NBS

Reference publications

NBSIR 87-3077

A 11 10 2 75374(3

NATL INST OF STANDARDS & TECH R.I.C.

All 102753748

Adams, John W/Time-domain system for ide QC100 .U56 NO.87-3077 1987 V19 C.1 NBS-P

TIME-DOMAIN SYSTEM FOR

IDENTIFICATION OF THE NATURAL

RESONANT FREQUENCIES OF AIRCRAFT

RELEVANT TO ELECTROMAGNETIC

COMPATIBILITY TESTING

John W. Adams

Arthur R. Ondrejka

Herbert W. Medley

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303-3328

November 1987

-QC

100

- U 5 6

87-3077

1987

Research Information Center

iNational bureau of Standards

Gaithersburg, Maryland 20899

NBSIR 87-3077

TIME-DOMAIN SYSTEM FOR

IDENTIFICATION OF THE NATURAL

RESONANT FREQUENCIES OF AIRCRAFT

RELEVANT TO ELECTROMAGNETIC

COMPATIBILITY TESTING

John W. Adams

Arthur R. Ondrejka

Herbert W. Medley

Electromagnetic Fields Division

Center for Electrons and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303-3328

November 1987

Sponsored by

U.S. Army Aviation Systems Command

St. Louis, Missouri 63120

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

1 . 0 Background 1

2.0 The Measurement System 2 2.1 Avalanche Step Generator 3 2.2 TEM Horn Antennas 5 2.2.1 Receiving Antennas 5 2.2.2 Transmitting Antennas 6

2.3 Waveform Measurement System 6 2.4 Use of Prony’s Algorithm . 7

3.0 Measurement Procedure Used at Ft. Rucker 8

3.1 System Setup 9

3.2 Selecting Appropriate Parameters for Time-Domain System.

9

3.3 Taking Reference Data 9 3.4 Rotating the Test Object 10

3.5 Filtering Analog Data Before Digitizing 10

3.6 Processing and Interpreting the Data 10

4.0 Sample Measured Data 11 4.1 Simulated Data 11 4.2 Apache Data 12

4.3 Black Hawk Data 12

4.4 Data From Other Helicopters 12

5.0 Summary and Recommendations 13

6.0 Acknowledgments.. 13

7.0 References 13

i i i

Time-Domain System for Identification of the Natural Resonant

Frequencies of Aircraft Relevant to Electromagnetic Compatibility Testing

John W. Adams, Arthur R. Ondrejka and Herbert W. Medley

A method of measuring the natural resonant frequencies of a structure is described. The measurement involves irradiating this

structure, in this case a helicopter, with an impulsive

electromagnetic (EM) field and receiving the echo reflected from the

helicopter. Resonances are identified by using a mathematical

algorithm based on Prony's method to operate on the digitized

reflected signal. The measurement system consists of special TEM

horns, pulse generators , a time-domain system, and Prony's algorithm.

The frequency range covered is 5 megahertz to 250 megahertz; this

range is determined by antenna and circuit characteristics

.

The measurement system is demonstrated, and measured data from

several different helicopters are presented in different forms.

These different forms are needed to determine which of the resonant

frequencies are real and which are false. The false frequencies are

byproducts of Prony's algorithm.

Key words: avalanche step generator; natural resonant frequencies;

Prony's method; TEM horn antennas; time-domain measurement system.

1 . 0 Background

If a structure is exposed to electromagnetic fields, resonances enhance

the fields by a factor of Q and often cause electromagnetic compatibility

(EMC) problems. Structures such as helicopters are built of highly

conductive materials such as aluminum, which typically yield Qs of 10 to

200. The quality factor, Q, is the ratio of stored to dissipated energy.

If the shape of a structure is complicated, as is the case with helicopters,

these resonant frequencies cannot be calculated. The only way to obtain

these resonances is by measurements. Fortunately, advances in antenna

design and solid state technology can be used with existing mathematical

procedures to develop a measurement system that can make the needed

measurements

.

A technological advance that will change some of the aircraft

character i st i cs is the increasing use of composite materials in place of

aluminum. For lossless structures , size - frequency scaling might be used for

the type of measurements discussed in this paper, but for lossy structures,

measurements should be made on full-size aircraft rather than scale models,

since size-frequency scaling does not work effectively for lossy objects.

Prony's algorithm has been in existence for about 200 years. Morf

recent applications to determine poles from time-domain waveforms have met

with varying degrees of success [1-5]. As a tool for target identification,

it has only limited success, since the quality of results degrades as the

1
si gnal -to-noise ratio decreases. If the target is not stationary with

respect to a transmitting antenna, only one time interval of data may be

recorded. However, if the position of a test object is fixed relative to

transmitting and receiving antennas, a large number of time intervals may be

recorded and averaged, which gives a significant improvement in signal-to

noise ratio.

Time-domain technology has been more easily handled in theory than in

application, but its great potential can now be realized due to the recent

improvements in the electronics and antennas needed for its application.

Higher speed devices such as gallium arsenide transistors [6-7] are one area where significant improvements are resulting in faster and more powerful

impulse generation capability. Antennas that radiate impulses without

significant phase distortion are fairly straightf orward to construct, and

the needed theory concerning differences between transmitting and receiving

horn antennas is now available [8]. These transverse electromagnetic (TEM)

horn antennas have been built and evaluated previously, but only for higher

frequency ranges. For EMC testing, the lower frequency ranges typical of resonances of larger structures had not been covered.

Electromagnetic compatibility (EMC) testing for incident fields should

be performed at all frequencies to which the device or system may be

exposed. The lower portion of the spectrum where large structures may be

resonant is often not tested. This is because common test facilities have

severe limitations which preclude their use in these lower frequencies.

Anechoic rooms have increasingly high reflections at lower frequencies. TEM

ceils or parallel plate structures can be used at low frequencies, but have

practical limitations for size of test object. Outdoor ranges cannot be

used for swept frequency testing, since use of field strength levels high

enough for immunity tests would not comply with FCC regulations. Even for

EMC testing under these constraints, the testing can be much more effective

if the resonant frequencies of the structure are known. Finding these

frequencies is the purpose of the work reported here.

2 . 0 The Measurement System

The measurement system used at Ft. Rucker on several Army helicopters

is shown in figure 1. The aircraft under test (AUT), whose resonances are

being measured, is located on a ground screen which is continuous from

transmitting antenna to receiving antenna. The transmitting antenna

launches an impulsive field toward the AUT, and properly polarized

reflections or reradiations are detected at the receiving antenna. The two

antennas are oriented orthogonally to each other to reduce the direct

coupling of energy between them. The AUT was in its flight configuration,

with no tow bars connected or doors or panels open, but in a power-down

condition

.

The actual resonant frequencies are unknown, so that it is most

efficient to illuminate a target with a spectrum that contains as many

different frequencies as possible. The impulse waveform has a spectrum

which contains a broad range of frequencies. The spectrum of other

waveforms usually favors a narrower band of frequencies.

2
Time-domain antenna theory shows that an antenna's characteristic in

the transmitting mode is the time derivative of the receiving mode

response [8]. To produce a radiated impulse field, it is necessary to

drive the transmitting antenna with a step waveform.

The outgoing impulse is produced by a step function followed by a slow

ramp which returns the voltage to its original value. The waveform is

repetitive at a rate determined by the clock generator. The trigger pulse

and dc power are fed to the step generator through a combiner.

The receiving antenna output can be viewed on an oscilloscope, which

also serves as a waveform digitizer. For better control of the scope's sweep

delay, the scope was synchronized externally to the clock generator. The

computer was programmed to record the digitized data so it could be

transmitted to a mainframe computer for further analysis at a later time.

2.1 Avalanche Step Generator

The step generators used on this project were of the avalanche type.

After testing many transistors for maximum applied voltage before avalanche,

consistency of avalanche voltage, and switching speed, we used a 2N390M npn

transistor in a single stage for the preliminary test. In the final

configuration, we increased the number of stages from one to four to

increase the output amplitude by about a factor of four. This was necessary

due to the low amplitude of the differentiated output pulse. The 2N390M

transistor switches slowly enough in the avalanche mode that a substantial

amount of the applied voltage is lost before the pulse can be formed. This

is due in part to the antenna's discharging before the transistor can be

fully switched on. Also some of the applied voltage is lost due a voltagedivider effect when the pulse passes impedance-matching resistors at the

input of the antenna. These resistors are necessary to prevent multiple

reflections if part of the pulse is reflected from the mouth of the antenna.

These effects caused the actual output pulse to be only 3 to M volts in

amplitude at the mouth of the horn and 1 to 2 nanoseconds in duration at the

transmitting antenna, and the received pulse with this configuration was

only 30 to ^40 millivolts in amplitude.

In subsequent testing, we found an experimental transistor that showed

signs of being much faster in the avalanche mode at substantially lower

applied voltages than others tested. That this transistor would avalanche

at a lower voltage is a convenience, but the faster avalanche time gives a much faster rise time as a step-function generator. This transistor has a part number HXTR-3615. Another transistor, the HXTR-510M, which is even faster, operates at MO to 100 volts dc with specified switching speeds of 20

to 80 picoseconds. In the single stage version, this transistor achieved an output pulse of M50 picoseconds with an amplitude of M0 volts. The

switching times are greatly reduced by shortening lead lengths and by

selective screening of components.

The step generator circuit shown in figure 2 is similar to the one that

drives the transmitting antenna, but can be modified to operate without th-..- antenna attached. The combined dc high voltage and a 5-volt positive

3
trigger pulse are applied to the input. The dc voltage charges the 220

picofarad capacitor to a voltage just a little less than that needed to

avalanche the transistor. The trigger pulse coupled to the transistor base

through the 1 000 -pi cofarad capacitor initiates the avalanche with very

little time jitter. For test purposes, the step output is taken across the

50 -ohm resistor at the output. In actual use, the 220-picofarad capacitor is

replaced with the antenna which has about the same capacitance, and the 50-

ohm output resistor is grounded.

During the tests performed at Ft. Rucker, we ran into several problems

due to the step generators, grounding, and the ground screen itself:

1. Without proper grounding of the step generators, the pulse would

radiate along the transmitting trigger cable and ground screen.

2. The ground screen was made of chicken wire, wired together and

staked to the ground. With wind, temperature and humidity changes, the

ground screen would shift relative to other physical components, causing

changes to the shape of the radiated pulse.

3. To achieve the relatively high dc voltages necessary for operation

of the step generators and to obtain a clean supply voltage, we used ten

67.5 volt dry cells in series. Even though the step generators drew very

little current, a few microamperes, the temperature and humidity changes

caused the available voltage to drop below the operating range of the step

generators under some conditions.

To solve these problems we have done several additional tests and

suggest the following improvements for any subsequent tests:

1. Work has been done on the component selection and mechanical

design of the step generators. After testing the various transistors, we have chosen two versions for a monolithic chip. Using these and selectively

choosing them for specific switching and avalanche characteristics, we can have them assembled on a substrate by a hybrid IC manufacturer. By using

hybrids assembled in a machined brass package with male and female SMA

connectors, we can achieve a small, 1.27 x 1.91 x 0.6M centimeter (0.5 x 0.75 x 0.25 inch), shielded package that can be bolted to the ground screen,

thus solving our grounding problem. The step generator can be optically

triggered, further reducing cable radiation.

2. In the immediate vicinity of the antennas we would construct i rigid ground screen from three sections of 0.91 by 1.22 meter, 0.16-

centimeter thick printed circuit board material with 2 ounce copper per

square foot (28.35 grams per 0.0929 square meters) on one side. We would

join these with 10.16 centimeter wide, adhesive copper foil tape. This

would give a 0.91 by 3.66 meter rigid mounting surface for the step

generators and antennas. This would stop the movement of the antenna

relative to the ground screen.

3. Although the new step generator design allows much lower operating

voltages, we feel that a well regulated and filtered power supply would be

the best choice to power the step generators. We have located a power
supply that delivers 600 volts dc at 1.5 amperes and has remote current and

voltage sense features. It is also IEEE 488 bus controllable. This source

would also eliminate downward dc voltage drift typical of batteries being

drained by use.

All of the above equipment works well with the half horn antennas which

are suitable for radiating pulses with vertically polarized E fields, but

the full-horn antennas needed for radiating horizontally polarized E fields

suffered signal loss due to ground loading when they were in close proximity

to the ground screen. To reduce this effect, tripod supported stands to

raise the antennas 3.7 to 4.6 meters above the ground are needed. These

stands would be adjustable from the ground in both the horizontal and

vertical planes so the antennas could be focused on the test object.

Tests have been performed with these new step generator designs on both

the indoor and outdoor ground screens at NBS and the results are very

promising

.

2.2 TEM Horn Antennas

The antennas used for these measurements have to transmit and receive

impulsive waveforms with minimum distortion. They were developed from a basic TEM horn design described by Lawton and Ondrejka [8]. In the

receiving mode they have a usable bandwidth from 5 megahertz to 1 gigahertz

over which the response is flat within ±6 decibels.

The antenna is constructed in two forms, a half horn that is mounted

directly onto a ground plane, and a balanced horn that can be used

independently of a ground plane. The half horns are useful when operating

with vertically polarized fields; the balanced horns can be used with

arbitrarily linearly polarized EM fields. Most of the measurements at Ft.

Rucker were made using the half-horn configuration.

2.2.1 Receiving Antennas

Figure 3 shows the construction of the balanced receiving antenna. The

two triangular conductors form a balanced 200-ohm transmission line, a simple modification of the parallel plate transmission line. The spacing

between the conductors tapers to a point where they connect to the 200 -ohm

input of a broadband pulse transformer. This terminates the antenna in its

characteristic impedance, which minimizes reflections. The output of the

transformer is unbalanced 50 ohms, which matches the coaxial cable we used.

The upper frequency limit is about 1.2 gigahertz due to the transformer.

The lower frequency limit is about 5 megahertz due to the antenna.

When the antenna is mounted on the ground plane, only half of this

structure is needed. The second half appears as an image in the ground

plane. Therefore, we refer to this as the half-horn antenna. For

convenience, the antenna is constructed to have a 50 ohm impedance so that,

the antenna can directly feed a 50-ohm measurement system. The upper

frequency limit of the antenna is 3*0 gigahertz, while the lower frequency

limit is 5 megahertz.

5
Other antennas are relatively broadband but often do not have good

phase response. With excessive phase shift, an antenna disperses a pulse by

delaying different frequency components by differing amounts. This phase

distortion makes it difficult to perform radiated time-domain measurements

and obtain meaningful results. The NBS antennas have a linear phase

response over the passband, making possible the acquisition of a high

fidelity waveforms.

2.2.2 Transmitting Antennas

The transmitting antennas are the same as the receiving antennas except

that a transformer was not used. Instead, the antenna elements were

connected directly to the step generator described in a previous section.

The antenna itself is the pulse-forming capacitor for the step generator and

is charged to the high dc voltage needed for breakdown.

Figure shows the half-horn antenna including a step generator. When

the step waveform propagates to the aperture, the antenna produces two types

of fields, a step-like function in the near field, and an impulse function

in the far field. Only the impulse radiates at a significant distance from

the antennas.

Not all the dc energy stored in the antenna is radiated. Some is

reflected from the aperture and propagates back to the step generator which

remains in a state of avalanche. The resistor R1 in figure 2, located

between the transistor collector and the antenna, matches the antenna

impedance so that multiple reflections are prevented. Figure 5 shows the

difference in radiated waveform for various values of R1 . There are very

few reflections in the waveform from the matched generator compared to the

unmatched one, and most of these are external to the antenna. However, the

peak amplitude in the matched condition is half that of the unmatched

condition since the matching termination for the source requires half the

voltage.

Because the received signal is always contaminated by noise, it is

desirable to increase the amplitude of the transmitted signal as much as possible. A modified circuit, shown dashed in figure 2, introduces a diode

shunting R1 to enhance the output step while still retaining the 200 -ohm

load resistor for reflections. The amplitude of the resulting pulse with

the diode is 50 percent larger than the matched pulse without the diode. No

additional reflections are produced by the diode.

2 . 3 Waveform Measurement System

Signals from the antennas are measured directly on a digitizing

oscilloscope. The input plugin unit to the oscilloscope is capable of

sampling waveforms as fast as 3 nanoseconds, with an equivalent bandwidth in

excess of 200 megahertz. At these frequencies, the oscilloscope has to be

operated in the repetitive sampling mode. The scope is capable of multiple

acquisitions and can calculate an average waveform. It took about a minute

to acquire an average of 1000 waveforms the way the scope was set for use at

Ft. Rucker. This amount of averaging enhanced the si gnal-to-noise ratio by

about a factor of 30 .

6
The digitized information was also transferred to a personal computer

via the IEEE-488 bus where it could be displayed or transformed to the

frequency domain. After this optional processing of the waveform, the

digitized data file was stored on a floppy disk for additional processing

using more powerful algorithms on a mainframe computer. The programs needed

in the personal computer included a data transfer routine to establish

communication between the computer and the oscilloscope, a program that

could calculate the fast Fourier transform (FFT) and graph both the timedomain waveform and the its spectrum, a file conversion routine that could

change the data file from that which was generated by the oscilloscope to a form that could be transferred to a mainframe computer, and a program which

could convert data from the mainframe computer into a form suitable for

graphic displays.

2. 4 Use of Prony's Algorithm

Prony's algorithm is a mathematical procedure to extract frequencies

and corresponding residues from a time-domain waveform which contains damped

sinusoids, as illustrated in figure 6. After the input data is processed,

the output data is given as frequencies and residues in the s plane. The

frequencies appear as conjugate pole-pairs in the second and third quadrants

of the complex s plane; only the second quadrant poles are shown in

subsequent figures, with radians converted to hertz.

The number of pole pairs is usually unknown. Since one of the inputs

needed for Prony's algorithm, in addition to the time-domain waveform, is

the number of poles, we had to experiment with known waveforms and try

requests for a different numbers of poles. We found no satisfactory

explanation or guidance in the literature. A heuristic guideline that we came up with works consistently, but for the mathematical purists, nothing

short of a rigorous proof is convincing. In any case, additional

theoretical work might be appropriate to evaluate the procedure we developed

by trial and error on known waveforms. This procedure is explained as follows

.

Repeated runs requesting different numbers of poles from Prony's

algorithm for each data set are a key to this procedure. The number of

poles is not known beforehand. If there are n true poles and m poles are

requested where m < n, Prony's algorithm breaks down completely and gives

randomly located false poles that are not even close to the true poles. If

m poles are requested, where m > n, then n poles are correctly located,

while m-n poles are randomly located. If p poles are requested where p > n, and p * m, n poles are again correctly located, and p-n poles are

randomly located. Repeating this request about four times seems to be

sufficient to tell which poles have identical locations and can therefore be

identified as true poles. The randomly located poles only overlap by

chance, and in the two-dimensional s (complex frequency) plane, this seldom

occurs, certainly not for all four requests.

These conditions are shown in four figures produced from a genera* ' • curve with 25 poles from 7 to 246 MHz. If m or p are greater than 50 (f r 25 complex conjugate pole pairs), the 25 frequencies are shown correctly

figures 7 and 8 by the repeated poles thqt form a tilted Z. In figur7
the solutions from request of 55 poles (x's) and request of 50 poles (V's) are correct; the solutions from request of 45 poles (#’s) are close in some

cases but substantially in error other cases; the solutions from request of

40 poles is grossly in error everywhere. Figure 10 shows the meaningless

scatter obtained when all requests were for less than 50 poles.

Although plots can give this information, it is much clearer to watch a buildup of the poles on a CRT display in order to separate actual poles from

artificial poles. For example, it is hard to distinguish between two, three

or four poles printed at the same location. For this we used a personal

computer with a high resolution video display.

We used this procedure and Prony's algorithm to determine roots of

these digitized time-domain waveforms. We generated three different formats

for each set of output data. These three formats are (1) a plot of the

poles in the second quadrant of the s plane, (2) a bar plot showing the

magnitude of the complex residues of the poles and (3) a bar plot of the Qs

of the poles.

The pole plot in the s plane shows the approximate natural resonant

frequency of a pole (proportional to the jw value) and the damping factor of

each pole (related to the o value). Poles near the frequency axis indicate

slowly damped sinusoids and will have high Qs . Poles further to the left

indicate more rapidly damped sinusoids and will be of little concern since

their Q values are low.

The bar plot of the magnitude of the complex residues shows their

amplitudes. The amplitude is related to the power of the frequency source

for the particular pole and is therefore related not only to the gain of

both antennas of our measurement system but also to the transmitting and

receiving characteristics of the AUT. The residues may also be used several

ways to assist in the separation of true poles from artificial poles. The

magnitude of the complex residue is one dimensional, so random repetitions

have a better chance of occurring than in the two-dimensional s-plane plots

above. The residues repeat for the four runs for the lower frequency poles

only if the algorithm has a true pole. The residues of the artificial poles

will not repeat unless the magnitude is extremely low. A very low residue

is typical of poles extracted from system noise. These show a very high Q

and may be fairly tightly clustered. The poles with low-residues appear to

be repetitive because visual displays of very small numbers seem about

equal . The high residues typical of poles in the lower frequency range are

not repeated for all four runs and are therefore relatively easy to use in

identifying true or false poles.

The Q of each pole is given by the ratio of imaginary and real parts of

the complex pole. For EMC applications this is a very important parameter

since it gives an estimate of how much unperturbed fields may be enhanced by

the resonance of the structure.

3.0 Measurement Procedure Used at Ft. Rucker

There are several steps to obtain the final answers. First, the timedomain system and transmitting and receiving antennas must be set up in a

8
way that minimizes cross coupling and reflected signals from unwanted

objects, and that maximizes desired signals from the AUT. Second, the timedomain parameters such as the sampling rate must be selected appropriately

for the preceding placement. Third, reference signals must be recorded with

no test object present so that this signal can be subtracted from signals

with test object present in order to remove the effects of reflections and

some time-domain system characteristics . Fourth, signals must be obtained

for several orientations of the AUT since coupling varies depending on the

antenna pattern of the test object and the two measurement system antennas.

Fifth, the filtered and digitized data must be recorded on disks. Sixth,

these digitized data must be processed using Prony's method and the output

data must be displayed in several different forms in order to obtain the

correct interpretation.

3 .

1

System Setup

The transmitting and receiving antennas were set up on suitable ground screens with a 90° angle between them, with both aimed at a center point as shown in figure 1. Typical distances are shown but some adjustments were necessary depending on the size of the AUT. It was necessary to use a dummy

target during setup to obtain large enough received signal to make the

initial setup of the measurement system.

3 .

2

Selecting Appropriate Parameters for Time-Domain System

The sampling rate, the time between samples and the number of samples

to be used for averaging were determined based on size of test object,

separation distances, received signal strength, and desired frequency range

to be covered. The most commonly used values at Ft, Rucker were the

following. The clock frequency was 10 kilohertz, the samel ing density was

set for 512 points per waveform, and the scope sweep speed to

100 nanoseconds per division. These settings gave a 1.953 nanosecond time

interval between samples.

The clock frequency was chosen to be high enough to allow acquisition

of a data set in less than one minute, but low enough that the average

current does not degrade the avalanche transistor due to overheating. The

scope sweep speed was chosen to capture all of the reflections from the

aircraft. The 512 points per waveform gives very good time resolution of

the reflected waveform.

3.3

Taking Reference Data

A reference run with no test object present was made at the beginning

and end of each data recording session. In addition to the measurement

system characteristics that need to be removed later by subtracting this

reference data, there were many other external signals that were removed

both by this subtraction and by averaging. The strongest signals came from

the air-to- ground and ground-to-air radio communications. These would

literally cover the screen of the oscilloscope at times. There were some F"

stations and other signals of unknown origin.

9
3.

4

Rotating the Test Object

The AUT was rotated through 145° increments for a total of eight

orientations. The natural resonant frequencies of the AUT do not change

with this rotation, but the coupling of energy in and out of the AUT would

vary depending on the patterns of the antenna formed by the AUT and by our transmitting and our receiving antennas. If any one orientation couples a very small amount of energy because of a null in an antenna pattern,

important information might have been lost. The optimum number of

orientations needed are not known due to the structural complexity of the

AUT. The eight rotations we used seemed to be adequate.

For each rotation of the AUT, requests for four different numbers of

poles (99, 98, 97 and 96) were made of Prony’s algorithm. Data from a single rotation is shown in the illustrations.

3.5 Filtering Analog Data Before Digitizing

Analog data must be filtered before it is digitized to prevent aliasing

[1]. Using a low-pass filter with sharp roll-off starting at least an octave below Nyquist's folding frequency will prevent signals at higher

frequencies from being imaged downward about this folding frequency and

contaminating the lower-frequency data. Once the data are digitized, there

is no way to remove these imaged frequencies or to tell which are imaged and

which are true frequencies.

We did not pay sufficient attention to this problem. One of the plugin units for the digitizing oscilloscope with built-in filtering was damaged

in shipment; a back-up, lower frequency plug-in unit only had minimal

filtering, and we did not have the proper filters along to use as backup.

Therefore, although the data illustrate the ability of the measurement

system to function as intended, the data may possibly be contaminated by

aliased frequency poles. This aliasing would not cause frequency-shift

errors in the poles we did detect, nor would it cause true poles to be

missed. Any critical use of these data should be verified by repeating the

measurements and including sufficient filtering.

3. 6 Processing and Interpreting the Data

The digitized data were then stored on disk for later processing on a mainframe computer. Some reformatting of the data was necessary before they

were sent to a mainframe computer. We used a personal computer for this

task. We also used this computer and a modem to transfer the formatted data

to a mainframe computer and also to retrieve the processed results. Again,

additional formatting was necessary on the personal computer in order to

display the results in the three different formats discussed in section 2.H.

We paid attention to the adequacy of the measured signals, the mechanics of

the processes, and the adjustments that could be made during measurements

subsequently. We overlooked the possible contamination of data due to

aliasing.

The key information to be obtained from the processed data are the

resonant frequencies and the Q of each resonance. Both are given
graphically in the plot in the s plane. A number of false frequencies are

also displayed, but the printed plots and CRT displays show clearly the

correct ones, indicated by an exact repeat of the pole for the four

different runs of Prony's algorithm. The exact numbers are then obtained

from tabulated data. Bar plot plots of the magnitude of the residues offer

additional help in identifying false high frequency poles, which are

indicated either by a very small residue or for larger residues by lack of

repetition for the four runs. The values of Q are given in another bar

plot. The Q plots can be used by EMC engineers to determine an approximate

enhancement of electromagnetic fields by the resonances.

^ . 0 Sample Measured Data

Three sets of sample data are given. The first is a simulation based on a generated waveform using known frequencies, damping factors and

amplitudes. These results are helpful in learning how to interpret the

plots. The second set of data is from the Apache helicopter. The third set

of data is from the Black Hawk helicopter. There may be contamination in

both of the real sets of data; the relatively few clear resonances

identified should be verified by additional, independent tests.

Data from the measurements on the other aircraft are summarized in

tables and figures.

4. 1 Simulated Data

Figure 11 shows a plot of a computer-generated, time-domain waveform

which contains 35 poles with frequencies of 7, 17, ...97, 101, 111, ... 191,

214, 23*1, ... 494 megahertz. This set gives an example of contamination

caused by Nyquist folding for frequencies above 250 megahertz. All the

poles have complex residues with an amplitudes of 0.08. Although the number

of poles is known in this case, we follow the procedure from section 2.4 and

request a larger number of poles than 35. Four computer runs were made

requesting 99, 98, 97 and 96 poles. The repetition of the location of the

true poles is shown quite clearly, while the randomly generated poles do not

repeat and hence do not overlay. The digitized waveform has 256 points with

a sample spacing of 2 nanoseconds. The Nyquist folding frequency for this

spacing is 250 megahertz. All the poles above 250 megahertz fold down and

contaminate the data below 250 megahertz. The pole at 294 megahertz is 44

megahertz above 250 megahertz; it folds down to 206 megahertz. The pole at

494 megahertz is 244 megahertz above 250 megahertz; it folds down to 6

megahertz. Figure 12 is an expanded view of figure 11. Figure 11 goes to

250 megahertz while figure 12 only goes to 60 megahertz. The residues of

the folded-down poles are not changed by the folding; this is shown in

figure 13. A bar plot of Qs is shown in figure 14. The computer-calculated

values of frequency are usually correct to about four significant figures.

The computer-calculated values of the residues repeat to about the th.rc

significant figure for true poles, but vary much mor^e for the created poles.

Table 1 is a computer printout of the numbers obtained from these runs.
. 2 Apache Data

Figure 15 shows the s-plane plot of poles to 256 megahertz, while

figure 16 is an expanded plot to 80 megahertz. The folding frequency for

the sampling interval of 1.953 nanoseconds is 256 megahertz. Resonances

appear at approximately 19, 38, 59 and 76 megahertz. The residue plot in

figure 17 also confirms these as real poles. Figure 18 shows Q values about

60, 200, 60 and 70, respectively. The printout of numbers in Table 2 shows

the exact frequencies to be 18.6, 38.3, 59. 1 and 77.^ megahertz. Whether

all these poles are real or are aliased is not known since the raw data were

not properly filtered before it was digitized, but if there is any doubt

whether the Apache helicopters might be expected to operate in locations

where external sources generate these frequencies, additional investigation

is prudent.

M . 3 Black Hawk Data

Figure 19 shows the s-plane plot of poles for the Black Hawk helicopter

for frequencies to 256 megahertz. Figure 20 is the expanded plot for poles

to 60 megahertz, and shows possible poles at approximately 11, 21, 28, 39

and 55 megahertz. These poles are not quite as closely clustered as those

of the Apache, but they do show up consistently in data taken with the

helicopter at other azimuths. Figure 21 of the complex residues casts doubt

as to whether these poles are real in that the amplitudes do not repeat as closely as those of the Apache. Figure 22 shows the Qs to be 10, 25, 23, 50

and 50 respectively. The exact frequencies from table 3 are 10.9, 21.3,

28.3, 38.2 and 53.6 megahertz. These data show some scatter and hence may

not be real. The 21.3 and 28.3 megahertz frequencies should be examined by

additional measurements, since both are in frequency bands authorized by the

FCC for amateur radio service, and in addition, the 21.3 megahertz frequency

is very close to the 21. M megahertz intermediate frequency which may be used

in various avionic systems.

4 . M Data From Other Helicopters

The Chinook we used for measurements had one rotor blade removed for

service, so the data were not taken on a complete aircraft.

One figure of the expanded pole plot is given for each aircraft in

figures 23 through 27. Tables M through 8 give data of the first 50 poles,

residues, and Qs for each of the aircraft following each figure. The same caveat applies to all of these data that applied to the earlier data - some

valid information is present, but before it is used in any critical

application, the measurements should be repeated with better analog

filtering to eliminate any possible contamination due to aliasing.

The processed data from the other helicopters and one fixed-wing

aircraft are summarized in table 9 to identify the resonant frequencies.

The data for the OH58 were taken with a larger time interval between

samples, giving a lower folding frequency (128 megahertz), and may be more contaminated by aliasing than the data for the other aircraft.

Specifically, resonances are indicated at 3 and 5 megahertz in figure 27,

lower than is possible based on the maximum dimension of this aircraft.

1 2
5.0

Summary and Recommendations

A new measurement system was used to determine the natural resonant

frequencies of helicopters by radiating the aircraft with short pulses,

receiving the reflected waveforms, and by using the mathematical transform

known as Prony's algorithm to extract the natural resonant frequencies of

these helicopters. Many improvements have already been made in all parts of

the system; more are anticipated. One procedural error was made in our

measurements. The analog data were not adequately filtered before

digitization. This casts suspicion on the data taken, but the measurement

procedure and system have been successfully demonstrated at frequencies and

for applications not possible previously.

Three additional recommendations are made for any subsequent work.

Adequate filtering should be applied. Full-horn antennas should be used to

measure horizontal E field polarization, since the major dimension of a helicopter is in the horizontal plane. The effect of the helicopter image

below the ground screen should be evaluated using scale models. This should

be done for both antenna polarizations.

6.0

Acknowledgments

This work was supported by the US Army Aviation Systems Command for

both the development of the measurement system and arrangements for the

testing at Ft. Rucker. Gilmore Krener of AVSCOM made special arrangements

for these tests at the US Army Aviation Development Test Activity at Ft.

Rucker. L. Eagerton, M. White and C. Mello provided excellent support at

Ft. Rucker.

Roland A. Sweet of the Applied Math Division developed the software to

implement Prony’s Algorithm and Linda Lindgren wrote the computer code.

7.0

References

[1] Poggio, Andrew J., et al , "Evaluation of a Processing Technique for

Transient Data," IEEE Trans. Ant and Prop., Vol AP-26, No. 1, Jan.

1 978.

[2] Van Blaricum, M.L., and Mittra, R., "Problems and Solutions Associated

with Prony's Method for Processing Transient Data," IEEE Trans. Ant.

and Prop., Vol. AP-26, No. 1, Jan. 1978.

[3] Van Blaricum, M.L., and Mittra, R., "A Technique for Extracting the

Poles and Residues of a System Directly from Its Transient Response,"

IEEE Trans. Ant. and Prop., Vol. AP-23, No. 1, Nov. 1975.

[M] Baum, C.E., "On the singularity expansion method for the solution of

electromagnetic interaction problems," Interaction Note 88, Dec. 11,

1971 .

[5] Tesche, Frederick M., "On the Analysis of Scattering and Antenna

Problems Using the Singularity Expansion Technique," IEEE Trans.

Antennas and Propagat., vol AP-21 , pp 53~62, Jan. 1973.

13
[6] Beneking, H., and Filensky, W., "The GaAs MESFET as a Pulse Regenerator

in the Gigabit per Second Range," IEEE MTT Vol . MTT-24, Jun.1976.

[7] Liechti, C.A., Special Issue on Microwave Field-Effect Transistors,

IEEE Trans. Microwave Theory and Techniques, Vol. MTT-24, Jun. 1976.

[8] Lawton, R.A., and Ondrejka, A.R., "Antennas and the Associated Time

Domain Range for the Measurement of Impulsive Fields," NBS Tech Note

1008, 1978.

14
GROUND

SCREEN

15

FIGURE 1

TIME

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MERSUREMENT

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17
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Figure

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antenna.
Voltage

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403 mV/div 20 ns/div 82.1 mV/div 20 ns/div

T i me

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(Diode Across R1

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Figure 5. Signal plots shoving the difference between matched and

unmatched antenna response.

19
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352 1

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Figure

6.

Sample

time-domain

waveform.
250|

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of

generated

data

with

25

actual

polea

and

request

for

99,

98,

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8.

Complex

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plot

of

second

quadrant

of

generated

data

with

25

actual

pole3

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request

for

99,

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and

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Figure

9.

Complex

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plot

of

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quadrant

of

generated

data

with

25

actual

poles

and

request

for

55,

50,

fl5

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Figure

10.

Complex

s-plane

plot

of

second

quadrant

of

generated

data

with

25

actual

pole3

and

request

for

>15,

^3

and

>12

poles.
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po 1

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d

66

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t> # o

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Figure

12.

Expanded

3

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plot

of

second

quadrant

of

generated

data.

B

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26

Figure

12.

Expanded

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plot

of

second

quadrant

of

generated

data.
Magnitude

of

Complex

Residues

L5 v5

Z5

25

15

IS

05

05

05

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Lb

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25

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cr

QJ Lu oo

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27

Figure

13.

Magnitude

of

complex

residue

of

poles

for

generated

data.
NX

cr

<D

Ll_

28

Figure

14. Q

values

of

generated

data.
Table 1. Data from main-frame computer of simulated signal. Table gives

processed data of real and imaginary parts of complex frequency,

real and imaginary parts of complex residue, Q, magnitude of

residue, sigma and frequency.

Complex Residue Q Mag Sigma Freq

Frequency

Real lm2 g Real Imag • Res (Np/ys)

-i4JU 1 5300 5 . 9629e 6 -1 . lle-2 - .010268 1 8. le-2 -1.1 v 6. 0

1 -1129900 5 . 9666e 6 -1 . 1 Oe-2 - . 01061

5

1 6.1e-2 -1.1 6.0

-1125600 5. 9917e 6 -1 .C7e-2 .010613 1 8. le-2 -1.1 6.0

-in 9000 5. 9982e 6 -1.1 le-2 .010357 1 8.16-2 -1/1 6.01

-oo7570 7 . 0002e6 3.297e-3 -.010193 13 8.1e-2 -.6 7.0

"557530 7.0003e6 3.272e-3 -.010176 13 8.1e-2 -.6 7.0

-557190 7.0003e6 3.273e-3 -.010176 13 6. le-2 -.6 7.0

-557190 7 . 0005e 6 3.260e-3 -.010175 13 6. le-2 -.6 7.0

-635710 1 .7e7 5.i03e-3 .010113 20 8.16-2 -.8 17.0

-635730 1 .7e7 5 . 1 2 3e -

3

-.010056 20 B.le-2 -.8 17.0

-635630 1 .7e7 5. ll le-3 -.010098 20 8.16-2 -.8 17.0

-635710 l .7e7 5.111 e-3 -.010106 20 6. le-2 -.8 17.0

-1661900 2 . 351 e7 -1 . lie-1 .0001063 5 1 .2e-3 -1.7 23.5

-337 6100 2.3569e7 1 . 071 e-1 -.000090 7 2 . 8e-l -3.3 23.6

-3625^00 2.1192e7 2 . 1 60e5

-.002111 6 l.Se-3 -3.8 21.5

-1505600 2.5662e7 -7.75e-3 .011553 6 9.1e-2 -1.5 25.9

-1156700 2.5999e7 -7.56e-3 .011936 6 8.56-2 -1.5 T87C)

-um2300 2.6027e7 -7.11e-3 .010599 6 8. 2e-2 -1.1 26.0

-Hi! 69000 2.6217e? 6. 11 le-3 .01117 6 8 . le-2 -1 .

5

26.2

-5197900 2.6283e7 — T.36e-2 .001551 5 2 . Se-2 -5.2 26.3

- 11

1

I 60 O 2. 6999e7 6.932e-3 .010021 21 8.16-2 -l.l 27.0

-1115300 2. 6999e7 7.C52e-3 -.010061 21 8.1e-2 -1.1 27.0

-1111300 2.6999e7 6. 937 e-3 -.039966 21 8. le-2 -1.1 27.0

-miooo 2. lei 6. 631e-3 -.039969 21 8.16-2 -1.1 27.0

-1392900 3-lel 8. i!3e~3 -.039771 27 8. le-2 -l.l 37.0

-1392800 3. lei 8.723e-3 -.039731 27 6. le-2 -i .1 37.0

-1392700 3. lei 8.7D3e-3 .039751 27 B.le-2 -1.1 37.0

-1392900 3- lei 8.697e-3 -.039766 27 8.le-2 -l.l 37. Oj - 151 1700 1 . 6*1 22e7 -1 . 13e~3 .011103 10 8. 9e-2 -1 .

5

16. l -1530600 1 . 6l 35e7 -3.706-3 .OH393 1 0 6.9e-2 -1.5 16.1

-1557500 1 . 6l 69e7 -5.l7e-3 .016555 10 9. le-2 -1.6 16.2

-11 611 00 1.6202e7 -3.23e-3 .01511 6 10 9. le-2 -1.5 1 6. 2i -1683900 1 . 699 6e

7

l .101e-2 .010191 28 8.1e-2 -1.7 17.0

-1 661800 1.6996e? 1 .l02e-2 -.010073 28 8.3e-2 -1.7 17.0

-1682600 1.6996e7 1 .1086-2 .010275 28 8.1e-2 -1.7 17.0,

-1 685200 1.6999e? 1.067e-2 -.01058 28 8.1e-2 -1.7 17.0

-2533500 5. 0027e7 1 .7006-1 -.000273 20 6. le-l -2.5 50.0

-3981600 5.021 9e7 -7 . 05e-l -.001 628 13 3.5e-3 -1.0 50.2

-6000000 5.0191e7 2.607e-2 - .001 157 8 5. 2e-2 -6.0 50.5

-3318600 5.0657e7 -5.03e-l -.000311 15 1 . 2e*3 -3.3 50.9

-3150000 5. 0905e7 -8.C6e-5 -.000032 16 1 . 7e-l -3.2 50.9

-1917900 5 . lei 1 . 225e-2 -.036999 29 8. 2e-2 -1.9 57.0

-1916600 5. lei 1 . 225e-2 -.039052 29 8 . 2e-2 -1.9 57.0

-1918100 5.7001e7 1 .2l5e-2 -.03903 29 8. 2e-2 -1.9 57.0

-1918200 5.700le7 1 . 230e -2 -.038955 29 6 . 2e2

-1 .9 57.

C

29
300|

1

1

i

i

t

1

x

99P 0. Q. 0l 00 r>. io cn cn cn

> # O

ft

3

ii

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'

4*£

8

M

9

a

ft

>4<X X

$

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in

CN

tKHf O

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CM

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8 JL

x*

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#

b< 4fr0t> tfOH- 0—E>*

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8

ft >#

o

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CM X>o

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in

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CO O

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(

Z HW) bsjj

m

3.

ftE

bo

co

30

Figure

15.

Complex

3-plane

plot

of

necond

quadrant

of

Apache

data.
d

66

CL OL £L

CO to

O) CD Oi

> # o

1

ft

M

ft

s X

X

&

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0

t>

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o o o o o

CO to ^ CM (zhim) bsjj

3

(CE

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00

\D

0) L.3

DO

U.

31

Expanded

3-plane

plot

of

second

quadrant

of

Apache

data.
Magnitude

of

Complex

Residues

r

7'7~7~/

zA

1 /

1/ 7 7-T

r / / / /. /

V2/77Z

V/////////

[//// / /////// / / / // // // // // /

N

n

cr

CD

coo

vOO

CMO

O

o

32

Figure

17.

Magnitude

of

complex

residue

of

poles

for

Apache

data.

Units

of

horizontal

axis

are

frequency

in

megahertz.
200

L9

65

65

65

65

55

Z5

Z5

ZS

St

St

St

517

Ot

65

65

85

85

85

85

85

Z5

15

15

15

05

PZ

PZ L_

PZ

PZ6 L 61

616 L L L L\9 l 66668PPP000 NXcr

d)

<D

S_ro

<nx

rocoo

SZo

03

ro 4J

ro •o . - n

0) ^

sz t_ o <y

re

m O- SOE

(_>O

C

<73 >,

a.' o 3 c ^ <13

cr <~

ao

<D3

tx Lx o o o o

to

O in

33
Table 2. Data

DrocpsspH

from main-frame

riat-o computer, ^ from

. Apache signal. & Table-L Rives

c

gives

real and imaginary parts of

residue, sigma and frequency.

complex residue . Q,

Complex

Frequency

Heal Imag

Res: cue

Real Imag

Q Mag

Res

Sigma

(Np/us)

Freq

(MHz)

-5C20900 3- 5375e6 3.293e-l -.221*5 l 7. 9e-l -5.0 3-5

-5608200 3.74B4e6 1 .29*6-1 .06251 1 1 3. le-l -3-8 3-7

-3026700 4 . 0499e6 9.029e-2 .03700* 1 2. Oe1-3.0 4.0

-2795 i 00 6 . 2202e 6 -1 . 06e1

- .055012 3 2 „ *e1-2.6 6.2

-26' 0900 6 . 6327e 6 -4.77e-2 . 07099* 3 1 .7e-1 -2 .

6

6.6

-235-! 00 8 . 6405e

6

-4 . 1 56-2 .0*7037 4 1 . 3e-1 -2.4 6.6

-2* 2-700 6. 951 5e6 -2.25e-2 - .0*2768 * 9 . 6e - 2 -2.1 9.0

-6000000 9. 2C29c 6 -4.25e-2 -.48068 2 9. 7e-l -6.0 9.2

-6000000 1 . 64 Be 7 -1 .22e-2 - .37131 O 7 . 4e- 1 -6.0 16.5

-5677200 1 . 669 6e7 -8. 2*6-3 .071 962 3 l . 4e-l -5.9 l 6.7

-6000000 1 . 6871 e7 ~D • 51 e~2 .1207* 3 2 . 6e - 1 -6.0 l 6. 0 -2 9*! 4 60 1 .555167 3.l30e-2 .00*5955 6* 6. 3 € - 2 - • 5 1 8.

6

-5*' 50-0 1 .857567 3.225e-2 - .006056 59 6. 6e-2 - < • ^ 16.6

-329*i 90 *1 . 6577e7 3.3136-2 -.0062 65 56 6. 7e-2 - .3 18.6

-32-520 1 . 6561 e7 3.28*e-2 -.006655 57 6. 7e-2 -

. 3 1 8 .

6

J -1715200 2.4044e7 -1 .4 6e-2 - . 006*51 1 * 3 . 2e-2 -1.7 24.0

- i 201 200 2. 4i45e7 -9 • 03e-3 -.001099 20 1 .6e-2 -1.2 24.1

-155*100 2.4l6c7 -1 .236-2 -.001 655 16 2.5e-2 -1.6 24.2

-*i 51 0200 2.41 9967 -l.23e-2 - .002689 16 2.5e-2 -1.5 24.2

-1286200 3.046367 -3. 39e-3 .00557 85 2* 1 .4e-2 -1.3 30 .

5

-1736100 3 • 056Se7 -5. 26e~3 .010131 18 2 . 3e-2 -1.7 50.6

-2182700 3.061 567 -6.35e-3 -.01 6769 1 * 3. 6e-2 -2.2 30.6

-1836000 3 . C696e7 -2.02e-3 .01 101 9 17 2 . 2e-2 -1.8 50.7

-6000000 3.1 694e7 6.51 4e1

-1 .2002 5 leO -6.0 31 .7 -6000000 3 . 5254e7 - 1 . 7 6e -

1

- .00*630 6* 3 . 5e1

-6.0 38.3

-205260 3.33*367 1 . 57 6e-2 . 012605 187 4 . 1 e-2 -.2 38.3

-1851 50 3. 834967 1

. *60e-2 .012157 200 3 . 6e-2 -.2 33.3

-163390 3.&355e7 1 .467e-2 .0119*7 200 3 . 8e-2 -.2 38. *1 -19051 0 3 • E357e7 1 . 53*6-2 .012027 200 3. 9e-2 -.2 33. *j

-5764 600 3.6577e7 -9.216-2 -.006505 7 l . 9e-1 -5.8 -6 0 -6000000 3. 94Q6e7 - 6. 64e-2 1.2659 7 1 eO -6.0 39.4

-6000000 3 • 9 63 6e 7 -2.09e-l -.092223 7 4. 6e-l -6.0 39.6

-1131 300 4. 5249e

7

1 .120e-2 - .00*36* *0 2 . 4e-2 -l.l 45.2

-1146700 4 . 5251 e

7

1 .109e-2 -.00*3*9 4 0 2.4e-2 -l .1 *5.3

-1044700 4 . 5264e7 9.217e-3 -.003933 *3 2 . Oe-2 -1.0 *5.3

-1140200 *.5353e7 6. 67 1 e

- 3 .00*7661 *0 2 . Oe-2 -1.1 *5.4

-1303700 5- 2354e7 3.120e-3 -.009651 *0 2. Oe-2 -1.3 52.4

-1354300 5.241 4e7 3.173e-3 -.01103 39 2.3e-2 -1.4 52.4

-1316700 5. 2456e7 2.097e-3 -.0108*5 40 2 . 2e -2 -1-3 52.5

-1421200 5.2504e7 2.42*e-3 -.010837 37 2 . 2e-2 -1 .* 52.5

-970550 5.90&e7 -S.Ole-2 - .01 9179 61 7.1e-2 -1.0 59.1

-960020 5. 90£4e7 -3 • 07e-2 -.018753 62 7 . 2e-2 -1 .0 59.1

-925420 5.9092e7 -2.93e-2 - .017021 6* 6. 6e-2 -.9 5S.1.

-965170 5. 91 667 ~3 . 21 e-2 -.0151 63 61 7. le-2 -1 .0 53, ?J -2567900 6. l 474e7 3 . 525e-2 .002912 2* 7. le-2 -2.6 61 .5

34
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35

Complex

3-plane

plot

of

second

quadrant

of

Black

Hawk

data.
Dl CL CL CL

CD 0 CO

CD CD CD CD

X 0 # o

2 %

” e a!

-6

-5

-4

—3

-2

-1

f

Sigma

(Np/jjs)

Figure

20.

Expanded

s-plane

plot

of

second

quadrant

of

Black

Hawk

dat

§

:< &

y\ * #

o &

#

0

X

c

x

V

TF x

X *

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o o o ' o o o o

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36

Figure

20.

Expanded

s-plane

plot

of

second

quadrant

of

Black

Hawk

data.
Magnitude

of

Complex

Residues z

CZzz

tzzEEE

czy / [27/ o 00o

M3O

CMo oo

09

>9

6P

8^

8fr

Zfr

t't' 8*89

88

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92

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921 2

1211 2

ZlZ l Z l Zll l l l l l l L 8888PP88000

a*

CD

Ll.

37

Figure

cl.

Magnitude

of

complex

residue

of

poles

for

Black

Hawk

data.

Units

of

horizontal

axis

are

frequency

in

megahertz.
I I 09

*5

*9

*S

frS

6*

8t>

8fr

9fr

89

89

89

89

8Z

8Z

83

83

LZ

93

93

93

13

13

13

13 L l ZlL L Lii L U

ll1 1 8888V*99000 NI o o o o o o o

iD If) "3" rn CM «—

38

Figure

22. Q

values

of

Black

Hawk

data.

Units

of

horizontal

axis

are

frequency

in

megahertz.
Table 3- Data from main-frame computer from Black Hawk signal. Table gives processed data of real and imaginary parts of complex frequency, real and imaginary parts of complex residue, Q, magnitude of

residue, sigma and frequency.

Complex Residue Q Hag Sigma Freq

Frequency

Res (Np/ys) [MHz)

n 6 cl Imag Real I mag

-2376*00 3 • 2662e6 3.963e-l -.30907 l leO -2.* 3.3

-20*8900 3.*379e6 2.302e-l -.26632 2 7. 0e-1 -2.0 3-*

- l 8“5B00 3-5203e6 1 . 67le-l .2*12* 2 5. 9e-1 -1.9 3-5

-188 9'i 00 3. 5592e

6

1 . 61 *e-l .25613 2 5 . 7e1

-1.9 3.6

-2036500 7 . 7 0 9

‘ e 6 -3-35e-l -.71232 * leO -2.0 7.7

-1902000 7 . 7 * 6 6e 6 -2. 5*6-1 - . 66255 * leO -1.9 7.7

-1895000 7 . 656Se6 - 1 . 66e1-.701

9

* 1 eO -1 .

9

7.9

-1905*00 8 . 0593-

6

1 .8016-2 -.7 651 1 * leO -1.9 8.1

-1056*00 1 . 067*e7 -* . 856-2 -.56773 10 leO -1 .0 10.9

-982720 1 . 0 6 E 1 e 7 -*

.

1

6

e -2 -.5202 1

1

leO -l .0 10.9

-95091

0

1 .0692e7 - * . 7 6e - 2 -.*6935 1

1

9 . 8e1

-1 .0 10.9

-893*10 1 .0909e7 -* . 97e-2 . *3*75 12 8. 6e-l - • 9 10.9

-2627900 1 . 6602e7 * . 660e1

.12658 6 9. 7e-1 -2.8 16.6

-25*3300 1 . 6S9e7 3.036e-l -. 050358 7 6. 2e1

-2.3 1 6.9

-2113500 1 .7009e7 2.5056-1 . 0C*6i 79 6 5. 0e-1 -2.1 17.0

-1997000 1 . 721 7e7 2.2026-1 .0360*9 Q * . 5e1

-2.0 1 7 . 2_

-551 170 2 . 1 26Se7 -2 . 22e -2 .12637 25 2 . 6e -

1

- . 9 21.3

-9107 60 2. 1265e7 -1 .966-2 . 1*1 67 23 2. 9e-l - 0 • « 21.3

-51 9090 2 . 1 295e7 -1 .76e-2 .11982 26 2 . *e1

-.8 21 .3

-1000200 2.1335e7 -.3 . 1 Se~3 .165*3 21 3. 3e-l -1 .0 21-3

-6000000 2. 5756e7 -5-216-2 •33773 * 6. 8e1

-6.0 25.6

-561 3200 2 . 6l 5Se7 -8. 2*e-2 -.112 5 2. Se-l -5.6 26.2

-5577500 2 . 6*8-67 - 6 . 1 6e - 2 .021 * 5 l . 3e-i - 5 . * 2 6.5

-6000000 2.7*35s7 -9.63e-2 - .005502 5 l . 9e-l -6.0 27.*

-12271 00 2. 607 5e

7

-5.87e-2 . 0061 802 23 l . le-l -1.2 28.1

-121 9500 2.8285e7 -*.936-2 -

. 01 6877 23 1 . 0e-1 -1 .2 26.3

-1236200 2 . 837367 -*.5~e-2 .026723 23 1 . 1 6 - 1 -1.2 28.*

-125—00 2 . 5* 3s

7

-*.27e-2 .0319 23 1 . le-l -1.3 20.*

-7*7200 3 . 6002e7 -1 .126-2 - .00*336 51 2. *e-2 -.7 *8.0

-752920 3.81167 -1 .2*6-2 - .001 672 51 2.5e-2 -.8 36.1

-761530 3- El 73e7 -1 . 32e-2 - .001330 *9 2. 6e-2 -.8 58.2

-8**630 3 • 8255^7 -1 .506-2 . 0005878 *5 3.0e-2 -.8 36.3

-3067*00 * . 32“e7 -* . 90e-2 -.15099 l* 3 • 2e1

- 3."1 *3.3

-2922600 *.565e7 -9.356-2 -.11273 15 2 . 9e - 1 -2.9 *3.7

-2928700 * .588267 - 1 . 2 2 e -

1

- .10*91 15 3 . 2e1

-2.9 *3-9

-2965600 * . * 1 7 1 e 7

- 1 . 60e- 1 - .076927 15 3. 6e-l -3.0 **.2

-31*3300 *.737Se7 9.5576-2 .0*80*1 1

5

2.le-1 -3.

1

*7.*

-2993300 * . 77 65^7 7.3836-2 - .010167 1 6 1 . 5e-1 -3.0 *7.6

-3030700 * . 509*e7 7. **56-2 - .020773 16 1 . 5e -

1

-3-0 *8.1

-3505000 * .66**e7 6.3*66-2 - .0718*6 l * 1 . 9e1

-3.5 *8.6

-1125500 5. S5- Be 7 1 . 699e-2 - .007965 *8 3 . 8e-2 -1.1 53 • 5

1 _* 0 O'

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J

0 0 5-35 6 9e 7 1 .*736-2 . 0072963 50 3-3e-2 -1.1 53.6

-10*7600 5. 36l 6 7 1 .5*2e-2 . 0050369 51 3. 2e-2 -1.0 5 ^ • w -1152500 5. 36£9e7 1 .7556-2 . 0056226 *7 3. 6e-2 -1.2 53.7

-1*1 “900 5.978667 -1 . 26e-2 .01 1*99 *2 3. *e-2 -1 . * 59.8

39
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t

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40

Figure

23.

Expanded

3

-plane

plot

of

second

quadrant

of

Chinook

data.
Table *4. Data from main-frame computer from Chinook signal. Table gives

processed data of real and imaginary parts of complex frequency,

real and imaginary parts of complex residue, Q, magnitude of

residue, sigma and frequency.

Complex Residue Q Mag Sigma Freo

Frequency Res (Np/ys) (MHz)

Real Inieg Real I mag

-1597900 6.4471e6 -3.67e-3 .0046071 4 .012 -1.6 6.4

-1 642300 6.4934e6 -4.80e-3 .0058017 4 .015 -1.6 6.5

-164 6300 6.5003e6 -6.56e-3 .0076565 1' .020 -1.6 6.5

-1 647700 6. 5i06e 6 -5.1 0e-3 . 00621 58 4 .01 6 -1.6 6.5

-1256100 1 ,5069e7 5.593e-2 .064353 1

2

.171 -1.3 15.1

-12B2400 1 . 509e7 6.7C2e-2 .06559 12 .168 -1.3 15.1

-1306000 1 .5D93e7 6.57£e-2 .07104 12 .194 -1 .3 15.1

-1485900 1 . 5 7 € 7 8.663€-2 .13048 10 • 3*6 -1 .5 15.1

-21 £3000 1 .55SSe7 -1 ,52e-1 -.14 64 7 .422 -2.2 15.6

-2510900 1 . 5754e7 -1 .37e-1 -.082069 6 .319 -2.5 15.6

-2556200 1 . 5767e7 -1 .44e-1 - . 066-55 6 .313 -2.6 15.8

-2567400 1 ,5669e7 -1 .29e-1 -.071765 6 .296 -2.6 15.9

-1723000 2.4i 02e7 -1 .74e-2 -.011679 14 .042 -1.7 24.1

-1766900 2 . 4i 92e7 - 1 . 93- "2 - . 01 0411 1 4 .044 -1.5 24.2

-1775600 2. 421e7 -1 . 99e-2 -.006336 1 4 .042 -1.8 24.2

-1766400 2.4236e7 -1 .96e-2 - . 006665 14 .043 -1.5 24 .

2

-1455700 2.62C2e7 -5.65e-3 - .036393 1 9 .078 -1.5 2 8.2

-1552400 2 . 62 69s 7 -1.13e-2 - . 036654 16 .077 -1 . 6 26.3

-1566600 2.6262e7 -1.34e-2 .033077 15 .071 -1.6 25.3

-15661 00 2.6306e7 -1 .44e-2 .. 0351 84 16 .076 -1.6 28. ’ -151 9200 3.270le7 3.6T2e-2 - .001 461 22 .072 -1.5 32.7

-1571100 3.2762e7 3-6l1e-2 .0040745 21 .073 -1.6 32.6

-1562600 3- 2799e7 3 • 592e-2 -.001453 21 .072 -1 . 6 32.8,

-1574700 3*2622e7 3.574e-2 -.006135 21 .073 -1.6 - 2 . £ -1677000 3. 676e7 -8.916-3 -.0113 22 .029 -1.7 56. 6

-1750500 3.657e7 -9.856-3 -.005659 21 .023 -1.8 36.9

-1766900 3. 669e7 -1.036-2 .0001536 21 .021 -1.6 36. 9 -1756700 3. 691 9e7 -1 .096-2 .00321 61 21 .023 -1.8 * 6 ^ -1706000 4.11 27e7 2.650e-2 .0031 861 24 .053 -1.7 41.1

-1754500 4.1213e7 2.41 56-2 - .000400 23 .048 -1.8 41 .2

-1602600 4.123367 2.320e-2 .0033633 23 .047 -1.6 41 .2

-1 7 $2000 4 . 1 262e7 2.3126-2 -.002306 23 .046 -1.8 41 .

3

-1750200 4 . 5966e7 -1.176-2 -.017226 26 .042 -1.8 4 6.0

-1611400 4. 607167 -8.1 96-3 .020635 25 .045 - 1.6 46.1

-1625100 4.6097e7 -6.22e-3 .0261 46 25 .054 -1.8 4 6.1

- 1 605000 4 . 61 2e7 -6.306-3 .022441 26 .047 -1.6 46.

1

-1656700 5. 0521 e7 1 .433e-4 -.009604 27 .020 -1 .9 50.3

-1937700 5.0422e7 -3*95e-3 -.006270 26 .015 -1 .9 50.4

-1 956100 5.04567 -4.206-3 - . 000375 26 .008 -2.0 50.5

-1934100 5.04?6e7 -5.3le-3 -.00-655 26 .014 -1 .9 50.5

-3336500 5.6£52e7 1 . 4326-3 -.01 4346 17 .029 -3.3 CA Q

-3463600 5.7l77e7 -6.6le-3 -.010936 16 . 02 6 -3.5 57 .

2

-3515700 5.727£e7 - 3 • 1 6e -

4

.002646 16 .005 -3.5 57 .

3

-3426000 5. 7323e7 -£.55e-3 .0061451 17 .024 -3.4 57.3

-6000000 5 . 91 96e7 - 1 . 071 eO 1.7663 10 1 .000 -6.0 59.2

41
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to in ^ ro CN *—

( z HIA|) bsjj

V)Cl

tx: E

hj

CO

42

Figure

2

fl.

Expanded

s-plane

plot

of

second

quadrant

of

Huey

data.
Table 5. Data from main frame computer from Huey signal. Table gives processed data of real and imaginary parts of complex frequency,

real and imaginary parts of complex residue, Q, magnitude of

residue, sigma and frequency.

Complex Residue

Frequency Q Mag Si gma Free

Real I mag Heal I mag

Res (Np/ys) (KHz)

-61 3420 6.7649e6 3-999e-3 -.003374 6 .01 0 -.8 6.6

-633190 6.6465e6 3-084e-3 .00351 33 6 .009 -.8 6.8

-532360 6.9223e6 2.365e-3 -.003536 6 .009 - 0 • 6.9

-9P5760 6. 9605e 6 1 .520e-3 -.0024 61 8 .006 -.9 7.0

-1 3-7300 1.11 72e7 4.852e-3 .00521 62 B .01 4 -1.3 11.2

-1406200 1 .1256e7 5.393e-3 .0042221 8 .014 - 1 . ^ 11.3

-1 469900 1 . 1469e7 6.446e-3 .0024664 6 . 01 4 -1.5 11.5

-',532500 1 . 1 55oe7 5.795e~3 .0037415 8 . 01 4 -1 .5 11.6

-2361 100 1 .704ie7 -1 . 69e-2 .0063307 n

1 .035 -2.4 17.0

-2479700 1 .7263e7 -1 .66e-2 .01 0923 7 .040 -2.5 17.3

-2666500 1 . 7757e7 - 1 . 32e-2 .01 6266 i .042 -2 .

7

17.5

-2757100 1 . 6001e7 -1 .25e-2 .0241 96 7 .054 -2.8 1 5 .

0

-1393100 2 . 31 32e 7 -2.22e-3 - .01 041

4

1

7

.021 -1.4 23.1

-1404200 2.3293e7 -6.25e-3 -.010731 17 .025 -1 .4 2 3-3

-141 6000 2.3549e7 -!.23e-2 - .0061 1

4

17 .030 « 1i ~ 1 . 1 23-5

-1432200 2. 3667e7 -l.49e-2 -.002872 17 .050 -1.4 25.7

-141 5700 2.6937e7 9.925e-3 .017273 1 9 .040 -1 . 4 26.9

-1 425200 2.71 33e7 1 .7646-2 .01 1 995 1 9 .043 -1 .4 27.1

1 Jr O f

T* O o 2.7426e7 2.346e-2 - .002476 19 .047 -1.4 27.4

-1410500 2.7554e7 2.2l6e-2 -.00 671 0 20 . 04 6 -1 .4 27.6

-1924900 3 . 0722e7 -2.44 € -2 .0031 683 16 .049 -1 . 9 30.7

-1962600 3.1076? -2. 52e-2 .017306 16 . 058 -2.0 3 1 • 1 -1697700 3-159367 -3.62e-3 .027581 17 .056 -1.9 31.6

-1664500 3 • 1 7 9 6e 7 6.596e-3 -.03067 17 .063 -1 .

9

31.5

-2696600 3.450967 -4.5ie-3 -.01 401

9

13 .029 -2.7 34 • 5 -5159400 3. 5226e7 -1 . 69e-2 .01685 1

1

.046 -3.2 3- . 2 -3660100 3.6637e7 -3.036-2 -.012832 10 .066 -3.7 36.6

“3652400 3.7473e7 - 7 . £ 1 e

-

3

.05266 10 .106 -3.6 57.5

-2051 900 4.038367 -6.69e-3 -.006421 20 .022 -2.1 ' n i; -2315100 4.055367 -9.96e-3 -.007693 17 . 025 -2.3 40.6

-30c6l 00 4.1C21e7 -1 .9Se-2 -.01 07 61 13 .045 "3*1 41 .0

-3756500 4.13le7 -6.056-2 .0026777 1

1

.121 -3.8 41.3

-1292000 4.54546? -7.69e-3 -.007070 35 .021 -1.3 *0 • D -1390300 4.5562e7 -5.74e-3 -.005397 33 .021 -1.4 45.6

-1795700 4 . 5701 e7 -1.136-2 - . 005595 25 .026 -1.8 45.7

-1635200 4. 5713e7 -7.96e-3 -.003308 28 .017 -1.6 45.7

-1347500 5.112267 -4.75e-3 -.010457 38 .023 -1 • 3 51 .

1

-1324 600 5.l264e7 -6.77e-3 -.005018 3-9 .021 -1 .3 51 • 3 -1337400 5.1476e7 -6.65e-3 -.004327 36 .01 6 -1.3 51 -5

-1397900 5.i546e7 -7.95e-3 .0024004 37 .017 -1.4 5i -5. -1455700 5.507367 -4.25e-3 .0051 749 40 .013 -1.4 c £ 1 -1219500 5. 6095e7 - 1 . 1 0

e

-

3

.004549 45 .009 -1.2 C C

. 1 -1*51 900 5.5i59e7 7.424'e-4 .0055395 49 .01

1

-1 . 2 55.2

-1650600 5.8i6e7 -6.12e-3 .0053045 56 .01 6 -1 .6 5 e.2

-6000000 5. 6662e7 4.455e-2 -.035165 10 .114 -6.0 c c

. 7

43
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a

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t=bO

00

44

Figure

25.

Expanded

3

-plane

plot

of

second

quadrant

of

Cobra

data
Table 6. Data from main-frame computer of Cobra signal. Table gives

processed data of real and imaginary parts of complex frequency,

real and imaginary parts of complex residue, Q, magnitude o r residue, sigma and frequency.

Complex Residue Q Mag Si gma Freq

Frequency

Real ifficg Real I ma g

Res (Np/ys

)

(MHz)

-506060 6.0793e6 -4.75e-3 -.052238 12 .105 -.5 6.1

-540610 6.0675e6 -5.94e-3 .055038 11 .111 - • 5 6.1

-567450 6. 1 1 5i e 6 -9.24e-3 . 057 526 1

1

.117 -.6 6.1

-544700 6. 1 32 2e

6

-o, 99 e -3 -.054799 1

1

.111 - . 5 6.1

-1067700 1 .0204e7 4.656e-2 . 034901 10 .116 -1.1 10.2

-1146300 1 . 0259e7 4.7056-2 -.041524 0 .126 -1.1 10.3

-1174300 1 .04i5e7 3. 646e-2 - .051 846 0 .129 -1.2 10.4

-1134500 1.0453e7 3.71 5e-2 .048755 9 .123 -1.1 10.5

-2341900 1 . 574 Be 7 6. 651 6-2 - .090385 7 .250 "2.3 15.7

-216E600 1 .564 6e7 7.685e-2 -.075234 7 . 21 5 -2.2 15.8

-1963600 1 . 5662e7 6.272e-2 .057383 8 .170 -2.0 * ~ O i D . r -213S3OO 1 ,5655e7 8.023e-2 .067666 7 .210 -2.1 15.9

-25' 4000 2.29167 -7.316-4 - . 1 9484 10 .390 -2.3 22.9

“ 2 i 0^0 j

0

2.2 91 967 - 1 . 56e-4 -.1497 1

1

.299 -2.1 22.9

-2260C00 2. 3l95e7 -5 • 07e-2 -.17953 10 . 373 "2 . 3 23.2

-2374400 2 . 3275e7 -7.696-2 -.20166 10 .432 -2.4 23.3

-6000000 2.599367 5.9336-1 .47565 4 1 .000 -6.0 26.0

-1 624500 2.6995=7 -2.54e-2 -.025419 17 .072 -1.6 27.0

-6000000 2.7 104e7 3. 569e-1 .3277 Z> .969 -6.0 27.1

-1974400 2 . 7 2 S 7 e 7 -.5 .5le-2 -*. 025256 14 .121 -2.0 27.3

-1690500 2.754567 -5.2le-2 -.012673 1

5

.107 -1.9 27.5

-1261 600 2. 7667e7 -1 .656-2 .0006369 22 .033 -1.3 27.7

-6000000 3. 1 66e7 4.2406-1 - . 1 64 65 5 .91 0 -6.0 31 -7

-6000000 3 . 3 4 4 6e 7 3 . 825e1

-.069592 6 .778 -6.0 33-4

-2274200 3.504567 -9.316-2 .085292 1 5 .252 -2.3 35.0

-2044600 3. 5203s7 -5.36e-2 .07178 17 .179 -2.0 35.2

-2010200 3 . 522 6e

7

-4.756-2 .074721 15 .177 -2.0 35.2

-2212 600 3 . 52?4e7 -5.406-2 .09371

4

16 . 21 6 -2.2 35.3

-1563100 4 . 3‘ 07e7 -2.93e-2 .01531 9 25 .066 -1.6 43.1

-1 665000 4.3"7 56 7 -3.226-2 .021537 26 . 078 -1.7 43.2

-1726500 4 . 3252e? -3.036-2 .023753 25 .077 -1.7 43 .

2

-1564600 4 . 3- 97e7 -2.316-2 .027017 27 .071 -1.6 43.4

-1172100 4. 5201 e

7

-5.33e-3 .01317 41 .025 -1.2 48.2

-1010300 4 . 521 5=7 -7.016-3 .010954 48 .026 -1.0 48.2

-1163300 4.52426? -7.606-3 . 01 3736 41 .051 -1.2 48.2

-1109300 4 . £47e7 -8.026-4 -.015656 44 .031 -1.1 45. 5] -6000000 4. 96l9e7 -2. 51e-1 .17015 8 .606 -6.0 49.6

-3456500 5. 327 6e7 5.654=-2 -.034299 15 .136 -3.4 53.3

-3299200 5. 355367 4.3966-2 - .042452 16 . 122 -3-3 53.9

-4076900 5. 41 02e7 3.394e-2 -.0771 63 13 . 1 69 -4.1 54.1

-4529900 5. 4'235e7 5.1536-2 - .09921

9

12 . 224 -4.5 54.2

-1411400 5. 5527e7 -4.396-3 .0033204 41 .011 -1.4 58.5

-1336000 5. 67 4 Be

7

-7.54e-4 .0052572 44 .01

1

-1.3 56.7

-677330 5.555567 -8.666-4 .0037235 67 .008 - . 9 58.9

-1446400 5. 55936 7 -5. 69e-4 .0052407 41 .011 -1.4 56.9

45
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Figure

26.

Expanded

3

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plot

of

second

quadrant

of

II

50

data.
Table 7. Data from main-frame computer of H~58 signal. Table gives

processed data of real and imaginary parts of complex frequency,

real and imaginary parts of complex residue, Q, magnitude of

residue, sigma and frequency.

Complex Resi due 0 Mag Sigma Freq

Frequency Res (Np/ys) (MHz)

Real Imag Real Imag

-442520 5- 5579e6 -5- 66e-2 .0061 112 6 .076 -.4 3-4

-458210 5.5556e6 -5-916-2 -.012678 7 .082 -.5 3-4

-449620 5 • 5994e 6 -4.02e-2 .01 0372 6 .063 -.4 3-4

-4521 00 3.4 655e6 -3.756-2 .01 6244 RW .063 - . 5

< c -520990 5 . 564 6e 6 -4 . 66e-2 - .062244 10 .156 — »-\ 5.4

-507540 5 . 4 1 7 Be 6 -4.9le-2 .054 61 1

1

.147 -

. 5

£ L> ^ -515740 5.4206e6 -5.15e-2 - . 05532 6 1

1

.151 - # c 5.

4

-47701

0

5. 455e 6 -5.1 4e-2 -.04 6613 1

1

. 1 39 -.5 5.5

~51 52500 6. 7557e 6 3. 641 e-1 .34146 1 1.000 -5 • 2 6.7

-6000000 6.6652e6 3.1 956-1 - . 51 61

1

1 1.000 -6.0 6 .

9

-750460 1 . 031 7e7 -5.056-2 .037332 13 .125 -.5 10.3

-71 6000 1 .04e7 -3-506-2 .039025 14 .105 -.7 10.4

-806090 1 . 04'07e7 -4.74e-2 .048036 13 .155 -.6 10.4

-924740 1 .04l?e7 - 6. a 36 - 2 .072567 1

1

.195 -.9 10.4

-5106200 1 . 1 659e7 8 . 0676-

1

- .27067 2 1 .000 -5.1 11.6

-755650 1 .I96le7 -8.65e-2 .066331 1 6 .224 -.8 12.0

-71 1 1 40 1 .205767 -6.066-2 .066407 17 .160 -.7 12.1

- 668690 1 .2064*7 -5.79e-2 . 0 621 33 18 .170 -.7 12.1

- 665500 1 .2115e7 -4.3Se-2 . 06684 16 .160 -.7 12.1

-6000000 1 .21 4367 6. S67e1

- .27404 2 1.000 -6.0 12.1

-1946000 1 . 555567 -3.30e-l .0431

4

6 . 666 -1.9 15.4

-21 25700 1 • 555567 -4.22e-1 .05478 7 . 851 -2.1 15.4

-21 67200 1 .5446e7 -4 . 3£e1

.11573 7 .905 -2.2 15.4

-2509600 1 .575567 -4 . 04e1

.2939 7 . 999 -2.3 15.6

-5647 50 1 . 7 5 1 6e 7 -1 . 616-2 -.078322 32 . 1 60 _ c,

• wS 17.6

-561450 1.752167 -1 .66e-2 . 082 655 31 .1 69 -.6 17.6

-565680 1.762767 -2.056-2 -.062037 51 . 1 69 -.6 17.6

-595120 1 .785167 -2.4 6e-2 -.064562 30 .176 -.6 17.9

-56945OO 2.2422*7 - 4 . 4 3 e - 2 - .43978 6 .664 -7.9 22.4

-4061 90 2.2609e7 1.4736-2 .044203 56 .093 - . 4 22.5

-5897 60 2 . 252567 1 . 591 e-2 .056692 s,0 .064 _ h 22.6

-565950 2. 2629e7 1 .7156-2 .036793 CO .065 - .4 22.6

-592540 2.264:2*7 1 . 690*-2 .036007 58 .065 )i 22.6

-4257200 2.517967 -2.606-1 -.471 92 5 1 .000 -4.2 23.2

-4064400 2 . 3566e7 -2.526-1 -.4091 6 6 .961 -4.1 23.4

-5027600 2-557567 -1 .$16-1 -.25647 6 .608 -3.0 23.6

-577710 2.636*7 3.1256-2 .00631 36 46 .064 -.6 26.4

-595550 2.639967 3.3696-2 .0031 636 44 .065 -.6 26.4

- 606650 2. 6439*7 3.534e-2 .001 453 43 .071 -.6 26.4

-577900 2.646367 3.1476-2 -.003601 46 .063 -.6 26.5

-41 6540 2 . 6625e7 2 . 1 60e-2 - .005478 69 .044 - . 4 2 ^ ! "w -427640 2 . 6652*7 2. 1 46e-2 -.005650 67 .045 -.4 2 5.9

-451520 2 . 685567 2.250e-2 - .00631 2 67 .047 _ It 28.9

-590240 2.5666e7 1 .905e-2 -.006660 74 .040 _ 1. 25.9

-596030 3 . 2262e7 4.201e-3 .0063212 62 .01 9

- . 4 32.3

47
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Sigma

(Np/ps)

Figure

27.

Expanded

s-plane

plot

of

second

quadrant

of

OV-1

(fixed

wing)
Table 8. Data from main-frame computer of OV-1 (fixed wing) signal. Table

gives processed data of real and imaginary parts of complex

frequency, real and imaginary parts of complex residue, Q,

magnitude of residue, sigma and frequency.

Complex Residue Q Mag Si gma Freo

Frequency Res (Np/ys

)

(MHz)

cl Imag Real Imag

-429040 6 . 2433a 6 - 3 • 4 6e - 2 -.028566 15 .090 -.4 6.2

-443560 6. 2452e 6 -3.56e-2 -.029179 14 .092 - .4 6.2

-494770 6. 2504'e

6

-3- 95e-2 -.031785 13 .101 -.5 6.3

-51 5

9*7 0 6.2772e6 -4.29e-2 -.031199 12 .106 - .5 6.3

- 1

1

9*i 400 1 .0476e7 1 . 799e-2 - .070894 0 .146 -1 .

2

10.5

-12* 61 00 1.05le7 l.533e-2 .073026 9 . 149 -1 .2 10.5

- 1 28237)0 1 . 06l 3a

7

5 . 675e-3 -.079524 8 .159 -1.3 10.6

-1 256200 l . 0653a

7

-l .20e-3 -.076331 0s .153 -1.3 10.7

-1729000 1 . 6703e7 -1 . 57e-2 -.009756 10 .037 -1.7 16.7

-1505300 1 . 671 9a

7

-2. 02e-2 .015513 0 .048 -1.6 1 6.7

-1796200 l . 6"52e7 -1 . 67e-2 -.012175 9 . 041 -1.8 *16.8

-*1663*1 00 1 . 6921e7 -1 . 95e-2 .01 9597 9 .055 -1.9 1 6.9

-1274600 2 . 25&5a7 2.6676-2 - .003257 15 .058 -1 • 3 22.6

-1291500 2 . 2 7 0 5a 7 2.8756-2 -.007253 16 .059 -1.3 22.7

-1441300 2 . 282 6 e 7 3.191e-2 - . 01

1

£62 1 6 .068 -1.4 22.6

-i 51 0000 2 . 26£5a7 3 • 2 5 1 e - 2 .01491 6 1 5 .072 -1.5 22.9

_ E Jj C £ 0 / w ^ 2.64 66e7 1 • 93 5a - 3 . 0091 £l 5 200 .01 9

- . 1 26.5

-52226 2.647e7 1 .94 :e-3 .0092226 200 .01 9 -.1 26.5

-109390 2.6474e7 2 . 2 7 1 e - 3 .009891 3 200 .020 -.1 26.5

-100720 2. 6477e7 2.31 6e-3 . 00-961 75 200 .020 -.1 26.5

-121 6000 3.31 64e7 -2 .25e-2 .0012635 27 .045 -1 .

2

33 • 2 -12264 00 3 . 322 6e7 -2. 2£e-2 .0029013 27 .04 6 -1 .2 33-2

-1249000 3 . 326£e7 -2.506-2 .0041 695 27 .047 -1 .

2

33-3

-1272100 3 • 3294e7 - 2 . 36e -2 .0056332 2 6 .046 -1.3 33 .

3

- 23602 OO 3 . 991 6e7 -1 . 39e-l .20763 17 .500 -2.4 *•9.9 -2364900 3 • 9 9 4 1 e 7

-

1 . 32 e-l .20776 17 .4 92 -2.4 •9.9

-2362500 3

. GC=Cfi7 -1 . 26e1

.20956 17 .489 -2.4 40.0

-2362 600 3.997la7 -

1 . 236-1 . 21 2 64 17 .491 -2.4 40.0

1

O' 0 0 0 0 0 0 4. 50 4 Be 7 -1.176-1 -.£5938 6 1 .000 - 6.0 45.0

-6000000 4.6005a7 - 3 . 00e-l -.95672 6 1 .000 -6.0 46.0

-6000000 4. 6553a7 -4.1 7e1

-1.0206 6 1 .000 -6.0 46.6

-6000000 4 . 6956e7 -5.426-1 -1 .0271 6 1 .000 -6.0 47.0

-3026200 5.062 6e7 2. lOOe-1 .25256 17 .62 7 -3.0 50.6

-2523200 5. 0644e7 1 .625e-i . 1 6975 16 .527 -2.8 cn £

^ U . V -2995600 5.064 6e7 2 . 0 £ 6e -

1

.2250$ 17 .614 -3.0 50 .

6

-291 1 900 5.06£3a7 2. 0 6£e-l . 201 34 17 .577 -2.9 50.7

- 639250 5.452 6e7 6.C49e-3 -.003495 £5 .01 4 -.6 54.5

-726760 5. 4536a 7 6. 342e*3 -.004370 75 .015 -.7 54.5

-41 9250 5. 4549e7 3 . 6926-3 -.002769 130 .01 0 -.4 34.5

-359300 5.457367 3.596e-3 -.002947 140 .009 - 1' 54.6

-2744O00 6 . 04 61 e

7

5 . 005e4

- .01 £441 22 .037 -2.7 60.5

-2512300 6 . 11 6le7 -1 .08e-2 -.016473 24 .043 -2.5 61.2

-1691100 6. 1 923e7 -1.37e-2 - .004663 33 .029 -l . 9 61 .

9

-1697900 6.2056e7 -1 .59e-2 -.003922 33 .033 -1.9 62 . l -2300400 6.679767 4.274e-2 -.014414 29 .090 -2.3 66.6

49
Table 9. List of Aircraft, natural frequencies, and approximate Q.

* Aliased frequencies (false).

Aircraft

Natural

Frequencies (MHz) Q

Chinook CH-47 15.1 12

24.2 1 4 28.3 18

32.8 21 36.9 21

ill .2 23

46.

1

25

50.

4

26

Huey UH-1 23.5 17

27.4 20

45.6 30

51 .3 38

Cobra AH-1 10.3 10

35.2 17

48.2 44

OH-58 3.4* 8

5.4* 1

1

17.8 31 22.8 58

26. 4 44

28.9 69

0V-1 (Fixed wing) 10.5 9 16.8 9 22.8 18

33.2 27

39.9 1 7 50.6 17

50
NBS-1 14A 1 REV. 2 -ec) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 87-3077

2. Performing Organ. Report No.) 3. Publication Date

November 1987

4. TITLE AND SUBTITLE

Time-Domain System for Identification of the Natural Resonant Frequencies of

Aircraft Relevant to Electromagnetic Compatibility Testing

5. AUTHOR(S)

John W. Adams, Arthur R. Ondrejka, and Herbert W. Medley

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8 . Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

U.S. Army Aviation Systems Command

St. Louis, Missouri 63120

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

bi bl iography or literature survey, mention it here)

A method of measuring the natural resonant frequencies of a structure is

described. The measurement involves irradiating this structure, in this case

a helicopter, with an impulsive electromagnetic (EM) field and receiving the

echo reflected from the helicopter. Resonances are identified by using a mathematical algorithm based on Prony's method to operate on the digitized

reflected signal. The measurement system consists of special TEM horns,

pulse generators, a time-domain system, and prony's algorithm. The frequency

range covered is 5 megahertz to 250 megahertz; this range is determined by

antenna and circuit characteristics.

The measurement system is demonstrated, and measured data from several

different helicopters are presented in different forms. These different

forms are needed to determine which of the resonant frequencies are real and

which are false. The false frequencies are byproducts of Prony's algorithm.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semco'c:'

avalanche step generator; natural resonant frequencies; Prony's method;

TEM horn antennas; time—domain measurement system.

13. AVAILABILITY

Uni imited

| | For Official Distribution. Do Not Release to NTIS

7] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

56

15. Price

U.S. GOVERNMENT PRINTING OFFICE: 1988-573-933 / 85033 U sc

O

mm-O C < 4
'