 M" NO 3 03 N- TT — a

3 Nv M- CM CM 03 CD 3 NO •

3 — 3 3 3 3

• —

— «

CD 03 CD 00 CO 00 00 03 N' N- N' N- 3 CO CO 3 3 3 3 3 in 3 in in

QQSSSSSSSSSSSSSSSSQSSSSSQSSSSSSSSSS SSCJSQSSSQSSSSQSQSSSSSSSSaSSSQSSSSSS QinsmsinSLnsifisunisunsLOQirisiLnsiosinsiosLnisiosiinsLnsi

roro'T^LnLncDcDr^r^oococncnsiS!' cMCMNONOM-M-inm33N'r'v33333

.— .— .— .— .— .— •— — '— «— — •— •— '— c\iO'jc\jCNjr\jCsiO'jcNjc\jr\jc\)C'jc\jc\<Cvjc\iOsJc\jc\jc\iro
- 97 -

CD p* — CM p- CD ro 00 CM CM CM — CD <r CO CM in p' — CO ro CO ro in CD _

05 PO (M ro CD ro CD <D CO in 1^ ro S) CM CM — CO T CO in — Pv (O S CO p* in in (M CO CM ro CM CM CO CD S CM (3 ro (M CO r- T S3 CM 'T ro CO ro CD T <r p> — (3 CM 3 "T 3 — ro 3 CM CO

CO CD r- S) CM CD ro CD CO CO CM CM CM 00 S CM 00 in CD •

p- 00 00 CM 3 T in CO 3 _ r- 0) Is- CO CO in 00 CO P" O) CM <r

p* in — p> CD CD ro — ro 3 CO •<r in ro CM P^ 00 M- CD

K) _ ro (3 CM M" M" r>- — <3 p- — r* •— CD CM CM •'T in ro CD ro in 00 00 CM in in in CO — P» CM

CO — in (M — CO ro 00 p» <3 S3 in CD (M <r — CD (\ in •sr ro CO ro 00 T ro O) 3 in CM ro in 3

CM O) S3 p- CD CO in ro in (3 00 ro CO CO ro 3 — (3 CO "T 00 p- 'C S3 CM (M CM 00 ro v CD r- p* in in

"T in CD CM in O) in 00 ro 00 S3 S3 CO in — CD T CO 3 T T ro p* in CD ro in O) in 00 ro CD CD ro in 1^ P' CO CD CM O) CM T r- S3 (3 CD CD CD in in CO CO r-v CO 00 00 CM 3 ro in •<r CO ro PCD CD CD CD CD CD CD S3 CD Q S3 S3 S3 — — 3 S3 (3 CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro 'T M" "T m- M" 'T T M- 'J' M- ”T "T 'T

i i i i i i i i i t i i t i i i i i i i i I i i i i i i i i i i i i t

ro in ro r^ ro 00 00 CO 3 in — r^ — CO <r 00 p' — — CM Pv in T in 3 in CM —

in in 3 3 in 03 3 03 CD 3 P" in 3 CO in ro 00 3 (M (M 00 TT —

CM 3 3 3 P* p' ro ro CD in p' P' CO ro CM r- CO — 00 s 3 — CO 00 — 3 P' m- CD 3 3 3 — CM 3 s •^r 3 CD

ro in in CD p' CD ro 3 CO in ro CO CO p- CM CO p> CO 3 ro 3 3 3 in 3 3 ro 3 3 (M 3 CM

ro CM (M _ (M ro CO in CO 3 CO CO p^ ro 00 p- CM 3 CM in 3 CM — V CM 3 ro 3 3 CD p. CM

p* 00 ro 3 ro p" ro in s 3 CM CO — in 3 3 CM 3 «

00 ro ro ro 3 in — 3 3 — p^ P- 3

00 <r ro ro ro P' — 3 3

ro 3 3 3 CD p- CM ro ro CO ro CM ro 3 Pv 3 p' in 3 3 CM in _ 00 3 in CM 3 <r 3 ro P> rr ro >

3 "'T in CO CM ro CM 3 3 •

V ro CM ro 3 in in CM

CD CM 00 in .

CM CD CM CD

ro 3 CM 3 p^

in p* P- ro 3 ro 3 3 ro 3 in 3 •'T 3 p- CM 3

CD 3 CD — p- T O

3 — 3 CO in rv — 3 3 00 CO 3 3 CM •'T 3 CM 3 — 3 3 3 CM — ro

P- 3 CD 00 CO CO CO in CO in CM CO (M 3 ro (M 3 ro 3 3 3 CD 3 — 3 3 3 3 P* p' pv in

CO P- CD CO CO CO CO CO CO CO CO CO CO CD CO CO CO CO CO CO CO CO CO 3 in in 3 in in in in in in in in

i i i i i i i i i i i i i i i t i i i i i i i i i t i i i i i i i i i

CM CM CM CM CM CM CM CM CM CM Csj CM CM CM CM

CM

CM CM

CM

CM CM CM CM CM CM CM CM CM CM CM

f

— — CM «

CM CM •

— •— • • * •

— — * •— — ^•— •— «— «— *

^

CM

1 i i i i 1 1 CM 1 1 1 1 1 1 1 1 — 1 1 1 1 1 i i 1 » 1 1 i i '

3 3 3 3 3 1 3 i 1 3 — 3 3 3 3 3 3 3 3 1 3 3 1 3 3 3 3 3 3 3 3 3 3 3 1 in — P* 3 3 3 3 "T 1 3 ln 3 CD 3 P' 3 3 O) CD 3 — 3 G) 3 3 3 p' 3 in 3 — 3

3 in — CM p- ro ro (M "T 3 ro p' 3 in ^r 3 3 — *— in 3 in *T 3 CM 'T 3 — p- in P- P- 3

’•T CM in S 3 — ro P- 3 3 CD «— O TT in CM 3 3 in 3 in p- — P-

in P- 3 CM 3 3 CM in

3 3 ro ro ro 3 — 3 in 3 O) CM ro

CM 3 P- P^ ro CD CT) ro «— in p- — -- <M P- P- CM 3 —

P* CM p^ CM CM 3 3 ro 3 3 3 3 CD 3 — P- 3 3 p' ro CM 3 3 3 ro NT ro ro P^ CM 3 3

in 3 3 3 3 CM P- p- m- 3 — 3 CM (M 3 CM

S O

CD O) in CM ro 3 3 3 p> 3 p- — in P- 3 3

in 3 in 3 3 3 CD CM P^ P- ro O) in (M CD CD 3 CD 3 3 CD — CM 'T 'T 3 3 3 s V 3 3 3 3 3 P' CM — 3 CM 3 ’T' 3 — CM CM 3 3 3 3 3 PJ ro 3 — ro — in ro ro 3 3 'T P' 3 3 3 in ro CM CM ro — CD — 3 CD 3 P^ in in 3 in in CM ro (M CM • CM — • 3 3 3 3 3 3 p' 3 Pn

in in in in in in in •'T in <r T •^r "T 'T 'T 'T rr ^r ro 'T ro ro ro ro ro ro ro

3 3 3 3 3 3 3 s 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 S 3 3 3 3 3 3 3 3 3

3 3 3 3 3 3 3 s 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 S 3 3 3 3

in 3 in 3 in 3 in 3 in 3 in 3 in 3 in 3 in 3 in 3 in 3 in S in 3 in 3 in 3 in 3 in 3 in

3 .

CM CM ro ro T <r in in CD CO P' p^ 00 CO CD CD 3 3 — — CM CM ro ro NT ^r in n CO CO rv. P' ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro rr T <T 'T "'T rr •'T 'T
-98-

i

cd in co CM no — n NO n CM — — n ao NO NO CD — CM NO NO CD — CD TT CM CD 3

CD CM in N- Q O) Q CO CM CD CM CD 00 oo CD CM CM NO NO CD CO CD CD 3 CD NO CD 3 CD CD CD n

in cd CM •

no 3 n n« no CD N' CD 00 CD r- n CM CD CM CM n N 3 CD CD NO — .

CO CD n CD co — CD CD NO CD M- CM CD (3 no M

- CD h' CD n M" CD 3 CM -NDQM- — M

- Ns S .

CD CM CD CO 3 — — CD cd M" TT no 3 n n cm CD CM CD ao Ns CD N' N- NO CM 00 3 Ns 00 3 TT . n 3 CD cm in •

CD r- cd CM NO CM S — 00 CD CO NO T 3 <

— NO NO Ns 3 NO M- — CD CD CO CD 00 Is* 3 -<r CD C\J NO M

- CD CM NO M- r- O) do r- CD n CD NO •

tt CD CO CM CD 3 fv NO M" — CO CO 3 — CD CD — co N- 3 <3 ID n n r>. in NO CD CD CD — 3 3 in CM 3 CD N~ CD CD Ns •— CD CM

CD — CD CD cd n r- CM ”T CD cm n m- n CD CD (M CD 3 DDQCON n n co n NO — NO CD T 3 NO 3 00 Is (\l K) CD CD cm co n NO CD N* CD CD tj- _ N' -- n NO V 3 CO •— M" s NO CD n

NO no NO CM CM NO ISO NO CD NO I'D NO CD M" NO NO NO NO NO M- V N" V V T m- n T M- M- n n M- M"

''T M" TT M" M" M" rr M" rr m- m- M- T m- T T M" M- V M" T V tt M- M- M" M" M"

I I I I I I I ! I I I I I

I I I I I I I I I I I I I I I

T n NO N'- 00 .

CD NO CD n ^r rr r- a

CD — Ns n 3 ,

M" CD n CD CD i\ CO CD 3 Ns n CD CD

CM CM 00 NO 3 n CD 3 3 3 00 Ns CD n CD 3 3

r- CD .

CO 3 NO 00 CD 00 3 CM in •

in M- CM

NO CD CD NO M" (M T CO CD — Ns M" — NO CD CM 3

n 00 00 M" 3 CD n NO m n 3 NO — n n r- n 00 S M" 3 CD CM CD s CO n CD CD — CD

NO .

CM 00 — 3 — n 00 N' n CD n NO CD CD

CM ao n .

CD CD NO NO NO CD CO 3 N' 3 a

in 3

CD N* — CO — CD CD rv N* CD CD M- CM CD — n 3

n CD n n CD n CD NO CD NO CD CD NO N- CD 3 3 CD CD CM 3 3 00 NO CD CO CD — .

NO CD 3

NO 3 n NO n T 3 3 M~ CO NO N' CO GO CD n NO

CM 00 M" CD CD n — NO n CD h* — CD n n _

NO CD TT — CD CD n Ns s 3 CD CD CD n CD 3 NO — r\ r' 3 00 »— CD n r- CM G) n

NO CD NO CD 3 3 — M- -- 00 3 CD CM ao CD N- CD

CM

CO M" 00 3 CD r- v r^- — M- CD 3 M" N* 3

M" 3 Os) CM n M* •— n NO 00 CD 3 P'- .

3

CM CO m in Ns — M- CD CM s CO CD — — M"

CD CM 00 NO 'r 'T CD — — CDNON03CMCD3'-CDCDCOa)CDNsCDNOCOM-COCONOCDNOM-CM

miDlDLOiDLDLOlDLDLD^lDlOLOiD^riDlD^^r'T'T'^'^r-^r^rTr'^-'^^r^r'^-Nr'^-Tr

I i I i I i ! I I i l I I l I l I ! I l l l I I I I I I i i i i i I i

CM CM (M 3 3 3 3 (M CM CM (M CM <M CM CM CM CM CM CM CM CM CM CM Cm CM CM CM CM CM CM — — — 2 2 CM — — CM •— *— •— —

1 LlI1 UJ

1 LU1 LlJ

1 3

1 UJ1 u i 1

1 uI UJ

1 UJ

1 UJ

1 UJ

1 LU 11 UJ

1 LlI1 UJ1 UJ1 UJ

1 u1 UJ1 u

1 UJ

1 LlI

I UJ

1 u

1 u1 UJ 11 UJ

1 UJ

1 u

1 UJ n 3 n CM 3 — u u -

in 3 — 3 3 UJ NO 3 T 3 3 — •3 CM in n n M

- 3 3 n M

- 3 — 3 3 3 3 n T NO V 3 r- NO 3

(M CM 3 n n N' CM NO CM CM 3 3 3 3 M" 3 — 3 n NO 3

r- CO n 3 h> — n n 3 — NO N- 3 3

n 3 3 n NO NO S M" NO N' 3 NO 3 M" Ns CM CM 3 3 n 3 — ''T — 3 3 3 n CM 3 3 M" 3 3 n 3 3 3 3 <r CM — n 3 — NO Ns 3 3

CM CM 3 3 NO 3 3 "T — r-' — CM — 3 CM 3 3 — in 3 NO — 3 3 3 3 — CM 3 3 CM Ns

-

3 V 3 r* CM M* 3 3 CM N' 3

in XT CM 3 3 N- NO CM 3 3 3 3 3 3 — 3 3 CM Ns NO CM — 3 3 M- 3 3 M" V 3 3 3 3 NO 3 3 3 — NO — 3 3 3 3 3 NO NO n n CM 3 Ns — M" 3 3 3 3 »— 3 r- CM n CM r- 3 3 3 r- (M CM 3 CD n CM 3 3 n CM Ns n 3 Ns NO n n 3 I s* n M" NO NO NO in CM M" 3 NO CM NO CM CM 3 — 3

3 3 3 3 3 — 3 3 3 3 3

NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO CM NO NO NO NO CM CM NO NO CM CM CM NO CM

S Q 3 Q N S QinQ

CO CO O)

v v ^r

3

s

if) CD

S 3 s 3 3 3 3 3 s 3 3 s 3 3 3 3 3 s 3 s s 3 3 3 3 3 3 3 3 3 3

3 Q 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 S 3 3 3 3 3 3 n 3 n 3 n 3 n 3 n 3 n 3 n 3 n 3 in 3 n 3 n 3 n 3 n 3 n 3 n 3

3 3 — — CM CM NO NO 'T rr n in CD CD Ns CO CO CD CJO 3 3 — — CM CM NO NO T m- n

n n n n if) n n n in n n m in n in n n n n m CD CD CD CD CD co CD CD CD CD CD

-

7957536996

-

45

.

0943050894
65500

2

.

78

1

360643E12

-4

1.6408720295

-45.2901029745

- 99 -

CD CNI CD oo p- O) CD — CM CO CO CD CD CM lD CD CD TT CD CM ro ro ro CD ro "T p- ID ID

00 — CD 3 CO 00 CD •'T 3 CO CD CD 3 CD LD CD 00 CM "T CD CM M" *— CD p- p- CD p- CD CM

CD P- CM CD CD TT CD CM —

TT — LD LD 1^ 00 LD CD ro CD CO TT CD 00 CD ro 00 00 p- 00 CD V r-v 00 ID CD CD CD CM <r p- «— TT LD ID

CD 00 SI — LD CM CM 3 3 CD 3 CD — ro ro CD CD ro — CM CD 00 (M id — CD CD CD CD CM — I s- CD T ro ID ro ro CD LD ro xr CD — CD •— 3 3

ro — cm K) ro 00 — 00 ro ro CM CD CD — 'T LD 00 r- LD CD ro CM CD CM ID CD — LD ID CO CD CD

P- CNJ CNJ 00 ro 00 O) ro r- "T CO CO CNI CD CD CM s ro — SI 3 CNJ ro LD 3 ro p* p- ID 3 3 3

r- id ro “T ro 3 (3 — CD 3 (3 — ID ID CD CD CD 'T M" 00 00 ro CM •— ro CM 00 p- Is* ro CNI ID CD CD (3 M" 00 ID — (MS) r- — ID *

— <3 ro 3 CO *— ro ID CD ID 00 CM S ro CD CD ro ro 3

NO TT CM s — O) CM CM P" 00 rj- CD CD CD 00 r- CD CO p- CD 00 3 3 CM CM CD CD 3 CD — ro

ID 'T ID ID CD M- ID ID ID ID ID ID LD LD ID LD lD LD CD LD LD ID ID CD CD CD CD CD LD CD CD CD CD ^ <r M" ^ t 'T TT 'T *r T "T <r M- T V 'T M- M- V "T NT V

r i l I i l i I i i I i i i i i i i i i i i i i i i i i i i i i i

CD CD — 00 LD ’T CD ro 00 CD CD p- P" 00 — CM ro p^ LD CD CM ID 00 CD CD ID CD — CD

CD CD ro ro — LD CD CD 00 3 CD — 3 CM CM — 00 3 CD p- I s- a) ro ro 3 OO 00 ro CD 00

CO rr Is- CD (M — 00 — — rr •'T p- — CM CD ID *— p- — 3 ro '<T ro — 00 CD CD r^ ID 3 ID 3

M" r- p- CD .

00 CD LD ro p- CM ro 00 00 CD "T 00 3 03 3 p- TT 3 3 CM 00 CD CD CO ao CD M- ro 3 (M — LD ro ID ro ID 3 ID CD 3 CD CM CM ro CD 00 CD 00 00 CD 3 (M — 'T O

CD ro CM 00

CM CD CD r» (M ro M- — ao CM 00 3 M" — 3 M- ID ro ro V ID 3 3 V CM — ro — CD CO CM 3 3 p- 3 — V «— <M — — CM ID CM 3 ro LD p- P* LD CM >

ro ro 00 00 00 V O) CM CM CD CM

CD CNJ CD ro ro 00 p- ro 00 ro CD ID CD — CM 3 — ro 00

CM — V •'T 00 — LD T CD CM ro CD CM ID — CD (M CD CO — CM — 00 3 3 LD — CD 3 CM LD CD 3 *— ro — CM P^ 3 TT CD M" ID CD CD CD CD ID (M T ro CM 00 CD CD P- — ro 3 CM 3 CO CD CD CD s ID CM CD Is- LD

cm ro to — cm — CDCM33a)p'COCM(DiDooLoaop'-rop'CDiDiDM-M- >'TroTrcMCD(M

M- ,<rM-M-M- ,<J’rOTr'<r'M-roioro'<rrororororororororororororororororocMro

i i I I I I I ! i i i i i i i i i i i i i i i i i i i i i i i i i i

C\l CNJ

I I Ld Ld

M" CD

P- CD

io p- ho p- — 3

CD CD

lo r^

LD '<*- s

CNJ K)

CM CM CM CM (M CM CM <N CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM

1 LlI1 LlI

1 U

1 LlI1 LlI

1 LlI

1 Ll!

1 LlI

1 LlI

1 LU1 u

1 LxJ

1 LlI

1 LlI

1 Ld

1 Ld1 Ld1 Ld

1 Ld

1 Ld 1

1 Ld

i Ld1 Ld1 Ld

1 Ld1 Ld1 Ld

! Ld

I Ld

1 Ld

1 UJ CD — CD — 00 I s- ID 00 CD LD P- OO CD LD CD CD ID "T Ld CM CD to CD P- CM LD P- CD .

CM ro ro M- I s- 3 LD 00 ro ID LD ro CD CO CM CM 00 — CD —

3 CM ro CM CD 00 — 3 CD P- 00

ID — LD 3 CM CM P" CM 3 ID 00 CD LD CD ao CD CD 00 ro CD 3 p^ CD •*r CD ro CM CD CD

O) p^ CD ro ro (M ro CD CD CO ro ro T CD LD 3 CD P- LCD LO CD ro CO ro CM CM ID ID CD P^ CD 00 — —

TT ro ro ID CO CD CD •<r CD CD CD ID CD 3 — — 00 3 — T p- CD — — CD — 3 — •

ro 3 LD CO "T — LD CD ro — CD P- T CM M" CD ID CD P- ao CO CD 3 LD (D <T 3 T CD

CD — CD (M CD ro 3 — CM h- CD 00 CD CM — CD CD CM LD ro CD CO CO ro 3 CM •^r CM T CM

s CD 3 CD 3 3 LD 3 ro P^ Is- CO — lD lD CM — ro CD 3 ro LD 00 3 S P- ro S CM 3

00 00 ID 00 00 00 CD CD P-- CD CD CD LD CD CD CD LC^ CD CD LD CD LD ID M- ID ro LD ID ro LD T

CM CM CM CM CM CM CM CM CM (M CM (M CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM

3 3 S 3 3 3 ssssss If) Q Ifl s in Q

cd r* co oo o> CD CD CD CD CD CO

3 3 3 3 s 3 3 3 3

ID LD ID

CD 3 3 — —

CD P- rv P^

3 s 3 3 3 3 3

3 LD lD 3

CM CM ro io NT P^ rv Pv

3 3 3 3 3 3 3 3 3 Q S 3 Q 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

UD 3 LD 3 ID 3 LD 3 LD 3 ID 3 ID 3 LD 3 LD

LD LD CD CD P^ P^ 00 00 CD CD 3 3 — — (M CM

P-. P^ P- Is* p- h- P- P- P- P- CO 00 00 00 00 ao

32.64819528)1

-46.5633598601
83000

2

457769592E12

-29

.

7265507238

-46

.

3644257402

- 100 -

.

LD CD CM — CD rr CO — CO I s- 00 p- — p- TT CM lD CD ro p- 00 CO — CO , CM CD ro ID CO ro CO r- -*r LD ro p- cm ro — ro 3 — — 3 00 LD CO — LD CD — 00 CM ID CM — CD 3 ID Is- PM" CD CD 3 ID ro CD 00 3 CD 3 00 — — (M LD CM ro LD LD CM —

'T 3 LD 00 ro CD M" CD ro 3 ID CD 3 3 CO Is- — M- CM s ro — LD p- 00 CO LD M" LD V ro CD CD I s- ro CD CD ID 00 00 ID ro 00 CD

CM 00 CD CD M- 3 CO 00 — CD Is- s 3 CM CD CD CD CD CD CD 3 ro Is- CD Is- M- rr — — CM LD CM CD

CD CM CD 3 ro ro M- 3 ro CM 00 p- 00 3 CD CO 3 CM ro 3 — 3 00 LD CM CD CD LD — Is- 3 Is- 3 — ro 00 CM CD — CD CD CD CD M" r- — LD 3 — LD LD LD 00 ro CM CM CM CO ro CD CD CD CD CD CD ID 3 ro ro r- M" ro 3 oo CD CO CD CM cm p- ro CO CM — LD LD CM ro — — ro — CD 00 CD ro 3 CD CD p- — CD ID p- M" CO Is- CM CO CO p- ro cd CM 00 CO CD ro 00 3 ro CD CO 3 CM I s- ID ID ro CD CD CD

CD CD CM CD •— CM CO •'T 00 T M- r- 3 CD 00 *

ld 00 CD p- CD CD CM LD 0) 3 — ro rr ro — S ro

CD LD CD CD Is- CO CO CO CD CO p- CO p- CD CD p- r- CO CO Is- CD CO p- CD Is- p- (\ p* p- p- p» P- 00

TT TT V M- m- rr M" M- M" M" M" M" T M" 3 T T "T xr M

- M- V T V

i i f i i i i i i i i I I I ! I I I I I I I I I I I I I

ro CD cd cm

r- p- m- — ld

Q Is* p- 3 ro

CD P- 3 CO CO

CM 3 CM CO CD CM LD P- LD CM 00 ID CD CO CO — PO P- CM

P- CD 00 CD 00

P- CO 00 ID CD

S CM 00 S CD

ro ro cm ro cm 111)1

CM (M CM CM CM

I I jJ LjJ 3 ID

DO 3

3) ^r M CD

3) 3

LD <3

30 P- M IT)

I LlI 00

p-p-ro

ro

I s- Q

3

ID

I Ld

in

S

(Mro

oo3

ID00

CM

ID

03CMro

coCDro

CM

M CM CM CM CM

CM I s- LD LD CM

3 r- ro CD LD CM 00 a

— 'T CD CM 00 — CD —

.

00 ro CM — CM CD

p* 3 CO CM — CM LD —

ro LD p- CO 3 Is- CM CD — CD — p- CM — LD rm- 00 3 CD CD M" 00

CD cr CD 00 P- CM 3 r- CD 00 CM CD CM 3 3 3

LD CM rr 00 3 00 3

ro CM ro CM CM ro CM ro

I I I I I I I I

CM CM CM CM CM CM

CM r--» CM

1 Ld1 Ld i1 u

1 OJ Ld 1

1 Id

CD CD Ld 00 CD 00 Ld 3

LD Is- vr CD ID CD LD

00 ro CO M" T P- CO 3

00 p- CD CM CD CM CD 3

ro ID 3 3) CO 3 P- 3

p- p- CD ro CD 3

ro 3 ro CD CD M" ID ID

oo 00 CM «— ro CD CO

m- ro M" ro — ro CM

CM CM CM CM CM CM CM CM

CMLDlDCOOOCOlDCOCOr-CMV LD 3 CO LD 00 CD POlOLD'M~33CMOOM‘3lDCO',3'IDCOCO'M'COP-3(M — SOOCMlDCMfOaOCMOOCO — [OiDSlDM-ro — Q — 3LD3 — CD3LDCOP-COP-CDCOLDSQ^rCMCDM-p*

CDrv-oocococo(\icDLD(M',T M"3ror^p^cop^roroco

rocDM-iDrocM — — (MrocscMr^roLDCDcoaocDoo —

33CMSP-LD3PMLD ,'TCOP''33' M" LD CO Q CO (SCOr-l^— rOCD'TLDM-’q- — LDCMCDM-CDCMM-rOCD oosr^CMiDCMM- — M-r-cMior-CDr-cDooroTj-GDiD

oo — oor-CDcocD^rcscMrocscocOLDro — qsld v

3 CO 3 CD ro — ro ro ro LD T ro ro 3 *— LD P- TT 3 3 3

CM

1 CMi CM1 CM

I CM

1 CM

1 CM

1 CM

i CM1 CM1 CM1 CM

1 CM

1 CM

1 CM

1 CM

1 1 CM

1 CM

1 CM1 CM

1

CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM

CM — CM — — — — — —

1 Ld

1 Ld

1 Ld1 Ld1 Ld1 UJ1 Ld 1! Ld

1 LlI

I LiJ1 u1 UJ 1

1 Ld1 LJ

1 Ld

1 Id1 Ld

1 Ld

1 Ld

CO —CM r- CD •

DJ

CD CO CM CD dJ ro ID p- CO CD ro CD

CD CO p* 3 3 ID CM ro CD S CD ro CD ro p- ro CM M" CO CD —

ro 3 ro CM P-

CM CD 3 3 — ro ro 00 CD 3 P- ro — CD CM

ro 3 CD CM 3 LD LD CO — ro CM ro T CD LD CD ro ro s P- p- P-. p- CD CD P- 3 CM 3 — CD CO I s- P- CD 00 3 s ro CO 3 LD — — I s- ID 00 CD M- CO

— T LD LD CO CO M" CD CD ro — CM LD 3 CO CO CO — ro p- 3 ro CM CO CO — CD CM CM ro

CD — LD ro CM CO 3 CD CD CM 05 03 LD CO CO CD M" M- — 00 ro ro CM — ro CM 3 ro ro CM ro 3 CM CM — — — CM CM 3 —

CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM

3 3 (3

3 SI 3

D <3 ID

M" 00 CO

3 3 3 3

3 S 3 3 LD Q ID

ID LD CO CD CO OO 00 00

3 3 3 3 3 3 3 3 3 3 3 3 Q 3 3 3 3 3 3 S 3 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3 LD 3 ID 3 LD 3 LD 3 LD 3 LD 3 LD 3 LD 3 LD 3 LD 3 LD 3 LD 3 LD 3

P- P- 00 CO 3 CD 3 3 .

— CM CM ro ro •^r LD LD CO 3 P- P- 3 CO 3 3 3

00 00 ao CO 00 GO CD CD 3 CD CD CD CD CD CD CD CD 3 3 3 3 3 3 3 3 3 —
- 101 -

(\j (M cd in oo cm O) O) in co cd cd in cm — ro — cd oo — — ld cd — ro oo t cd in ^iDinoooQQMKiQ^cniD'Troro roinscosh'i^cM — — cDCMinscM — — q

inoo"TCDT — ’^•rN' ,r(MCJ) — (SCSor^TTNiinoorocMinscMr^^r — o)N^cocoro(MK)

cd — coin^cnr^sin — — horoco’^’N^Q — (MNin — cm — cdki — Kiinoor^ca — ooTr

CMin^o) — qcmocd — cDoorocMCMcoroscDOor^inrocDcDQoocoajoxDCDO) — o)

inininroro — (DCOQCoroincDS — mcDCDC3rocDhoooo)Ln ,Trooor^QQin — incM

K)^r — cd^t — (MC^r^OhocD — (MQincsinoohococncM — inr^.'-Qror^ooQCMcocM

0)(DinroooiN'K)Q(D»sos — cm ro — ocDCMinor^cDinininsrorocoinin^r^cj)!^

CDf^CMr^lOO) — CO^T — 3CDCM3 — — 0)L0L0<N’T00inrorv.r>nSQ00I^CMinC0in’-

^r-«rcDS)^rin<\KD — ojor^Tcor^ooo — (MOcohomh'CMTCMcDCMCDCDr^incDS

Is- Is- 00 rv l\ CD 00 00 CD 00 r^. rv. CO r'v 00 CD 00 00

M1 ^r

i 'Ti ^r

i mi i i M1 V

i ^rI i M"

1 t

i 'T1 l

•<r

i M1 M"1

•'t

1 T

1 TT

1 I i "T

1 "T1 i 'T

1 'T

1 T

1 T1 TT

1 TT

1 i ^r

I M"

1

CD r* in in "T 00 CM CO 'T CD CO CD CD CD CD in CD CM CD CM CD CD 00 ro

•«r CD CD CD s <3 in CM CO rv ro ro — 3 1^ ro ro T — CM in 00 — CM — 00 in in CO in

M

- in — CD 3 — ro ro CO S) M" r- CD CM CD CD (3 CD S3 SI CD CM (3 r- in 00 CD — CD ro 00

r* r— ro 00 CD S ro — M- CM in CD 00 CD ro S3 03 in (3 ro — — •— CM in in Q CM M" 3

0) 3 CD 00 in M" 00 CD 00 CD CD 00 00 — CD CD CD CD ro CD in S3 CD r^ CO CD 00 CD «— 00 CD CD CD

in 00 CD ro O) 00 CD — CD CM CM CM CM in *— T <s 00 ro 00 CD s CD ro CD CM CM CM

CD CD «— SI 3 in in 00 CM 3 in 00 0) ro ro 00 S CM CD in I s* CD 3 3 3 CM 00 in M- ro CD

in s 00 00 r* m CD r- CD CO 3 •

00 s *— CD CM CM CD CD •

3 in CD in O) CD 00 3 in CD

00 S — 00 bn ro (M CD 3 M" V in ro CD 3 — CM CD *— CD TT CM CO ro in 00 CD ro 'T CO CM in CM

CD 00 <3 a) <3 in T r- CD CD CD CD — Si S) CD in S3 CM ro 00 00 ro in in ro CD CD ro CD r\

in

ro 3 • T O) . CD

00 in 00 in 3 in CD CD in CM CD S3 CM CM CD si CM 3 — ro 3 . 3 s

CD

i i i i i i i i i i i i i ii i i i i i i i i i i i i i i i i i i i i

CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM

1 1

1 ! 1 1

1 t 1 1 |

I

| 11

» 1 1 1 |1 i 1 1 Id

1 Ld

1 UJ1 bJ1 UJ 1

1 UJ

1 UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ Ld 1 Ld UJ Ld Ld Ld Ld Ld Ld Ld Ul UJ

1 Ld1 Ld Ld

1 Ld

.

CD CO r* Ld 00 CD — ’T 'T r\ CD CM CD — M- 1

CD Ld CD — 00 CO CO in CM in M- ro CM CM ro

M* 3 00 ro ''T — CD 00 ro CD ro •— ro ro CD CM in 3 ro CD in CD 00 in CD — CM 3 CM T CD

CM ro ro CD 3 I s* CO CD 3 in 00 3 CD 00 ro >

CM in CM in 3

CD 00 CM CD CD CM •

ro CD CD

in 3 CD ro 3 — CD s 3 r^ 3 CM -

00 CD CD — ro CM .CM CD ''T 3 CD — 3 in 1^ ro

CM CM CM CD — 00 CD 00 CD CD CD CD 3 rr CD 00

CM 00 in in CM CM CD 'T 3 3 in CO CD

r* CD ro s CD in CD CD 3 — CM 00 CD 3 00 CO CO — in CD r- CM 00 CD ro 00 in — CO CM •^r CM 00

CD .

in CO CM CO CD CO CO T CM in — M- <

00 M- m- r- CM 00 CM ro •CD

'T in |\ —

in CD CD CD ro (M — in 00 in ro 3 in •

CD m CM M- CD r» ro ro CD CD CD ro

ro — — 3 CM *— — CM — (M 3 CM CD — —

s ro CD CD s ro CD — 3 CD *— CM — CD ro CO 3 — — 3

CM CM CM CM CM CM CM CM CM CM CM — CM CM CM CM CM — — CM CM — CM CM — CM CM CM — CM — CM CM CM CM

SC3QSQSQSQSSSSSSSS SSSQSSSSSSSSSQSSS insinsinsjinsinQiDQinsinQ^

S)*-^-C\j(M|sOhO^rM-inLOCDCDr^r^CDC0 8SSSSSQSSSSSSSSSS

s 3 3 3 S 3 3 3 3 3 3 3 3 3 3 3 3 3

3 S 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3 in S in 3 in 3 in 3 in S in 3 in 3 in 3 in

CD CD 3 3

— CM CM ro ro T <r in in CD CD r> S 3 _ _ _
- 102 -

CD '=r CD r- r- bn CO r- 00 — CM in CD NO — T CM CD v CM

CD CD — (\l — 00 00 LD — CD — NO CD NO CD CO TT 00 NO NO

r- ^r 00 3 m- CD — CM in s CM n- m CD r- NO rr CD 3 CD s CD CD CD CD CD (M in — CM N- — -

NO (M CM 3 CD 00 NO

r^ CD T NO bn CNJ NO 00 CD — CM S in 3 3 — .

CNJ no 3 — CD M" C\l CM — CM

NO M" CD NO CD 1X0 CD 3

(M NO bn 00 LD 00 — M" NO in CM CO 00 CD in TT N- in CM 00 N' — 00 CM bn CM r- CD CD NO i^ rr NO s in oo 00 'T CD CD N' (M CD ID 00 CM CM CO CD s in 00 00 M" r^ T — M- (M XO

CD CD CD CM CD r^- NO LO CM CD CD CM N- s CD NO XO M

- CD

i^i^i^CDi^r^r^r^r^cor^Nr^r-oor^r^cDr^cor^

T'«j-rr'T^Tr'^-rrTr^r\r'r^r'T'^r'T'^-'T'^r'^r^r

I t i i i I i i i t i i i i i i i i i i i

cocNJCDr^^cDr^mf^

SSCDNOCMN'-NO — 3

in c\i CDXO'TCOCO — XONOr^-CD CD

COS — COC^-— X0 — SOOCD I CD 3 CD 00 CD — NO — 3 — CD M" CD 00 NO CD NO CM 3 XO Ld

CD QO NO N- M

- NO NO CM >

Q CO ’T ID N Q NO co r* XO

in (M •'T 3 CM CD NO NO NO XO 00 CD NO CM S NO M- xo m- NO

00 NO 3 00 CM XO N- CM CD N* M" — 3 NO N- CD CD cm r>- CD

CM XO N' XO rr CD .

N- T — CD XO NO "T M" NO CD CD M- —

NO CM XO N* NO CM CD tt CD NO — CD 3 NO (M CD CM S CD CM

CD CM M" CD NO s NO — — 00 s 00 S3 CD 3 NO NO XO 00 N- CD

cm r- 3 — CM NO CM NO CO M- NO XO XO CM 00 rr CD P- CM CD X)

NO 3 N' 3 — 3 CD CD n* r- 3 CM QO — CD Q — CM — CD —

- * • • • TT • • -

- IT) —

CM 00 XO M" NO Is- CM CM cm r- CM 0 fr 0 2 CM •

1 1 1 1 1 1 1 1 i i 1 1 1 1 Q 1 l 1 1 * NO

(M CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM

CM —

1 CM1 — CM

|

| | | | | | |

- 1 12 2

1 LxJ

1 Ld Id 1

1 Id IdI Ld Id 1

1 Ld Id UJ Ld Ld Ld Ld Ld Ld l i LjJ M- CD Ld NO M* CD CD id NO XO OO N- CD CM CD CD U Id

NO — CD 00 CD M" CD XO NO CM h- CM NO CD N' — N- CD T 00 M" — NO NO s Nv — CM XO 3 CD (M XO N XO CM CD 3 3 CD 00 in

CD NO — — •

CD in CD N- 3 M" ^ N S S ID D X S CM CD

r- in NO 00 r- XO CD CD 'T CD — 00 N 3 CM 3 (M OO Nv CD CM

'T NO — M" — CD «— NO CD 00 CD — CD 00 00 CD CD NO NO S CM

rr NO N' S M" 00 s CD m- 00 CD — CD N- NO 3 CM TT 00 CD

in m- V r- XO CO s NO CO 00 — M- — 00 CD CD CM CD V NO

s s 3 CD 3 3 CM ~~ 3 CD * 3 CM S CD (M — CD — CD —

CM CM CM — CM CM CM CM CM — CM CM (M CM — (M CM — (M — CM

S s s s Q Q Q S Q Q Q S S S S s Q S Q SJ 3 S s s s S S S s S Q S Q Q Q S s S S S s 3

S xo s xo S XO Q xo Q XO Q XO S in S xo C3 in <3 LO 3

00 00 CD CD <3 Q — *— CM CM NO NO •^r XO xo CD CD Nv r^. CO — — — — CM CM (M (M CM CM CM CM CM CM 12 (M CM CM CM CM CM
THE

nAXIMliri

VALUE

IS

5.11

4020372E- 10

AT

LOCATION - 103 -

ii

III|

<3I LlI (M

in8

I-o

_1

CL

CXO

Li- en

LlI Q3

h-

«—

_J

Cl

TL<X<EQZ<

LlI I

CL

LlI I

Z
- 104 -

The following ten pages show the results of applying the software contained

in Appendix C to a step-like waveform with endpoint not equal to zero.

The first page shows the waveform as acquired from the DPO and the difference

waveform obtained by subtracting successive points of the original waveform.

The frequency spectrum of this difference waveform is tabulated on the next

eight pages and plotted on the last.

This software correctly transforms waveforms of this type.
- 105-

o-T

CD > > - —f •—

CNJ

aa

N \ '

(/) o CD X «

Q (X ~ — 00 i in - UJ • "T <S G> ' CNJ

CNJ • '

(_D ’

CD • Z

K) o »-• • 

z \- CL

in HO

t- UJ (— - Z f— CO U ^ CQ UJ < .— CO u_ CO s a Ld Z z

00 z CO Id o 1 o < CO J—

CJ CQ H—

u

U

O (- Ld h-

—' 1 CO z o: Q — Ld . Ld Ld

K> h- l- > QL
- 106 -

— CD CO LD X LD g LO CM X — NO — CM X g X X g X NO X g — CO CO X CD X X CM X X NO g — X X — X X N- g X NO

z s O' — CM g CO lD O' O' X NO — N* X N- — s CM NO CM X X g 3

10 CD X 'g- X CD X CM 3 — X X X X X X CM 3 X <3 X CM X CO LD g 3 3 3 N- g CM X X g 3 X X X X CM X (53 NO g <3 X

X CM CD X LD 3 g NO LD n- X X X X 3 X CM NO X , X NO X X (3 3 g X ID X cm X r-v NO — s X N' N- N' X X X — 3 CM g NO X

m 00 g X NO X X g X X N- X X X X X s NO s X CM X g X

X s N- X — Cm g CD X X 3 g X NO g X CM <3 rv- •— g CM NO

g * n- r-' NO LD CO NO X X NO X X X — CM X NO X NO CM <3 <3 <3

jC- X NO 3 s CM CM CD g X CM 3 g X X X g X CM X CM .

- X X CM

h- CM NO g g X LD X X X X X X X X X X X X X X X X X

1 X

h- 3 1

1 1 1 1 l 1 1 i 1 1 1 l 1 1 1 1 1 1 1 1 1 1 <

3

3 3

CD ID CXI — Q

UJ

***N < X

N X N S _l LJ ieis

j

a

Z Z X X

Z _l UJ 3 — Z • < .CO 3 — —' — X <

S3 — N X

CD X UJ X

CM U > Z X

— Z U

UJ Z Z _J

CO X UJ — _J — a x -

uj a a

>- co uj z

LJ X X O CO

Z X — hLU CD h- Z X

CD UJ Q 3 —' Q

a h- X X O X

X <1 H- O X K— QC X < CO —

X X J x > z

X x CL X X XXX z <

—• <. x -x z — LO X < O X

LD > X X a

XI- Ct X

X < (Jl cr Lx. QC

g Z X x X

•• z < dl x a

g m o x X X — ••ExXCClfl

- X —'CM

S O X UJ Ld UD 00 Z — X x X X

I OXl— 1 00

I— X <

x z x cr a. >- o f— X X X X o

I x x i— *— i~ x X

— X I Z z Z X

NO I— I— X X X <C X

X no cm no g x g no x

CM LD ID - CD N N (NJ (NJ CO - XXXCM — NO — NO SCOLD 'ftD(JQ'-O)(\lCM(D ,TSN-'-GgL0(\|MrON'<r(NJSrd) n - in g s s CDCDCMgcoo) 0)LniD - hosr^ — s no M(jDCD(JlDg^NDMnLDCDO)LDMN(\JLD(3-C0gC0(I)(i) -LDCOCOSCOOlCOOOSSWM^SCOgCOCDgKIMD-r' MJlDCfiCDCOODmOlQM-ODCDCOaOMSMOKiGinKllO

(MXNO — N-XN'NOXXSXSXCMr^X'-NO — x cm g cm —

OOCD'TSLfXMrOSLDCOLnLO CM3XX3XX — X g NO U)lDv03'rLl300WLn^(\JLn-S(\INl(\jKlCO'TO)CDO)U)M

•

• s •

- s s x • cm n- • - cm x x x • co ki - x x

(\i s co g • - • - -

• g n- • x • s • • xr'-xr'-xr-'-— scMNOXgxr^xxgNoxxsxcMxr''

I 1 — 1 I ID GO CO LD I 00 00 I I — N- g X I X NO I | tog3 — CMCMCMNONONONONONONogNONo no no no no no no

I I I I I I I I I I I I I I I — I ! I I I — I — — XXXXXXXXXXXXXXX I XXXXX I X I I Vt'TlD'-LONQNNUMLnCDOJfMXLOinNLIKDXgXX

NgC)LDC\J(\UON-SCDgg-COggroCO(JO-'TC]Of\l(\l NGgOO^-QM(\jNgC\JNCD(\jGNCD-CO'TLn-gg

LDONODCVJLOKlCDffiLnLOMCOKKD'-aOJhO^Oj COlO NgQg(Sg5)f\lDNOO ,nDlDrONggNDCDOJNCTNCri

CONON'T'<rNKl-CD'T(\lCnrOWO)CO-SSI(\)QNDCOLD

h' soiMoiQ-CDgQtNjcoaDNMnMSiKiLnojSNicoiiD MSS(MlD01CDO)S(\)CMSlCDWL£iLmr)ginuLO'JUD'-Q N(\jLniog(Nj-Ng-coQNDcoc)QgsMcoMir)-(\jg — — X < g g — NO CM g — O) CM CM — NIX — X — — K) OJ -

SSSS3S3SSS3

CJ s s 3 3 s s s s s 3 s SQlDQlOSlflSinOLOQ

ID CMCMNONOggXXX

3 3 S 3 3 3

<S (3 3 3 3 3 3 3 3 S 3 3 3

3 <3 3 3 3 3 3 3 X 3 LD 3 X X 3 X 3 X 3 X 3 3 — — 3 3

X N* N- X X X X
-107

— Goro^cotOT — (jdcd't CMP'CDCDCNriDCDfOiDPococQ'M-ro — cooo cd cm — c\i p'<ocD(\iiDcocMrO'TP'rocDp-p-cDCDr--OMQ^ Ln-rroco'T33CMCDcOM-iDLDroco

't^-'J-OOCOK)0)inM^COinN1COrO'TSOJCJ)LDMS ,rCDO)(SC75SrOhOTif)(\JMf)

Si — — SCDcocdtP'-co — cmco (Nr 3 — p-cd cm cnjidpo.— rocoM-CDrocoooiDCD

cocoroaocDrocMSP'-CMCOSio — P'-p-com-idscdlopo — pvlo^-oocoomco — co —

OJCflOOQf^lOhOCOCT — — lDK)CDO) Tflv CDSi^LDCnO)OOCDSQir)M(s-K)CD'rfvG

PO 00 PO CJ) ID S — lDrOrorOCMC0 C0 SLDLDCMP~C0 tDCM >'TC030MC0 CDlD'<rfO 0)(M(M'<r 'TioiDCMCOtO’T — — ro(srv>Lnc\JCDiDr^cDcDcoa)f\jLncncor'hoisooo(a(\jr^TrTrcD

ro — cocororo — — cD ,T”,TOosi(SO)TrcoLomcD(LD^rco'TS3(S p^ ro <s cm QOMP'-S — (M — CDCD"^ — CO — CMM-OMfOQOOP'COP'-S — LDP'-CDCMr''CDrO — 3POQO

cmidldcoP'IDP'P'CO' — PO PO CD CD PO ID P- CO P* *- CO ID 00 CO CO ro P CM CD - T LD — P' ID iocoidldidididldidcoi^

i i i i i i i i i i i ID

1 LD1 CO CO

1 1 LD LD ID

1 1 l CO1 CO

1 LD1 CO

l LD

1 CO1 CD

1 CD

i CO

1 CO ID CO

1 1 1 P

1 CO CO1 1 ID CO

1 1

p*— CD PO PO LD I s* CO CD 00 CO CO CD CD CO

(M — 3 CO lO 00 — P* — iD m- (3 P* CM ro oo v "T CO co p* P- lO CM 00 v P CD p CM CM ro id

cd ro — cd m- CO CD — PO CO (NJ PO CD LD CD CD 3 PO CM CO 00 p- CD (Nl 3 CD — CO LD p M- ID (Nl ID

(\J (M I s* CD — CO — 3 ID P- — (NJ P' 3 3 3 3 ID PO p* p- CM ID m- LD CM CO S ID (Nl ID 3 — (NJ r- (Nj f\j ni (NJ ^ PO P^ CD P- 3 ID "T CM CO 3 M- CO M" 00 CO 3 PO CO 3 3 ID (Nl CD ld ID 00 00 00 Q — P* CM CD PO CO CO (NJ pn p. CD CD P- — CM 3 (NJ 3 3 LD CO CD rr CO p — lO CD M" P- 3 P- CD

rr co co r-" ro CD P- ID P" CO — CM PO ID ID V PO CO CO T -— CD (NJ CD p- ID ID — 3 P 00 ld — (Nl

(NJ CO CD P* PO PO 00 P' Q CO CO CO ID

co co po 00 CD CD LD LD CM 00 CD — LO ID CD 00 P^ M' ID 3 3 ID PO LO CD CD CD rf Q CO P- (NJ CM CD CD ao 3 CD 3 CO ID p- CO CO CO P T - 3 M" CO

id po 'T ro ID P* PO CD CNJ "T CM CO CO CD V 3 co 00 3 •

CD pv ID 3 po ID M- M- ID CO TT 3 ro — PO CO - — (NJ • • • P* 3 ro 00 3 00 • CO 3 00 CO 3 ro - LD • co •

• • CO • — CO ID — PO • 00 CD CD LD CM • M" p • 'T P- 00

co co 3 m- ro 3 CO P" (NJ P- 00 CO CM p~ (NJ PO CM "M" (NJ PO — PO P* M" CD rr 'T ro co co i^» CM CD CM —

PO (NJ 1 1 CO (NJ 1 1 1 1 *

1 (Nl p- PO (Nl 1 1 1 l 1 (Nl Pv LD 00 1 i p i i ro i 1 1

po po ro po PO PO PO PO po PO PO PO ro po to PO po ro po M" "T PO PO M"

1 1 — PO —

1 1

f 1 PO ro "T — — —

1 1 1 1 I U Ld LlI Ld LU III*

UJ LlI Ld UJ

1 1 Ld Ld

1 LdI u1 Ld

1 LlI Ld i ill Ld Ld 1 Ld

1 Ld1 u

1 Ld i 1

1 1 1 LjJ Ld LlI

1 LlI

1 1 Ld U

1 1 iLi U

0) CD CO CO PO CO r* CM — P* «

— Ld ID rr T UJ CD CO p- Pn Ld UJ CD ID p 00 CO CO CO 00

cd 3 cd ro m- co co co <3 CD CD PO — 3 P- PO (NJ "T — p — CO CO CO P PO lD CO — — CO — p- CO PO Tj- rr PO p- co p* PO 0) CO CM

3 CD T ’T PO O) (NJ CD 3 ^r — CO rr CD LD CO V LD CO p- p-

(NJ "M

- ID 'T CO m- 3 — PO LD

P* CM PO T CO CM 3 ro P' ID CO CD CD P 3 3 3 PO —

CD (NJ CO CD ID S If) Q ^ Cm O) CM LD 3 p. p' — CO p. — cm ID CM P- ID ID CO PO CD ID LD (NJ CD M" CO (NJ ID (3 CO CO (NJ PO CD LD M" M* TT CO 3 CM CO ^ 3 — PO (Nl — — CD rt — CM PO CO CO 00 — LD (Nl O) — Ps

CO CO ID 3 LD CD LD i

PO 3 p- ro ld PO LD TT p •— p "T CD PO CD 00 CO — ro co M- CD

S ID CD CD P* PO 3 (Nl CO CO PO CD 00 CM co 3 P* CD (NJ ro CO (NJ p* ro (nj (Nl CD P' (Nl 00 3 co p- m- 3 'T (M LD ID 0) CO CD — — Q'TP (NJ *T S — (NJ p- ro — — ro co m- P- LD M 3

•<rO)C\J(M(N)rO(M(M(M — rOK)- CO — fO (M CM P' — CM CD CM CO 00 — P' — PO CD — CM CD

QSSSSS 3 SQ 3 S 3 SSSQSSSSSQQS QinsiDSiosinsinsin

roK)^r^LntDa)CD(v'(^coco

3 3 3 3 3 3 3 3 3 3 S 3 3 3 3 3 3 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3 LD 3 ID 3 LD 3 LD 3 'X) 3 LD S LD 3 LD 3 ID 3 LD 3 ID 3

CD CD 3 3 — — CM CM lO NO T LD LD CO CD r-N Pn CO CD CD CD 3

CM (\ \ NJ Cm CM CM CNJ (N! CM CM CM Cm CM CM CM Cm (NJ CM (Nl Cm ro

I
- 108 -

V CO O' CD ID m

- CD CD 3 *

CD 3 o- 00 3 — 3 — D D 3 3 D "T o> D 3 3 3 o* ID CD 00 co LD DO 3 3 3 LD r-~ — DO 3 3 DO — M" — 3 3 D 3 3 3 3 D 3 3 D O' 3 D

CD 00 o- DO DO M- 03 DO 3 3 ao CO DO 3 D D M- 3 V — 3 3 3 3 OJ D 3 3 , 3 D •*T 3

a> M" (M S3 00 LD 00 DO CD 00 o< — — 'T DO 3 3 CM DO NO OJ D 3 — CD 3 3 3 TT 3 3 3

'T 00 .

CM — CD V (M M- 3 — 3 o* 3 CD D DO M" CM 3 DO D 3 3 M" 3 3 D 3 —

D 3 O' O' ^ O) — O' CM DO CD DO CD DO — r- CM 3 LD 3 CD M" 0- — rr 3 3 3 OJ 3 3 3 — 3 CD 3 3 rr 3 ,

ID 0) DO CO CM rr CD CM •<r O' OJ CD M

- CM CD — D 3 D O' 3 D .

3 — 3 3 3 O' 3 D 3 OJ

C\) 3 T O' M- <3 M- 3 o T co CO LD 3 DO D 3 3 CM D 3 3 CM 3 M- O' 3 3 3 3 V M" D 3 — •^r "T CM 00 00 CM — TT ID V CM DO — 3 3 3 O- 3 3 3 3 — 3 3 TT 3 3 3 O' 3 3

O' — CD CO CM — 3 CO ID CO o- CD 3 D 3 «“* 3 * D 3 3 * 3 3 — D 3 OJ 3 3 3 OID CD T DO DO DO CM CM 3 CO DO DO 3 O' — r- 3 OJ 3 3 O' T 3 CM 3 3 3 3 3 D 3 O' 3 3

CD ID CD CD O' CD CD CD CD (JO CD CD O' D D rv D 3 3 3 D 3 O' 3 3 0" 3 O' 3 3 3 3 O' 3 3

i i i i i i i i i i t t i i i i

>' i i i i i i i i i i i i i i i i i

33 o- cd cd — in in — c\jt id coq) ^-unNDLncocD ’rr^vcO'^rtD — cni^)r-CD ddoojm-cdcm(MO'CD03d3m-cm — codd30'0'33do — cdm-m-oj — — 3— ^tcd — D <'rO'CDCON3M-3QO)s

OJCD3 — — C03CD3 3CDCQCM 3O'O0CJ)M-Cr) — COCX>3CMO'OJDM-a)3(MCM G0330joi0'0jcooj ,,r

,'3-V00'0jcn — C0 m-ojqo)3CDD3ojO' — 333 — dcd

OJ — 003O-DCD ,?-CD3OjM-DaC)C0M-CDSCD-'rS3D00 — DCDCOOjv-iD — — — 3

OJSDCDCDCDCDDOjCmDO' — COCDCDCDCDCDCDCDCODDCOOJDSO'S — COCDDOJ r'OjcD-coa)3cc^rD-rco-ojr-0'30'CncDO)3Da)3a)CQM-CM'TS3333

COCDCDSO)C03DCOO' — O 00 D 3 3 OJ O' — ODCD'^-^r^CDCD'TlD — CD CM 00 — CD

''T3QCD — 300 — CDDCOSCOCOCOCD — 'T OD MS ID N M W N 'f - VSSh'TS 3 3 • -CD • OJ — M" • D 3 • CD — • 00 V - CD C\l F^- -— O' — • -O' CD •

• 3

c\i • -cd • • — • -3 • 3 — • -co -3 • -3 (\j ki v • co • — oj •

• ^r(\iisoiD',Tr\)CDa) 00 CD(S)(\iho 3 d 3 -<r co cd 3 o- d d m- o- co co cd

(M — I I3I3COOOICOO'ICO — I — 03 I CD ID N I (\J I Q I iNDi^ri | 'T

"T 3 3 3 M

- 3 3 3 T 3 3 ^ NDTTNDNDhO Nl’T'T^Kl'TNlVMKlTT 3 'T lllllll — lllll — lllll — llllllllllll — II

IxJ UJ LlI UJ ID UJ LiJ I Id UJ LU UJ LU I Ld Ld Ld UJ Ld I Ld Ld UJ OJ Ld UJ LU IjJ LiJ UJ LU Id I Ld UJ

co — ojCM30'OidDM-003DLd — dcm — CDidO'OCDDM-30'^rD'TCOOOuJOJCO

f^- 30- — D — 33D''TM-CDDD33CDOj3DCDCDCO — — CDOJCDO-COr-'M-CQS — (Dross - ojM-SM-oicoO'DOjcoD'q-CM — — 3D — roscMCMcococos^cDcr) 3SCMQDDC)33COC03C03DOJM-33^COCOQ30-3 M- — CO CO CD S

•'TDO'— CDCD3333''r0'D0'^r3D'CD3OJCD30'3CD'<rCDGDD — 0^003-^-

CJDCOSOOCDCDQN'TSVDQ - CDNDCDCO'-lD^TNDr-'^rCDrO^-NNCDSCDD — LD 0)&3333LD3^r-'T— 3CJ)CDCDOJOODM-M-SCD3COSOJOJ3tOOJ3aOCDa)3 QMSO'COtDO'Cns — ooM-DDD-nrrco^rcoojO' — o- o co o co od — co oj s

cmoo — — O' — 33m-^ ojooojr'3co3cDa)''rojcD30'CD"<r — — co co m- cm cm

O) — — — 3 — — > CD DO — OJ-'TOJ — — CO — 0'3D — 3 — T — — CD — Ol — 00

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

S 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

D 3 ID 3 D 3 in 3 D 3 in 3 in 3 in 3 in

3 — —~ 3 3 3 3 M- •^r in D CD CD rv o> CO co 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

SSQCQSQQQQSQSQSQSS SQSSSQQSSSSQSQSQQS SLDSuDQLDQlDSKOSlDQlDSlDSlD

CD CD 3 Q OJOj33T'<rDDC0C00'O- MKi'T'T^'T^T'Txr^'rTTTrTr’r'TTr

!

1

I

1

:
- 109 -

in IO CD CD 00 CM •*T «— ^r 00 CM CM 00 — — ro in 'T 00 3 O) CO CM in _ 03 in 3

CNJ CD 00 CD in O) S3 CM — SI S3 CM — CM T CD in •

3 ro CD CM ro 3 <M S3 S3 03 S3 03 ro CM

CM ID 3 CNJ ro 'T 00 CD r- — Q CD in •

ro CD CO CO in ro in CD CD CM 3 — CD S3 co — — ro CD CD

r* in 00 in — CD in — h- in «

O) ro CD CD 00 CO ro

3 CO ro in 3 ''T CO 00 CM 3 CM CM 00

o ro O) CD CD in I"' ro CD m- ro co ro ro O) 3 T ro ro ro 3 V — co co 3 CD CD CD ro in (3 CM

r- fO CO K> 'T 00 ro r* CD CD 00 Is" CD co co CO 3 CO CD co ro S3 3 CO CD 3 co 03 3 CO 00 3 3 in in

0) Q <3 3 I s* ro CD in S CD in CD co — CD in S3 in TT 00 — in ro in in CD in 00 r— 03 CD in ro V

in CNJ CD hO in — CM co ro CD

00 CO CM s CM CD 00 — inCD CD ro 03 3 in CM ro 3 0) (3

00 3 00 S3 — ro

cd in in CM 3 3 3 —

ro 3 CO CD co — CM CD in 00 ro CO 03 _ ro in ro

CD 00 "T CD Si rv — co CM S3 T CD s CD m 00 m in CD S3 «— in m- — 03 ro S3 s CD

fO CD S3 in CD Is- 00 in co lD 00 S3 CD in CD 3 T 3 — in 3 3 CD S3 00 03 ro - in 9 3

CD in CD CD in in CD cd in CD CD in 3 in co CO co CD 3 CO co CO 3 in CD CD in in CD CD CD CD CD

i i i i t I i i I i i i i i i i i i i i i i i i i i i i i I i i i

hO

in 00 ro CM in 3 — M" CM CO co 00 in

CD 3 rr ro in 3 CD 3 CM 3 — ro ro CD ro "'T CO "T ^r — T ^r 00 in in CD .

ro ^r — — .

CM 00 r^ 03 0) ro CM co ro 3 CM CO S3 CD ro CM 03 00 ro — 3 ^r r-. s CD in ro ro ro un ro 00 CM 03

M- CM in CD in S3 ro 00 M" CO 3 3 CM CD S3 CO 03 "T ro 00 3 00 00 CD M- CD *— rv in S3 00 — CM 03 ’'T 00 ro — — CM 03 00 3 ro \r M’ *

S3 03 00 03 I s* ro V CD 3 CM 00 co CD

r^ 00 CM 00 03 3 M

CD CD 3 M" CO ro 03 03 ro CO CO CO CM s M

- — V CM CM CM — T CM ro >

00 00 ro M" CD in CM M" CD ro 00 CD 03 CD CM ro in CD T 03 S3 00 CO 00 in in M- in 'T in CD — 03 00 co s <3 03 00 CO S 3 3 ro T in in 00 3 ro 03 «— 00 T CD s 03 00 'T

CM in 00 »— in 03 in in 00 ro 03

ro .

in ro 3 (3 CD — co ro CD 'T M- 3 in CM — m- 03 S3 CM in — CD in in r^ in in in _ ro in CM ro m- 3 M

- 3 <3 — S3 <r — 03 00 co

CD M* co 00 S3 00 Q CO Q <

s s CM ro >- r- M- 03

M- CD - <M CD «— 00 rr 03 co - ro • 3 03 in • CD • .

. 00 . 03 . ro

in • (3 00 — in ro. S3 3 CO • • CD m- (3 CD "3- 1^ CM CM 3 03 ro CD S3 —

CM — 3 — •— 00 CO 00 CO CM in V in • ro CM 00 CD CD (M in Q co ro 3 ro ro

• I s* CM 1 i 1 i 'T co 00 S3 i 3 1 in ro 1 in i i 3 i 00 co 1 ro 1 i co 00 i CO i co

ro ro ro V ro ro ro ro ro 'T ro ro ''T T ro ro M- ro ro ro ro ro ro ro M ro

i lx!

i Ixl

i IxJ

1 Ixli ixl T 1 LJ

i ixl

i Id

I Ixl

i Ixl

i Ixl

1 u

i Ixl1 Ixli Ixl

i IxJ

1 Lxl

1 Ixii IxJ

1 Ixl

i lxl

1 Ixl

1 LJ

1 IxJ

i u

i lxl

i u

i LJ

i Ld

i ui lxl

1 LJ

i Id i in co CM in 1 ro ro ro 'T CM ro CD in 00 CD — in M" CM in 03 CD in 00 ro CD 03 — CD CM — CD lxl in 3 3 CD ixl «— co in <

— ro 3 CD

CD 3 CD ro 03 CM 03 3 3 T T in ro in CD 0) 0)

CM ro T ro r* CD CM — CM CD CO in ro — 03 — CD CD 3 CD — in CD ro 'T CD "T 00

CD 3 r- ro CM 03 ro ro CM ro CD 3 CD •'sr CD — 00 ro CD 00 "T 3 — in 'T ro CD 'T in r-' CD ro — CD ’T ro 3 CD 3 CD CM 3 in 'T 3 — CM •M" ao (M ro T 03 r- — CM r- N") —

in ro .

T 3 03 CM ro — — r- ro CD "T 00 TT CO CD 03 CM

CD 00 — 3 03 ao CD (M CM in CM

S3 00 — ro CM LO co — —

00 CD M" 3 ao V in 3 M-

<

3 ro CM — — 03 »— in CD CO ao 00 (M

03 CD 00 ro .

CD ro (M 03 *— M" — CM — ao CD ro — in 00 S <

— 00 m 3 3 in 1^ CM CD CM — in CD in 00 ro S- 3 in — — 3 CM ro in 03 CD 3 CM ’T 3 03 in 00 CD in 3 03 CM in 00 00

,

CM _ 03 .

CM CM — 03 CM .

03 CM in CM 03 m — in — 03 in — — »— CM .

— *- 03 »—

3 Q 3 S 3 3 3 Q 3 3 3 3 3 3 3 3 3 3 3 3 s 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3 in 3 in 3 in s in 3 in 3 in 3 LO 3 n 3 n 3 n 3 n 3 n 3 in 3 in 3 in 3 in 3 in 3

00 CO 03 03 3 3 — (M CM ro ro T *T in n CD CD r*' 00 co CD CD 3 3

— 3 3 ro ro T T in

TT in in m m in in in in !n in in n n n in n n in n n CD CO CD CD CD CD CD CD CD CD CD
-110-

co — — (MinKir^mm — cn — cor^- m in ro in v in no 't 05 co ino

NO^TNO(JOtj-(_D — ><Tr^COC3 CDCDCD — CD CM in — SSlD'CCMrv' ,r^QvCOO) — CO —

CDC£)a)oomK)rv'f\j(DSr'rs-— ros^CDcx)c\:cocD(LDc\iooc\j'^M(D(\jK)CD(Mr^r^in

in — Mcoc\i(\iCD — incococ\jcD — '^•Qr^cnv — — ^r^sioDCMrocncDCDcocDcnMr^

o)^_^_fv»Q(\ii^Ln(\jfso ,^riv'CDr^rv'03 ,3‘(\ir^corohocD — 10 — Tj-in^rfMincDOhocNj

CD CD m- 1^ r^sr^ — Lnr^sc\Jinooi£)CDScnr-cooo(M^r(\icot£i(X)'rr^incDO)Q — co^incD’^r(\irv-(Nj(MCD — sincMQ — — co^rinsiDr^r^cDCDCDcoM — m — —

CDCDrOCOhOO)K)r^r-'r^lDlsOCD(SLn(Dr^cni£ir\j(\iCSl — Q'TCD-q-CO'TlDCDOor^K) — 'TinQroi^si(\jr^(joininr^ini^iniDODr^co(\iCDco'q- — n — ^mdsid

ininr-cDODiDCsjoQCOQ^r — cdcd rocD^rr^r^coco — oincDTCD vsodinjmo

(\iiDr^hocococ\jf\i^cDincDin(\iC3 Nnc\jsc\jcD co co co — 00 — cn co —

crjcjDinf^ioincocoiDcocococDf^cDiDiDr^iDCDr^ijDiDaDr^r^r^coinaDijoaDuDr^r^

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

co cxiinr^ r^-inror^ in co no no cm in cn co co CDhO— in'TIDCMCDCDaD — CD COCO CO CD — S)C\l'n-OOr^CO-^-(\ICOCD'^-CD — inco

sin — fMincoLOQininro — r^— NooaoiM^rQ — c\JLOC\iooc\jNo^rrrcosic\jCDO)^-

fo — foco^rcnhnr-soooKi^rcoQCDcoi^ro^rooNocDincooof^cMr^oo — horocDin

'rcocDQroaor^Nooocjor^NocDQ'T — sjr^incxj — ^rincoQOCDcosojNor^Qinr^ro

(N/rocMNOCDCOCDCDro — cDiorsJin^ — OvJCDCocooco — r^r^ — scor^rofsiincNjinin ror^s — inooo^r^oomcoNONocDr^Qinin^co — coin — cn no — no cn — in in — co no r^aohocDSNoa)Qc\jr\icomrvihoin^rQr-r--cD — CDCMr-cDLnrMSi^rNi — (\icoq —

^cNjcoMcsjcn^cor'^rinuor^inhOLnroooisiis^r^r^r — '<Troino)ioisioco — cooo
- 111 -

) 03 CM no 00 CD ro — CD CM 00 m- CO ro — n 00 CO CD 00 CD ro ro M- V n CM CO CD

CM <3 f CM — CO 'T in F CM NO CM 00 — <3 n T CO ro CM CD CM CD CM T 00 ro M- CO CM

CD CM f — to 0) f 00 ro 3 ro — ro f CM n ro — CO oc M- — CD 00 — — f n — CO ro 3 CD CO 3 3 in 00 f — CO ro ro F "T ro CD n CO F CD •— M- 00 r- CD ro f n f 3 "T n CO ro 3 3 F F

CD CD M" CM 00 CO O) — ro (N CD in (M ro CD n CD CM CM CM (3 V f n ro ro f n T— — CO V 3

O) in 00 m — CM CD 3 — CO — M" 00 ro CM ro 00 00 CD CM 00 n CO 3 00 f F F M- n 00 00 CD F 3 f S 00 T .

f 3 00

— 0) CO CM n — <

F ro ro f CD n n f 00 CM CD ro M" CD CM CO F ro 3 CO CD 3 — ro (3 00 f — M- CO 00 CD CO CM — F CO CO CO CD f CM ro ro ro 00 .

00 n F M- M* CO

"T in CD M" f 00 CM (M 00 (S 00 CO CO CO 00 n CO 3 CO CM "T TT T CO f n ro CD CO 00 M- F ro n

ID CO <3 cm f — 00 3 CO CD CD CD CO CD 00 CO — n n V 00 CM CM ro n (M ro CD — M- — CM (M n

in no CD cm in ro (3 CM (3 — ro CD CM CM ro f (3 00 CO CM (3 ro — 00 3 CD F 00 CO j- - CM 3 3 n

0) CO in CO CO CO CO CO CO CO CO n F CO GO f (\ n CO CO CO CO CO CD CO n CO CO F CO CO CO f CO f

I I I I I I I I I I I I i I I I I I I I I I I I I I I I I I I I I | |

cm CD — t no ro n CO ro CM ro — — — CD 00 F

rocDsrofMQioro — m- n F ro F n CD CD n ’3- n CD F CD CD M- .

00 F

ncooocDro — rococo CD M" — co ro M- ro ro "T n CO ro 00 s — 3 3 F CO M- 00 00 CO CD CM

Tf — rOCMM-CDCOF'CD 3 — CM CM S CO CD CD CM M" F CD — CM F n n 00 CD — F CD ro 3 3 M" — QCDrorOOOCMCMCM 00 — ro CD F CM 3 3 T 3 — n CO — n 00 M" 3 n CM n 3 F Q CD Q 'T ^ CD CM - in CO CD 3 3 F CO — — 00 00 CM 'T M" CD CM CD CM CM — n CD 00 s CO ro oo FSinSJOOCO-lDF 3 — co — CM CO TT •

3 ro — F T 00 3 n 00 n CO CO n CO n oo 3 — COSQSM-COn ro CD S n cd ro F 00 s CD 00 n T ^r — CO F 00 ro 3 CO — 3 S CD

CM 3 NO 3 F CO ~- CDn CD 3 CO n cm rr CO F CO ro n F CD CO CD 00 — CD 00 F CM F CO co n

00rorO3003(MC0(D co t ro F CM "T 00 ro »— F CO n 00 3 "T — 00 00 ro CD n CO — CD n co CM • CO • • - — 3 CO - F • CM n CD

ro CD • CO 00 F - ro CD CD • ro — F- — 00 3 •• • • — CO CM • - — 3 • ^r - 3 CD 3 CD 3 CD ro • CD ^ in • CM CM F' 3 CD 3 ro • co ro n • CO 3 00 CO ro F '— CM ro CM n n M" CM ro 00 n — F

CM 1 1 (M 1 1 1 in 00 F 1 3 i rr — 3 1 CM CM n 1 I 1 n 1 1 1 ro 1 n F 1 1 1 F

•'T ro ro ro ro ro ro ro ro ro ro M" NO NO ro NO ro ro ro ro NO NO T

1

1 1

A NO ro

1 1 1 1

1 1

1 1 —

1 L1 LlI1 Ld

1 LlI1 LlI

1 UJ

1 UJ LlI UJ

1 LlI UJ UJ 1 1 1 LlI u UJ LlI UJ UJ UJ LlI u LlI UJ

1 UJ1 UJ1 u

1 Ld1 u 1 Ld1 Ld1 Ld

.

rr F CO n — <T n M- n — F UJ UJ UJ NO n (M CO 00 — CD CD F 00 — CO ro — — in Ld CD n CO ro CD V — s CM F CM CM F — CM n

F CO V CO ro 00 ooF n CM CM 00 n CD CM T vr CO ro F F CD F n CO CD CO n F F ro CM F CD s CD CO CD n NO CD CM M- 'T 3 "T CD n ro CO

CM 00 s s CM CM — CO n F 3 ro CO CO n

M- CD F ro — M- CO — T M" F 3 CD CO 00 n 3 CD NO

CO TT CO ’'T CO 00 CD ro — CD n CO n CO .

CD F n — CO CD CO CM — CO CO ro NO (M M- .

— CO CO

CD GO CD M" 3 CM ro M" ro CM CO CD CD ro M" 00 3 •'T n F F ro 00 NO •

ro 3 CD — ro n CM 3

CM CO — ro F CM F F CM CD ro V CM CO CD n 3 F M- CM CM T CO CM — 3 CD 00 ro CD 00 CO 3 n

CD CO F F M- ro «— s M" CM CM 00 (M CO ro CM 3 — M" M" — (M 3 CO 3 F ro n CM n CD 00 M- ro CO ro — CD ro — CM CO CO M- *— F *— CM — NO n •

ro NO CO CM n 00 F 00 F F n n 'T ro TT F CD

CD — — — CD — — — — — — — — CM n CM 00 — —

— CO — — F CO CM

— — n — CM

SSSQSSQSQSSQQQQS3 3S33SS33S333Q33S3 3n3n3L0Sl03n3nSnSnS roro'-TTrnncocoFFOooo3333 —

CDOOCOOOOO<DCD(DCDOOaOOOa000333

3

3 3 3 3 3 3 s 3 s 3 3 3 3 s 3 3 3 3

s 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

n 3 n 3 n 3 LO 3 n s n 3 n s n 3 n 3 — (M CM ro ro ’T TT n n CD LD F F 00 CD 3 3 3

CD CD CD O) cn CD CD CD 3 3 3 3 3 3 3 3 3 —
-112

CD ro ro M" CO in CD CO — CD CD CM M- LD — ro LO 00 CD in Is* ro CD CM CD D — a a m . ro CD CD M- CD — CM — CO in ro CD CM — CO CO CO CD in — co N CD M- CO CM — IN a co CM a — ro 00 in CD S3 CD IS V CD (M CD CD CM CM in M- V CM M” co LO a NO CD M" NO CM ID ro NO a co a a

CNJ Q ID — in ro M" — CD — cn CD S V

in TT ro CM in a a NO M- CM O

CO NO CM CD a a LO ro CD T Q CO a co ro CM — CO CD CO ro CM in a in CM — in CD 00 in NO IN NO ro CD a M- CD NO NO N- CM

ID r- co LO CD LD CD (M LD CO — CD n co in CD — CD CM co (XJ |N a ro a a CO a CM NO a

CO <r — — CD CO •'T — CD CM CD CO in ID CM co CD

LO in <r — CD |N 00 CM a 00 a a ro CM

(M CD — — CO CO 00 CD CO CO LD M" (NJ — ro 10 in LO — CM M- NO a a — CM CD a 00 co IN co ro a LO

CD CM CO LID — CM — CD ro CO CM •

CD in ro CD T ro CO CO CO ro CM CM a CO CD CM ID a CO |N a a a

rxi CO ID CD CO in CM a CXI CM <S LD CD *

in ro LO ID a ro co in co LO CO CD 00 LO CM a |N a a

in ID M- in ro ro ID "'T ID — C3 CD CO 00 ro in ro Cxi . LO a CD CD ,CD CO CD T a co M" CM LO

in CO CD CO co (0 CD in CO CO CO CO CO CO CO CO LO CO CO CO LO co co co CO LO CO CO LO LO LO LO a a a

| I t I I I I I I I I I I I I I I I I

I

I I I I I I I 1 I I ! | | | |

ID OK) CD CO — CM NO — NO CO CM CD COCXlSCD'TCO — Q^rC\lDCOCDr-(\ir^r^lDCDrOrOCnrrMO'jNDCDCOCDCD(\J — hOCO

fOCM — S — NO(MCDrOCOIN(\jM" 0)CMS',;3"CDrO -*j-Q(\jLOSCMCO — IDSOD — — 0)00 nocm — M-CDinrocoaLOLDiDco — — cnooM-NocMacoacocococoiDCDCMCDoo — noid

CDlOCM — CDLOCDNOCMCDCDCDCOIn— (MaNONOCDCnacOCOCMCOaQCO — (IWM- — N

NO — OOCDNOGONOCONOa)r^COM-COacOM"CDNO — OOCO(\IM-a — O)N0C0N0\rQCDrrQ

LONO — QOCO — CDC0CDCMCDfNN0O)a(M’'TSCD — CD — a^COINCOCOaM-lDLO — — CD

NO CM a ''T CM NO — (MCMNOCMCDaCO — ^QLOhO - ID 00 |N CD id — tDLDOO'TN'CDNOOONO

colonott — cd — nocmcmnocdcoinoononoi^cmio — lOCMCOLOLDLONOCDr-cDcoiNcniN

CD — CMlDINCOaCOLOa — — iDaCMCDCOCOINCOlDOONCMCDCOCOaOlONWCDCDCDCD

• ro • - 'T <s — .

• — m- in cd • • — a — co a -cm • • • tt co • cd • cnj • • • — co cd co s r- • • • -inr^ co • cm no cd a N • — n» • lO CO M -- LO — aM'NOM’CM — M’SCMM'INNO — COlDlDCM',TM‘M‘ — COlDM" ' CD CO CO

ir^i i co co no i i i i i i in co m- — i i inro-Mco i in i i i icnr^i 110

no m- no m- no ro m- 'T m Ki M-M-rorororoNONoro'<r'q-NoroNOTr — Illllll — III — lllllllllllllll — llllll

I L±J Ixl Ld lxJ LlJ LlI Ixl I IxJLULlI I LJUIxJLJLJlxJLdLiJLJLJLJlxllxJLiJlxl I IxJUJLiJlxJlxILxl

Ld-^riDCOaOCO — (MlxJr^(MhOLdCOr-CODrOCDrv'h'NDOOCOCOr^OO(XJlxJ^rOO'TCDCOK) — cDinisoinisococ\JCDCxjNDc\jiDNDS3r^rsjsiS'-CDLnr^covr^D ,^(soc\ic\iTrQ^c\i

a ro co to CD — id — co — roDr^iDfxjrooor-CDror-coooiMr^scoD'TKiD^-CDisro — NO CO NO — a — (NJS - QCO'^COCOCXJCDLOCOhOISCDCOSJCDlDCXJOOCDQQ^r^rr'h'

'TOJSKNJ - h'D(Sr^LOr^h-COCDK)OvJ(\j'rr^rrOOCO^CDCOCOCDDCOCOCDSCDCDr^)

CD CM CM CO LD CO M- — COCOCOCO — iDlDlDCDr^COCOr^CO — lD(\|TrroiDfN00 — D NO (M LD (^•S — CSI^r^OOLnCO^rND'^COCOCxlQNDQM'-r^SCDDCOCnNDDCOD^rCD'T^r-

(MM-tN^cDCDiDCD — CDM-r^CDcororos — (Mcoro — aoar-cocoQaM-rocDrocD —

'T’^rOJ3lsO — — S3 — CjDLDr^CDCDr^CXlNDCXJK)'^- — I^DCO^rCO^rSCOKlCDCDSCXJCSJ

C\J — CD — r-' — — NO — CD ID N CD - M - *0 — CO LD — CD — NO — — CD

1

a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a

a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a

ID a LO a ID a ID a ID a D a LO a iD a lO a lO a D a iD a LO a LO a ID a LO a LO a ID a _ «— CM CM ro ro •'T V ID LO co CO |N |N co 00 CD CD a a — — a a NO NO M- TT LO LO co co in a a a a a a a a a a a a a a a a a a a — — — — — — — — — — — — — — — —
- 113 -

i

r- 00 CD 00 p* ro ro p* CD ro CD in CD CO CO ro in

in .

CNJ CNJ CD in CNJ M" 00 — 00 CM ro 00 CNJ CD 00 CNJ S —

ND ro O) ro O) p* CNJ •*r TT >

— CO CD CM CD ao C2 ro — *r 00 ro .

CD TT Q 00 'T S CD CNJ in 00 00 •'T ID "T — p- S

00 <NJ in ao in ro ro <\l CD ro 00 CNJ CD 'T s CO Q CD ro — CNJ CD in Q CNJ CO CD CD CD P» CNJ CNJ CD CD in — p- ro 00 ro CNJ S

G> CNJ ro CD CD CD CNJ r* 00

CD CNJ LO ro CD s CNJ CD V CO

S p* — Q CD CD CD in p> CD ro ro P'- in CD ro p'- CD ro CD 00

S CO (D CNJ 00 p* 00 CD p* CD ro p* 00

CD CNJ CD CNJ in CD — 00 00 — CD O) CD CNJ CD CD —

CNJ co 00 in in M"

(a <a in ro in 00 S ''T CD . CD "T S 00 00 CD ro T CM CO

CD r- p* CD CD (D CD CD CD CD CD CD CD CD in in CD CD CD CD CD

i I l i i I i i i i i i i i i i i i i i i

in p- CO in CM — CM "T CM — —

00 CD p* — ro .

CD CM in — "T CM in 1

CO SI p- 1 s CM CO in ro CNJ 00 p- LO ro CD p- I s- r- CD in CM 00 CD UJ

s 00 — 00 p* M" LO Q CD <

CD CD ro CO ro in s <3 CD •

r- CNJ ro 00 p* CM p- Q O) CD CD CM CM in CD M- p* in

M" CD p* 00 in in P s CD "M- — CD 00 rr — CD — M" CNJ s 00

CM CNJ — (a 00 CO CM — in 00 CD — 00 in p- ro S ro —

.

CD CD ao M" ro CM in in CD 00 CD — S3 in 00 in CM — ro

CNJ •M- CNJ 00 00 in CD — ro 'T r* — CD CD CD in CM p» ro CD T

p- CNJ — p. s 00 p* CD 00 CM CD CD ro «— T CD s CD in

OD 00 • - - S CD s ro —

CD

CNJ in •

1 CM

• p- CD CNJ - • • CD rr CD in

CD CD

CD P* in M’ CO P^ CM CD CO 00 CM CD CNJ CM CNJ 00 ro CM

00 in i 1 1 1 CNJ ro in in ro 1 1 i 1 1 ro ro i i CO

ro ro M" •m- ro ro •"T ro 'T ro ro ro ro "T ro ro

i u1 UJi Ixl

i U

1 UJ

i UJi LJ

i u

1 LJi u1 UJi LJ

i UJ

1 u

i UJ

i LJ

1 U 1

i U

i u

I LJ CD CD CD CD Pv CD CD p- — CD CD CD CD CO CD 00 LJ ro M" p- CD in •— Q — Q s s «— CO rr ro S CM in CD 00 p*- CD

Q 00 CM CD — in in p* — S — s in CD in ro CD -M- CO

(NJ — ro S 00 CD — CD CD CM V p- in ro CO p* CD P* in

r>. — *r V S 00 CD M" in S CM in p* Q 00 CD s — ro V

-M- CD CD ro S O) »— CD — CD CD p*

CD CM CM ro s (M

p* (NJ 00 ro — CD ro "T T CM .

CO s ro S CM CD M" CM

CD S CD in CM ro 00 s in ro in T •M- CD p. S CD in CM 00

CD in 00 — Q CD in Q CO in CM s P^ 00 S CM — — Q ro CD

.

in (NJ — CD CD — — in — 00 — CD CM CM CO — — — CD

SQSQSSSSSSS SSSSSSSSSQQ SinsmSinSinSinS

00 00 CD CD S S C\J CNJ ro — CM CM CM CM CM CM CM

S s S S s s S s S S

Q s s S s s s s s S

in s in s m s in s in s

ro M- vr in in CD CD p- CO

CM (M (M CM CM CM CM CM CM CM
- 114 - ii

<3l UJ

ao

r* zo *• >—

l

1— o < 3 u CL o3 cro

h- Li. <

CO

<3 t— .

—

1 z 3 t—

3

r- 3

ina

r- 3

03 (—

r- 3

CL - Z — <

in

X •—

<z

Ld3 az < < > z Z *—

3 z z 3 X T < h- z

cr Ld 3 X t— h- z3 -
- 115 -

The following ten pages show the results of applying the software contained

in Appendix D to a step-like waveform that begins at zero and ends at some

nonzero value.

The waveform, as acquired by the DPO, is shown on the first page. The

transformed spectrum is tabulated on the next eight pages and plotted on

the last.

This software correctly transforms waveforms of this type.
> > 0

•—> 1—

CM

CDQ rD \ X ' o) o CD X — s cr '

*»- CD 1 ID * n LiJ • M" UJ <S <S ' •—

CXI U. CM •• > *—

O —

—

O • Z — LD ~ - n Z h- cr. ID — t— o

fO

H 1— LJ - Lu l- CD

u

V lx. LJ c

•• CD • M- CD

Q

Q lj 2: z

CD Z LO

U 1 O < cn 1 t- U CD » U LJ C *- UJ i— ID i id x cr Cj — UJ •—« LJ lJ

K> t- )— > Z
3

!

-OCT-80

14:38:28

TEST

COND

. :

FFT

MODIFIED

THE

MAXIMUM

ANALYSIS

FREQUENCY

IS

128000

MHz

A

SET

OF

25G

FREQUENCY

POINTS

WILL

BE

CALCULATED

-117-

E

LlI crCD

•o

NO 00 CM 00 CD 00 ft — ft 00

NO — CO CD <

NO S3

D s — 00 — CM LD CD CO CO N- CD ID CD CO f?- 00 CO CO CM Q —

00 LD ft SJ <s Si ft 0\: CD

CM CD 00 ID SI fT NO iD n- ID

ft CO ID 00 CM 00 fv NO —

00 FT CO NO 00 CD ft CO CD N- S) r- 00 •— CM V CD ID CO S3

'T — N- NO LD 00 NO CD CD

CO rW^ ft ID — — X

cr> CO CO CD 'T CD S FT NO — N' CO N. — — CM

CO CO CO X X N- CT

CM

CO ft s CD X X X CM

ID CD 00 S CD CM NO X

S (O CD X X

CO CD CO CD CD S3 NO Q

"T CD NO ft CO CM S3 N' NO CD CD ID — CM X NO

x r* 00 s

NO X

S3 CO

CO (S — CD — S

ID CM

CD NO

IT

C£ N- CD — S

NO tt NO CD CM ft CO — T CM CM S

X NO S Q — (MCMCD',TLOC\l'S rTDlDCD^rCOCMLDCM — IT h- CMXFTFriDLOlDiDlDtDXCOlDlOlDlDlDXlDXXlf

I— Q I I I I I I I I I I I I

i I I I I I I I I | <

ID X X X LD LD CM NO CM T |N» (N* LD FT <

FT NO CM — 1

— X NO X X — NO ,

—

rr ID CD Q — s S SI CM ft X — — X NO X CM NO NO X ft CM X N' CD LD FT S3 S3 •

— X X CM FT X X X ID LD .

NO s N' NO X X X ID 'FT X NO ID ID X X LD NO N' CM ID Si — X FJ X — ID X X (3 X X X X S SI NO N' NO Q X FT X X ft NO 1^ ID X N- X ID X X X X X X X S NT X X X X NO S3 N' NO NO X ID

LlI CM ID NO »— r- X NO X X S X <3 X CM r-> ID — NO — X CM FT Q X X 'T S ID CM NO S3 ID X LD NO — — CM S3 X ID <3 X X — X .. X HO 'T X FT X X NO ID fJ- CM ID — s CM NO CM NO X FT X X X

LlI S3 • SI s> X N- • CM N>. CM X X X X NO . X CM- S X fT - fT r-v • X (3 I s* < X N' X ID r- r— S) CM NO X ft ID r- X X ft NO X X S3 X CM

X

CL

1 J i l LD X X ID 1 X X 1 i N- ft X 1 X NO 1 l

S3 — CM CM NO NO NO NO NO NO NO FT NO NO X X X X X X

1 1 1 1 1 » 1

| 1 1 1 | 1J

1 X X X X 1 X X X X X X X X X X 1 X X X X

1 X 1

1 X

\r FT X X X ID X X N- NO CM ID N'- OJ CM X X ID N' X X X ft N' FT X ID CM CM LD N- •

X X FT FT «— X FT FT X X X — FT X X X NO — X NO CM N- FT CM N' X CM X r- X — X FT ID — X ID ID r* X CM X NO X X LD X NO X NO X X CM X FT CM — — o N- FT X FT S3 FT X CM X N- X FT D ID NO r- FT FT X X CM N' X 3 X CO h* 'FT •FT N- NO — X "FT CM X NO X X X •

s S) CM SI X

l~ <s X NO X X — X T X CM X X f" D N- <s X LD CM S3 X

»—

s X CM LD X X X s CM CM X X NO X ID D FT ID FT X ft ID

N* CM ID X FT CM — N' FT X X rv. X X X X FT S3 NO X X LD —

LJ<

z: — — ID — — 'T •FT — NO FT — X CM CM — X CM — CM — — X

S S (3 C3 QSSSSiGlSiaCJQSCiJCiSiaSlSSSSlSS

O SQQSSSQSSSS'SSSSSQSSaifiQLO

uj s q uo s in s uo s 'ao s uo s m s in s ^ s ins s - -

on ID — — f'j(MNlrn^'ruOiOC£U3NNCOOOD05

I

2000

2.21

887842E13

59.9642318006

-58.074380949

2500

1

.

40558542E13

47.933:576308

-62.0399062057

2000

4

009892699E13

38.1452407288

-52.9343960493

2500

9

751

224

304E14

26.3506612233

-65.2158681489

4000

2

.

894

5654

99E-1

3

-0

.

6309672712)6

-55.

7653834515
- 118 -

CD CD CD in X CO CD in CM CD — ps m >s. n CD cc X n X — CM V CM X ,T X CM

M

- Ns SI M" in CD CD in

CD CD CM CM CD TT NO CD rv. CD in S3 X CM CM n CM X X N- N* in X Ns X

00 00 M- CD in I s* in CO CO NO 00 M- in 3 CM CD (X- !\ (S T 3 X cs X 3 X M" in CM X n X X M- rr — 3 CD cc CD N' CD — CM CD CM 3 — N' x CM CM X X •— X X M" X X X X in X X M" CM

CD CD X CM s ps CM 00 3 X — ps X CC M" in 3 CD n NO — N- n — X X CM X — X N» M- X

3 r- in X CD CD «— — in NO CD CD Ps CD s NO in CD CD X X 3 3 n X ps X X T h> X X Ns X i

Q — in x NO NO CM CD CC IS m in CM CD in CM M X s CM X X n -T X X CM CM T in X

CM CD in rr — — M 3 ps in CM (JO ICO ps CD CD CD CD CM n X X ps X X X 3 CM Ns M- M- X CM X

CD X X .

ps NO M" — CD T CO 3 3 CD V CD m m n X M- X M" <s (3 .— X 3 CM M' 'T 3

CM — CD CD "T — CD • CM M- CM NO <3 CO ps CD 3 n N- X Og X X X — 3 X X X N'

CD ps in ps rs. CD X NO CD CD NO in Ps CD N- — CO m 00 X X X X CM X M- in Ns in in X T

ID ID in in in in CD n~ in in CD CD m in m CD CD n CD n X X X X X n X N' X X n X X in X

I I I I ! I I I I I I I I I

I I I I I I I I I I I I I I I I I I | | |

X X CM — X X X CM — X X X X X X

X X X — X «— n Ns X n CM X ^r T X X X X X X X T n X X M" X "T in CM in X X X — X X 3 Ns X X n X X 3 X C\J X Ns Ps X — X

X n ps M- in og in X . X

X — X — 3 n Ns — CM Ps 3 s 3 X in X "T ps Ps CM n M- in CM X 3 in CM n 3 CM X (M X

X X CM T X ps X Ns 3 n M" CM X s •x X M- X X 3 X X s X n CM X n n X CO CO Ns X X

(M X X X X CM Ns Ns M- X X ps — CM S CM 3 3 n X X M- X Ns — X X T Ns 3 Ns X CM — X

N> X X Ns n Ns M

- X — CM X in n X X X X T — X CM X Ps in in — 3 ps X n 3 X 3 in

N> X X CO ps 3 X X M" X n

X X X X M" X X n n CM X X

T n n X X ps M" Ps CM X

in X in X X X M" 3 X ps 3 CM X X X X •x X X 3 X n Ns X X X rr — 3 T X X X X

X X n X X CM T 3 X Ns X X *T 3 X X 3 *— X Ps n 3 X n M- 'T n X M" 3 f'O 'T X 3 — CM Ns 3 X X 3 X X 3 X X 3 X • n X X 3 X — X n — X X X X in CM T N- - M" ps X (M Ns M- X 3 X Ns CM X X 3 Ns CM X CM M- 3 X — X Ns T X M- M" X X X Ps CM X CM — • X 3

1 X CM 1 1 1 1 — 1 CM X X CM 1 I 1 1 1 CM n X M" 1 1 Ns I i X 1 1 1 CM — 1 x m- x t x xxX’'3-m-xxm-m-xx

i i i i i r i i i i i i i *— i i i «— i i i i i t i i i i i i i i i UUJUJULjJUULiJLiJUJlJJUJU I LJIjJLJ I LaJUJUJUJ I ! IjJULLlUJUJLLiLLJLiJLLlUJUJ

x x x - — x N* cm — r- uJinM-M-LuxxpsNsLdujxinNsXXXXXX — CM
- 119-

00 NO CO 00 T CO TT 00 — O) CM NO NO in CM NO — — — CO CD 00 CD CO — CD in

00 — 00 I s* CO C\l CM «— r- CD <r m N- CM in NO CO NO 00 m CD — 'T — Is- (3 •<r Is- CD — CD M" CD

Is- NO O) NO CD NO 00 CO NO 3 LO in 3 TT — s 3 CD CD NO in "T 3 CM CO in M- (M CD CM in (3 3 CO in 00 NO CO 00 — — rr NO CO IS cm NO NO CM in NO

CO NO CO CD 'T NO NO CO N- in 00

C\i «CO ’T CM M“ CD

CD r- CM CO in NO CM 00 NO m CO CO V o NO m (3 — in CM 1^- Is- _ CD NO CD

<M NO CO NO CO NO — r- (M 3 lO CO CD M" — M" CO CO 00 CM CD 00 (3 .

NO CO 00 (3 — M" 3 h* NO 00 no 00 CM M- CO CM TT r- CM CO M" CM CO — m NO in 3 in

300 NO ao (3 in (3 CM CD (3 (S

r* M* 3 m* no Is- CO 00 in 3 ro N' LO CD NO CM m CD (O CM NO 3 NO CO CO T in 3 M- in

CM 00 00 CM «— T in M- CM NO — CD Is- 3 CO Is- CO <s 00 CD — CD 3 M- (3 00 00 — Nv (3 CM 00 (3 00

CD rr CO CM — 3 00 m 00 Nv CO CD V LO CO *

l\J •

in CD CD — CO CO •— m CO CM 00 3 CM 00 N" NO NO NO CM CM CM 00 NO NO 'T CD r- .

rv 3 CM CO CD rr CD CM NO 3 CM NO NO in (3 r- NO CO NO CO (3

CO CO CO CO CO CD CO CO N' in in Is- in CO CO CO in CO CO CO Is- CO N- CO CO CO 00 r- CO CD CO in CO

I I I I I I I I I I I I I I

l l < I I II I i I i I I I I I I I I I I

CM (M CD — NO CM NO in CM m- 'T in

NO CD 00 *— «— 00 CD CO *r CM — — — in ao in NO N- in CM in 00 CO CM — CM 3 in 00 ao •'T CD

in in NO Is- CO NO (3 CM — CO •<r NO — — NO Q CD CO 3 in NO CO rv NO CM 3 oo CD CD 00

NO — 00 (3 CD NO NO CD CO CM 3 -

NO N- 00 CD NO 3 •

00 O) NO CM h- (M in M- ao 3 CM — M- CM in

CM CM r- CM 00 CM •'T rr M- CD Is- CM CD — CD V CM (3 CD 3 G) in 3 CM r^ •

NO ao NO — in 00 00 NO

NO N- in CO M" CO S CM M- in 00 00 TT CO <3 CO M- Q NO in 00 «— in CD CO CM ^r in — — — NO CD CO

CO CD CD CO in CM iM in Is- — CD CO CD CD CD CD CD 00 CO in in CO OJ in 3 rv 3 — CO CO in CM CO NO 00

00 CD NO CO M“ in vr CO — CM Is- NO CD CO CD 3 in CD 3 ao 00 M" CM 'T 3 3 NO NO 3 s

(3 CM 00 NO in CO N* ^r — r- 00 in NO NO CM Is- — CO ao T -<T CO CO V in — ao CM CO — CD NO .

,

00 (3 CO — CD in CO Q CO 00 CO CO >

,^r CO 3 in r- OsJ |\ CO M- — M- s 3 3 in CM NO

i CD . CM .

M- in NO CO — 00 M- * CO CM N- — • — r- CO NO M CO

M" CD . • — NO - 3 — CO • 3 NO • Cm M- NO M* 00 - — (M in

NO in M- CM CD 00 00 CD 3 (M NO NO in (3 rr CO 3 3 in in ^r 00 »— r^- CO CO O) NO CO 3

1 NO 1 NO CO 00 1 CO 1 00 — 1 — 00 i CD in T r- i CM i 3 1 i NO 1 'r 1 1 V i CM

NO NO NO NO M" ro NO M- NO M" NO NO NO NO •M- NO NO NO NO T NO rr NO NO NO

1 i 1 1 ! 1 1 1 » 1 1

| 1 LlJ

I UJ

1 UJ1 UJ 1

I U

1 UJ u UJ UJ 1 UJ UJ UJ Ul Ul 1 u LJ Ixl Ixl Ul Ixl UJ U Ixl UJ Ixl UJ 1 txl

1 UJ Ixl1 UJ1 Ul

(M NO r- U in CO NO ICO UJ — in CM — CD Ixl Is-- CO in •’T NO 1^ TT in TT CO CO u CM CO — in CO

Is- — in — NO 3 in T M" CD in in s 3 CD CM NO m 00 CD CO — «

CO CM CD r- CO r- V CD 3 m 3 r- 3 3 .

CM 'T 3 ’T CM 00 in CM CO in "T CM •

— 3 in — NO 3 CM CM 00 CO CO 3 V CO 00 CM NO

3 in in CD 3 3 ao CO NO CO NO in CM NO 3 CO CD 3 NO NO — <

T .

ao NO CO 3 CO 3

CO CD NO 3 3 NO T r- m Is- T 3 r^- CO NO CM 00 3 3 ao M- 3 a

in — M" CO NO "T CO NO —

CD CD ao 3 1^ M- 3 M" CD 3 — CO NO O) 00 .

in M- NO Is- ao NO rr r-. Is- CO s LO in .

in in NO .

3 NO NO CO NO -M- M- ... NO ao CD CD CM CO in TT 3 CO NO 00 3 CM CM NO CO CM NO OD CD CD 3 3 CO

CO CO OO S — CO 'T 10 ao NO •<T CD •'T 00 CM

» ^ Is- 00 .

•

r-- CO CO — ao CM 3 CD CO 00 — r- — NO NO 'M'

CM CO CM r-. ro CD NO CO CD TT CM CO NO Is- CO M" •

•

ao CO T CM CM ’

in CO

NO — — CO — — NO — CM •^r OvJ — CO •

r-. NO ua -- NO — 'T — — ao — CM — CO — CM

SSSSQSSSQSSSSQSS3SSQQSSESSSSQSQSQSS SSSSSQSQSSQQSSSESSSQEQSQSSQEQQaQQQQ QinQiflsifisinsLf)SLOSLnQ'vns^smsi^QLnQLnsLOQinQLrjSif)Q

(MOvjhOM-q-'q-iDiocDcc^-r^cococncnKJS cMCMNONo-q-xTinincocors'rs'aoaoao

forr)^^rON^rohON^isorohON^hO lvo^',T

,^-^r'^r^r'^-'r'^-Nr ,^- ,T'^"'^-'r'<7''^-'^rTr'T
- 120-

— CO CO CD CM CO ro CO q q CD ro ro V CM CO CD — r>- LD CO V CD r>. CD CO ro — CD r-

CM q ro CM CM CD LD ro q o o f'-v ro CD ID — q CO CM ID (M CM — CM ,

q LD q CO CO LD IO K) q CD CD I s* — S3 CO ID — ro CD CD CO LD b LD CD S3 CM o — XT CO Q o .— CM ro CO CD CO CO CD

h' ID ’ CO LD r- — r-' LD q — CD O CD CD CO CO ro • • CD 0 LD q CO CO CM CM CM CO LD ro

CO CD ID r* K> CD q IO CO ro ro CD S3 q ro ro ro o q — 00 CO n CD CD CD ro LD q S3 CM CD

fO q OD ro CD CD CD r- CO CO CO CO o CO CD CO ro S3 rv. CO CO o CO CD o CD CO S3 LD LD CD CD q

S3 r- ro CO ID S CO ID CO CD •

CD lD s LD V CO — LD ro LD ID CD LD CO — CD CO LD ro q CO q

CM CD ro ID — CM CO ro CO •

CD CO CM <s CM CO 00 — ldCD CD ro q CD o LD CM ro CD Q CD CD ro

>

S

IO — CD ID LD CM r*> [S — ro CO CD CO CM CD ID CO ro CO CD — ro q ID ro ro q q

q CO q CD S3 — CO CM S3 q b s CD LD 00 LD LD CD s * LO q — CD ro S3 <3 — CO ID LD r* in CD r- _ CO — LD CD q LD CO s CD LO CD q 53 ID 63 CD s .

CO CD ro mmm. LD r n CM CD

CO LD r- LD CO CO LD CO CO LD LO CO CO CO CD CO CO CO LD CD CD LD ID CD CO CO CO CD CO CD LD

i ! I I I I I I I I I I I I i

I I I !! I i I I I I I i t I I | I I I

CM

r'' cm — O) — m r-' co 10 — cm in o co ro co r^- r'- ro • q q cn cd — comm- — ro q q cd cm cm — incDincM — srocoro —

rOfMCOfOr'CMCTCOCOOsjCMCMCDqCOrO — 'T'TNSlCDlOrorOKn.D^rOOOroCDQlDCOlDSNir-M-ODCDr^CMCOQCDCDM-r'OCDr^CDCDCD^rCjO — I^LOQCD — CMCDM-ND — Nn — (Mcnoor^roqq~s30) 03a)r^roqcor''CMcococo — r''i^cor''CMoocns3qqaocj3 r''qCOrOCDa)rO(OCOCOCMS)q — qqfMCMCM — qCMCO — COCDrOqO)inCMq(MrO(M O)O)O)(MfOlDC0qqCDS200G0C0lOLnqLnr''qtnqC0--0)C0C0S2C20)CDC0ror^Q

hOM-M-lDLOCOr^^O) — OOqCOS3qCnCDqq — (MlOOO — ina)LDinCDror'.CJ)r''COro tnfor''S3a>'-coroa)qqr''incM'-qa)QCMio — CQiOh'qinr''LninLD — roqojoo qr^qr^SJ-Siq — cdooco — coqcocoscosicos — sscMro — r^qr^cncMao —

• • • (M CD — CD • q • CD CO • IO -S3 CD ID CO •— • I"' 00 -CD NO CD • • Q OD — LO IO • • -CD •

‘

• CD -TStD^ • • -CM -CM •

- S3 -CD • LO CM

q — CM — • f"* — • — COCOCOCOCMlDqiO •rO(Mr''COCOCO(MinS)COrOQrorOCOCOq

i I i i 'tcoods i n i unw i d i ir''iODcoiNDir''icDcoicDiccr''i i

q ro q ro ro q

- ro ro q ro q ro q q q ro q ro q q q ro ro ro ro ro ro ro q ro q

ro q

ro

l Ld

l Ld

q l u

i Ld

I u

i u

1 id

i Ld

I Ld

l Ld

1 Ld

i Ld

I Ldl Ld

l Ld

i Ld

i Ldi Ld

I Ldi LdI Ld

i Ld

i Ld

i Ld

1 Ld

i id

i Ld

i Ldi Ld1 Id I

1 Ldi Ld i CM LD 1 ro ro ro q CM ro CO LD CO CO — q ID q CM LD CD CO LD 00 ro CO CD — CD CM — CD Ld CM — Ld

S3 CO Ld h' — CD ID — — ro S3 00 — CO S3 r-' CO ro CD CM CD S3 S3 q q LD ro LD CO CD CD CD CD —

r* T ro CO r- CM — CM q CO 00 ID Is- ro — CD — CO q CD (3 CO — LO CO q ro q CD q CD — ID S' ro CM q CD ro o ro CM q ro CO Q q CO q CD — 00 ro CD 00 q Q •

to q ro CO q LD CO ro s

CO q ro q S3 CD — — Q CD CM <s lD q q Q — CM q q CO CM ro q CD — CM ro — CO — LD q S3 O) CM ro — *— r^ ro CO q 00 q CO CO CD CM

CO CO q — S3 CD 00 CO CM CM ID Cm Q — S

ro r- CM LD CD .

CO CD q r- S 00 q ID S q .

— S3 ro CM •

-

CD .

ID CD 00 CO 00 CM S' ro LD ro .

— CO ro o CM CD — q — CM — CO CO ro — LD 00 <3 — — r^ 00 LD S3 S3 ID s» CM CO CM CM CO S3

ID 00 ro o Q ID — — Q CM ro ID CD CO q S3 CM q Q CD lD 00 CO LD Q CD CM LD 00 q CD ro ro ro 0)—*(Mq(M — 0)(M — 03<MlDCMO)LOr'' — LO — CDr^iD — f\j — — — 0) — — 00 CM

S3 S3 Q S3 Q Q S3 S3 S3 S3 (3 S3 (3 S3

S3 S3 S3 C3 S3 a S3 Si S3 S3 Si S S3 62 ID S3 ID S in S3 LO G3 LD <S ID 62 ID S3

CD S3 S3 —

_ CM CM ro ro q q LD lD CD

q ID LD iD) LD ID ID ID in LD ID ID in LD

a (S3 s s

Si Si <5 3 D C. D S

CD ^ 00

iD iD iD ID

S3 3 S3

S3 G3 Q 62

LD Si LD 62

oo CO 03 S3

iD ID L

CD

S3SSQ

S S S <a LTSlOQ I'T' I CD CD CO CD

S s S3 S3 S3 S3 Q S3 S3

S3 S3 Si Si S3 <S S3 S3 S3

ID S3 LD S3 ID S3 LD S3 LD CM ro ro q q ID ID CD CO

CO CD CD CO CD CD CO CO CO
- 121 -

no 'T CO in 0) 00 CM CM CM — CD CD CM CD co in CD tn r-s CM CO in 3 .NO CD CM CM N« — NO in

00 CD 00 NO CO 0) 3 3 — 00 — NO 00 CM m- Ns NO CM CM rv. CO ’T CD co in NO CO 3 — NO 3 "'T CM CD

00 in K> CM CO -00 00 — rr (3 sr CD CO CM co CO CO CM CO CM NO CO CM NO NO 00 in CD CM Ns 00 CM CM O) — in CO 00 CM CO — T (3 r- CD — — <r Ns 3 00 CM NO CD CO CO 00 00 CD NO Ns S in 00 3 (M r" in CM NO Tf CD N- 00 M- CM 00 NO NO CO •

CO •

T in TT CM in 00 CD NO CM CD CD M"

•p— .

r- S N- — in 3 CM in 00 CO CD 3 CD Ns CO 00 CM m- CM 00 CO 00 'T N' in CD CD 3 CD in 00

in 00 C\l N* CM CM 00 — s in CM 3

— 00 •*r in 3 CD N* N* CD CD CD CO NO .

in — — r-s CD Ns 3

00 K) O) ro Ns Ns 'T CO NO 00 (3 in CO r- CD CO 0>J CM 3 •— 3 'T CO CO CO CD CM N' NO 3 co CD

.

'T in 3 no r- S CM co in in r- m N' in CD ao 00 CM CD CO •M

- — N-* — m- 1^ CO 3 CO m- in CD

CO CD CO CM 00 00 Q M- — CD CD — NO co V N^ CO 00 CD m CO 00 3 CO CM N- CO in co 3

ro CO CO CM CM CD in CD in cm s NO CM 3 CM CO .

— CO CO CO .

00 — CD CO in NO CD

Ns CO in CO CO CO CO CO CD CO N' CO CO CO CO CO CO CO CO Ns N Ns CO in CO CO CO CO Ns Ns- co co in

l i i I i i i i i i i i i lit i i i i i i i i i i I

— in oo cm CD CD in G N CD 3

CD ^r 00 CM CO Ns NO Ns Ns

Ns CO NO

NO

Ns |Sx

CM

CD 00

CO

CO

NO

in

00 NO

Ns s

"TCO 3 CO

CD

<r CD in

NO CO S —

*— in co co cd in co NO — Ns 3 NO CD LO CM M" — — in CM 00 CM NO M" NT Ns 3 NO CO CD CM T N- 00

CO CD NO CD S CD 00 NO "T CO 3 CO CO NO NO CM 00 NO CD in CO CO Ns CM Ns 00 — NO NO CD in — NO Q NO 00 Ns NO 00 CO N- NO CD 3 m- •— S Ns in CM *— in co CO CD CO 3 CM NO Ns 3 in N NO — 3 CD

NO 00 00 CD CD NO — CD CO CM in — CM CD 00 CO 3 CO — rs Ns — 3 00 Ns NO CM in CM in m 3 CO 3

— in oo cd Ns oo in CO NO NO CD 3 m in ’T CO «

00 in •

CD NO — NO CD .— in in — 00 NO Ns s in

CO S NO CD 3 CM CM oo in CM NO in 3 Ns Ns CO — CD CM CD in CM 3 m- NO — CM CO 3 — 3 CO

NO CM CD CO P's 'T in co Ns in NO in NO 00 3 s T "T T — M" NO in CD CO 3 CO co 00 00 CM CD NO

CD NO S 00 N 3 in NO CD CD NO s sr CO — r>. — 3 NO 3 co NO Ns 3 s— in N> co CD in CM 00 NO NO — • - 3 • •

' • in CD T 3 CO m- •

CO CM • • CD CO CM .

- — 00 CO • — Ns coco • Ns NO • 00 — 00 NO CD in 3 M

- NO NO — Ns CD CM NO NO 00 00 in M- CM — NO — — Tf- CO M" - Tf — N- CO 00 CM Ns CM CM CM CO NO M

- "T M- CD M" m

in i i i — i i 1 1 N- — co Ns in 1 CM CM 1 CM CO 1 1 1 1 1 1 1 1 1 CM 1 CM CM i i

M" NO NO NO NO ’T T NO NO V NO T M" M" "T M- T V NO NO M- NO 'T NO NO

* -

1 1 l 1 1 1 1 1 1 1 1 1 1 NO 1 . 1 1 1 p— 1 1 1 1 p— 1 1 1 1 1

1 1 1 1 1 Ld UJ LlI Ld Ld Ld Ld Ld UJ LlI u UJ Ld — Ld Ld Ld Ld 1 Ld Ld Ld Ld 1 Ld Id Ld UJ Ld 1 UJ Ld U UJ Id — CO in in Ns p— 00 N in CD Ns NO CD 1 NO Ns LO CD Ld 00 T — CD UJ M" in CD in Ld (D (M M- N- CD CM co CM CM NO 3 CM m NO CD 00 M- LlI CM (M N- CM NO •<T NO NO 00 3 CD co CO — in — NO CO M- CO CM NO 3 3 in CO — Ns in 00

in Ns 3 CO NO — CO 3 NO CM 00 Ns Ns CM CM — Ns — (M CD Ns N- CD

in in — in T in CM m in Ns Ns 00 NO Ns in p- NO Ns CD 3 3 Ns CO CM CM 00 in M- NO 00 CM 00 3

in CO in CD NO co Ns s co 3 CO 00 00 CM Ns m CD S 00 — 3 — 00 CO T m 00 v CM T p- CD CO ^r CO — CO NO CM 00 NO NT Ns in Ns p— NO NO CO CM CM n NO in Ns 00 m M

- 3 NO CM — (M M" CD O) 00 CD

CO m- p— O) CM NO "T CD s Ns. 00 Ns NO m a) CD CD CO CO 3 in NO NO CD 3 NO CD CM in Ns 00 in CM CD — 3 00 .

Ns 00 p- 3 •- 00 "T CD NO in CD NO Ns N CD ICJ 00 p— 00 CM — 3 CO CO co NO — 00 CD CO Ns

Ns 3 CO NO (M 3 NO in — O) CD rs. CM NO •

NO TT in M- 3 pSp in CO s in CO 3 a) <T in CO CM NO

CD

NO 00 CM

p— — CO CD CO OO NO p— T— -- m — CO — 00 00 iM CM — p— — CO — p- ro CD — ps 3 3 3 3 3 3 S 3 S 3 3 3 3 s 3 3

3 3 3 3 3 3 3 3 3 S 3 3 3 3 s 3 3

3 in 3 in 3 in 3 in 3 in 3 in 3 n 3 in 3

Ns Ns 00 00 CD CD 3 s

p— CM CM NO NO “'T ’T in

CO CO CO co CO co Ns. Ns Ns Ns Ns Nv r>s Ns. Ns. Ns Ns

S^RKQSSSSQSSQQSSQS SoiaijS 3 QQSSSQlSQSSSQ lOSLoainainQiDSinQinsinQiOQ

m co co Ns Ns co co cd cn s 3 cm cm ro no ^

rv.r^.'vr^r^rN.r^fv.rvaOQOCOGOOOOocDCOOO
- 122 -

no — in ro CM — NO CO in NO CM NO cc CD CD — — CM — CM 00 NO in CO O' NO O' CD vr in no o> CO O' CD in LO in <3 NO NO CO CM O' CO CD 3 in a") O' «— in CM — t}- CO 3 in CO 00 V CO CO — no O) r" 00 NO 3 NO — *r O' CM in NO

CO 00 •'T — CD CO CM — o- CO • CO T 3 CD CO S NO CD

-

CO NO -

NO O' T no CD lD CO O' CD •

T 00 r^s CD NO r^ in O' 3 in CO NO 3 3 O' O' CM 3 in

CM CO CO O) — no CM CD LO CM no CD in CD T CM CM CM 3 T n NO NO O' in — — 00 M' ... Q CO V Q

in .

(M O) O) — CO •

M" M- CO NO CM NO 00 00 CD <M CO in CO <3 00 O' O' r- in CD 00 CD O' M" in M" 00 — r- (3 CO — .

CD CO CM in -

— o* NO NO O' CD in m O' 00 CM CD NO CD CM CO O' NO CO V

s *— NO Q 00 O' — CO CO CD CO CM — O' CO CO CO CD CM NO NO NO CD — CO in o* T CO CM 00 . T O' CO CM CM 00 3 00 CO 00 CO 00 in CO s CO CM V M- CO O' in NO CD M- CO 00 MT O' NO in CD CM CO

CM O' — 00 Q CO 0) CD CD CO CD CD CO ID in 'T 00 (M (M NO in CM NO CD — M" — CM CM in CM 00 in

CM in no (3 CM 3 .

no CD CM CM NO O' 3 00 CO CM (3 NO — 00 3 CD O' CO CO — CM 3 3 in O' w

. in

CO CO CO CO CO CO CO CO in O' CO CD r- O' in CO CO CO CO CO CO CO in CO CD O' CO CO CO O' CO O' CD CO

I i i i i i i i i i i i i i i i i i i i i i i i i

CD "T — CO in M- o- CO CO — o> CO 3 in in CD 3 CM — CO CO CM M- M" O' — cmcdoo in *

^r CM 3 NO in 00 CO 00 NO CD — NO in CO CD 0) O' in CM — NO — NOOOr^CO'T'TCOCMCMin NO T V in MT 3 V CD — — 3 in CO NO CO 00 O' 0) 3 NO

CM M- 00 CO N' CD 3 CM 3 00 CO CD CM "T 3 — CM CO in in CD CD ... O' CD NO 3 3 NO CM _

NO NO CD CM C\J CM CO NO 3 O' CM 3 3 3 •— *r in CD — m 00 M" 3 in CM in 3 O' 00 in CM ’T^CDCM'-IOIOCDSiQMO- — 00 CO (M T V CD CM CD CM CM — in CD 00 3 CO NO 00 NO CO

qcoco — no-3 — m-co — cmco <r T — 3 NO — O' CO 3 m CO in CO CO in CO in CO in NO sss^DinNoaisincDNor^ CO 3 CD 00 in M" M" — CO r» 00 NO v 3 00 3 3 3 NO CM 3

s O' co — cDincDScoincMTCo O' CD M" NO in r> CD CO CD CO — CD 00 O' CM O' CO 00 in CD in NO

SC03(MC0CDC0M-NONvfM”T00 NO — 00 in 00 3 'T -

CO 00 NO CD in CD — CD in CO CD CM

CO - • • — 3 CO -O' -CM in CD -

NO CD CO 00 • • O' NO CD CD NO NO — — 00 3 • - —.CO CM- — 3 "r 3 CD 3 CD 3 • 3 NO CD O'

- (M CM O' 3 3 3 NO • CO NO in • 00 3 00 CO NO O' *— CM NO (M in in T CM NO 00 m — O' in LD NO

(Ml I l inCON l S 1 "T-S 1 CM CM in 1 i l in 1 1 i NO 1 in O' 1 i i 0' 1 O' 1

NO NO NO NO NO NO NO NO M" NO -'T NO NO NO NO NO NO V NO NO M" NO M- NO 'T

1 1

4 13 13

|

1 1 1 1 I 1 1

1 |

1 1 i 1 Ld

1 Ld

1 LxJ

I LlI

1 LU Ld Ld Ld Id i i 1 Ld u Ld Ld Ld Ld1 Ld Ld U Ld Ld UJ Ld Ld1 Ld Ld 11 UJ1 u

1 Ld i LdI Ld

CO in — n NT in Ld UJ Ld NO in CM 00 00 — CD 0) O' 00 — CO NO — — in Ld CD in O' Ld T in 3 CM 0- CM CM . CM in — O' (O M" 00 NO 00 CO — O' in CM (M 00 in CD CM M" V CD NO — CO in

r- in CO CD CO in — O' NO T CM O' CO 3 CD CD CD in NO CD CM M" M" M" 3 •'T CD in NO CO 3 NO 00 3 CM CM — 00 in N- 3 NO CO CO in •

V CD NO — TT CO — M" O' 3 CD CO CO in 3 CO NO — NO CO

M" CO 00 a

NO — 3 in CO in cc — cc O' in <— CO CD CD CM

CO CO NO NO CM — .CO CO CM s 3 CM NO NO CM CO CD 0) NO •M- CD 3 Lf; O' O' NO CO NO «— NO s CD — NO in CM 3 00 CM CM

NO CM h' CM CO NO M" M" CM CO CD in 3 O' M- CM CM M" CD CM •

3 a) CO NO 00 CD CO 3 in O' 3 —

M" NO — 3 M" CM CM CO CM CO NO OJ 3 — M" V — CM 3 CO 3 O' NO n CM in CD 00 M- NO CO CM M" O' NO — CM CO M" CO O' •— CM * NO in •

NO NO CO CM in CO O' CO O' m in M- NO O' a

M" M" NO

CD — — — — — 'T T— — OvJ uo CM CO .

— .

CO r— — O' CO CM — — — m «— CM CM — CD

Q Q <3 <3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 s 3 3 3 3 3 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 S 3 3 3 3 3 3 3 3 S 3 3 3 S in 3 in

in S in 3 in 3 in 3 in 3 in 3 in 3 in 3 m 3 m 3 in 3 in 3 in 3 LO 3 in 3 in 3 3 — —

V m m CO CO O' O' CD CD CD CD 3 3 — — CM CM NO NO T TT in m 3 3 O' O' 3 00 3 3 3 3 3 3

00 CD CO CD CO CO CD CO 00 00 CD CD CD CD CD CD CD 3 3 3 3 3 3 3 3 3 3 3 3 3 3 — — — —
- 123 -

CD CD eg *— eg 00 ro CM — 00 g CD 00 eg g p* — CO 00 n — g 03 pN g CM CM .

03 03 3 CD — g g g CD X in eg eg TT PO 3 CO S3 S3 03 g 03 03 — CD — g ro 03 X ro — g X p* ro 00 CD — CD 3 g 00 CM X CD fO eg p- in g NO n 00 n 3 fO <3 g g eg n ro ro 3 03 X 3 ro ro — p- ro g .

CD — O) CD 3 g — p- g fO CM fV S) S3 NO g ro 03 CD ro CM 03 3 X n ro ro —

00 s CD fO eg — 00 CD CD fO CM p- S3 pn eg — p> 03 •X p- ro fO ro X 3 g X ro ro PN CM X CM

CD in CD in O) eg in CD

CD p- CD p- 03 <

p- 03 CM CD eg p- S3 ro — 3 CD X s CM ro 03 03 in

.

00 00 g «— CD eg CD CD P* in g CM CD 03 g

n p* g — 03 P* CO eg 03 00 3 X ro _ CM 03 CM

.

CO 00 CD 00 CD CD in g CM — ro in p* n

ej g ro (3 3 — CM 03 03 X CD r-N X ro 3 in 3 1^ lO — eg — CD ro CD eg — CD p^ PO 03 g hO CD CD CD NO eg eg 3 CO 00 CM n 3 X p- 3 X CD 3 X

CD CD T P* eg 3 CM eg 3 in CD g p- ro n n S3 ro X p^ LO n CD 03 X n eg 03 PN 03 X g

g p* ho ro in g in — S3 CD CD CD NO ro CM .

in S3 00 03 03 X 03 g 03 X g eg m 3 3

CD CD CD CD p* CD CD CD CD CD CD CD CD in CD CD CD n CD CD (D CD n CD X n n in n X X X X

l l t l i i i I i i i l i i i t <11111 < i I i

CD ro X X X CM — g X P' — X

CD X ro g ro n ro X PN X ro p. X X 3 X ro X CM X CM X X X X 3 n g g X Pv X X 3 3 CM r— X ro X PN CM g X —

X ro X g CM X

n X eg p^ «— n 3 X g S X X X X s

g X in ro X p- n n If) X

X X g ro CM X X s n X X X n X CM PN X — ro g X X _ X in X ro eg X X X X P- — CM 3 ro ro X X 3 X X CM X 3 3 X — X g- V — p- X eg

0) ro X ro X ro X p- X g X 3 X g X ro •

X X eg g 3 >

X ro X ro g 3 00 g- 3 g- X X X — X X X CM X pN ro X 3 CM g 3 X — X — 3 g X pv X X 3 V n n — .

X eg eg

g- CM ro — eg CM ro eg X p* 00 -

g 3 n ro — in X P^ X n — in n X g p* X ro X ro —

X

g _ X — ro CM eg ro X X P' X ro ro p* CM n — n CM X n n n ro X X X PN X p- eg g- in p- X 3 X in 3 — — n 3 CM X X X r^ X n X P- eg X X X X n ro g X X X X pN eg

• g 3 — — g X •— s «

X CM eg • g X . rv X X

CM . - 1 - — X X X 3 PN in p- X • eg ro X 3 p- • — p> in — 3 g ro g eg — g 3 eg g p- ro — X n n eg T g g

X n g - X CD p. X X

1 X X ro 1 i i i 1 i P- X g — i i n ro — ro X i in i

i i l X p* 1 1 n X n

ro g ro ro g g ro ro g g ro ro ro ro ro ro ro g g ro ro ro g ro ro ro ro ro g ro g g

i I 1i

| 1 i |

l

1 1 X

1 LlI1 liJ

I X X i X

1 X X 1 X X X X X X X X X X X X X X X iI X

1 XI X

1 X

1 X

1 X

1 X

1 UJ

1 IJ X X X ej X X CM ro X X p- X n ro X PN p^ ro X X X p- X eg X g X g X X ro X X X

ro in ro X CM X CM ro eg n ro 3 Pn CM 3 3 — X n pN X g p- n g ro eg CM g 3 ro Og X in .

in X *— n — X <

ro n p- n CM ro X pN X ro X X eg p- 3 X m g ro n g X 3 ro 3 X g

ro 3 — eg 3 — 3 X g X X CM X n X ro s X X 3 X n CM X X 3 3 g g p> p- eg — ro

CM P' n 3 P' in P> p- X X ro ej CM g p- g X X g X X X X n X X X 3 X CO ro — g X in X g — X X X X — m n in X PN X X p- X — n eg g ro n Pn X — n ro eg in g X X 3 g P- X in X g ro g X X CM 3 ro 3 ro — p- 3 X n X X ro n X in g X g g p" — eg

g- X X n X — X g p- X X ro ro 3 — eg X ro ~ X 3 P- X X 3 3 g ro X ro X — X 3 X 3 ro — — 3 — X in pv X X p^ CM ro ej ro g

n X g X g 3 X ro X X 3 CM 3 X in CD _ — — ro X — n p- X .

ej -- ro X n — — CO ... ro .

— — — X — in eg

3 S 3 3 3 3 S 3 s 3 3 S 3 3 3 Q 3 3 3 3 3 3 3 S S 3 3 3 s 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3 m 3 in 3 in 3 in 3 in 3 in 3 in 3 n 3 in 3 in 3 LO 3 m 3 in 3 in 3 in 3 in S in 3

CM CM ro ro g g m in X CD P' p. X X X X 3 s — — CM eg ro ro g g in in X X P' p* X X X

3 3 3 3 3 3 3 3 3 s 3 3 3 3 3 3

.

429

1

73

1

G69

-75.861

705995
- 124 -

CD CD LD CD V ID — 3 CD CD CM CD — ID in •

P- M" CD 3 po «— m- LD <3 *T CO 3 m CM PO PO

PO (3 p* CM 'T ID — CM 00 CD PO CD 00 — PO — V CD — CD ^r 3 CD CM V LD CD CD TT ID 'nT — P" 3

CD ID po hO CM CD po CO CM CD M

- 3 CD 3 CD PO — CM

CM CD CD O) CD CM CM CD CD ID <

3 PO CD PO CM 3

PO O) CD CD CM CD — CD CM ID PO CD 3 (M CD "T CD

(3 CD CD CD ID p- CD po PO I s* ID CD po CD PO CD 00

CM CD CD CD p" CD PO P" CO .CD CM CD CM LD CD

I s* CO — CD O) CD CM CD CD — CM P" CO 00 *T LD ID V

PO ID CD 3 T CD CO M" S CD CD p- CD PO ''T CM CD

CD CD CD CD CD CD CD CD CD CD CD ID LD CD CD CD CD CD

I I I I I I I I I I I I ! I I I I I

CD p- ID CM CO P' CD CM p' —

CM PO — CD 'P — ID CM CM CD .

CD LD — — 1 ID PO CM CD ro CD M" CM CD P- P- CD PO 3 CD p^ LJ CD p" V ID 3 CD — CD CD PO 00 ro ID 3 3 P- CD PO

0D p» P' CM P- 3 CD CD CD CM CM ID CD M" P- PO

00 ID LD P" 3 CD T — O) 00 M- — CD — M" CM 3

Q CD CD CM — ID CD CD — CO ID p* pv ro 3 ro P- PO

CD T PO CM ID ID CD CD CD — V 3 LD 00 LD CM —

00 00 ID CD — PO M- P' — CD CD CD LD CM P* ro 00 —

"P — P- 3 CD CD CO CM CD CD ro — M- CD 3 CD TT 3 CD 3 PO (M LD CD — CD CM 00 CD 'T CD iD * «

CD CD

00 P- •^r CM CD P* 00 CD CM CO CM CM CM 00 PO CM

1 1 1 CM PO ID ID PO l 1 1 1 1 PO PO 1 1

PO PO PO M" PO PO PO PO PO M" PO PO "'P

I I t I I I I

I I I I I I I — I I I DJ LJ LjJ LJ LJ LJ LJ U LJ U LJ U LJ LJ 1 LJ UJ u

CD P- CD CD P- CM CD CD M" 00 CD ao CD CD LJ PO M" 3 3 — 3 3 3 — CO PT PO 3 CM in CD 00 P' O) M" CM CD — ID LD P'

3 — 3 M* lD CD LD ro CD M- CO 3 00 CD — CD CD CM M" P^ M" ID PO 00 p> CD P- ID

rr 3 00 CD rr LD 3 CM ID P' 3 00 O) 3 — PO

PO S CD — CD — CD CD P' P- — CD CM CM ro 3 M- CM

00 PO -CD PO M" vr V CM — CD 3 PO 3 CM CD V CM

ID CM PO 00 3 ID PO LD M" M" CD Pv 3 CD LD CM CD — 3 CD LD 3 00 LD CM 3 p» 00 3 CM *

3 PO LD — CD CD — — ID — CD — CD CM CM CD — — CD

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 S 3 3 3 3 3 3 3 3 3 3 3 3

ID 3 LD 3 LD 3 LD 3 ID 3 LD 3 ID 3 ID 3 LO 3

CD 3 3 — — CM CM PO PO T 'T LD LD CD CD p*. P* CO

CM (M CM CM (M CM CM 3 3 3 3 3 3 3 3 3 3
- 125 - ii

GJI LlI 00

r*

NBS-114A (rev. 2 »ec) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

81 -2235

2. Performing Organ. Report NoJ 3. Publication Date

4. TITLE AND SUBTITLE

1980 Annual Report: Technical Contributions to the Development of Incipient

Fault Detection/Location Instrumentation

5. AUTHOR(S)

W. E. Anderson and J. D. Ramboz

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

A063-EES

8. Type of Report & Period Covered

Oct. 1 , 1979 - September 30, 1980

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State, ZIP)

Department of Energy

Office of Electric Energy Systems

Washington, D.C. 20461

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Technical barriers exist in the development of instrumentation to detect and locate

incipient faults in underground transmission cables. Knowledge is required of the

physical, chemical, and electromagnetic properties of cables which precede breakdown, of the manner in which characteristic rf signals propagate in cables, and of

» appropriate methods of coupling detection systems to operating transmission cables.

A measurement program has been initiated that will provide data on the rf

properties of cables and on the characteristics of some forms of incipient faults.

Preliminary measurements demonstrate the limitations of frequency- or time-domainreflectometry techniques in the detection of incipient faults. Software is presented which permits the Fourier transform of step-like waveforms.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semi colon s) aging; cables; dielectrics; electric insulation fault location; time-domain--

ref lectometry ;. underground transmission.

13. AVAILABILITY 14. NO. OF

| "ft Unlimited

j | For Official Distribution, Do Not Release to NTIS

PRINTED PAGES

130

1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402. 15. Price

| Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $ 12.50

USCOMM-DC S043-P80

NBS-I14A irev. 2-ac) U.S. DEPT. OF COMM.

4.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

81 -2235

TITLE AND SUBTITLE

1980 Annual Report: Technical Contributions to the Development of Incipient

Fault Detection/Location Instrumentation

5. AUTHOR(S)

W. E. Anderson and J. D. Ramboz

JH8 . Type of Report & Period Covered

Oct. 1, 1979 - September 30, 1980

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. Z/p]

Department of Energy

Office of Electric Energy Systems

Washington, D.C. 20461

S. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. SUPPLEMENTARY NOTES

f | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Technical barriers exist in the development of instrumentation to detect and locate

incipient faults in underground transmission cables. Knowledge is required of the

physical, chemical, and electromagnetic properties of cables which precede breakdown, of the manner in which characteristic rf signals propagate in cables, and of

appropriate methods of coupling detection systems to operating transmission cables

A measurement program has been initiated that will provide data on the rf

properties of cables and on the characteristics of some forms of incipient faults.

Preliminary measurements demonstrate the limitations of frequency- or time-domainreflectometry techniques in the detection of incipient faults. Software is presented which permits the Fourier transform of step-like waveforms.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words try semicolons)

aging; cables; dielectrics; electric insulation fault location; time-domain--

refl ectometry; underground transmission.

13. AVAILABILITY

| X Unlimited

| | For Official Distribution. Do Not Release to NTIS

j Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

14. NO. OF

PRINTED PAGES

130

15. Price

i

|

1

1

: Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $ 12.50i

i

USCOMM-OC «04c-P80
i