NBSIR 78-892

THE TIME DOMAIN CHARACTERISTICS OF A TRAVELING-WAVE

LINEAR ANTENNA WITH LINEAR AND NON-LINEAR LOADS

Motohisa Kanda

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

February 1979

NBSIR 78-892

THE TIME DOMAIN CHARACTERISTICS OF A TRAVELING-WAVE

LINEAR ANTENNA WITH LINEAR AND NON-LINEAR LOADS

Motohisa Kanda

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

February 1979

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

ABSTRACT 1

1. INTRODUCTION 1

2. TRAVELING-WAVE LINEAR ANTENNA 2

3. TRAVELING-WAVE LINEAR ANTENNA WITH A LINEAR LOAD 4

4. TRAVELING-WAVE LINEAR ANTENNA WITH A NONLINEAR LOAD 6

4.1 THEORETICAL CONSIDERATION 7 4.2 NUMERICAL RESULTS 9

5. CONCLUSIONS 10

REFERENCES 11

iii

THE TIME-DOMAIN CHARACTERISTICS OF A TRAVELING-WAVE LINEAR

ANTENNA WITH LINEAR AND NONLINEAR LOADS

Motohisa Kanda

Electromagnetic Fields Division

National Bureau of Standards

Boulder, Colorado 80303

This paper discusses the time-domain characteri sties of a travelingwave linear antenna with linear and nonlinear loads. The fast Fourier

transform (FFT) is used to analyze an antenna with a linear load. A

numerical time-stepping, finite-difference equation method is used to

analyze an antenna with a nonlinear load. The nonlinear effect is treated

by the Newton-Raphson iteration technique. Effects of various linear and

nonlinear loads are examined. Physical insight into the nonlinear loading

of the antenna is also given in terms of detected time-domain sinusoidal

electromagnetic (EM) waves.

Keywords: Fast Fourier transform; Newton-Raphson iteration method ; linear

load; nonlinear load; time-domain measurements; time-stepping finitedifference technique; transient; traveling-wave antenna.

1. INTRODUCTION

It is well known that a conventional linear antenna, which supports an essentially standing-wave current distribution, is highly frequency sensitive

because its antenna characteristi cs (e.g., current distribution, antenna

admittance, radiation pattern, etc.) are strong functions of frequency. On the

other hand, an essentially travel i ng-wave current distribution can be produced

on a linear antenna by inserting a suitable loading resistor one-quarter

wavelength from the end of the antenna, as indicated by Altshuler [1]. The

correct value of loading resistance is not, however, easy to calculate since the

antenna does not have a characteri sti c impedance analogous to TEM transmission

line theory. Moreover, since the value and the location of the loading

resistor are functions of frequency, this type of a linear antenna cannot be

considered broadband.

Wu and King [2] demonstrated that a travel i ng-wave antenna can be realized

by continuous resistive loading, where the internal impedance is a particular

function of position along the antenna. Shen and Wu [3], Taylor [4], Shen [5],

and Lally and Rouch [6] have modified and improved the original Wu-King theory

and have done experimental work on a relatively long (more than 25 cm)

traveling-wave antenna.
The author [7,8] applied the nethod-of-mor.ients technique to numerically

solve the wave equation of a traveling-wave linear antenna. The current

distribution, antenna admittance, near-field and far-field radiation patterns,

and radiation efficiency of the antenna were calculated and compared with

results calculated from Wu-King's current distribution. More recently,

transients in traveling-wave linear antennas analyzed by the author [9,10] have

been compared with those in TEM horns and conical antennas.

In this paper, the time-domain characteri sti cs of a traveling-wave linear

antenna with linear and nonlinear loads are discussed. The characteristics of

the antenna with a linear load are described first in the frequency domain.

Various combinations of resistors and capacitors are used as linear loads. Very

short, incident electromagnetic (EM) impulses of 100-ps duration and 1 .5-ns

duration are used for the analysis. Time-domain characteri sties are then

obtained using the fast Fourier transform (FFT) technique.

Traditionally, the characteristics of a linear antenna with a nonlinear

load have been analyzed in the frequency domain by considering spectral

components of solutions at harmonic frequencies [11]. For example, Sarker and

Weiner [12] have used the Volterra series analysis to obtain the scattering of a nonlinearly loaded antenna. Calculation of the transfer fuction of a nonlinearly loaded antenna, however, becomes very tedious, particularly when

circuit models for such a combination are very complicated. For this reason,

recent analyses of nonlinearly loaded antennas have been evaluated using a direct time-domain technique [13,14]. In this paper, the time-domain

characteristics of a travel i ng-wave linear antenna with a nonlinear load are derived by solving the time-domain, nonlinear equations using a time-stepping,

finite-difference equation technique. The nonlinear effect is treated by the

Newton-Raphson iteration method. The transfer function and the dynamic range of

a travel i ng-wave antenna with a nonlinear load are derived. Physical insight

into the nonlinear effects on an antenna is gained by an examination of the

detected time-domain, sinusoidal EM waveforms.

2. TRAVELING-WAVE LINEAR ANTENNA

In this paper, a traveling-wave linear antenna is realized by depositing a thin film of resistive material on a glass rod. The film thickness and,

therefore, the resistance vary with position along the linear antenna. Although

various types of resiti ve-1 oading profiles have been examined, the best are

2
related to the Wu-King theory. That is, if the internal real impedance (i.e.,

resistance) per unit length V (z) as a function of the axial coordinate z is

given as

( 1 )

then the current distribution I z

(z ) along the linear antenna is that of a travel i ng wave; i .e.

,

The symbols have the following meanings: h is half the physical length of

the dipole, k is the wave number, V 0 is the driving voltage, and T is given

by

where a is the radius of the dipole, and C(x,y) and S(x,y) are the

generalized cosine and sine integrals, respecti vely

.

In recent work by the author [7,8], current distributions on a travelingwave antenna are calculated by solving the one-dimensional wave equation

numerically using the method of moments [15]. Figure 1 shows a traveling-wave

linear antenna and its resistive-loading profile. Current distributions

calculated from the method of moments and Wu-King's approximation are shown in

figure 2 along with some experimental results. Theoretical and experimental

results indicate that the current distribution along an antenna is indeed that

of a travel i ng wave. Once the current distribution on the traveling-wave antenna is given, the

effective length and the driving-point impedance of the antenna can be

determined. These quantities are needed for analyzing the time-domain

characteri sties of the antenna with linear and nonlinear loads. The effective

length, h G (f), of the antenna is given by the moment of its current

distribution, divided by the driving-point current; i.e.,

( 2 )

T = 2[sinh

-1^

- C(2ka ,2kh) - jS(2ka,2kh)] + ^(l-e"j2kh

) (3)

h

( 4 )

3
Using the approximate current distribution given in eq (2), the effective

length h e (f) and the driving-point impedance Z 0 (f) of the traveling-wave

linear antenna are given by

h (f ) = 4- (l-jkh-e'jkh

) , e rh

(5)

and

Z 0(f) = GO Ml - ^) • (6)

The effective length and the driving-point impedance of the antenna were also

calculated using the current distribution obtained from the method of moments.

The results are shown in figures 3 and 4.

3. TRAVELING-WAVE LINEAR ANTENNA WITH A LINEAR LOAD

The characteristics of a traveling-wave linear antenna with a linear load are analyzed first in the frequency domain, and then the time-domain

characteri sties are obtained using the FFT.

Using the effective length h G (f) of the antenna, the open circuit

voltage Vg(f) of its equivalent source is given by

Vf > = - he

(f) E inc (f > - (7 >

where E. (f) is a normal incident electric field. The thevenin's

equivalent circuit model for the antenna and a linear load is shown in

figure 5. The receiving transfer function S r (f) of an antenna in the

frequency domain is defined by

V (f) -h (f) Z (f)

$r(f) " ^7^ = z^TT^T-ffT • ( ">

where V[_(f) is the induced voltage and Z|_(f) is the load impedance of the

antenna . Figures 6a and 6b show the magnitude and phase of the transfer function of

the traveling-wave antenna with various combinations of linear loads. Th<> magnitude of the transfer function drops rapidly above 1 GHz due to a rapid

decrease in effective length as indicated in figure 3. This rapid decrease in

4
effective length above 1 GHz prevents the antenna from resonating. Figure 6a

shows that the magnitude of the transfer function of the antenna becomes

constant with high impedance loads in the lower frequency range. Figure 6b

indicates that the total phase dispersion of the antenna up to 1 GHz is still

only 180° for various linear loads, although a large phase degradation takes

place above 100 MHz. This nondi spersi ve characteri sti c is very useful for fast,

time-varying, transient EM impulse measurements.

The time-domain characteristics of the traveling-wave linear antenna with

a linear load were obtained using the FFT. Two incident EM impulses, one having

a duration of about 100 ps and the other having a duration of 1.5 ns, are used

for time-domain analysis. The time-domain waveform and the amplitude spectra of

an incident EM impulse with a 100-ps duration (50%) are shown in figure 7, The

amplitude spectra are relatively flat up to 5 GHz. The time-domain EM impulse

waveforms received by a traveling-wave antenna with various linear loads are

shown in figures 8a and 8b. Figure 8a shows the EM impulse responses of an antenna with various resistive loads. Figure 8b shows those with various

capacitive loads and capacitive-resistive, parallel combination loads. For

capacitive loads of 0.1 pF and 1 pF, which represent typical capacitances of a sampler or of a high-frequency detection Schottky barrier diode, the resistive

load predominantly determines the EM impulse waveforms, since the impedances

corresponding to capacitances of 0.1 pF and 1 pF are very high. The lower the

resistive load, the more predominant the down-shoot of the EM impulse waveforms

becomes due to the low-frequency roll-off as shown in figure 6.

A low-frequency, incident EM Gaussian impulse with a duration of 1.5 ns was

also used in the time-domain analysis. Its time-domain impulse waveform and

amplitude spectra are shown in figure 9. The amplitude spectra are very flat to

200 MHz. The time-domain response of the traveling-wave antenna with various

linear loads are shown in figures 10a, 10b, and 10c. Figures 10a, b, and c show

the time-domain responses of the antenna with various resistive, capacitive, and

capacitive-resistive, parallel combination loads, respectively. The figures

indicate that, as the loading impedance of the antenna decreases, the received

time-domain waveforms become time-differentiated and exhibit a predominant

down-shoot. Thus, to reproduce the original incident EM impulse waveforms, a traveling-wave antenna should be terminated with a high, linear impedance load.

5
4. TRAVELING-WAVE LINEAR ANTENNA WITH A NONLINEAR LOAD

Thevenin's equivalent circuit models for the traveling-wave linear antenna

with a nonlinear load are shown in figure 11. For both models in the figure, the

traveling-wave linear antenna is modeled as an open circuit voltage source

|

G | E inc , and its driving-point impedance is represented by R

a and

C a , in a series configuration. From the driving-point impedance given in

figure 4, R

a is 250 ft and C a is 0.5 pF, for the purpose of the time-domain

analysis of the models indicated in figure 11.

In Model I of figure 11, the characteristics of the traveling-wave linear

antenna are determined by the nonlinear load, v/hich is modeled with a nonlinear

resistance R

n and a linear capacitance in parallel configuration. In reality, a beam lead Schottky barrier diode, which is often used as a nonlinear

load, is better represented by Model II shown in figure 11. Model II consists of

a nonlinear resistance R n and a nonlinear junction capacitance C j , as well as

a linear series resistance R

s , linear package capacitance Cp, and lead

inductance L.

The nonlinear resistance R

n in Models I and II can be described by the

diode I-V characteristics, modeled as

The symbols have the following meanings: i is the current (amperes), V is the

voltage (volts) across the diode junction, i s is the saturation current

(amperes) which is assumed to be 2 x 10 -9 A, and a = q/nkT = 38 V" 1

, where q is the electronic charge (1.6 x 10“1 9 coulomb), n is the diode

ideality factor (-1.05), k is Boltzmann's constant (1.38 x 10“ 33 J/K), and

T is the ambient temperature (-290 K).

The nonlinear capacitance Cj in Model II is represented by

where Cj (0 ) is the zero bias function capacitance, typically 1 pF , and V>, is the built-in potential, typically 0.45eV for the beam lead Schottky barrier

di ode.

(9)

Vv)

c

.i<°>

( 10 )

( i-v/v

b

) 1/2

6
The package linear capacitance C p in Model II is typically 0.1 pF. In Model I the nonlinear junction capacitance Cj and the linear package

capacitance C

p are combined, where the total diode capacitance C<j is

assumed to be linear and to be 0.34 pF. The linear series resistance R

s and

the lead inductance L in Model II are assumed to be, respectively, 8 ft and

0.1 nH . These elements are totally neglected in Model I.

4.1 THEORETICAL CONSIDERATION

The method used for analyzing time-domain characteri sties of a travelingwave antenna with a nonlinear load is a time-stepping, finite-difference

solution technique for obtaining the numerical solution to a time-domain model

equation. The nonlinear effect caused by a nonlinear load is solved by the

Newton-Raphson iteration method. The basic idea of the time-stepping,

finite-difference equation technique is briefly discussed below. More detailed

discussions on this subject are given by Calahan [16].

Linear and nonlinear elements are converted into a resi stance-current

equivalent network in the nodal equation method. For instance, in a regular R,

C, and L circuit, we have

and

i , , = C

n+1

V

n+ 1 - Vn

V

n + 1 ' L Vl "n

( 12 )

03)

where T is

Vi and i 2 , therefore.

a sampling-time interval. Once the initial V 0 or i 0 is given,

then V 2 and i 2 > etc. can be determined; such a method is,

called a time-stepping, finite-difference equation method.

7
In order to deal with nonlinear equations that result from nonlinear

elements such as diodes, the Newton-Raphson iteration is used. The basic

technique is discussed below. Given a nonlinear equation f(i, V), the solution

of f(i,V) = 0 yields the solution of the nonlinear equation. First, f(i , V)

is expanded about an initial solution CT that is,

f(1,v) = f (1°, V°) + J[f(i,V)]

where J is the Jacobian of f and has the form

(14)

J =

3 f i 31

3 f -i

3 V n+m

3f n+m

Now, f ( i

, V ) = 0 determines

31

as

3f

3V n+m

n+m

J[f(i>°)] P’

0

1= - f(1°,V°) .

The solution Ai

AV

( updates the initial value of

. o

Al

AV

C

, via

r.n+ll r - n i i

1 -

v n+l

_ —

. n Al

AV

n

The operation is repeated for n = 0,1,2,««», until the change

significantly srnal 1 .

Al

AV

IS

(15)

(16)

8
4.2 NUMERICAL RESULTS

An incident, EM sinusoidal wave was used to examine the time-domain characteristics of a traveling-wave linear antenna with a nonlinear load. In the

analysis, a single time-domain, sinusoidal EM wave was divided into 16 discrete

digitized points (17 points including both ends). To arrive at the detected

time-averaging of the sinusoidal wave excitation, 400 sinusoidal waves, which

correspond to 6400 discrete points (16 points per cycle), were applied

successively to a traveling-wave linear antenna with a nonlinear load to

compute 6400 discrete induced voltages at the antenna terminal. These 6400

discrete voltages were then numerically averaged to arrive at the detected

time-average of the sinusoidal EM wave excitation.

Figure 12 shows the detected 1st and 400th sinusoidal waves using Models I and II. Because of the nonlinear element, the detected sinusoidal wave is

clearly skewed, and there is more negative than positive charge accumulation.

Figure 13 shows the time-averaged, detected dc induced voltage at the antenna

terminals as a function of normal incident sinusoidal EM field. The experiments

were performed using the traveling-wave linear antenna with a beam lead

Schottky barrier diode as a nonlinear load, and the results are shown in this

figure. From the theoretical and experimental results given in the figure, the

detected dc voltage is shown to be precisely equal to the square of an incident

EM field below a detected dc voltage of about 0.1 volt (square-law detection).

Above a detected dc voltage of about 1 volt, the detected dc voltage is

precisely proportional to an incident EM field (linear detection).

Figure 14 shows the transfer function of the traveling-wave antenna with a nonlinear load as a function of frequency. The transfer function of an antenna

is defined in eq (8), with E-j nc of 1 V/m. The theory and experimental

results are in general agreement. The discrepancy between the theoretical and

experimental results below 100 KHz is mainly due to the effect of the resistive

leads used as a dc pick-up in the experiments. The very sharp cut-off indicated

below 100 KHz and above 1 GHz can be easily explained as follows. Figure 15

shows the detected time-domain EM sinusoidal waves at various frequencies. This

figure shows clearly that the detected sinusoidal waves are more skewed and

distorted at 10 MHz than those at 10 kHz and at 10 GHz. In turn, this skewed

and distorted sinusoidal voltage causes more negative charge accumulation,

leading to a very high detection efficiency. On the other hand, the smaller

9
skeweness and distortion at 10 kHz and 10 GHz, cancel positive and negative

charge, and the net charge accumulation is almost zero, leading to a very

low-detection efficiency.

5. CONCLUSIONS

This paper discussed the time-domain characteristics of a traveling-wave

linear antenna with linear and nonlinear loads. The theoretical technique used

for analyzing the time-domain characteri sties of an antenna with a linear load

is the FFT technique. Very fast impulses with durations of 100 ps and 1.5 ns were used in the analysis. Various combinations of resistances and capacitances were used as linear loads. In general, the traveling-wave linear

antenna with a high impedance load preserves incident time-domain, transient EM

waveforms. On the other hand, an antenna with a low impedance load causes tine

differentiation in the time-domain waveform due to a 1 ow-f requency roll-off in

its transfer function.

The theoretical technique used for analyzing a traveling-wave antenna with

a nonlinear load is the time-stepping, finite-difference equation method with

the Newton-Raphson technique. Differential equations are solved using the

time-stepping, finite-difference equation method, whereas the nonlinear effect

is treated by the Newton-Raphson iteration technique. The dynamic range and

the transfer function of the traveling-wave antenna with a beam lead Schottky

barrier diode used as a nonlinear load were evaluated. The physical insight

into the nonlinear response of the antenna can be gained by a qualitative

discussion of the effects of skewness and distortion of detected time-domain EM waves .

10
REFERENCES

[1] Altshuler, E. E., The traveling-wave linear antenna, IEEE Trans. Antennas

Propagat. AP-9 , No. 4, 324-329 (July 1961).

[2] Wu, T. T., and King, R. W. P., The cylindrical antenna with nonreflecting

resistive loading, IEEE Trans. Antennas Propagat. AP-13 , No. 3, 369-373

(May 1965).

[3] Shen, L. C., and Wu, T. T., Cylindrical antenna with tapered resistive

loading. Radio Science 2 , Mo. 2, 191-201 (Feb. 1967).

[4] Taylor, C. 0., Cylindrical transmitting antenna: Tapered resistivity and

multiple impedance loading, IEEE Trans. Antennas Propagat. AP-16 , Mo. 2,

176-179 (March 1968).

[5] Shen, L. C., An experimental study of the antenna with nonreflecting

resistive loading, IEEE Trans. Antennas Propagat. AP-15 , No. 5, 606-611

(Sept. 1967).

[6] Lally, J. F., and Rouch, D. T., Experimental investigation of the broadband

properties of a continuously loaded resistive monopole, IEEE Trans.

Antennas Propagat. AP-18 , No. 6, 764-768 (Nov. 1970).

[7] Kanda, M., The characteristics of a relatively short broadband linear

antenna with tapered resistive loading. International Symposium on Antennas

and Propagation, Digest, 230-233, Stanford Univ., CA (June 1977).

[8] Kanda, M., A relatively short cylindrical broadband antenna with tapered

resistive loading for picosecond pulse measurement, IEEE Trans. Antennas

Propagat. AP-26 , No. 3, 439-447 (May 1978).

[9] Kanda, M., Transients in resistively loaded antennas, and their comparison

with conical antennas and TEM horns. International Symposium on Antennas

and Propagation, Digest, 13-16, Univ. of Maryland, MD (May 1978).

[10] Kanda, M., Transients in resistively loaded antennas and their comparison

with conical antennas and TEM horns, MBSIR 78-876, National Bureau of

Standards, Boulder, CO (March 1978).

[11] Wiener, N., Nonlinear Problems in Random Theory (Cambridge, MA, MIT Press,

1959).

[12] Sarkar, T. K., and Weiner, D. D., Scattering analysis of nonlinearly loaded

antennas, IEEE Trans, on Antennas Propagat. AP-24 , Mo. 2, 125-131

(March 1976).

11
[13] Lin, T. K., and Tesche, F. M., Analysis of antennas and scatterers with

nonlinear loads, IEEE Trans, on Antennas Propagat. AP-2 4

, No. 3,

131-139 (March 1976).

[14] Kanda, M., Analytical and numerical techniques for analyzing an electrically short dipole with a nonlinear load, NBSIR 78-898, National

Bureau of Standards, Boulder, CO (Nov. 1978).

[15] Harrington, R. E., Field Computation by Moment Methods (New York: The

MacMillan Company, 1968).

[16] Calahan, D. A., Computer-Aided Network Design (McGraw-Hill, Inc., New York,

1972).

12
RESISTIVE

LOADING/O.

5

cm

UNIT

LENGTH

(kfi/0.5

cm)

I

DIPOLE

Fig. 1. A traveling-wave linear antenna and its resistive-loading profile.

13
MOMENT

METHOD

(S33d03a) no i in a i y is i a iN3yyno 30 3S\/Hd

o

c

o

z

o

I cr

ono

CL

o

00 o

C\J o

o

C\J

O'

(a/vuj) NounaiMisia iN3dano jo 3oniiNDvw

14

Current

distribution

of

a

traveling-wave

linear

antenna

at1

GHz.
(IU) HJ.9N33 3 A 1 10 3 3 3 3 30 lH\/d AdVNIOVWI

(lu) H19N31 3AI133333 30 IdVd 3V3d

15

Fig.

3.

Effective

length

of

a

traveling-wave

linear

antenna.
RESISTANCE

(fi)

FREQUENCY

Fig. 4. Driving-point impedance of the traveling-wave linear antenna.

16
RECEPTION

ANTENNA IMPUT IMPEDANCE

I L (f

)

LOAD IMPEDANCE

LOAD 1 — ANTENNA

h

e (f)E INC (f)

v

L (f) = -h

e (f)E INC (f) Z

L (f)

Z

0

(f) + Z

L (f)

Fig. 5. Thevenin's equivalent circuit for a traveling-wave linear antenna

with a linear load.

17
oULi

cc.

VO

CT>

ooo

I

(ap) NOiioNnd aadSNvai do 3aniiN9vw

18

a)

The

magnitude

of

the

transfer

function

for

a

traveling-wave

linear

antenna

with

a

linear

load.
19

b)

The

phase

of

the

transfer

function

for

a

traveling-wave

linear

antenna

with

a

linear

load.
FREQUENCY (GHz)

Fig. 7. Time-domain waveform and amplitude spectra of 100-ps EM impulse.

20
11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4 —I 1 I I I I I 0.1 0.2 0 3 0.4 0.5 0 6 0.7 TIME (ns)

0.8 0.9 1.0 11 1.2

a) Transient responses of a traveling-wave linear antenna with 100-ps

EM impulse with various resistance loads.

fr /x -ini') 1

21
01 pF

Fig. 8 b) Transient responses of a traveling-wave linear antenna with 100-ps

EM impulse with various capacitance loads and capacitanceresistance, parallel combination loads.

22
FREQUENCY

Fig. 9. Time-domain waveform and amplitude spectra of a 1.5-ns Gaussian EM

impul se.

23
12

Fig. 10. a) Transient responses of a travel i ng-wave linear antenna with a 1.5-ns Gaussian EM impulse for various resistance loads.

24
RELATIVE

AMPLITUDE

11

Fig. 10. b) Transient responses of a traveling-wave linear antenna with a

1 .5-ns Gaussian EM impulse for various capacitance loads.

25
11

10

9

8

7

6

5

4

3

2

1

0

-1

2

3

0 1 pF + 1 Kn

1 pF + 1 Kn

0.1 pF + 100 Kn

01 pF + 10 Mn

0.1 pF + 1 Mn

_L _L

6 7 TIME (ns)

J

10

i12

Transient responses of a traveling-wave linear antenna with a

1 .5-ns Gaussian EM impulse for various capacitance-resistance,

parallel combination loads.

26
TRAVELING WAVE LINEAR ANTENNA

MODEL I

Fig. 11. Thevenin's equivalent circuit for a traveling-wave linear antenna

with a nonlinear load.

27
RELATIVE

AMPLITUDE

RELATIVE

AMPLITUDE

Fig. 12. Detected EM

a nonlinear

si nusoi dal

1 oad. waves by a traveling-wave linear antenna with

28
Fig. 13. Dynamic range of a traveling-wave linear antenna with a nonlinear

load.

29
-40

rMODEL.

I

30

Fig.

14.

Transfer

function

of

a

traveling-wave

linear

antenna

with

a

nonlinear

load.
Traveling-Wave

Linear

Antenna

model

II

31

Detected

EM

sinusoidal

waves

by

a

traveling-wave

linear

antenna

with

a

nonlinear

load

at

various

frequencies.
NBS-114A (rev. 5-78)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 78-892

2. Gov’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

THE TIME DOMAIN CHARACTERISTICS OF A TRAVELINGWAVE LINEAR ANTENNA WITH LINEAR AND NONLINEAR LOADS

5. Publication Date February 1979

6. Performing Organization Code 723.03

7. AUTHOR(S)

Motohisa Kanda

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 7233281

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP

)

Same as Item 9.

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information If do < ument in c ludt < Mtfni/n .tn( bibliography or literature survey, mention it here.)

This paper discusses the time-domain characteristics 01 a traveling-wave linear antenna with linear and nonlinear loads. The last

Fourier transform (FFT) is used to analyze an antenna with a linear

A numerical time- stepping, finite-difference equation method is used to

analyze an antenna with a nonlinear load. The nonlinear effect is treated

by the Newton-Raphson iteration technique. Effects of various linear and

nonlinear loads are examined. Physical insight into the nonlinear loading

of the antenna is also given in terms of detected time-domain sinusoidal

electromagnetic (EM) waves.

17. KEY WORDS (six to twelve entries; alphabetical order. apit.ilizc only Of lir t h tt r l thi hr i » min/ onlcBM • proper name; separated by semicolons)

Fast Fourier transform; Newton-Raphson iteration nu-thod : linear

load; nonlinear load; time-domain measurements; time-stepping

finite-difference technique; transient; travel in.'-v.iv' mti-nu.i.

18. AVAILABILITY [

' Unlimited 19. SEC URITY a K (THIS REPORT)

21. NO. OF PA(.F'»

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