NBSIR 73-305

SINGLE STRAND MODEL COMPUTER PROGRAMS

FOR THE TRANSMISSION LINE PROPERTIES OF

THE MOORING LINE DATA LINE

D. R. Holt and N. S. Nahman

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

April 1973

Final Report

Prepared for National Data Buoy Project

National Oceanic and Atmospheric Administration

NBSIR 73-305

Single Strand Model Computer Programs

For the Transmission Line Properties of the

Mooring Line Data Line

D. R. Holt and N. S. Nahman

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

April 1973

Final Report

Prepared for National Data Buoy Project

National Oceanic and Atmospheric Administration

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

CONTENTS

Chapter Page

CONTENTS iii LIST OF ILLUSTRATIONS iv

ABSTRACT 1

1 INTRODUCTION 2

2 MLDL PARAMETER CALCULATIONS 4

3 MLDL PROPAGATION CALCULATIONS FROM 6

GIVEN LINE PARAMETERS

3. 1 Attenuation Phase and Quarter Wavelength 6

3. 2 Input Impedance 7

3. 3 Voltage Amplitude 8

3. 4 Current Amplitude and Phase 9

4 COUPLER LOADED MLDL CALCULATIONS 11

5 SINGLE COUPLER MLDL UPMODE TRANSMISSION 14

REFERENCES 17

APPENDIX - PROGRAM LISTINGS 47

A. 1 PROGRAM ZY 47

A. 2 SUBROUTINES FOR ZOGAM 48

A. 3 PROGRAM RESPDATA 49

A. 4 PROGRAM CURRESP 51

A. 5 PROGRAM ALLCPLR 53

A. 6 SUBROUTINE ABCD 55

A. 7 PROGRAM UPMODE 56

iii
LIST OF ILLUSTRATIONS

Figure Number Page

Figure 2. 1 Equivalent circuit per unit length, 18

Figure 2. 2 Cross section of single strand line. 19

Figure 3. 1 General equivalent circuit per unit length of 20

MLDL.

Figure 3. 2 Equivalent circuit per unit length of MLDL in 20

terms of R, L, and C.

Figure 3. 3 Attenuation versus frequency. 21

Figure 3. 4 Phase versus frequency. 22

Figure 3. 5 Quarter wave length versus frequency. 23

Figure 3. 6 Equivalent circuit for input impedance of 24

MLDL terminated in arbitrary load impedance.

Figure 3.7 Real part of input impedance versus frequency 25

Z termination,

o Figure 3. 8 Imaginary part of input impedance versus 26

frequency termination.

Figure 3. 9 Real part of input impedance versus frequency 27

chort- circuit termination.

Figure 3. 10 Imaginary part of input impedance versus 28

frequency short-circuit termination.

Figure 3. 11 Real part of input impedance versus frequency 29

open- circuit termination.

Figure 3. 12 Imaginary part of input impedance versus 30

frequency open- circuit termination.

Figure 3. 13 Equivalent circuit for source voltage response 31

of MLDL with short termination.

Figure 3. 14 Input voltage amplitude response versus 32

frequency short-circuit termination.

IV
Page

Figure 3. 15 Equivalent circuit of current response for 33

variable positions on the MLDL.

Figure 3. 16 Current amplitude as function of position on 34

line 7. 2 KHz sine wave generator short-circuit

termination.

Figure 3. 17 Current phase as function of position on line 35

7. 2 KHz sine wave generator short-circuit

termination.

Figure 3. 18 Current amplitude as function of position on line 36

7. 2 KHz sine wave generator open-circuit

termination.

Figure 3. 19 Current phase as function of position on line 37

7. 2 KHz sine wave generator open- circuit

termination.

Figure 3. 20 Current amplitude as function of position on line 38

7. 2 KHz sine wave generator characteristic

impedance (Z^) termination.

Figure 3. 21 Current phase as function of position on line 39

7. 2 KHz sine wave generator characteristic

impedance (Z ) termination,

o Figure 4, 1 Equivalent circuit for coupler loaded MLDL. 40

Figure 4. 2 Current amplitude as function of position on 41

loaded and unloaded line for 7.2 KHz sine wave.

Figure 4. 3 Current phase as function of position on loaded 42

and unloaded line for 7. 2 KHz sine wave.

Figure 5. 1 Equivalent circuit of MLDL with coupler 43

source down line.

V
Page

Figure 5. 2 Thevenin equivalent of MLDL circuit model 44

in Figure 5. 1. Figure 5. 3 Received voltage amplitude versus discrete 45

coupler positions upmode using 6 KHz

coupler source.

Figure 5. 4 Received voltage phase versus discrete coupler 46

positions upmode using 6 KHz coupler source.

Figure 5. 5 Received current amplitude versus discrete 47

coupler positions upmode using 6 KHz coupler

source.

Figure 5. 6 Received current phase versus discrete coupler 46

positions upmode using 6 KHz coupler source.

vi
ABSTRACT

Equations and computer programs are presented for calculating

the propagation properties of the Mooring Line Data Line (MLDL).

The development is based upon a single-strand inner conductor model

for the MLDL structure. Propagation parameters, input impedance,

voltage amplitude, and current are developed from the complex

impedance/meter (Z) and the complex admittance /meter (Y) of the

MLDL. A matrix formulation of the voltages and currents along an

MLDL loaded with couplers at arbitrary positions is developed. The

received voltage and current at the water surface produced by a single coupler down line at an arbitrary distance is presented.

Key Words: attenuation; characteristic impedance; circuit model;

computer program; computer printout; coupler; current; impedance;

load impedance; mooring line data line; phase; propagation characteristics; sea water return; series impedance; shunt admittance; single

strand; transmission line

1
CHAPTER 1 INTRODUCTION

The objective of the work reported here was to develop computer

programs for calculating the propagation properties of the Mooring Line

Data Line (MLDL). The programs were based upon a single- strand

(inner conductor) model for the MLDL structure. This report is divided

into five chapters as described below.

Chapter 1 is the present introduction, and Chapter 2 presents the

equations and computer program for calculating the MLDL transmission

line parameters Z and Y, the complex impedance/meter and the complex

admittance/meter, respectively. Given the MLDL dimensions and

material parameters, the complex Z and Y values can be computed for

any frequency of interest.

Chapter 3 presents the equations and computer programs for calculating (1) the propagation parameters: ql > attenuation (dB/m); B,

phase (radians/m); and \/4 , quarter-wavelength (meters), (2) the

MLDL input impedance, (3) the amplitude of the MLDL input voltage,

and (4) the current along the MLDL as a function of distance from the

sending end. (2), (3), and (4) are computed for the MLDL distant

end terminated in a short circuit. Given Z and Y, (1) through (4) can be

computed for any frequency of interest.

Chapter 4 presents a matrix formulation of the voltages and

currents along an MLDL loaded with couplers at arbitrary positions.

A computer program is presented for calculating the current at each

coupler. Given Z, Y, the positions of the couplers, and the coupler

impedance Z^ , the complex current at each coupler position can be

computed for any frequency of interest.

2
Chapter 5 presents equations and computer programs for calculating the received voltage and current at the water surface produced by

a single coupler placed at an arbitrary position along the MLDL (the

MLDL is loaded with only one coupler). Given Z, Y, and the

coupler position, the complex voltages and currents produced at the

water surface terminals can be computed for any frequency of interest.

3
CHAPTER 2

MLDL PARAMETER CALCULATIONS

In this chapter, given the MLDL material parameters, the series

impedance/m Z and the shunt admittance/m Y are calculated in terms

of the single strand model.

The equivalent circuit per unit length of the MLDL is shown in

Fig. 2. 1 in which s is the complex frequency variable, L is the external inductance, C is the capacitance, (s) is the inner conductor

impedance, and z (s) is the outer conductor (sea water return)

impedance. The line parameters have the definitions

r L = 1 n —- (henrys/meter), (2. IJ 2 TT r^

C = 27r€'Un(

]} (farads/meter), (2.2)

z^{s) = R (ohms /meter), (2.3)

(s) = "^^•{in^'r? s + y I (ohms /meter), (2.4)

^ 4 71" ' ^ o o

^ Definitions (2. 1), (2. 2), and (2. 3) are given in [ Ij

.

The impedance expression (2. 4) is easily derived from considering

the low frequency expansion of the sea water return expression

1/2

^2<^> = 777 V f ^ ^ r— TTT. "^^^^ ^ ' ^1 ' o 2 ( y ^

r^ s )

modified Bessel functions of second kind [2, 3].

4
where r and r denote radii of outer and inner conductors, respeco 1 tively. The parameter 77^ in (2. 4) has the definition

- = CT r ( cr , conductivity of sea water)

'o 4 2 o 2

y

where y is Euler's constant, and /» = C

' o

^

The computer program ZY calculates the series impedance Z

and the shunt admittance Y for the circuit model above. As an ex- ample consider an isolated single strand of low resistance cable with

the dimensions and material parameters shown in Fig. 2. 2. The

cable has 16 strands of number 28 AWG helically wound on a nylon

core, from which we conclude the center conductor impedance is

z^(s) =5 n/iooo ft. A sample output for f = 1 KHz and f = 7. 2 KHz appears below,

SINGLE STRAND LINE PARAMETERS

SERIES IMPEDANCE AND SHUNT ADMITTANCE CALCULATIONS

IN MKS UNITS

Z Y F

OHMS/ M OHMS/M MHOS/M hZ

1.73870-002 1.04368-002 0.00000 + 000 2.14464-006 1.00 + 003

2. 35061-002 6.62145-002 0.00000 + 000 1.54414-005 7.20 + 003

This calculation is performed in the Fortran program XY given in the

Appendix (A. 1, page 49).

5
3. MLDL PROPAGATION CALCULATIONS

FROM GIVEN LINE PARAMETERS

In this chapter circuit models, equations, curves, computer print

outs and programs are presented to illustrate the following specific

propagation characteristics of the MLDL: (a) attenuation, phase,

quarter wave length, (b) input impedance, (c) voltage amplitude, (d)

current amplitude and phase.

3. 1 Attenuation Phase and Quarter Wavelength

For the general equivalent circuit model in Fig. 3. 1 the propagawhere a. , jS are attenuation (dB/m) and phase (rad/m) respectively.

The characteristic impedance has the definition

For the specific equivalent circuit model in Fig. 3. 2 the series

impedance Z(j (ji) and shunt admittance Y(j co) are calculated in the com

puter subroutine ZOGAM. This subroutine appears in two versions in

the Appendix (A. 2, page 50). Version 1 computes Z{i ^) = R + jajL

and Y (j oj) = j W C where R = ^ /lOOO ft. , L = 500 pi H/1000 ft. , and

C = . 2 M F/lOO ft. Version 2 of ZOGAM calculates Z(j OJ ) = R ( ) +

j W L ( ^) and Y (j 60) = j C from equations (2. 1) through (2. 4) of Chapter 2, For the sample calculations of Chapters 2 through 5 we have

selected version 1.

tion fxinction is defined as

r (J Oi) = v/ Z(j to ) Y (j CO )

= a ( co) + j i3(aj) (3. 1)

(3. 2)
A computer printout of attenuation, phase and quarter wave

length for one frequency (100 Hz) appears below.

F(HZ) ATTENUATION(DB/M) PHASE (RAD/M) QUARTER WAVE

WAVELENGTH (M)

1.00 + 002 4.894 - 004 5.999 - 005 2.618 + 004

The curves of attenuation, phase, and quarter wave length for

0 < f < 10 KHz are shown in Figs. 3.3, 3.4, 3.5.

3. 2 Input Impedance

The input impedance for the MLDL terminated in an arbitraryload impedance Z has the quivalent circuit shown in Fig. 3. 6.

For Z =Z , Z =0 (short termination), Z = =° (open terminaL o L L

tion) the expressions for Z. are m

[z.^(ja3)]= (j ^) (3.3)

2 iyii oj)

z, =z L o

and

z^=o

r, i - e

respectively.

A comj

line length i = 500 meters appears below

A computer printout of Z^^(j ) for one frequency (100 Hz) for a

7
HZ

INPUT IMPEDANCE VERSUS FREQUENCY

FOR THREE TERMINATING IMPEDANCES

TERMINATION SHORT TERMINATION

REAL(ZIN) IMAGKZIN) REAL (ZIN) IMAG(ZIN)

OHMS OHMS OHMS OHMS

1. 00 + 002 1. 455 + 002 1. 367 + 002 8. 20 5. 106-001

F

HZ

1. 00 + 002

OPEN TERMINATION

REAL (ZIN)

OHMS

2. 733 + 000

IMAG (ZIN)

OHMS

4. 852 + 003

The curves of each termination for Real (Zin) versus f and Imag

(Zin) versus f are shown in Figs. 3.7, . . ., 3. 12 for 0 < f < 10 KHz.

Note that when Z = Z , the input impedance is in fact equal to Z ; L o o consequently, Figs. 3. 7 and 3. 8 show the real and imaginary parts of

Z^, respectively.

3. 3 Voltage Amplitude

Consider a one volt sine wave generator with 5 0 ohms impedance

driving the MLDL with a short termination. The circuit model is shown

in Fig. 3. 13 where E(jo))is the voltage response at the source end.

The amplitude | E (j ^) | has the expression

E (j CO)

Z^(j CO )

CO ) + 50

1 -2 (j CO

)

1 ^^-2^y(jco)

(3.6)

The computer printout for a line length of 5 00 meters of

E(j 2irf) I for one frequency (100 Hz) appears below.

8
SOURCE VOLTAGE AMPLITUDE RESPONSE

USING SINE WAVE GENERATOR WITH 50 OHMS

IMPEDANCE . . . CHARGING DOWN LINE

F AMPLITUDE RESPONSE

HZ VOLTS

1. 00 + 002 3. 444 - 002

The curve of jE (j 2 f) | versus f for 0 < f < 10 KHz appears

in Fig. 3.14.

The computer program which performs the calculations of sections

3. 1, 3. 2, 3. 3 is entitled RESPDATA and is given in the Appendix (A. 3,

page 51).

3. 4 Current Amplitude and Phase

Consider the MLDL being charged down line when terminated in an

arbitrary load impedance Z . The circuit model appears in Fig. 3.15. L

The current response at any point x-meters from the generator

for load impedances equal to 0, , Z is given by

CO,x)] = z^.o

^-xy (j CO ) . -{2 a -x)y(j CO ) e + e Z^(j CO)

1 - e

- 2 ^ y (j CO )

(3.7)

[l(j CO,x)] =

and

^-xy(jco) ^-(2 ^-x)y(j CO

) e - e

Z^=co ZJj CO)

[l(jco,x)j = E e

g

1 + e

-xy (j CO )

-2 £ y (j CO )

Z = Z

L= o

Z ( j CO)

• o

(3.8)

(3.9)
The computer printout for current amplitude and phase appears

below for a total line length of 1500 meters for a 1 volt sinusoidal

generator.

CURRENT RESPONSE AS FUNCTION OF POSITION ON LINE

FOR THREE DIFFERENT TERMINATIONS

OPERATING FREQUENCY IS 7. 2 + 003 HZ

ALL AMPLITUDE AND PHASE UNITS IN AMPERES

AND RADIALS, RESPECTIVELY

DISTANCE FROM

TOP

METERS

3

6

OPEN TERMINATION SHORT TERMINATION

AMPLITUDE PHASE AMPLITUDE PHASE

2.445-002 -9.821-001 1. 594-002 1.196 + 000

2.452-002 -9.841-001 1.586-002 1.194 + 000

1500 0.000 + 000 0.000 + 000 2.402 _ 002 -1.649 + 000

DISTANCE FROM TOP

METERS

ZO TERMINATION

AMPLITUDE

1. 976 - 002

PHASE

1. 088 - 001

1500 1.548 - 002 -2.130 - 001

The curves of amplitude and phase versus distance from the top appear

in Figs. 3. 16, . . . , 3. 19; these curves were computed using the computer

program entitled CURRESP which is given in the Appendix (A. 4, page 53).

10
CHAPTER 4

COUPLER LOADED MLDL CALCULATIONS

In this chapter an equivalent circuit for the n coupler loaded

MLDL and voltage- current expressions for any coupler position are

developed. Computer printouts, progranns and curves of current

responses are illustrated.

To carry out propagation calculations of the coupler loaded MLDL

consider the circuit of Fig. 4. 1 where each coupler has the equivalent

circuit

Z^(j 60) = R^ + j COL^ (4. 1)

E is a 1 volt sinusoidal generator, and Z =50 ohms,

g g

Using the ABCD 4 terminal network parameters enables a matrix

equation of the form t

1 Z

0 1

1 Z

0 1

' A B

n n

C D

n n

1 Z

0 1 "L

(4.2)

Now the kth section of line has the definition

^ The dependence of network parameters on jco is omitted for space

economy.

11
1z

o

Z cosh y Z sinh y

sinh y a Z cosh y

o k

(4.3)

where C k " \ " "^-1 • We are interested in computing the voltage and current at each

coupler position x^. From (4. 2) notice = 1 = BI DI ^

and I

Therefore I = D/B.

g

At X = the voltage and current are given by

K] :;]"[:->] [.;]

At X = x^, the voltage and current expressi

(4. 4)

>ions are

(4. 5)

The computer program ALLCPLR performs the current re - sponse calculations and is given in the Appendix (A. 5, page 55) along

with the subroutine for calculating the overall ABCD matrix of the

coupler loaded transmission line (A. 6, page 5 7). The computer printout from a sample calculation of (4.5 ) appears below for current re- sponse, t

^ Additional coupler configurations, line lengths, and operating

frequencies were input to this program by request of the Sponsor.

The results were delivered to Mr. E. Kerut in June, 197 2.

12
SINGLE STRAND LINE WITH 12 COUPLERS

DOWN MODE WITH GENERATOR AT SURFACE

GENERATOR CHARACTERISTICS. . . EG = 1 VOLT ZG = 50 OHMS

F = 2 KHZ

THE FOLLOWING LINE PARAMETERS ARE USED --- R = 5 OHMS/10^ FT L = 500 MICROHENRYS/ 1 0^ FT

C = . 2 MICROFARADS/ 10^ FT

THE FOLLOWING CURRENT RESPONSE IS COMPUTED

AT EACH COUPLER POSITION

DISTANCE FROM TOP AMPLITUDE PHASE

(METERS) (AMPS) (RADIANS)

0 1.94719-002 -2.88721-001

10 1.9495-002 -2.92767-001

500 2.00345 -002 -3.63656-001

Current versus line position curves are also presented in

s. 4. 2 and 4. 3.

13
CHAPTER 5

SINGLE COUPLER MLDL UPMODE TRANSMISSION

In this chapter equivalent circuits, equations, computer printouts, programs, and curves are presented for upmode transmission

on the MLDL from a single coupler at a given position.

Consider the circuit shown in Fig. 5. 1. The voltage generator

has been moved from above water to the coupler position x meters down

line and a short has been inserted for the terminal load impedance.

Since the coupler impedance is in series with the input impedance to the

short circuit section of the MLDL an equivalent impedance is used.

Z ( -X, j oj ) = Z (j ^ ) + Z ( - X, j UJ)

eq c m

An equivalent circuit to the circuit of Fig. 5. 1 is shown in

Fig. 5.2.

Now the input impedance to the short circuit section of MLDL is

given by

Z. ( je-x, j oo) =

1 - exp i -2(£-x) yjjco)

}

1 + exp

I -2( l-x) y (jco) }

(5. 1)

The voltage response at the above water level is given by

E(x, jo) ) = E

c Z^(jco)+ Z ( Ji-x, joj)

1 -Peq(jw)Pg^

-2 zyijcc)

(5.2)

where p eqand P are voltage reflection coefficients, i. e. , g

14
z -z z - z

fJ = Q and p = • (5.3)

eq Z + Z "^g Z + Z

eq o go

The current expression at the above water level is

-xy(jCO) 1 - p (jco)

(5.4)

The computer printouts for voltage and current are displayed

below and have been calculated using the computer program UPMODE

given in the Appendix (A. 7, page 5 6). -f

SINGLE STRAND LINE WITH ONE COUPLER

UPMODE USING 1 VOLT 6 KHZ SOURCE

R = 5 OHMS/1000 FT L = 5 00 MICROHENRYS/ 1 000 FT

C = . 2 MICROFARADS/1000 FT

THE FOLLOWING CURRENT RESPONSE IS AT SURFACE

AS FUNCTION OF DISTANCE FROM COUPLER SOURCE

DISTANCE FROM TOP

(ME TERS)

50

AMPLITUDE

(AMPS)

1. 17647-002

PHASE

(RADIANS)

3. 83396-001

2000 1. 39387-002 •2. 47144+000

t On request of the sponsor different coupler levels, operation frequencies, and line lengths were input to this program. The results were

delivered to Mr. E. Kerut in June, 197 2.

15
THE FOLLOWING VOLTAGE RESPONSE IS AT SURFACE AS

FUNCTION OF DISTANCE FROM COUPLER SOURCE

DISTANCE FROM TOP

(METERS)

50

2000 5.96933-001 -2.47144+000

The amplitude curves for voltage and current versus distance are

shown in Figs. 5.3, 5.6.

AMPLITUDE

(VOLTS)

5. 88233-001

PHASE

(RADIANS)

3. 83396-001

16
REFERENCES

1. Ryder, J. D. , "Networks , Lines and Fields", Prentice-Hall, 1949.

2. U. S. Coast Guard National Data Buoy Development Project, Report

No. 601107, "Data Line Analysis and Telemetry Specification",

Arthur D. Little, Inc.

3. Weeks, J. L. , "Electromagnetic Theory for Engineering Applications", John Wiley and Sons, Inc., 1964, pp. 482-493.

17
sL

-nnnnn- Z2(s)

sC

Figure 2. 1 Equivalent circuit per unit length.

18
LlJ z a:

LU 1— LU

a: >- • CO o

o

1— l-H CNJ UJ z

>- uo

I o

_J

o o s- >-z

03

+->CO

I—

I

Pi

O

f-i

-i-> o

COO

U

:i

•i-i

19
Figure 3. 1 General equivalent circuit per unit

length of MLDL.

R(oo) L(w)

Figure 3. 2 Equivalent circuit per unit length of

MLDL in terms of the parameters R, L,

and C.

20
r-O

i—OOOOO r— O O O OO

O OOOOO OO

(lu/gp) N0iivnN3iiv

21
31

LlJ

o

cr

CO

Hi

en

^(>

CO

•i-i

(m/pBJ) 3SVHd

22
u

cr

<Du

CO

>

.—

I

>

a

00

IP

o

CM

(lii) H19N31 3AVM yBiaVnt)

23
o

Z .1 n

X = 0 X = £

Figure 3. 6 Equivalent circuit for input impedance

of MLDL terminated in arbitraryload impedance.

24

N

>-O

cr

UJon

o

o

I

o

o

I

o

o

LO

I

>>o

Pi

(U

cr

0)u

tn

COu

0)>o

Oh

>^

Ofl

CO

CO

?H

• r-(

(sujqo)"-

z

26
o tn o Lf) o LT) o CO CM CM I— I—

(sujqo) '^^z JO iyvd IVBy

27
JooI ooooooo \ I I I I I , cor>. 1^ ir> CO c\i <—

28
f— <— ^

o

COo

ego

a»

:icr

<u

cn

CO

^1>

0)o

,—

M «i tj

<ua

>-

•f-i

-i-> LlJ cr

UJ -1-1 o

+->

::5 o

;h

. w

C)

I SH

o

CO

(smqo) ^^z JO idVd IVBy

29
o

X

o

(A

o

o

>-

cr

o

o

cr

M-l

CO

CO

>

o

<uOh

13Ph

.1-1 m

O

CO

0)

^3O

fH •iHU

I

<ua,o

(siuqo) ^4 dO lyvd AyVNIOVWI

30
50^

Figure 3. 13 Equivalent circuit for source voltage

response of MLDL with short

termination.

31
(s^LOA) 3SN0dS3y 3anindwv

32
I ( j0J,K)

Figure 3. 15 Equivalent circuit for current response

for variable positions on the MLDL.

33
1

ro CO CM cvj 1— I— o

o o o o o o o

(sduie) 3SN0dS3y 3anindwv

34
1 1 1 1 \

1 o

EO

o

in

Olo oloo ldo id CMIII— I—IIO O

(spBJ) 3SN0dS3y BSVHd
(sdiue) 3SN0dS3y 3anindwv

36
X

O

o

• t-l o

0)

(/J ci -aa

4->

^1 U

o

00

(Ua,o

uo

->-> nJu

0)

CiJD

>

o

I o

I o

I (spej) 3SN0dS3y 3SVHd

37
SI X

CO

S4

o

o

+-> o

COoi

o

<M

CO

0)M-r-l

N

o

0)Oh

D

O

nJ

-au

^1o

-l-> nJ

OJn

&J0

OJ>

(sdwv) 3SN0dS3y Baniiidwv

38
o

o

enUUJo

1—

I—

I

Q

enO

o

•1-1 4-> O

nm

03

x:

a.

+->

0)

^1 U

CO

a;u

tiC

•1-1

N

u

a

• iH

(U

-l-i u

nJ

?-( nJo

u

o

+-> nJ

^^(U

(U

>

(Ti

(speu) 3SN0dS3y 3SVHd

39
A 11

Q

i X

11 X

T3

0) Xia

o

I—

I

u

<u

1—1

:io

oo

a

O

IT)

A

0 0X

t—

I

>.1-1

cr W

u

-r-(

40
CO CM — O O O O

(sdiiiB) 3SN0dS3b 3anindwv

41
Ln o un - I— o

I I I (spp^) 3SN0dS3y 3SVHd

42
Figure 5. 1 Equivalent circuit of MLDL with coupler

source down line.

43
eq

I (x, joj)

OE ( X, joo)

Figure 5. Z Thevenin equivalent of MLDL circuit

model in Figure 5. 1.

44
0 t- o

r— a

^ .— o

f~ ^

+ a 3: 3= u • o

ro <a- ^ TX 1

0

0

CM

00

0

OJ

0

VXD '

- E

X

0

0 1—

t

I—

C\J 1—

(

' 000

Q.

a;

LU

_i

D_

ZD 0 0

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48
APPENDIX

PROGRAM LISTINGS

A. 1 Program ZY

Program listing for computing series impedance (Z) and shunt

admittance (Y) of the MLDL in Chapter 2 , page 5.

PROGRAM ZY

DIMENSION F{2)

TYPE COMPLEX Z,Y

C0MM0N/DL0CK1/Z,Y

c—— — —— —

C COMPUTE SERIES IMPEDANCECZ) AND SHUNT ADMITTANCE (Y) IN MKS UNITS

C

PRINT 220 $ PRINT 225 $ PRINT 230

F(l)=l.E + 3 $ F (2> = 7.2»1.E*3

DO 1 K=l,2

CALL ZOGAM (F (K) )

' "

1 PRINT 2jQ,Z,Y,F(K)

CALL EXIT

20 0 F0RMAT(2 3X,C(F12.5,E12.5) , 6X , C ( t 1 2 . 5, E12 . 5) , 1 IX , E 8 . 2

)

223 F0RMAT(57X,»SINGLE STRAND LINE PARAMETERS*//)

225 F0RMAT(36X, •SERIES IMPEDANCE(Z) AND SHUNT ADMITTANCE ( Y) CALCULATIO

INS IN MKS UNITS*///)

230 FORMAT (t»0 X ,»Z» ,2 8X,»Y» , 26X ,»F»//30X ,*OHMS/M» , 7X , OHMS/M* , 23X , MHOS

1/M»,17X,*HZ*//)

END

49
A. 2 Subroutines for ZOGAM

Version 1: Program listing for computing the characteristic impedance

(Z ) and propagation function (r) of the MLDL. (3. 1, page 6).

SUbKCUTINL ZOr.Ar (F,LSWCH)

Trpi COIIPLtX GAM0,o,20

CO )MON/iJLOCK3/20,GAM10

TrPC KuAL L CC ALL PAk'ftMLT£RS IN MK3 UNITS

C COMHUT^ CHARACTLRISnC IMPcUANCt. ANU PROGATION FUNCTION OF LiNt

IF (LSWCH.LQ. 0)GO TO 1 o[=3.1i,l5>3 i f TPI = SORTF (PI)

L= (.j;»l.L-6) »^.£d i C=(.2»l.E-9)»3.2-8

(5.»l.c-3) *3.^8

1 S= (0. )*F»2,,»FI

3AlllO=CSakT ( (L»L+K:)*C*S)

ZJ=GAM10/lC*S) % K;£TUKN i CND

Version 2: Program listing for computing the characteristic impedance

(Zq) and propagation function (r) of the MLDL. (3. 1, page 6).

SUBROUTINE ZOGAM{F)

TYPE COMPLEX GAMIO ,S, ZA , ZB, ZO , Z,

Y

COMMON/BLOCK1/Z,Y

C0MM0N/0L0CK3/ZC ,GAM10

TYPE REAL MU,L

C - C ALL PARAMETERS IN MKS UNITS

C

PI = 3.1«*159 $ RTPI = S0RTF(PI) $ MU=«» . • PI 1 . E-7

B=. 08/39. 37 $ A=. 055/39. 37

EPSR=2.3 $ EPS=EPSR*8.85»1.E-12

L=MU/(2.»PI)»L0GF(B/A) S C=2.»PI*EPS/L0GF (B/A)

GAM5=, 57721 t C0 = 1.7811 S RO = SQRTF(L/C)

ZA=(.016«»,0.) $ SIGMA2S5.

ET A0=MU»SIGMA2». 25* (B*»2)

1 S= (Q.,1.)*F*2.»PI

Z8 = -MU»S/(t*.*PI) <CLOG(C0»ETA0»S)+GAM5)

GAM10=CSQRT ( ( {L»S)+ZA+ZB)»C»S)

Z=L»S+ZA+ZB $ Y=C*S

Za=GAMlG/ (C»S» $ RETURN S END

50
A. 3 Program RESPDATA

Program listing for computing attenuation, phase, input impedance

and voltage amplitude of the MLDL in Chapter 3.

PROGRAM RESPDATA

DIMENSION ALPHA (100 0) ,BETA(10 00) ,ZNOT(10 0 0) ,QTRLM(10 00) ,REZO (10 00)

1,FIMZ0( 100C),RINSHRT( 10 00) , X INSHRT ( 1 0 00 ) , RI NOPEN ( 10 0 0 ) , XI NO PE N ( 1 C

0

2C),A'1PE0(1C00),FREQ(2)

TYPE COMPLEX ZO , GAM 1 0 , ZNOT , E5 0 , Z I NSHRT , Z I NOP EN , EX ,EL MX , A I

X

TYPE COMPLEX VOLTRESPtDNOM.S

CCMMON/BLOCKl/ZO ,GAM1Q,R0,S

COMMON/ aL0CK2/PI ,KPHAS

c

- C ALL LINE PARAMETERS VALUES ARE FOUND IN SUBROUTINE ZOGAM

C LSO IS OPTION FOR COMPUTING ATTENUATION AND PHASE

C LSI IS OPTION FOR INPUT IMPEDANCE

C LS2 IS OPTION FOR VOLTAGE AMPLITUDE

C LPO IS OPTION FOR PRINTING ATTENUATION AND PHASE

C KFQ IS NUMBER OF FREQUENCY POINTS BETWEENO AND 10 KHZ

PI = 3. l^i 159

100 FORMAT( klkXtli) ,5X, 15)

22 READ 103, LSO, LSI, LS2, LPO, KFQ

IF(EOF,60)'t5,'»6

kS CALL EXIT

i»6 KFQS=KFQ I PRINT 220 1 IF (LSO.EQ.O) GO TO 5

C COMPUTE ATTENUATION AND PHASE

C

- —

DC 1 K=1,KFQ

F=K* (1. Z*k) /KFQS

IF(K-2) 2,3,'«

2 LSWCH=1 t GO JO k

3 LSWCH=0

k CALL ZOGAM(F,LSWCH)

ALPHA (K)=REAL (GAMIO)

BETA (K) =AIMAG (GAMIO)

ZNOT (K) =Z0

IF (BETA (K) ) 32, Sit, 32

3k QTRLM (K )=1. E+lOO $ GO TO 1 32 QTRLM(K) =PI/( 2.»BETA (K)

)

1 CONTINUE

IF (LPO. £Q.0)GO TO 5 PRINT 200 S KCNT=0

00 20 K=1,KFQ

KCNT=KCNT+1

IF(KCNT-'t6) 36,37,37

37 KCNT=1 S PRINT 222 J PRINT 200

36 ALF03=8.686»ALPHA(K)

F = K» (1. E***) /KFQS

20 PRINT 202,F,ALFDB,BETA(K) ,QTRLM(K)

C - 0 COMPUTE INPUT IMPEDANCE OF LINE FOR SHORT , OPEN, AND ZO TERMINATIONS

C

5 IF (LSI. EQ. 0)GO TO 7 DC 6 K=1,KFQ

6AM10=ALPHA(K)+(0.,1.)»BETA(K) " Z0=ZNOT(K) J E50=CEXP(-2. 500. 'GAMIO)

2INSHRT=Z0» (1 .-E50) / (1.+E50)

51
R£SPDAf A' ZINOPEN = ZC* (1 . + E5 0) / (1.-E5 0)

REZO (K) =KEAL{ZO) J FI MZ 0 (K ) =A IM AG ( Z 0

)

RINSHRT (K) =REAL ( ZINSHRT) $ XI NSHRT ( K ) = AIM A G ( Z INSHRT

)

RINOPEN (K)=REAL(ZINOPEN) J X INOPEN ( K) = AIM A G ( ZINOPE N

)

6 CONTINUE

PRINT 220 I KCNT=0 $ PRINT ZQk

DC 2^ K=1,KFQ

KCNT=KCNT+1

IF (KCNT-i*6) 39 fWO ,t»0 KCNT=1 S PRINT 222 J PRINT ZQk

39 F=K» ( 1. E+U) /KFaS

Zk PRINT 2 06,F ,REZO (K) , FI MZ 0 ( K ) , RI NSHRT ( K) , X INS HRT ( K ) , RI NOPEN ( K )

,

IXINOPEN (K)

COMPUTE VOLTAGE AMPLITUDE RESPONSE

7 IF (LS2. EQ. 0 )G0 TO 22

PRINT 222

DO 10 K=1,KFQ

G;iM10=ALPHA (K)*(0. ,1.)*BETA{K)

Z0=ZNOT{K) S E5D=CEXP(-2.»500.*GAM10)

VOLTRESP=Z0/(ZO+5a.)»(l.-E5O)/(l.+E50)

10 Af^PE 3 (< ) =CABS ( VOLTRESP) . - - KFPT = KFQ/3 t F CTR= { 1 . E* ) / KFQS

KFPT=KFPT»3 $ KCNT=0 J PRINT 208

DO 26 K=1,KFPT,3

F1=K»FCTR $ F2=FCTR+F1 J F3=2. *FCTR+F1

PRINT 2 1C,F1, AMPtO(K) , F 2 , AMPE 0 ( K f 1 ) , F 3 , A MPE 0 ( K+ 2

)

KCNT = KCNT + 1 S IF (KCHJ-kb) Z(>i kk,

ki^ KCNT = 1 $ PRINT 222 J PRINT 208

26 CONTINUE

GO TO 22

20 0 FCRMAK 25X, F (HZ) 1 i^X , ATTENUAT ION ( DB/M ) , 1 IX, PHASE (RAD/M) ,10X , 1*QUARTER WAVE L E NGT H ( M

) • / /

)

202 FORMAK 2i+X, E9 .2, 3{15X,E10. 3) ) 20'* FCRMAK 35X, *INPUT IMPEDANCE VERSUS FREQUENCY FOR 3 TERMINATING IMF

1ECANGES»//29X ,»Z0 T E RM I N AT I ON* , 1 i^X , SHORT TE PMINATION* , 13X, OPEN

2TERMINATI0N*///! CX, F (HERTZ) , 3 ( 6X , RE AL ( ZI N

) , 6X ,^IMAG(ZIN)»)/27X

3,*0HMS^ ,5 (IIX ,^0HMS*) ///)

20 6 FCRMAT(11X,E8.2,6(6X,E1C.3))

208 FORMAK 16X, SOURCE VOLTAGE AMPLITUDE RESPONSE USING SINE WAVE GENT

IRATOR WITH 50 OHMS I MPE D ANC E . . . CH ARGI NG DOWN L I NE // 1 2X , 3

( F* , 1 2X

,

2^ AMPLITUDE RE SPO NSE , 7 X ) / 1 OX , ( HZ ) , 1 6X , ( V OLTS ) , 12X , {HZ)»,1'»X,

3* (V0LTS)*,12X,^ (HZ) , 15 X ,( VOLTS )//

)

210 FCRMAT(3(eX,E9.2,llX,E10.3))

220 FORMAK IHl, 17X, SINGLE STRAND LINE PARAMETERS. R=5 OHMS/iQOO FT

1 L=500 MICROHENRYS/1000 FT C=.2 MICROFARADS/100 0 FT'//)

222 FCRMAT(lHl)

END

52
A. 4 Program CURRESP

Program listing for computing current amplitude and phase of the unloaded MLiDL in Chapter 3.

PROGRAM CUR'^E^P

DIMENSION Ar3SIX£ (innn) ,AESIX3(lU0n) ,PHE2 (11)110) ,PHE3 (luon)

TYPE COMPLEX t^X,ELMX,FLT

TYPE COMPLEX Z-: ,GAM1j ,ZNCT,AIX1, AIX2,AIX3

GOMMOM/LLOCKl/Zt. ,&AM10 ,kC

C0'^M0N/BLGCK2/P1 , KPH AS 2 , KPHA S3

PI = 3.1'«159

C

C KX IS TOTAL Nb'MLEP OF EQUIDISTANT POINTS ON LINE WHERE CU'vlPENT

C 13 CCMPUTciD

C XLT IS LENGTH OF LINE

C F IS OPERATING FFEQUENCY

C

IGG F0RMAT(5X ,I5,ttX ,F6.1,3X ,E7.1)

REAU l.o,KX,XLT,F

IF (EGF,b(j ) ttS, V5

tt^ CALL EXIT

tf6 CONTINUE

C

-

C COMPUTc AMPLITUDE AND PHASE OF CURRENT AS FUNCTION OF POSITION

C ON LIME FOR Zi, OPEN, AND SHOl^T TcRMINATIONS

C LSWCH=1 i CfLl ZtlGAM (F ,LSWCH) $ KPHAS2 = KPHAS3 = -1

AIX1 = 1,/ZU t ABSIXi = CA&S (AIXl) S A NGl = C ANG ( A I X 1

)

PRINT 220 i DO 12 K=1,KX

X1C = K»XLT/KX $ EX = CrXP(-i.»Xllj*GAMlt!)

£LMX=CEXP{-(2.*XLT-Xin) GAMIO)

£LT=CEXP (-2.* VLT»GAMlf,

)

AIX2=1./Z.* (LX-cLMX) / (l.+ELT)

AIX3=l./Zu»(EX+tLMX)/ (i.-ELT)

A.3SIX2 (K) =CABS (AIX2) 5 AB3 I X3 ( K ) =CABS ( AI X3 ) ANG2 = CANG (AIX?) $ A NG3 = CANG ( A I X 3)

PHL2(K)=ANG2 i PHE3(K)=ANG3

12 CONTINUE

LCNT = '.) 5 PRINT 2nn S PRINT 202 $ PRINT 203,

F

P'ilNT 'diik $ PFINT 2l<6 $ PRINT 2u8

00 in K=1,KX

X=K*XLT/KX $ LCNT=LCNT+1

IF(LCNT-«+6) 13,1*4

Ik LCNT=U $ PRINT 222 $ PRINT ^CS " $ PRINT 2D8

13 PRINT ?in,X,A'SlX2(K) ,PHE2(K) ,AbSIX3(K) ,PHE3(K)

10 CONTlNUr

P <INT Llf7,A8SIXl, ANGl

2C'0 F0RMAT(it2X,F5.1,» KHZ SINE WAVE GENERATOR AT TOP CHARGING DOWN MOD

IE*//)

202 FORMAT (:^3X, CURRENT RESPONSE AS FUNCTION OF POSITION ON LINE*, IX

1,*F0R THi'.EE DIFFERENT TERMINATIONS*//)

2'.'3 P"0RMAT(52X,*0PFf:ATlNG FREQUENCY IS*,Ee.i,* HZ*//)

ZCt* FORMAT ('2X , ALL AMPLITUDE AND PHASE UNITS IN AMPERES AND RADIANS*/

1/)

206 FORMAT (26X, DISTANCE FROM TOP* ,i3X ,*OPEN TERM INA TI ON* , 16X ,SHORT T lERMlMATION*//)

207 FORMAT (26X, *DISTANCE FROM TOP*. 15X, 1 ZO TERMINATION *111)

20 8 FORMAT (32X,*MrTERS^, 13 X, 2 (AMPLITUDE* ,7 X,*PHASE*, 11 X)//

)

209 FORMAT (32X, METERS*, 13X, *AMPLITUDE*, 7X, *PHASE ! 1

)

53
210 rOKMAT(29y.,Fe.C),15X,2(tlC.3,UX,il0.3,6X))

22n F0Rr,AT(lHi,l7X, SINGLE STRAND LINE PARAMETERS ... R = 5 OriMS/iOOG FT

1 L = 5C: nlCROHf- Mf-.YS/l ]C"J FT C = .2 MICkOFAPADS/lP n 0 FT*/)

222 FORMAT (IHl)

ZUD

54
A. 5 Program ALLCPLR

Program listing for computing current amplitude and phase of the

loaded MLDL in Chapter 3.

P^or,kAM ALLCPLk

UlMtNSiON R(5C),L(50),OcLX(50),T(50,lC),U(50,10),V(50,10),W(5C,10)

l,A(10)t-'(10>f<' <10) fU(10) ,atT5(lu) ,ZN0T(1[)) jGAh'dO) ,dl(l(J), 11(10),

2£2(1C) ,2C(50,10)

J£ Mth 310N 12 ( IC ) ,Ffti.U (10) ,X( 51) , F I ABS ( 5 1 , 1 0 ) , PHEI (51,llj),ZIN(lC),

lI^x(^;l)

CO .-lilON/uLoCKl/A, C,C,U,Ol.T ,0ET5,ZN0T,GaH, DELX

CO 1MGIJ/LL0CK2/T,U,V,H,ZC ,NCPLk,NFt?Q

CaMMUh/t:L0CK3/ZC ,GAM10

TYFc: CO:iPLEX A,i , C , 0 , DET , T 5 , ZNOT , GA H , T , U , V , V! , 1 1 , 1 1 , t^a , 1 2 , ZC , ZI N , 1I2X,ZG,GAM10

rvpi. k:.al l c

C MAXIMUM 50 COUPLERS AMU 10 FKtQUtNGlIrS Af t ALLOWEU

C NCPLk LTAfiUS FUk NO. OF COUPLEki

C NFPU STANL.S FCK NO. OF UOWN MCb^ CHAKGING F.iLQUENCIES

C £UI;H CCUPlEK has a semes inductance OF ^40 illCKO hENhYb AND A C SiRUS f ESlSTANCE OF 3.3 OHMS

0 —

lUO FORMAT (5X, 15, f.X, 15)

102 FOKMAT (16F5. 1)

lO^f FIPMAT (6(^X,Ff>.l) ) C — --

C CJUPL^F. VALUL5 IN MKS UNITS

D'\TA((L(I),I = 1,!;0)=50(,0J00*»))

i)A TA ( ( 1 ( I ) , I = 1 , '„ 0 ) =5 0 ( 3 . 3 ) )

25 li-.hO ico,i^cpl; ,NFkQ

IF ttOFjcO) '5,'»fc

1*5 ClLL EXIT

^6 RiAU 1G2,(DELX(1) ,I=1,NCFLR)

IF (t.OF,&0) ««5,««7

k7 R-:AD 10*«, (FPLQd) ,I=1,NFRQ)

IF (EOF,oO) '«5,li6

<*8 D'J 11 J=l,NFRf:

00 16 K=1,NCPLR

18 ZJ(K,J)=R(K) + 2.»3.1*fl59» ( 0 . , 1 . ) L (K ) FREQ ( J)

11 CONTINUi:

0) 1 J=l,i^FRC

If (J-2) 23,19,22

23 LSKCH = 1 i> GO 10 22

19 LSWCH=0

22 Call ZObAM(FRCC( J) ,LSk^CH)

ZNOT{J)=ZG $ GAM(J)=GAhlG

1 CONTINUl.

CALL At.r,D $ Ni,0 = NCPLR+l

DO 3 J=1,NFRQ

E2(J)=0. i E1{J)=1.

12 (J) =cl (J)/B(J) $ IKJ) =0 (J)/B(J)*E 1 (J)

DO k K.=1,N50

IF (K. EG. 1) GO TO 6

<Q=K-1

CALL lNVL.kT(KO,J)

I2X(K)=L.(J)»I2(»^) i GO TO 5

6 I2X(1)=I1(J)

55
5 FIAbS(K, J) =CAt S(I2X (K) ) $ PH CI ( K , J) =C ANG ( I 2X ( K )

)

k CUNTlNLc

3 CONTINUl

00 an K=1,N5C

IF (K.&l .DGO TO 6

X ( 1) = 0. * GO TO 20

8 X (K) =X (K-U+DTLX (K-1)

20 ^ONTINU:.

UJ IC J = l,NFKt;

F=FRta(j)/(i.:*3)

HslNT ZC+tNCPLF $ PRINT 206 j. PkINT 212, F $ P^INT 2il»

PilNT 216 i PkINT 218 t> PRIwT 220 i. PKINT 222

00 12 K=1,N50

12 P UNT 2G2,X (K) ,f- IADS (K, J) ,PHtI (K, J)

10 CONTINUE

ZIN(l>=o(l)/LMU $ Z1N(2) = B(2)/D(2)

DO lb J=l,NFkO

15 ZiN( J) =t'(J)/D(J)

P<INT 2L8

0 it j=i,NFRr;

F=FKLa(J) / < 1.'. -fS)

16 P<INT 210,F,ZIN(J)

GU TC 2:p 20 2 FOKtiC r(26X,F5.0,l5X,i;i2.£,12X,L12.5//)

20'* FORMAT (IHl ,39X SINGLE STRAiJD LINE WITH *,I2,» COUPLEKS'//)

206 F )R,-l<iT(39X,*DnwN t^OUt WITH OtNLKATOk AT SURFACE*///)

20d FORH&T (Hl,tt3X INPUT I MFcQA NC E ( ZI N ) / / 3 OX , F (HZ) ,10X,*R£AL (ZIN)»

1, iX,»Ir!AG (ZIN)*///)

213 F JKhA r { 50X ,£c .2 , C (E16« 3, t 16. 3)

)

212 F jRMAT (27X,»GiM KATOR CHmIRACTERISTICS . . . EG = 1 VOLT Z& = &0 OHMS

1 F = »,F5.0,» KfZ*///)

21«» FORMA r (^5X,»T^b FOLLOWING LINE PARAM£lti<S A.<t UStO ///)

21b FOR.:AT(:0X,»k=5 OHMS/1000 F T» , 5X , L-5 C 0 MICRO HENi^YS/1000 FT»,5X,*

1C=.2 Ml.i^O FAKALS/IUDO FT'///)

218 FORMAT ( 2bX , •(HE FOLLOWING CURRENT RESJ-ONSE IS COMPUTED AT EACH COU

10l£r PCoIl ION*///

)

220 FOKI'A r (21X,*DIS1 ANCt FROM TOP* , 10 X , 'AMPL I TUOfc , 15 X , FH A SE* ) 222 FORMAT {2tiX,*( Ml ERS) »,16X,*(AMPi) *fl6X,* (F. AOI ANS ) *///)

56
A. 6 Subroutine ABCD

S'Jt3R0UlINL ADCD

Q£M£NSIGN ZC(E:0,1C),T(50,10>,U(50,10) ,V{50,10),W(bO,10) ,DELX(50) , lA(10),B(lC),C(lt),D(lD),U'£Ti5(10) ,ZNOT (10),GaM(10)

C J.iMDN/!3LOCKl/A,8,C,D,DEl , Dt T 5 , Z NOT , G A H , Dl L X CO lHCM/t L0CK2/T,U,V,»J ,ZO,NCPLR,NFI^Q

TrPu COMPLEX ZL,ZOfGAMiO,E50,AO,BO,GO,DO,Al,Bl,Cl,Dl,A2,B2,C2,D2,

lA3,b3,C3,Lt3»At,,f if ,C'*,D'4,IJtT,UtT5,T,U,V,W,A,8,C,D,ZN0T,GAM

C

C CALCULATE OVEFALL ACCD PARAHETEkS OF COMPLETELY LOADEU LINE

C CJUPL^:' iMPED^NCu IS ZC

C T,U,V,W AkE the INV£|<S£ MAT.<1X cLt:Hi.NTS IN POSITION^) (i,l),(l,2),

C (2,1), (2, 2) Ri SHECTxVtLY AND THEY ARE DEFINiiD IN THL RcPORT ON

C P^Gt

C

- 00 1 J=1,NFRQ

A3=U3=1. i n3=C3=0.

Gf»MlC = GAM ( J) i Z0 = ZNOT(J)

01 2 <=1,NCPLK

5 E30 = CtXP(UELX (K) GAHIO) S A 0 = ( E5 0 +1 . / £5. D » / 2 . .3-i=ZC»(c50-l./Et 0)/2. i C 0 = B 0 / ( Z 0*» 2) i CO = AO

'A1=1. 5 B1=ZC(K,J) $ C1=0. $ Ul=l.

AZ=AC»A1 + -. C»C1 I u2 = AO*01+dO*ul

C2=C0* A1+LC*C1 $ D2=C0*B1+D0»D1

AH=A3»A2+t3»C? i j't=A3»e2+b3*U2

C'+=(;3»A2+-03»C;2 S Li'+ = C3*82 + D3*U2

A1 = A'» t)3 = t.'i+ tC3 = C*+ i D3 = D'» O_T=A3»L.0-B0*C0

T(K,J)=(DU+CO*ZL (K,J) )/DET $ U ( K , J ) =- ( E G+ A

0 *ZC ( K , J ) ) / DET

\/ (K, J) =-Cu/OEl i W(K,J) =AO/DE'l

2 CONTINUA(J)=A3 I E.(J)=r!3 $ C(J)=C3 i D(J)=U3

1 JiTS ( J) =A3*D3-C5*S3

RiTUF.N i END

3JBr<0UTINE INVEl.T(K,J)

' DIMENSION T(50,10),U(50,10),V(6U,10),lr. {30,10),A<10),B(10),C(10),

10 ( 10 ) CO 1!10N/[>L0C<1/A,B,C,0,0ET,D£T5,ZN0T,&AM,DELX

C ) ^M0;J/ijL0CK2/T , lJ,V,W ,zc,ncplr,nfrq

TYP£ COMPLEX T , U , V , W , A , 3 , C , D , A 0 , B C , C 0 , D

0

AO=T(<,J)*A(J)*b(K,J)*C(J>

GJ=T(K,J)»B{J)+U(K,J)*D{J)

CJ=V{<,J)*A(J)+H(K,J)*C(J)

O0 = V (<, J) B(J) (K, J) J)

A(J)=Aa b D(J)=BO i C{J)=CO i 0(J)=DO

K^TUkN S END

57
A. 7 Program UPMQDE

Program listing for computing the upmode voltage and current response

of the MLDL in Chapter 5.

P'?OGR'i'i UPMOOE

DIM-I^JSr ON F'5-:'J(?5) , X^OS (5r ) ,G^" (21) ,7r.'0T (25 ) , 7C ( Z: ? ) , c HQ G ) , rlZ_

1 (5 J, 25.) ,F2(5: ,2S)

jYpr CD "1 PL EX Ga'^l"j,7"';&aM,ZM0T,ZC,;^H0G,7SH, ZCA__PC , ry , ^H OC, - I.? , E2

CCM-10N/ 3LCC<.: /Zb ,GftMl': ' '"

'

TYD-: -^:al Lc

c

C CO-IPUTE VOLTfiG-: AMD CUf<'^cNT F;c:SFOMSt: IM IJC^MOO"

C F0L.L3WING LIN-: P/i;aMETEPS UC.FD

C R=5 QHHi/ir.Cj FT _ C=.2 M TCi^IOF AJA OS / 1 00 r FT L^J- ^JCRO^^N^

~c~"" /i: ij FT " ' ~" ^' -

- -

-

C FCLLOWIMG COUPLER pAkAMETlFS ARE USED

C R=^.5 OrirS L = ^''- MICROHFfJRYS

C KG =3. 3 ? l':-, :i.!oU i I = 3. mi 59 I ZG=Bi.

IOC FTR^AT( 2"(5X,I v) ,F-5. 1)

102 Fc-< i;t( 3 (i*x ,?:o. 1 )

)

IQi* FOR'nT{ ISt^S . 1

)

18 REA3 12 : ,MF.n ,NPOS, XL-: IF (ZJF, 6 j) -6

U5 CALL EXIT

U6 Rl^:) IG 2, (FR"':(n_, I = 1,NFR,Q) ^ IF (EOF, 6. ) it5, ^7

L,7 READ 10 (XPOSd) ,I = l,tJPOS) _ _ _ IF (cOF, cjC ) ttS, '+9 CONTIlU: _ c

C TH^! FOLLOWING P^,0GRA^1_ PAP AMtT'PS^ARE EVPLfliriEn [ C NF;?'J IG TCT Al 'JUM lER C'- ^CHARGIKG FR-ZOUEhrOIES"'"''' c fpos 13 rjuMi:"' OF gi'k'ator posttioms now) linf _ _ C X5y IS Ov'-i^ALL LIME LENGTH - -

-

c DO 1 J=l,nFRO

F = =^REC(J) _ _^ _ IF ( J-2) 2, 3, 1+

.

- - . — - - - -

2 LS'-J:h = 1 GO TO i+

_ 3 LSWCM = j

' ""

I* CALL Z'J GA;-- ( F, LSWCH) ^_ _____ GAM ( J )= GAMl 0 I ZNOT(J)=ZC "

ZC ( J) =RC + Lr* ( , 1.) F*2.*PI__

1 KHOG ( J) = (ZG-Z / ( ZG + Z''

)

EC = 1. _^ _

DC ^ K=1,^IP0S

X = XPOS(/v) _ _ _ DC j J= 1 ,KFRO ' ^

"

Z5H=Zi^» (1 .-C£XP (-?_._*_(X50-X) *GAM ( J) )J / ( 1 • + CE X ^

( - 2_. ^ (X5 D-X) *GAm ( J ) ) ) ZCAPC=ZC(J)+Z"sh" S EX = CEXP(-X»g'an ( J)T "

" R'JOQ=(ZCAPC-ZNOT(J))/(ZCA?C + ZN'OT(J))

FI2(<,J)='^C*E''/(2JOT(J) +ZCAPC) *((l.-PHOG(J))/(l.-rHOC*RHCG(J)*(EX

1*»2) ) ) E2(K,J)=EC*ZMCT(J)/(ZNOT(J)+ZCAPC)»EX*((1.+RHOG(J))/ ( 1. -RHQC* RHOG

1 ( J) * (E< »2) )

)

6 CCniNdE

5 CCNTIMJE

DC 1 J J = i ,nfi;q

58
F = r ?£Q( J)/(1.L*3)

PRINT :iu 1^ PRINT ZlcjF ? PPir;T 21*+ _ P^INT 2 16 I PRINT 216 PRINT 22j ? PRI^.'T 222

DO 12.. K = 1,NPQ^

FiaT3=: Af.'S:(FI2{K,J) ) dH!£I=CANG (FI2 (K, J) ) 12 P-iINT 2 :2,XP0S(K) ,FI.a.iVS, PHEI . PRINT I PRINT 22i:' ? PRINT 226

DO 16 <=1,NP0S . . , E2'\ i3=aa?.s(F? (<, J) ) ^ PHe2=";/^Nr,(E2 (K,j)

)

16 . PRINT 2 J2,XPD.S.(K) ,::2AiS,P.HE2 . IC CCNTINJE

GO TO 13 . . . ..

2Q2 FC:=l^AT(26X,F5,:,l3X,::i2.'i,12X,El2.5//)

23U FOR^ar( Ihl, J9X,*5I^iGi.C: STf-'/^NO LINF WITH.l C C U^L P // / ) ZZt FO'^MAK 39X, ^Ut^.-ICHc* USING 1 V0LT»,F5.C,' KHZ SOURCE*///)

22 8 PD:RM ATCIHI , -3X,.* INP.UT I^PIC A!rL.CZJN) .//li.X.^* F .(.HZ ) Xa.?P£AlXUJ.}J:

1,3X,»I:-1AG(ZIN)*///)

21!: fori;t( 3:x, -:3.2,C(ii':3,3,-:ie. 3) ) . . .. 212 FG ?'14T( iLX, G^Nt f'ATOiO. C H A?' t CT E R 1ST I CS . . , EG = 1 VOLT F = »,F5.C,* KH

IZ*///) __ _ 214* FOR"l-*,T( 35X, ThL FOLLOWIIlG LINE PAPAMETERS ARE USED «///)

21C F i:.T( 23X, ^ = 5 OH-lS/1 '. ; FT* , f.X, *L = 5 ^10^0 I'^fS / 1 Z i FT*,5X,»

1C=.2 MICkO FV.AUS/l ~ ' FT*///)

21« F:^,HiT( nx,*THi FOLLOWING rU'?R.ENT PESP^^'SE IS ?T SURFATE, AS. FUNCTJO

IN OF DISTANCE Ff<C'-t COUPLER S0UF':E»///)

22C FOR'UT( 21X, DISTANC" ^^RO-^i T OP * 1 - X , * A '^PL I TUO E* , 1 E v , * PH A SE ^)

222 FC^'^AT(2pX,*(r^ETE^3)*,16X,*(A'iF3)*,lbX,*(RAni.'N?)*///)

22i* FO^ -1 AT( HX ,* The FOLLOWING V0LT3Gr REIS^^ONSI IS__/"'T SURFAC E A S FUNCTIO

IN OF DISTANCE FROM COUPLER SCUFCE*///) ~ '

22 1 FG="IAT( 2bX, ( MET'^S ) *,iex ,* (VnLTS)*,15X, * (RADIAN'S) *///)

END

59
FORM NBS-114A U.71)

U.S. DEPT. OF COMM. 1 . PUBLIC ATION OR RE PORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA ^^^^^ 73_303

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

SINGLE STRAND MODEL COMPUTER PROGRAMS FOR THI

TRANSMISSION LINE PROPERTIES OF THE

MOORING LINE DATA LINE

5. Publication Date

^ April 1973

6. Perfonning Organization Code

/• AUlrlUK(.o; J_J X\ . ITLOJ-X- ctllCl IN, O. IN cLllliictll 8* Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS, Boulder Labs.

DEPARTMENT OF COMMERCE

10. Project/Task/Work Unit No. 2722424

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

National Data Buoy Project

National Oceanic and Atmospheric Administration

13. Type of Report & Period

Covered

Final Report

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant,

bibliography or literature survey, mention it here.)

Equations and computer programs are presented for calculating

, the propagation properties of the Mooring Line Data Line (MLDL).

The development is based upon a single-strand inner conductor model

for the MLDL structure. Propagation parameters, input impedance,

voltage amplitude, and current are developed from the complex

impedance/meter (Z) and the complex admittance/meter (Y) of the

MLDL. A matrix formulation of the voltages and currents along an

MLDL loaded with couplers at arbitrary positions is developed. The

received voltage and current at the water surface produced by a

single coupler down line at an arbitrary distance are presented.

17. KEY WORDS (Alphabetical order, separated by semicolons) attenuation; characteristic impedance;

circuit model; computer printout; computer program; coupler; current; impedance;

load impedancej mooring line data line; phase; propagation characteristic^; sea water

return; series impedance; shunt admittance; single strand; transmission line

18. AVAILABILITY STATEMENT

UNLIMITED.

[^FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

22. Price

USCOMM-DC 66244-P7t

USCOMM lU.