A111DE 7 b 5 3 E

NBS

PUBLICATIONS

NBSIR 88-3084

POSSIBLE DESIGNS FOR

ELECTRIC-FIELD-STRENGTH PROBES

FOR MILLIMETER WAVES

J. Randa

M. Kanda

D. Melquist

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303-3328

February 1988

jvesearcn miormation L-enter National Bureau of Standards

Gaithersburg, Maryland 20899

NBSIR 88-3084

POSSIBLE DESIGNS FOR

ELECTRIC-FIELD-STRENGTH PROBES

FOR MILLIMETER WAVES

J. Randa

M. Kanda

D. Melquist

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder. Colorado 80303-3328

February 1988

Sponsored by

Naval Ocean Systems Center

San Diego, California 92152-5122

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

POSSIBLE DESIGNS FOR ELECTRIC -FIELD- STRENGTH PROBES

FOR MILLIMETER WAVES

J. Randa, M. Kanda , and D. Melquist

Electromagnetic Fields Division - 723.03

National Bureau of Standards

Boulder, CO 80303

Various designs are considered for electric - field probes for

the frequency range 26-110 GHz. Two particular designs are investigated in some detail. A resistively tapered dipole

antenna with a diode detector shows promise for frequencies

up to about 40 GHz. The second design is based on a fiberoptically sensed temperature sensor to detect the heating of

a resistive strip. If its sensitivity can be increased

significantly, this design may be capable of operating to

frequencies above 100 GHz.

Key words: electric-field probe; flouroptic temperature

sensor; millimeter waves; resistively tapered dipole.

1
I. INTRODUCTION

With the growing importance of millimeter waves in both military and

civilian applications comes an increased demand for electric - field probes to

operate at frequencies up to 100 GHz and beyond. Such probes would be

useful in many applications, but the one of interest in the present study is as a transfer standard, enabling secondary calibrations facilities to trace

their measurements back to a primary standards laboratory. Transfer

standard probes of this sort which the National Bureau of Standards (NBS)

has developed in the past include the EFM-5 [1] and the 8-mm resistively

tapered dipole [2], The frequency ranges for these two electric - field

probes extend to 1 GHz and 18 GHz respectively. There are electric - field

probes available commercially which are claimed to work to higher

frequencies, but they are not suitable for our purposes.

In developing a probe design for electric fields up to 110 GHz, we will

pursue three different lines of attack. The most conservative approach is

to attempt to extend a successfull lower- frequency design into the frequency

range of interest. The resistively tapered 8-mm probe, whose highest

operating frequency is about 18 GHz, will be the starting point for this

attempt. The dipole will be scaled down from 8 mm to 4 or 2 mm, and a diode

whose range includes the higher frequencies will be used as a detector. The

second approach is to use an antenna other than a short dipole -- a commercially available broadband antenna better suited to the millimeter

wave region. We will present estimates of the parameters and performance

required for a spiral antenna. Attempts to obtain a suitable antenna

commercially have been unsuccessful thus far, but there is still at least

one possibility. The third line of attack comprises new, unconventional

probe designs. We suggest several possible designs and briefly consider

each. The most promising of these novel probe configurations appears to be

the one based on the fiber-optic monitoring of the heating of a resistive

strip, and this design is pursued in considerable detail. The idea is to

deposit a thin film of some resistive metal such as nichrome on the tip of a

f iber-optically sensed temperature probe. When placed in an electric field,

the thin film will be heated by the induced current, and the resulting

temperature rise can be measured by the temperature sensor, yielding a measure of the electric field intensity. Calculations to determine the

feasibility of such a design and the optimal values of variable parameters

will be presented, as will the results of some preliminary measurements.

The remainder of this report is organized as follows. The next Section

is devoted to what we consider conventional approaches. We discuss the

resistively tapered dipole probe and present results of preliminary

measurements up to about 30 GHz. We also consider designs based on other

antennas, such as the spiral. Section III deals with less conventional

designs, with a heavy emphasis on the fiber-optic- thermometer based design.

We also suggest several other possible designs, with an assessment of the

practicality of each. Section IV contains a summary and recommendations for

future work.

2
II . CONVENTIONAL APPROACHES

A. Background

Numerous configurations for electric field probes have been suggested,

tested, and even marketed. It is not our intent to discuss them all here.

A thorough review can be found in [3]. For present purposes it suffices to

consider the two most successful and popular probe designs relevant to

frequencies above 1 GHz.

The basic configuration used at NBS in developing the isotropic

electric-field probe [1], and used in subsequent NBS and commercial probes,

is an electrically short dipole with a diode detector (typically a beam-lead

Schottky diode), connected to a metering unit by a high-resistance filter

line. The small antenna(s) and high-resistance line do not perturb the

fields being measured, and the transmission line does not itself pick up

spurious signals and transmit them to the metering unit. For dipoles

constructed from a highly conducting material, the resonant frequency of the

dipole establishes an upper frequency limit for the probe since the response

of the dipole becomes very frequency dependent as the resonance is

approached. Thus, for example, the EFM-5 [1], which uses 5 -cm dipoles

(resonant frequency about 3 GHz) , can only be used up to 1 GHz before its

response becomes frequency dependent.

There are (at least) two ways to go to higher frequencies with this

basic design. The obvious manner is to use shorter dipoles. Very small

dipole probes (0.6 mm) have been used at lower frequencies for biological

implantation purposes [4], For such small antennas, however, it is not

always clear that the detected signal is due to the antenna and not to

spurious effects . Another way to suppress resonance effects is to use resistive dipoles rather than good conductors [5-7], This fact can be seen quantitatively in the simple model presented in the Appendix and used in

Section III. Basically the resistance reduces the magnitude of the currents

induced and also damps them so that they do not persist long enough to build

up a resonance. Thus for a given length dipole, one can achieve a greater

frequency range by using resistive dipoles [7], but the price paid is a reduced sensitivity due to the smaller induced currents. The sensitivity

loss can be ameliorated by tapering the resistive profile of the dipole [3.

6], achieving a travel ling -wave antenna effect. By having the resistance

grow continuously to infinity as one approaches the ends of the antenna, one can preferentially damp current reflected from the ends, thereby suppress i s,- the resonance while not sacrificing too much sensitivity. Using resistive lv

tapered 8-mm dipoles, a probe has been constructed which can measure 1 to

1600 V/m fields up to 18 GHz [2].

The other probe design in wide use at frequencies above 1 GHz employs < themocouple detector to detect the temperature rise in thin resistive f i 1

:

. [8, 9]. Use of a thin film accomplishes two purposes, as will be seen explicitly in Section III. It increases the resistance of the strip, thus

increasing the heat generated (for the same amount of current). It also

reduces the thermal mass of the material to be heated, thereby allowing

faster response times. The geometries of the configurations used in

3
[9] differ, as do the methods used to obtain a cold junction in the

thermocouple, but in both the hot junctions are heated by the currents

induced in the junction material.

The major drawback of the thermocouple -based designs is their

sensitivity to fluctuations in the ambient temperature and to other heating

mechanisms. The individual thermocouple detectors are also not as sensitive

as diodes, leading to the connection of many individual units in series to

obtain detectable signals. That in turn raises the question of interaction

between the individual units due to electromagnetic scattering. Also,

because of their relatively slow response time, they cannot be used in peak

or quasi-peak detectors. In their favor, probes based on thermal detection

are directly sensitive to the time average of the electric field. The

dipole-diode design, on the other hand, is only indirectly sensitive to the

ambient temperature and has a faster response time. In the presence of

waveforms more complicated than a single sinusoid, however, it does not

necessarily indicate the true electric field [10]. Typically this is not a serious shortcoming if the probe is to be used as a transfer standard since

such applications are usually in single- frequency cw fields. Probes based

on electro - optical technology [11] promise to overcome several of the

problems noted above, but they will not be operating at millimeter-wave

frequencies in the near future.

Because of the success of the resistively tapered 8-mm dipole as a transfer standard up to 18 GHz, we have chosen to attempt to extend this

design to higher frequencies in the hope that it can cover at least the

lower portion of the frequency range of interest -- up to about 40 GHz.

Results of preliminary tests and measurements are contained in the next

subsection. In addition to attempting to extend the range of the resistively

tapered dipole design, we also consider the possibility of using an antenna

other than a dipole as the sensing element. Such an antenr.a would need to

be broadband, of course, and it would also have to have a rather large

beamwidth. The large beamwidth is necessary if it is to have any chance of

serving as the basis of an isotropic probe. In the third part of this

section we will consider the possibility of such an alternate antenna, with

special emphasis on a cavity-backed planar spiral antenna.

B. Resistively Tapered Dipole

The resistively tapered 8-mm probe is well documented in [2], It

consists of three orthogonal sensing elements, each of which is a resistively tapered 8-mm dipole. The resistive profile which was used for

the dipoles was

60 x 6 , 34 12/mm

4 mm -

| x |

| x | <4 mm

.

( 1 )

This resistive tapering was achieved by tapering the width of the resistive

strips that constitute the dipole arms, as shown in figure 1. The tapering

required to eliminate reflected currents depends on the frequency, and

therefore eq (1) will not be the optimal tapering for frequencies above 18

GHz.

4
Extension of this design to higher frequencies requires shorter dipoles

with appropriate tapering for the desired frequency range (up to about 40

GHz). We are in the process of obtaining such dipoles. Preliminary tests

have been performed on a 4-mm dipole obtained by cutting 2 mm off each end

of an 8-mm dipole. The resulting 4-mm dipole has a resistive tapering which

is not at all optimal, but measurements were made on it nonetheless to

obtain a quick indication of the feasibility of this design. A Schottky

diode was ultrasonically bonded across the gap, as is done in the 8-mm

probe, and the frequency response was measured up to 40 GHz. This was done

by immersing the unit in a 20 V/m electric field in the NBS anechoic

chamber. The results of these measurements are shown in figure 2. As can

be seen, the response is quite flat up to almost 30 GHz. Considering the

crude tapering of the dipole, this is an encouraging result, which augurs

well for the performance of a properly tapered unit.

In addition to the frequency response, a property of great interest is

the antenna pattern, the angular response of the unit. For an electric

dipole, the voltage across the gap should vary as cos# , where # is the angle

between the dipole axis and the polarization of the incident electric field.

Any deviation from a cosine squared pattern for the voltage squared is an indication of the presence of undesirable effects, such as pickup by the

leads or scattering from the substrate. Since such effects were the major

obstacles in developing the 18 GHz probe, it is crucial that we check for

them as we go to higher frequencies. Measurements of the angular pattern

were performed at several frequencies in the anechoic chamber. A computerdriven positioner rotated the dipole, taking readings every 8.78°. Results

of the measurements at 20 GHz and 30 GHz are shown in figure 3. The results

in this case are mildly encouraging. The angular patterns could be

smoother, particularly at 30 GHz, but they do exhibit a cos# behavior. With

a smoother resistive profile, better patterns should be achievable. In the

8-mm probe problems were encountered around 20 GHz and above due to

scattering from the support to which the dipole substrates were attached.

This problem was eliminated in the measurements of figure 3 by switching

from a delrin support to one made of foam with a dielectric constant of 1.1 or less at these frequencies.

The results obtained with the tapered 4-mm dipole obtained by

truncating an 8-mm dipole are grounds for cautious optimism. A properly

tapered 4-mm unit should display better characteristics, and it therefore

appears possible that it will be able to serve as the sensor for an electric - field probe covering frequencies up to about 40 GHz.

C. Other Antennas

To cover the entire 26-110 GHz range with a single traditional antenna

sensor, it is probably necessary to abandon the dipole-diode design in fav< : of a more broadband antenna with a correspondingly broadband detector.

Patch antennas are popular in many applications at these high frequencies,

but they are not suited to use in broadband probes due to their narrow

bandwidth. Even patch antennas with relatively large bandwidths, such as

5
the electromagnetically coupled antennas [12-14], are much too narrow for our purposes.

A broadband antenna which may be suitable is the spiral. (See, e.g.

,

[15, 16].) Spiral antennas are bidirectional unless backed by a cavity (or some other reflector). Even for an isotropic probe, unidirectionality of

individual elements may be desirable in order to reduce the effect of

scattering from the other antennas in the probe, and so we shall consider

cavity-backed spiral antennas. The cavity reduces the bandwidth, but this

disadvantage can be ameliorated somewhat by lining the cavity with absorbing

material. That in turn results in a loss of power gain, but decade

bandwidths are then achievable. As for the beamwidth, for a cavity-backed

Archimedean spiral the beamwidth is typically between 60° and 70° at 2-5

GHz; and it is not likely to be larger at 100 GHz. That is a problem if

isotropy is a concern. It would take five or six such antennas just to cover two dimensions. To cover the full 47r solid angle would require ten to

twelve spiral antennas.

The physical size of the spiral is determined by the range of

frequencies it is to cover and by the tightness of the spiral (a, where the

spiral is described by r = r 0 e ) . For efficient radiation or reception, a relatively tight spiral seems desirable, a=0 . 2 . The radius of the feed

region is required to be much less than the minimum wavelength; the Antenna

Engineering Handbook [17] suggests • That would require an inner

radius ^<0.214 mm for 100 GHz operation. Relaxing that requirement a bit

would lead to a feed region of diameter <0.5 mm. The outer diameter of the

spiral needs to be a bit bigger than A /ir. If f . =10 GHz, 2r o >0.95 cm, max mm 2 whereas if f . =25 GHz, 2r 9 >0.38 cm. mm 2

Regarding the detector, most applications of spiral antennas have

emphasized transmission rather than reception or use as a probe. There has

been considerable difficulty developing broadband baluns at high frequency,

which could pose problems for our application. For the detector, if one uses a Schottky diode as at lower frequencies, the requirements are that it

be physically small (length of about 0.1 mm or less) and that its cutoff

frequency exceed 100 GHz. It is not overly difficult to meet the size

criterion, but the cutoff frequency could be another matter. Present

detector diodes used at and above 100 GHz tend to be whisker diodes, whose

mechanical instability poses a problem. An alternative would be to use thermistor detectors. It would mean sacrificing sensitivity and response

time, but it might be acceptable if the required diodes could not be

obtained or fabricated.

Thus far, our efforts on spiral -probe development have been directed

toward locating, purchasing, and testing commercial units which operate up

to 100 GHz and above. These efforts have not yet been marked by success,

but the outlook is not entirely bleak.

6
Ill . UNCONVENTIONAL PROBE CONFIGURATIONS

A. Design Based on Fiber-Opt ically Sensed Thermometer

A.l General Design

The electric-field probe configuration considered in this subsection is

based on a fiber - optically sensed temperature probe [18]. The temperature

sensor consists of a small quantity of a phosphor affixed to the end of a optical fiber. The phosphor has the property that the lifetime of the first

excited state is temperature dependent. In the temperature sensor, the

phosphor is excited by a pulse of light transmitted down the fiber, and the

rate of the subsequent decay back to the ground state is monitored by

detecting the photons emitted and transmitted back down the fiber. The half

life of the excited state determines the temperature of the phosphor and of

any material with which it is in thermal equilibrium. An electric-field

probe can be built around this by placing the temperature sensor in contact

with a thin film of resistive material which will heat up when immersed in an electric field [19]. The resulting temperature rise is measured by the

temperature sensor and gives an indication of the magnitude of the electric

field. In [19] the authors used a carbon-based spray paint to paint narrow,

thin crossed dipoles on polystyrene foam. The temperature probe was sandwiched between two slabs of foam with the crossed dipoles painted on one

of the faces in contact with the temperature sensor.

The configuration we consider is quite different. Our idea is to

deposit a thin film of a resistive material directly onto the tip of the

temperature sensor, in thermal contact with the phosphor. Such a design

has the advantage that it minimizes the amount of material in contact with

the film which is being heated. This is important because the sensitivity

of the electric field probe will depend on the amount of heat transferred to

the phosphor for a given electric field. Any extra dielectric material in

contact with the resistive film will absorb heat from the film, thereby

reducing the amount available for the phosphor. The extra dielectric

material increases the effective thermal mass which must be heated, while

generating no additional heat itself. Initially it was intended that the

resistive film coat the outside of the end of the fiber (about the last 1 mm) so that it formed a cylindrical tube as in figure 4a) . (The phosphor

would be located at the tube center.) As will be seen below, a better

geometry may be a thin rectangular strip on a flat surface on the end of the

sensor, figure 4b).

Calculations have been done to assess the feasibility of this design

and to determine the optimal values for the various parameters. These

calculations require a simple model for the power absorbed by a resistive

cylinder or strip in an electric field. Such a model was previously

developed in [20]. Since that work is not generally available, the model is

presented here in the Appendix. In addition to the theoretical work, son.' preliminary measurements have been performed. Both calculations and

measurements are presented below.

7
A. 2 Theory

The simple algebraic model (SAM), developed in [20] and presented in

the Appendix, leads to the following expression for the power absorbed by a resistive tubular cylinder of length 2i in an electric field with component

parallel to the axis of the cylinder,

abs

2 2 E L _ R

z e f f abs ,

2 Z. 1 m1

where

"ef f

2 (1 - coski)

k sinki

R

abs

r

ac

2 2 sin ki

(1 2ki sin2ki)

,

Z.m

=R U + R + iX , abs r r

(2)

(3)

k = 2n/X .

In eq (3) and Z .^

are, respectively, the effective length and the input

impedance of the cylindrical tube considered as a dipole antenna. In the

equation for R , , R is the usual ohmic resistance. R , is an effective

3.DS a.l< abs

ohmic resistance, given the current distribution assumed on the cylinder.

Since we will be dealing with resistive films which are much thinner than

the skin depth of the material used, R is given by

R

AC

_J

<77rRt

’ (4)

where a is the conductivity of the material from which the cylinder is made,

R is the radius of the cylinder, t is the thickness of the cylinder wall,

and we have assumed t«R. The radiation resistance and reactance, R and

r

, are given by

R = - — - {2(1 + cosb)S 1 (b) - cosb S : (2b) + sinb [Si(2b) - 2Si(b)]},

sin k

I

30 n 22

x _ . M {sinb /R ) . 2Sj(b) + S 1 (2b)] - 2(1 + cosb) Si(b)

sin ki + cosb Si(2b) }

,

8
b - 2ki. (5)

The expressions used in evaluating the sine integrals, S^b) and Si(b), are given in the Appendix, as are details of the derivation of eqs (2-5).

The SAM can be used to estimate the amount of power absorbed by a resistive tubular cylinder and the consequent rate of temperature rise, and

also to determine the optimum value of parameters such as t and o. Beginning with parameter optimization, the first question is what quantity

we wish to maximize or minimize. What will determine the sensitivity of the

electric - field probe is the total amount of heat transferred to the phosphor

temperature sensor for a given electric field, but that calculation would

introduce dependence on too many additional parameters . The total

temperature rise of the resistive film is somewhat simpler, but it is still

complicated by heat- transfer problems. In order to isolate a manageable

number of parameters of the resistive cylinder, we shall consider the rate

of temperature rise of an isolated cylinder in an electric field. For the

purpose of optimizing the parameters, neglect of the heat loss to the

dielectric substrate and to the surrounding air is permitted since values

that maximize the rate of temperature rise in the absence of heat loss will

also maximize it in the presence of heat loss. This is because the heatloss mechanisms do not depend on the parameters being optimized. All that

will change is the actual rate of temperature rise (dT/dr) achievable.

The power absorbed by a resistive cylinder was given above, eq (2).

Neglecting heat loss, the rate of temperature rise is the power absorbed

divided by the cylinder's mass times its specific heat capacity,

dl = 1 dr 47riRtpC abs ’ ( 6 )

where p is the density and C the specific heat capacity (at constant

pressure) of the material of the cylinder. Using the full expressions, eqs

(3) and (5)

,

for the effective length and the various contributions to the

input impedance would result in an expression for dT/dr that was too

cumbersome for analysis. We therefore resort to the approximation that the

cylinder is electrically short, 2i«A . This approximation will be adopted

only for the optimization procedure, not for the computation of power or for

subsequent calculations. For ki«l we can write

J eff

R , * RAr,/3 , abs AC

R ~ 20 0 k

2 / r

X

r ~ -120 0 [ln(i/R) - 0.653].

Equation (6) then takes the form

9
2 2 2 2 2 7* (i E /24tt pCoR t ) { [ dr z 37raRt + 20 Q (ki)]

2 + (120 Q)

2

[ ln( 2 /R)

2 -1

- 0.653] } . ( 8 )

Equation (8) contains six parameters which can be adjusted to maximize

the rate of temperature rise: a, Z, R, t, p, and C. Not all six are independent, however. In practice, the choice of a will constrain the

achievable values of p and C, and could even determine them uniquely. The

relationship between C, p, and a for available materials is hopelessly

complicated. To keep the problem tractable, we will treat C and p as constant in the optimization process. This amounts to treating them as dependent variables of a and then neglecting the additional (implicit)

dependence on o that they introduce into eq (8)

.

Of the remaining four

variables, the optimum value for Z can be determined by inspection: the

larger Z is, the larger dT/dr is. Since we want to stay below resonance,

this fixes Z to be a little less than A/4 at the highest frequency, or A=0.67 mm.

Once these constraints are imposed, we are left with the problem of

maximizing a function of three variables, o, R, and t. Except for the

argument of the logarithm, R and t always appear in the combination Rt

.

Since the logarithm is a very slowly varying function for the range of

parameters we consider, as a first approximation it can be considered a constant in the maximization process. In addition to being a reasonable

approximation, treating R as a constant corresponds to the actual situation,

in which the cylinder radius is dictated by the radius of the temperature

sensor on which the resistive film is deposited. Letting s=Rt , the function

to be minimized is then

dT

dr

(s.ct) =

K

2

s a

Z 2 2-1

[ (^ + R ) + X

Z

] \ 37tcts r r (9)

where K, R and are all independent of s and a. The function in eq (9)

approaches infinity in the double limit s->0 first, then There is no extremum in the finite s -a plane. If we consider just the finite

rectangular domain sefs . ,s ] and oe\a . ,a 1, then the maximum of mm max

dT/dr over this domain occurs for

mm max

s = s mm

Z 222 2 2 -1/2

a = 77— {(20 Q k Z ) + (120 0) [ ln(i/R) - 0.653] } ' J7rRt

( 10 )

2 2 2 The value of a corresponds to the requirement that ^

a^ s=^r+^r

- Physically

what is happening is that for a fixed thickness and radius if o is made too

small then very little current is induced and very little heat is generated,

whereas if a is very large then the induced current is also large, but the

generated heat is again small because of the small ohmic resistance. The

10
optimum value of the conductivity is somewhere between the two extremes, and

it happens to be the value for which the effective ohmic resistance ( R

abs )

is equal to the radiation impedance of the cylinder. Thus, to maximize the

rate of temperature rise of the cylinder -- which with our assumptions is

the same as maximizing the power absorbed per unit volume --we should use

the smallest possible value of the product Rxt and then choose the

conductivity according to eq (10)

.

What then is the maximum rate of temperature rise that can be achieved?

For a given radius and thickness, the optimal conductivity can be computed

from eq (10) and then substituted into eq (9) to obtain the rate of

temperature rise. In figure 5 the rate of temperature rise in a 1 V/m, 40

GHz field is plotted as a function of the thickness t for fixed radius, R =

0.5 mm. Representative values for the optimal conductivity used to obtain

4 5 these rates are o=2

.

72x10 S/m for t=100 nm and ct= 2. 72x10 S/m for t=10 nm.

3 3 In obtaining these results, the values C=377 J/(kg K) and p=8xl0 kg/m were

used. These correspond to the approximate specific heat capacity and

density of bulk nichrome . Nichrome was considered the appropriate material

because the optimal conductivities were found to be close to the

conductivity of bulk nichrome. It should be noted that the conductivity of

thin- film nichrome is not necessarily equal to that of bulk nichrome. This

will be noted further in the discussion of the preliminary measurements.

The temperature rises displayed in figure 5 are not terribly encouraging.

Even if a coating thickness of 10 nm can be achieved, and if the optimal

conductivity is used, the temperature will rise at the rate of only 0.009

K/s in a 1-V/m field, which would be quite difficult to measure in a bulk

material, and almost certainly impossible in a thin film. A 10-V/m field,

however, would result in a 100-fold increase in the power absorbed and the

rate of temperature rise.

The amount of power absorbed by the resistive cylinder is also of

considerable interest, since once the cylinder has reached its equilibrium

temperature any power absorbed will be transferred to either the

surroundings (air, substrate) or to the temperature sensor. The power

absorbed, therefore, places an upper limit on the amount of power

transferred to the temperature sensor. In addition to the magnitude of the

power absorbed, we must know its frequency dependence. If the electricfield probe is to be frequency independent, the power absorbed must be

independent of the frequency of the incident radiation. In figure 6 we plot

the power absorbed by a resistive cylinder as a function of frequency for

4 S three sets of cylinder parameters: [a(S/m) , t(nm)] = (10 , 10), (10 ,10),

5 and (10 , 100), all with 2i=l mm and R=0.25 mm. In each case the

conductivity used is optimal given the values of R and t. The absorbed

power was computed from eqs (2-5). The electrical shortness approximation.,

eq (7), were not made in this computation. Instead, the full expressions

for the effective length and input impedance, eqs (3-5), were used. Firm.

6 contains good news and bad news. The good news is that a very flat

frequency response is predicted for a coating thickness of 10 nm . The !>.,.! news is that the amount of power absorbed is miniscule, about one half

11
nanowatt. This will probably be insufficient to heat the phosphor

appreciably. Furthermore, it may not be possible to obtain a film as thin

as 10 nm.

As an alternative to the resistive cylinder, we also consider a thin,

flat, resistive strip on a dielectric substrate. We do so because it may

prove to be a better configuration, and because it corresponds to the

geometry used in the preliminary measurements to be discussed below. The

expression for the power absorbed by such a resistive strip in an electric

field is the same as that for the resistive cylinder, eq (2), except that

the input impedance, , is different. Equation (4) holds as before, but

eqs (4) and (5) must be modified. For the resistive strip of length i,

thickness t, and width w, R is given by

A.L*

R

AC

21

CTWt (ID

King has shown [21] that for a cylindrical dipole of noncircular cross section the radiation resistance can be obtained from that of a circular

cylindrical dipole with an equivalent radius which depends on the dimensions

and cross sectional shape of the dipole of interest. For a very thin,

narrow, rectangular cross section the effective radius is one fourth of the

width. This is obtained by considering the thin rectangular cross section

as a highly eccentric ellipse, so that

R

eff ' 2 (a

e + V “ V2 - “/4 ' (12)

where a^ and b^ are the major and minor radii of the ellipse [21, 22], The

derivation of this result assumed that the width is much less than the

length of the dipole, which will not be the case in the applications below.

This approximation, therefore, is suspect, but we shall use it nonetheless

to obtain an indication of the size of the input impedance for the resistive

strip configuration. The approximate input impedance of the resistive strip

is given by eqs (3), (5), and (11), with the radius R replaced by the

effective radius of eq (12)

.

The power absorbed in an electric field can

then be computed from eq (2) and compared to the result for a circular

cylindrical dipole. Figure 7 plots the absorbed power in a 1-V/m field for

thin-film tubular and strip dipoles of two different thicknesses. The

length, thickness, specific heat capacity, density, and conductivity were chosen to be the same as in figure 6. The strip width was taken to be 0.5

mm, and the tube radius was R=(0.5/27r) mm so that equal amounts of material

are present in strip and tube.

Two features stand out in figure 7. The strip configuration absorbs more power, and it also has a flatter frequency response. Both effects are small for the 10 nm thickness, but are quite pronounced for 100 nm. Both

features are due to the smaller radiation impedance, particularly the

radiation reactance, of the strip as compared to the tube. The ohmic

resistance is the same for the two configurations, but for the tube the

12
radiation impedance is comparable to the ohmic resistance, whereas for the

strip the radiation impedance is considerably smaller. Consequently, the

tube has less current induced and less heat generated (since same ohmic

resistance). Furthermore, the power absorbed by the tube will also reflect

the resonant behavior of the radiation impedance and will therefore be more frequency dependent. Because of its slightly better behavior, we are led to

choose the rectangular strip configuration over the tubular cylinder as the

sensing component of the probe.

Thus far we have neglected the effect of the dielectric on which the

thin films are deposited -- the fiber filling the middle of the tubular

cylinder and the substrate on which the resistive strip resides. Ideally,

we would like them to have no effect on the response of the thin film, but

it is necessary to check whether this is the case. The effect of the

dielectric substrate on the power absorbed by a rectangular strip is the

easier of the two to analyze, and so we consider that case. The substrate

is assumed to have large transverse dimensions so that it can be

approximated by an infinite slab of thickness d. We wish to calculate the

field just outside the dielectric when a plane wave of amplitude E 0 is

normally incident. This is a standard problem in boundary- condition

matching, whose solution is

E = E 0 (1

6 - 1

€ + 1 + 2 ij e cotk '

d

), (13)

where k' is the wave number in the dielectric. To assess the size of this

effect, we plot in figure 8 p=E/E 0 for e=4 and 5, which are typical values

for glass. Two disturbing features are evident in figure 8. The dielectric

substrate decreases the field by as much as 60% at some frequencies, with a corresponding decrease in the minimum field level that can be detected.

Even more serious is the fact that the effect is frequency dependent. A

frequency variation of ± 4 dB or more, as in figure 8b), is unacceptable.

The permittivity of the substrate cannot be made small since we wish to

deposit the thin film on the tip of the temperature sensor. Therefore, the

only way to eliminate the frequency dependence introduced by the substrate

is to make it much thinner than a wavelength. This may be achievable by

using a tapered tip for the temperature sensor. If the thickness of the

dielectric cannot be made small, the frequency dependence evident in figure

8 would seem to rule out this design for a broadband probe.

A. 3 Exploratory Experiment

In the theory section above, we avoided detailed consideration of heat

transfer mechanisms and the actual rise in the equilibrium temperature of

the resistive structures in electric fields. To address this question, as well as to test the general feasibility of this approach, an experiment

designed and conducted. Rectangular strips (2 mm x 1 mm) of nichrome weir

deposited on 1-cm square slabs of glass. The thickness of the nichrome f : was not measured during deposition; it is believed to be between 10 and 1

nm. Two sets of samples were made, one with surface resistivities ram- i m; from 740 ft/sqr (i.e. the resistance across a square section is 740 h) t.>

13
Q/sqr, and the other with 3.1 to 3.9 kQ/sqr. Because the strips are so thin

the conductivity of the strip is not that of bulk nichrome , and the

thickness cannot be inferred from the surface resistivity. The glass

substrates are about 1 mm thick. The length and width of the strips were chosen to be about two to three times the dimensions which would be used for

frequencies up to 110 GHz. This scaling was done so that measurements in

the NBS anechoic chamber, which only extend to 40 GHz at present, could be

scaled up to the frequency range of interest.

The samples were irradiated with electric fields parallel to their

lengths, and their temperature was monitored by the fiber-optically sensed

temperature probe described above and in [18]. Initial measurements were

made in a small, portable, absorber- lined chamber at 20 GHz. No detectable

temperature rise was observed, even for field levels as high as 300 V/m

2 (24.35 mW/cm ). The sensitivity of the temperature sensor was limited by

fluctuations in the ambient temperature, which were approximately 0.3 K.

Additional measurements were made in the anechoic chamber at 16 GHz.

o With no incident field, the temperature was measured to be 22.5±0.4 C. For

o an electric field of 658 V/m, the temperature rose to 23.7±0.2 C. When the

field was turned off, the temperature fell back to its initial range. These

measurements were performed on a sample with surface resistivity 3.7 kQ/sqr.

A larger effect was observed with a sample with 780 Q/sqr. In an electric

o field of 662 V/m, the temperature rose to 23.5±0.4 C from an ambient of

21.510.2 °C.

To test whether the effect observed was due to the heating of the

resistive strip and not to the dielectric substrate, measurements were also

made on a plain glass slab without a thin film present. At 16 GHz, for a

o 658 V/m electric field, the temperature rose to 23.010.2 C from an ambient

o of 21.510.2 C. Comparing this with the results above indicates that the

entire temperature rise observed in the resistive-strip samples could have

been due to the generation of heat in the dielectric substrate rather than

in the thin film. We also tested the temperature sensor alone in the

electric field and observed no effect. This is to be expected since in the

experimental configuration the fiber of the sensor is oriented perpendicular

to the field.

In the measurements above, the time it took for the sample (with or without thin film) to reach its equilibrium temperature after the field was turned on was about one to two minutes. Such a slow characteristic time

indicates that it is the thermal mass of the glass, rather than of the film,

that is controlling the rate of heating. This fact is confirmed by other

measurements made with the infrared camera system of Professors Norgard and

Sega at the University of Colorado at Colorado Springs. This system has

sufficient resolution to see the temperature distribution across the sample,

showing whether the entire glass slab or only the resistive film is heating.

At field levels sufficient to heat the sample, it was observed that the

14
temperature of the entire substrate rose, indicating that either the heat

transfer between film and substrate was sufficient for the film to heat the

substrate, or that the substrate was heated directly from absorbed

radiation.

A. 4 Summary

The theory and results of preliminary measurements indicate that there

are several sizeable obstacles which must be overcome before this probe

design can be considered feasible. The overriding problem is to obtain an observable heating effect in the resistive strip for reasonable field

levels . Even if the heating effect observed in the measurements so far is

due in part to the resistive strip, which is possible but not certain, an improvement of about four orders of magnitude in (power) sensitivity would

be needed. Two ways in which an actual probe would achieve sensitivity

improvements over the preliminary experiments are clear. The present

temperature sensor is in principle capable of measuring temperature rises of

0.1 K, and improved models are expected to be able to measure 0.01 K, but

the measurements described above were limited by fluctuations in the ambient

temperature of order 0.3 K. In the probe design the resistive strip could

be thermally insulated from the ambient, thus eliminating these fluctuations

and allowing smaller temperature changes to be observed. Another tactic to

subtract the ambient- temperature fluctuations would be to use two

temperature sensors, one with the resistive film and one without. The

uncoated sensor would respond to ambient fluctuations, which could then be

subtracted, provided the fluctuations did not vary significantly over the

distance between the two sensors.

The sensitivity would also be increased due to the smaller effective

thermal mass of the probe configuration compared to the experimental setup.

2 In the experiment, the 2 mm thin film was in thermal contact with the 0.1

3 cm volume of glass substrate, whereas in a probe there would only be of

3 order 1 mm of optical fiber and phosphor to be heated by a film of about

the same surface area. Another possible source of increased sensitivity

would be improvements in the temperature sensor, which are quite possible.

If reasonable field levels can be made to produce observable effects,

the next problem would be to eliminate the frequency dependence introduced

by the dielectric on which the film resides -- the glass slab in the

experiment and the fiber in the actual probe. The obvious way to achieve

this would be to use a thinner substrate/fiber. It might also be possible

to reduce the effect by using a different geometry, such as a rectangular

strip on a wedge-shaped sensor tip, as mentioned earlier and shown in figure

4b) .

A problem which will remain, even if all the aforementioned

difficulties can be resolved, is the fact that this is a thermometric

design, and as such it is subject to the problems of all such designs:

variations in the ambient, drift during continuous use, and the like.

15
B. Other Unconventional Probe Configurations

In addition to the probe design described in the preceding subsection,

several other designs were considered and subsequently discarded. We note

them briefly here.

If a phosphor which would itself heat in an electric field could be

found, the probe design of Section III. A could be simplified to a strip of

phosphor whose temperature was monitored optically, eliminating the need for

the resistive strip and the problem of transferring sufficient heat from

strip to phoshphor to heat the phosphor. This avenue has not been explored

at this time.

The idea of a semiconductor probe in which the incident radiation would

raise additional electrons to the conduction band was dismissed because

characteristic thermal energies at room temperature are about 60 times

larger than the energy of a 100-GHz photon. Consequently, even if a material could be found with the correct band gap, the conduction band would

already be populated at room temperature

.

The birefringence of lithium tantalate crystals is temperature

dependent. By coating such a crystal with an absorptive material, one could

hope to measure the temperature change of the material in an electric field

by monitoring the birefringence of the crystal. One immediate problem would

be how to heat the entire crystal uniformly. If that could be overcome, the

sensitivity of such a device could be sufficient. For a crystal of 1 mm

length, we would expect a full cycle shift for a temperature rise of about 5 K. Since shifts of 0.01 of a full cycle can be detected, this would allow

detection of temperature changes of about 0.05 K, which is competitive with

other thermal detection methods, and which could be improved further by

detecting smaller fringe shifts. A thermometer based on this concept has,

in fact, been developed [23],

Another optics-based idea for thermal detection is to measure the

thermal expansion of a lossy material by use of a Fabry-Perot

interferometer. Again, however, the sensitivity does not match that of

other thermal detection methods. Using representative values for thermal

expansion coefficients and assuming an expansion of one tenth of a wavelength is detectable one concludes that a temperature rise of 16 K is

required to obtain a detectable expansion.

IV. SUMMARY AND RECOMMENDATIONS

Development of an electric - field probe to cover the frequency range 26-

110 GHz does not promise to be a simple task. The results obtained thus far

with the resistively tapered dipole design are encouraging, and it appears

probable that this design can be extended to cover the bottom of the

frequency range of interest, up to 30 or 40 GHz. Beyond that, however, the

picture darkens considerably. It is not clear that suitable high-frequency

broadband antennas and detectors are available commercially, which makes the

development of a conventional probe design for these frequencies very

16
difficult. The most promising unconventional design, based on the

optically- sensed temperature sensor, has major problems which must be

overcome before it can be considered a real possibility. Since there is a definite need for elec trie - field probes in the millimeter-wave range, we recommend the following.

1) The resistively tapered dipole design should be extended to the highest

frequency possible. This will involve fabrication of properly tapered 4- mm and 2-mm thin-film dipoles, identification and purchase of suitable

diode detectors, assembly of components, and testing, characterization,

and calibration of the units.

2) Efforts to obtain high-frequency broadband antennas commercially should

continue. If they can be obtained, their frequency response and

beamwidth need to be measured and suitable detectors obtained and tested

before final design of a probe based on the antennas can be done.

3) Investigation of the design based on the optically- sensed thermometer

should continue. The next step would be to make further measurement,

using thin-films on smaller substrates in a more stable thermal

environment. If these are successful, the choice of geometry

(cylindrical or rectangular strip) must be made, and a thin film should

be deposited on a temperature sensor and tested.

REFERENCES

[1] Larsen, E. B.; Ries , F. X. Design and calibration of the NBS isotropic

electric-field monitor (EFM-5), 0.2 to 1000 MHz, NBS Tech. Note 1033,

March 1981.

[2] Kanda, M. ; Driver, L. D. An Isotropic electric - field probe with

tapered resistive dipoles for broad-band use, 100 kHz to 18 GHz, IEEE

Trans. MTT-35, no. 2, 124-130, February 1987.

[3] Tell, R. A. Instrumentation for measurement of radiofrequency

electromagnetic fields: equipment, calibrations, and selected

applications, in Proceedings of a NATO Advanced Study Institute in

biological effects and dosimetry of low energy electromagnetic fields,

M. Grandolfo, S. Michaelson, and A. Rindi, eds . New York: Plenum,

1983.

[4] Batchman, T. E.; Gimpelson, G. An implantable electric - field probe of

submillimeter dimensions, IEEE Trans. MTT-31, no. 9, 745-751,

September, 1983.

[5] Wu, T. T.; King, R. W. P. The Cylindrical antenna with nonreflecting

resistive loading, IEEE Trans. AP-13, no. 3, 369-373, May 1965.

[6] Kanda, M. A Relatively short cylindrical broad-band antenna with

tapered resistive loading for picosecond pulse measurements, IEEE

Trans. AP-26, no. 3, 439-447, May 1978.

[7] Hopfer, S.; Adler, Z. An Ultra broad-band (200 kHz-26 GHz) highsensitivity probe, IEEE Trans. IM-29, no. 4, 445-451, December 1980.

[8] Aslan, E. Broad-band isotropic electromagnetic radiation monitor, I i. Trans. IM-21, no. 4, 421-424, November 1972.

17
[9] Hopfer, S. The Design of broad-band resistive radiation probes, IEEE

Trans. IM-21, no. 4, 416-421, November 1972.

[10] Randa , J.; Kanda, M. Multiple - source , multiple - frequency error of an electric field meter, IEEE Trans. AP-33, no. 1, 2-9, January 1985.

[11] Chang, J., ed. High bandwidth analog applications of photonics, Proc

.

SPIE 720, 1970.

[12] Hall, P. S.; Wood, C.; Garrett, C. Wide bandwidth microstrip antennas

for circuit integration, Electronics Lett. 15, no. 15, 458-460, July

1979.

[13] Suzuki, Y. ; Miyano , N.; Chiba, T. Expanding the frequency bandwidth of

a microstrip antenna, IEEE AP-S 1981 International Symposium Digest,

366-369, June 1981.

[14] Sabban, A. A New broadband stacked two -layer microstrip antenna, IEEE

AP-S 1983 International Symposium Digest, 63-67, May 1983.

[15] Dyson, J. D. The Equiangular spiral antenna, IRE Trans. AP-7, 181-187,

April 1959.

[16] Rumsey, V. H. Frequency independent antennas. New York, NY: Academic

Press, 1966.

[17] Deschamps, G. A.; DuHamel, R. H. Frequency- independent antennas, in

Antenna Engineering Handbook, ed. H. Jasik; New York, NY: McGraw-Hill,

1961.

[18] Wickersheim, K. A.; Sun, M. H. Flouroptic thermometry, Measurement and

Control, p. 132, June 1987.

[19] Martin, V. M. ; Sega, R. M. ; Durham, R. Fiber optic microwave power

probe, Optical Eng. 26, no. 2, 170-173, February 1987.

[20] Randa, J. Reflection and absorption properties of a sparse, planar,

random array of lossy wires; unpublished report to sponsor, January

1987.

[21] King, R. W. P. Chapter 1 in The Theory of linear antennas. Cambridge,

MA: Harvard University Press, 1956.

[22] Elliot, R. S. Chapter 7.12 in Antenna theory and design. Englewood

CLiffs, NJ: Prentice-Hall, 1981.

[23] Cetas, T. C. A birefringent crystal optical thermometer for

measurements of electromagnetically induced heating, in Biological

effects of waves, Vol. II, C. C. Johnson and M. L. Shore, eds

.

Rockville, MD : HEW Publ. (FDA) 77-8011, 1977, pp. 338-348.

[24] Pistolkors, A. A. The Radiation resistance of beam antennas, Proc.

I.R.E. 17, no. 3, 562-579, March 1929.

[25] Stratton, J. A. Chapter 8 in Electromagnetic theory. New York, NY:

McGraw-Hill, 1941.

[26] Jordan, E. C.; Balmain, K. G. Chapter 14 in Electromagnetic waves and

radiating systems. Englewood Cliffs, NJ : Prentice -Hall , 1968.

[27] Einarsson, 0. Chapter 12 in Electromagnetic and acoustic scattering by

simple shapes, J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi,

eds. Amsterdam, The Netherlands: North Holland, 1969.

[28] Cassedy, E. S.; Fainberg, J. Back scattering cross sections of

cylindrical wires of finite conductivity. IRE Trans. AP-8, no. 1, 1-7,

January 1960.

18
APPENDIX

We consider a hollow, circular cylinder of length 2i and radius R, with

a thickness t and conductivity a (fig. 9). The radius is much smaller than

the length and the wavelength of the incident radiation and is much larger

than the thickness: A, 2i » R » t. To treat the scattering from and

absorption by such a cylinder we assume a sinusoidal current distribution

along its length,

I(x) = I sin[k(i - | x | ) ] , (A.l) m

and use a simple algebraic method to compute the amplitude of the induced

current, I , or equivalently the current at the midpoint of the cylinder,

1(0). The simple algebraic method (SAM) is based on the EMF method, as found, e. g., in [24-26]. The current at the midpoint of the wire, 1(0), is

the short-circuit current for a receiving dipole. It is given by

1(0) =

Ex L

eff , (A. 2)

Z.m

where is the component of the incident field parallel to the dipole, cf.

figure 9b) , and we have assumed that the incident field does not vary along

the length of the dipole. Z ^

is the input impedance of the dipole used in

the transmitting mode, and L ^

is the effective length. The effective

length is given by

L

eff I(x) dx

2 (1 - cos ki)

k sin ki (A. 3)

The input impedance Z^ has three components -- the radiation resistance, the

radiation reactance, and a contribution from the ac resistance. The

radiation resistance (R^) and reactance (X ) of a center- fed tubular dipole

with sinusoidal current distribution are well known [26],

R

r = (2(1 + cosb) S

x (b) - cosb S x (2b) + sinb [Si(2b)

s in ki

- 2 Si(b) ] )

,

{sinb [-7 + ln(~^) + 2 Ci(b) - Ci(2b)]

sin ki kR

- 2(1 + cosb) Si(b) + cosb Si(2b)},

(A. 4)

where

19
b = 2ki, k = 2n/\ , 7 = 0.5772147

The sine and cosine integrals have convenient series representations (for

computational purposes)

,

c • / N C sin V , S ( -1) Si(x) = J dv = E

o

n 2 n+l v n=0 ( 2 n + 1 )

(

2 n + 1 ) !

’

x i i

N

n 2n

c / n r 1 - cos v « (-1) x

S x (x) = J dv = - E, v n=l 2 n ( 2 n) !

’

Ci(x) = - J ~ dv = In x + 7 - S 1 (x)

(A. 5)

Use of eq (A. 5) allows us to simplify the expression for slightly,

10 (1 2 2 x = - 2

{ sinb [ ln(T /R )

- 2 S^b) + S 1 (2b)] - 2(1 + cosb) Si(b)

r sin kZ + cosb Si(2b)}. (A. 6 )

Because we shall be dealing with cylinder thicknesses that are much

smaller than the skin depth at the relevant frequencies, the ac impedance

per unit length of the cylinder is entirely resistive and is given by its dc

value

,

1_

2i

R

AC

1 <727rRt (A. 7)

R cannot be added directly to the radiation input impedance. R relates

AC. AC

current to voltage for a uniform current distribution, which is not the

present case. The voltage drop across the length of wire for the current

distribution given in eq (A.l) is

Ay = J (JJRac

) I m sin[k(i - |*|)] dx

2 RAC (1 ' 2k£

Sln 2ki)

1(0) R

abs ’

where

Rabs - rac 7“y- (1 - 517

2 sin kf

(A. 8 )

(A. 9)

20
Since Z. relates the voltage applied at the terminals of the dipole to the

in

input current 1(0), R , is the contribution to Z. from R . We can

r abs m At

therefore write Z. as m

Z. = R , + R + i X , (A. 10)

in abs r r

with R , X , and R , given by eqs (A. 4) and (A. 9).

r r abs °

Having determined L eq (A. 3), and Z^, eq (A. 10), we know 1(0) from

eq (A. 2) for a given incident field E . That enables us to write the power

absorbed and power scattered by the resistive tubular cylinder,

P

scat 2

I no) I

2 R

r

1

2

2 2 E

R

r

abs

1 ( 0 ) R

abs

2 2 E L

1 x eff

Z.m1

R

abs

(A. 11)

The scattered power is the power that is reradiated by the current induced

in the cylinder, and the absorbed power is the power dissipated in ohmic

heating. The powers in eq (A. 11) are time averages, whereas E^ is the

amplitude of the x component of the incident wave. Note that although the

expressions for L ^ Z. , R , and R , all diverge for sin ki -*• r 0 , they eff m r abs &

enter eq (A. 11) in such a combination that the powers remain finite.

Equation (A. 11) is what we shall need in our analysis of the heating of

a resistive cylinder. Before using the model, however, we should check that

it is reasonable. To do so, we use the model to calculate the radar cross section (RCS) of resistive wire and compare it to published results, both

experimental and theoretical. A review of the RCS results for lossless

wires can be found in Einarsson's chapter of [27], which also contains

references to the original papers. Figure 10 (taken from figure 12.8 of

[27]) represents theoretical and experimental results of interest to us. The curves represent calculation results, and the circles are measured

points. The quantity L is defined as I-kSL/X, so that the resonances at L

(2n + 1 )tt/ 2 correspond to 2H = (2n + l)A/2. The general features are clear:

2 a first resonance at 2i ~ A/2, with a peak value of a/A = 0.8-0. 9, followed

2 by a plateau with a/A = 0.1-0. 2, a second resonance at 2i = 3A/2

,

a second

(higher) plateau, and so on. Calculations and measurements have also been

done for lossy wires [28], In figure 11 we reproduce their figure 10, which

plots the RCS for lossless wires (theory) and for a particular lossy wire

(theory and experiment). The lossless result resembles that of fir, nr.- !

21
as it should, and for the lossy wire theory and experiment agree quite well.

The lossy wire that was used had an ac resistance of 2800 Q/m. For a resonant length of 2$. = 5 cm (3 GHz), the wire had a resistance of 140 Q.

The effect of the resistance is to decrease the resonant RCS by a factor of

about four. In addition, the resonance becomes broader. These two trends,

the resonance becoming lower and broader, continue as the resistance is

increased, until the resonance is washed out altogether.

We now turn to calculations of the RCS using the simple model described

above. The RCS is defined as the effective area required to intercept an

2 o amount of power equal to 4ttR times the backscattered ( 9 = 180 ) power per

unit area for a given incident field,

RCS lim

dP

dA

(9=n)

R-t-co

( —

)

dA' me

2 x 47rR . (A. 12)

2 (The quantity 47rR times the backscattered power per unit area is just the

total power scattered assuming isotropic scattering.) Equation (A. 11) gives

the total power scattered by a (tubular) wire; to obtain the RCS we need

only relate that to the power density scattered back to the source. The

angular distribution of the power radiated or scattered by an electric

dipole is

dP

dA (r

z

7T c COS (-COS0)

2 2 > r sin 6

(A. 13)

where C is related to the total scattered power by integrating over the

surface of the sphere,

P scat

f 77 dA = 4tt (0.6093) C . J dA (A. 14)

Equations (A. 13) and (A. 14) can be used in eq (A. 12) to write the RCS in

terms of the total scattered power for an electric dipole,

RCS

P scat

dP

0.6093(77)

.

dA me

(A. 15)

Using eq (A. 11) for P and writing the incident power density in terms

s c a 1

1

of the incident electric field, we have

(^) v dA' inc

1 Ei 377 fi,

(A. 16)

22
RCS = 1.641 L

eff

2

Equation (A. 16) is the expression for the RCS of a tubular cylinder in our

SAM, with R and determined by eqs (A. 5), (A. 9), and (A. 10) and by

eq (A. 4). To compare to the results of figure 11, we use a cylinder radius

of 12.7 j^m. This is the same as was used in obtaining figure 11, so that

capacitive effects will be the same. The material of the cylinder is taken

to be silver (a =6.17 x 10^ S/m), and a thickness of 72.5 nm is used. This

yields a fiber with an ac resistance of 2802 £1/m, compared to the 2800 12/m

bismuth wire used in figure 11. To generate predictions for the lossless

case, we assume a solid silver wire of radius 12.7 fim, by taking 27rRt -> 7tR in eq (A. 7). This yields a wire with 32 fi/m, which is close enough to

lossless for our purposes. Figure 12 displays our predicted RCS for these

two cases, which should be compared to the curves of figure 11. The

agreement is excellent for both the lossless and the lossy cases. The

location, height, and width of the resonances all agree very well with the curves in figure 11, which represent the results of more exact calculations

and of measurements . The success of the SAM in predicting the RCS for both

the lossless and the lossy wires gives us confidence in its ability to

predict scattering and absorption of lossy wires with different parameters.

We should note the limitations of the model in predicting the RCS of

wires. If we consider higher frequencies than those represented in figs. 11

and 12, problems are encountered. In particular, a spurious maximum occurs just above 2,0/A = 1. Consequently, the model should not be used above about

22/A =0.8. It can, however, be trusted through the first resonance, for

the location and strength of that resonance, and for the height of the

plateau after the resonance.

2

23
Diode

Bonding

Pads c

05

54

COwco

•rHcnc

a)e

•rH Q4-> C

05E

<u o

cx

•rH X)

X3

a)54

<uex

cO

W

4-1 Q) X, <J pH C

ai •H >

•t—1

X)

4-1 c

CO cfl •rH — w

05

w

5-1 5-1 <u P 4-5 £ ai i E

oo •rH

T—H

a) r-H rC • rH H E

a)

5-4 3

DO

•H

Ct,

24
Frequency

Response

of

4-mm

Resistively

Loaded

Dipole

25

Frequency

response

of

a

4-mm

resistively

loaded

dipole.
Figure 3a) Angular pattern of 4-mm resistively loaded dipole at 20 GHz.

The abscissa is the angle between dipole axis and direction of

the incident plane wave.

G 90 18G 270 36G

Figure 3b) Angular pattern at 30 GHz.

26
Phosphor

27

Figure

4

Two

resistivefilm

configurations

considered.

a)

Cylindrical

coating.

b)

Resistive

strip.
(K/s)

0.02

0.01

0.005

0.002

M H

0.001

0 20 40 60 80 100

t(nm)

Figure 5 Calculated rate of temperature rise for resistive tubular cylinder

in a 1-V/m 100-GHz field, as a function of cylinder thickness.

The optimal conductivity was used for each thickness and the

cylinder radius was 0.5 mm.

28
oo

oCT>

Ooo

o

o

CD

o

in

o

o

00

((mu)ap)sqBd

29

Figure

6

Calculated

power

absorbed

by

a

tubular

cylindrical

dipole

in

a1

V/m

field

as

a

function

of

frequency

for

three

different

choices

of

thickness

and

conductivity.

The

radius

and

full

length

in

each

case

were

0.25

mm

and

1.0

mm,

respectively.
oo

05Oooo

1^o

COomoboo

(Mu)sqB

d

30

Figure 7

Comparison

of

the

powers

absorbed

bya

resistive

tubular

cylinder

anda

resistive

strip

of

the

same

thickness

and

surface

area.
o 0

to ^H T> H C o m ia g

as s-i ^ o o o

tO 3 *t“1

4-1 x:

tO 4-> <v X ME *-> C E

•H

•U E r-H

to 3

CO <u T) co jQ i—1

to (0

O

•rH - 4-> 4-1 >-a ’ TJ

4J c - c <u E

<0 3 3

X) cr to •M a) CO o S-l to c 4-1 •H co 4-1 •M 4-1 0) O c X J2 (V 4J c CO 4J o | X o •H to (V •u •uu a) (V TJ c — to r—< 3 H S-I as 4-1 (V •M >

4-( to CO (V c

»—4

CO > to

cfl to to 4J

4J 5 O -Q

V

M to IV 60 G s-l <v co (0 to JZ •— r-1 u o —

•M Cm M jj O u c IV o <v > o a> o

•M rH '»M IV M <u u >

cfl •M c <0 a: TJ lp^ (jC

tO oo

0)

60 L

31
32

Figure

8b)

As

in

figure

8a),

in

dB

.
Figure 9a) Dimensions of resistive tubular cylinder.

A

X

Figure 9b) Geometry for scattering from cylinder.

33
(a) (b)

Figure 10 RCS of a single perfectly conducting wire as a function of L =

InH/X. Curves represent different calculations; circles are measurement results. Taken from [27].

34
Figure 11 Calculated and measured RCS for a lossy wire. Taken from [28\

35
Figure 12 RCS for lossless (continuous curve) and lossy (dashed curve)

wire, computed using SAM.

36
HBS-1 1 4A [REV. 2- U.S. DEPT. OF C O MM

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 88-3084

2. Performing Organ. Report No, 3. Publ i cation D ate

February 1988

4. TITLE AND SUBTITLE

POSSIBLE DESIGNS FOR ELECTRIC-FIELD-STRENGTH PROBES FOR MILLIMETER WAVES

5. AUTHOR(S)

J. Rartda, M. Kanda, and D. Melquist

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s)

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)

Naval Ocean Systems Center

San Diego, CA 92152-5122

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)

Various designs are considered for electric-field probes for the frequency range

26-110 GHz. Two particular designs are investigated in some detail. A resistively

tapered dipole antenna with a diode detector shows promise for frequencies up to

about 40 GHz. The second design is based on a f iber-optically sensed temperature

sensor to detect the heating of a resistive strip. If its sensitivity can be

increased significantly, this design may be capable of operating to frequencies

above 100 GHz. 12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate

electric-field probe; flouroptic temperature sensor; millimeter waves; resistive!

tapered dipole.

13. AVAILABILITY

ly~l Unlimited

| 1 For Official Distribution. Do Not Release to NTIS

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

20402.

|X1 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

40

15. Pr

A U.S. GOVERNMENT PRINTING OFFICE 1988—574-717 85.101 REGION NO 8