National Aeronautics and Space Administration

Langley Research Center • Hampton, Virginia 23681-0001

NASA Technical Memorandum 4694

Reflectometer Distance Measurement Between

Parallel Conductive Plates

Chase P. Hearn and Robert T. Neece

Langley Research Center • Hampton, Virginia

November 1995
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Introduction

Microwave reflectometry can be used to make distance measurements between a directional antenna and a

reflecting target. Distance is derived from the complex

reflection coefficient, Γ(ω, d), which is measured at the

input of the antenna and is a function of both distance d

and the radian frequency ω. Such a technique was proposed and developed for measuring the “stand-off” distance between the highly ionized plasma that occurs in

front of the heat shield of a reentry vehicle. In this application the plasma may form a highly conductive target

parallel to the metallic spacecraft skin. This paper considers the measurement problem in which the reflectometer target is a highly conductive surface parallel to the

antenna ground plane, as illustrated in figure 1. These

parallel surfaces constitute a parallel-plate waveguide

(PPWG) which can contribute parasitic perturbations to

Γ(ω, d) that, if ignored, seriously degrade the accuracy of

reflectometer measurements (ref. 1). Two distinct PPWG

phenomena are described, and their effects on both frequency and time-domain reflectometers are discussed.

Techniques for defeating these deleterious mechanisms

are presented. Experimental results (of measurements

made in a controlled PPWG environment) are presented

that yielded distance-measurement accuracies on the

order of 0.025 cm (0.01 in.) after the application of these

corrective measures.

Symbols

c velocity of propagation

d distance

du unambiguous full-scale range

d0 fixed distance

F(ω) transfer function

f frequency

f (t) inverse Fourier transform of F(ω)

g(t) impulse response

k multiplicative constant

M magnitude of Γ

m an integer, 1, 2, 3, ...

n an integer, 1, 2, 3, ...

Sinc ( ) sin ( )/( )

Tp propagation time delay,

Vi (i = 0, 1, 2, ...)

W(ω) rectangular frequency domain window ∆ω

wide centered at ω0

X,Y,Z axial coordinates

β imaginary part of complex propagation

constant

Γ(ω, d) complex reflection coefficient dependent on

radian frequency and distance

λ wavelength

λ0 wavelength of ω0

ω radian frequency

ωm radian frequency of modulation signal

ω0 constant radian frequency

Φ(ω, d) phase of Γ(ω, d)

ΦD differential phase between signals at ω0 − ωm

and ω0 + ωm

dΦ

dω –-------

Abstract

This report presents an analytic and experimental investigation of the measurement problem in which a reflectometer is used to determine the distance to a target

that is a highly conductive surface parallel to the reflectometer antenna ground plane.

These parallel surfaces constitute a waveguide (WG) which can contribute parasitic

perturbations that seriously degrade the accuracy of the measurements. Two distinct

parallel-plate-waveguide (PPWG) phenomena are described, and their effects on

both frequency and time-domain reflectometers are considered. The time-domain processing approach was found to be superior to a representative frequency-domain

phase-measurement approach because of less susceptibility to perturbations produced by edge reflections and immunity to phase capture. Experimental results are

presented which show that a simple radiating system modification can suppress

parallel-plate (PP) propagation. The addition of a thin layer of lossy mu-metal “magnetic absorber” to the antenna ground plane allowed a measurement accuracy of

0.025 cm (0.01 in.) when a vector network analyzer (VNA) is used as a time-domain

reflectometer.
2

Abbreviations:

CW continuous wave

PP parallel plate

TEM transverse electromagnetic

TM transverse magnetic

VES vector error subtraction

VNA vector network analyzer

WG waveguide

Ideal Reflectometer Concept

A reflectometer distance measurement is based on

transverse electromagnetic (TEM) wave propagation

along the Z-axis (fig. 1). With no reflections except the

one from the plate and with no parallel-plate (PP) propagation, the phase of Γ(ω, d) at the aperture plane is a linear function of frequency and plate spacing, ω and d,

given by

(1)

where β is the imaginary part of the complex propagation constant, λ is the wavelength, and c is the velocity

of wave propagation. A fixed-frequency (ω = ω0) reflectometer distance measurement based on Φ(ω0, d)

becomes ambiguous when d > λ/2 and Φ exceeds 2π.

When d < λ/2, only the TEM mode can propagate along

the X- or Y-axis and contribute to Γ(ω0, d). This propagation mode is often ignored in theoretical models because

energy loss via radiation is very small if the aperture

diameter is at least 1λ (refs. 2 and 3); the measurement of

d through Φ(ω, d) is nearly ideal.

Multiple Z-Axis Reflections

In practice, additional Z-axis reflections will occur,

as indicated in figure 2. The “local” or first aperture

plane reflection V0 and multiple reflections between the

plates (with V2 the largest) contribute to Γ(ω0, d). The

magnitude and phase functions become nonlinear in d

and vary about −2ωd/c with λ/2 periodicity (refs. 3

and 4). The local reflection V0 remains constant as d

increases, while V1 and the multiple reflections decrease.

Thus V0/V1 increases and V2/V1 decreases with d.

Parallel-Plate-Waveguide Effects

When d > λ/2, a modulated excitation signal can

eliminate ambiguity, but PPWG propagation occurs

along the X- or Y-axis. This PPWG propagation affects

Γ(ω) and a distance measurement. The effect of PPWG

propagation on Γ(ω, d) has been well documented for

fixed-frequency (ω = ω0) excitation of infinite parallel

Φ ω( ) , d – 2 2βd 2π

λ

------     – d 2ωd

c == = –----------

plates (refs. 1 and 2). It was shown that energy is most

efficiently radiated from such systems at plate separations within about ±λ0/8 of

(2)

and that radiation is ideally zero at the “critical points”

that are defined by equation (3).

(3)

With ω constant, variations in the magnitude and

phase of Γ(ω0, d), which are periodic in λ0/2 are

observed as d is varied (as sketched in fig. 3). Similar

behavior is observed in Γ(ω, d0), with d fixed and ω varied. The latter case, with ω variable, is of interest here

because it is applicable to measuring distances greater

than λ/2.

Each critical point corresponds to the introduction of

a new PPWG transverse magnetic (TM) mode (ref. 1). At

those points, the new mode in the waveguide (WG) channel presents such a poor match to the aperture plane that

the incident wave is largely reflected and radiation is

squelched. With d fixed, varying f changes λ. As equations (2) and (3) are alternately satisfied, Φ(ω, d) and

M(ω, d) ≡ Γ(ω, d) exhibit large periodic variations as

the 1-way electrical path length changes by λ/2. Thus,

PPWG propagation imposes a characteristic “signature”

(modulation) on Γ(ω, d). This modulation is periodic in

λ/2 and much larger than the modulation that is produced

by Z-axis multiple reflections. These effects are demonstrated in figure 4. Removal of the ground plane eliminated the PP propagation channel and reduced the λ/2

variations in M(ω0, d) from 17 to 3 dB at d = 20 cm.

Although PPWG propagation and Z-axis multiple reflections disturb Γ(ω, d) with the same periodicity, the wave

forms are quite different. Figure 5 compares a typical

PPWG response (ref. 2) with the computed vector sum of

a primary reflection plus the first multiple reflection (corresponding to V1 and V2 in fig. 2).

In theory the PPWG signature intensifies as d and

the number of WG modes increase; however, this

increase is partially offset in practice by reduced peaks in

M(ω0, d), as illustrated in figure 4. Reduced deviation of

Φ(ω, d) from linear was observed to accompany a reduction of PPWG variations in M(ω, d).

Edge effects in finite PP fixtures produce the rapid

fluctuations (“trough ripple”) in Γ(ω0, d) evident in figure 4 and which can affect a distance measurement. Just

above its cutoff, the electrical length of a WG for a new

mode is very sensitive to d or f. Wave propagation along

the X- or Y-axis in a PPWG is highly mismatched near

d ( ) 2m + 1

λ0

4

-----     = ( ) m = 123 ,,, ...

d n

λ0

2

-----     = ( ) n = 123 ,,, ...
3

WG cutoff (ref. 5). Reflections at the edges of a PP fixture impose a series of “resonant loops” on Γ(ω, d)

between critical points. Figures 6 and 7 are from a narrow span which includes only two critical points to illustrate these effects. Dispersion in the interconnecting WG

(and horn) and the linear-phase term were empirically

removed from Φ(ω, d) by using processing features of

the Hewlett Packard (HP 8510C) vector network analyzer (VNA). The result shows the remaining deviations

of Φ(ω, d0) from linear.

Resonant loops occur when the PPWG presents a

high shunt conductance to the aperture plane. This shunt

conductance strongly modifies the aperture plane admittance produced by Z-axis transverse electromagnetic

(TEM) propagation. Complementary (low-conductance)

resonances have relatively little shunting effect on the

Z-axis response. The loops may be over coupled (encircling the origin) or under coupled (nonencircling), as in

figure 6 and impose step changes on Φ(ω, d0) and large

impulsive “spikes” on the phase delay −dΦ/dω, as is evident in figures 7(a) and 7(b). If the trough ripple is

ignored, figures 7(a) and 7(b) show the same general

behavior that is sketched in figure 5. Therefore, distance

measurements where d > λ/2 based on Φ(ω, d0) or dΦ/

dω are affected adversely by PPWG propagation in a

way that cannot be completely “averaged out.”

In summary, the impediments to making accurate

distance measurements beyond d = λ/2 with a PP reflectometer are (a) local reflections from the aperture plane,

(b) multiple reflections between the reflecting plate and

the antenna, and (c) two PPWG propagation effects. All

impart nonlinearity to Φ(ω, d) that is periodic in λ/2. In

addition, dispersion in the interconnecting waveguide

adds additional phase nonlinearity.

Local reflections can be negated with a tuner at the

input port in a fixed-frequency system (ref. 2). Vector

subtraction of the “free-space” response (with no reflecting plate) from a measured response, defined here as

vector error subtraction (VES), can negate the contribution of local reflections to Γ(ω) over the operating bandwidth of a modulated system—provided the system is

linear in the sense that if input x produces output y, then

input kx produces ky. More complex error-correcting calibration schemes have been developed that effectively

compensate for both Z-axis multiple reflections and local

reflections (ref. 6).

Numerous systems that have different modulation

formats are applicable to making distance measurements

when d > λ/2. Some systems are less susceptible than

others to PPWG effects. This difference is shown here by

a comparison of two approaches: a frequency-domain

phase-measurement approach and the inverse Fourier

transform time-domain approach that is used in modern

VNA’s.

Frequency-Domain Approach

A simple way to extend unambiguous range in the

phase-measurement approach is to use double sidebandsuppressed carrier modulation (at ω = ωm) to generate

two continuous wave (CW) signals separated by 2ωm and

measure the differential phase ΦD that is accumulated by

those signals in traversing the path to and from the

reflecting plate (ref. 7). In the ideal case of a reflection

from one target in a nondispersive media, the phase

difference,

(4)

can be determined without ambiguity when 0 < ΦD < 2π.

It can be seen in equation (4) that ΦD/2ωm is the two-way

time delay Tp.

For an unambiguous full-scale range of du, ΦD = 2π

and ωm is given by

(5)

This approach was found to be highly vulnerable to

the effects described previously, and the approach performed poorly in a PP configuration. The phase nonlinearity associated with each sideband caused large

variations in ΦD(ω0, d) around the value given by equation (4). An analysis of two constant-amplitude reflections predicted a phase error given by

(6)

(See ref. 4.) This expression has the same compound

periodicity related to ω0 and ωm that is observed in laboratory experiments. It was also shown that sweeping the

carrier frequency across a bandwidth ∆ω >> ωm and

averaging the resulting phase measurements reduced

phase error by the factor Sinc(∆ωd/c) (ref. 4). This

reduction was verified experimentally by stepping the

carrier over 51 points within a band ∆ω = 10ωm (ref. 6).

Examination of phase and phase-delay measurements from several different PP laboratory fixtures

revealed that fluctuations in Φ(ω, d) and dΦ/dω that

were produced by edge reflections were seldom zero

mean and hence could not be eliminated completely by

averaging. The limited value of averaging is believed to

be one weakness of this approach to distance measurement in a PP environment. Another weakness is that

amplitude limiting, normally used in a phase-only

measurement approach, makes VES inapplicable. This

ΦD ( ) IDEAL

2ωm

2d

c

-----     2ωmT

p = =

ωm ( ) u

πc

2du

= --------

ΦD 4ωm

d

c – --     k 2ωm

d

c

--     2ω0

d

c

--   ≈ sin cos  + ...
4

inapplicability is a severe limitation if the local reflection

is sizable compared with the primary reflection, as

occurs when the horn aperture is covered with a highly

reflective dielectric heat shield (ref. 7). The phasemeasurement approach described here is not linear, making VES inapplicable; signal-to-interference ratios of

0 dB result in “phase capture” by the interfering signal,

and the average phase delay of the combined signal

becomes the one that is associated with the interference

instead of with the primary response. It has been shown

that a periodicity related to the primary response remains

in Φ(ω) after phase capture. That periodicity can be

exploited to extract target distance in the presence of the

larger interfering response (ref. 8).

Time-Domain Approach

Measured frequency response data that are obtained

from a real system (either continuous or discrete) over

the interval (ω2 − ω1) = ∆ω define a “transfer function”

F(ω), which is assumed to be zero elsewhere. (No physical system can have such a transfer function which produces an output before the input is applied.) The inverse

Fourier transform f (t) of the physically unrealizable

transfer function F(ω) is then computed. This “time

response” would result if a unit impulse was applied to

the input of a system having the frequency response

function F(ω). The time-domain approach differs from

the previous approach because it is linear with respect to

the amplitude of the reflected signal and uses both the

magnitude and phase of Γ(ω). Thus, VES can be used to

negate local reflections.

A unit impulse that passes through a purely real, uniform band-pass “window” function W(ω) having a value

of unity within the bands ±(ω0 ±ω/2) and zero elsewhere

produces the output:

(7)

Thus, f (t) can be interpreted as the response that

Sinc-pulse excitation of the real system would produce.

The output response of a system that has a transfer function with constant magnitude M and linear phase across

∆ω (simple weighting and delay) to g(t) is Mg(t − Tp),

where Tp is the time for a pulse to propagate through the

system −dΦ/dω. The location of the output-pulse peak

t = Tp can be converted to distance if the propagation

velocity in the medium is known. In the time-domain distance measurement approach, Γ(ω, d0) can be thought of

as the transfer function between the reflected and forward voltage waves, with Tp the round-trip propagation

time 2d/c. When Γ(ω, d0) is inverse transformed, reflections V0 and V2 (fig. 2) produce interference pulses that

are separated from the primary pulse by multiples of Tp.

g t( ) 2∆f Sinc ∆ωt

2

---------     ω0 = cos ( )t

Figure 8 is the corresponding time-response measurement, without linear phase or dispersion extraction, from

which figures 6 and 7 were generated. Figure 9 is the

same case with linear phase and dispersion extracted.

The secondary reflections are easily identified. Increasing ∆ω sharpens the time responses and increases timedistance resolution. The time-distance discrimination and

linearity characteristics of this approach allow it to operate in the presence of local interference reflections that

are larger than the primary response. This discrimination

requires that Tp = 2d/c exceed 2/∆f, which is clearly true

in figure 8.

The theory of pulse distortion in linear networks can

be used to explain how phase and amplitude fluctuations

in Γ(ω, d), caused by secondary Z-axis reflections, PP

propagation, and dispersion affect the location and

amplitude of the time response to a hypothetical Sincpulse input. Although the infinite plate PP signature is

not a reflection phenomenon, it influences the amplitude

and location of the time response much the same as multiple reflections do.

Periodic variations in either M(ω) or Φ(ω) that are

caused by multiple reflections, PPWG propagation, and

dispersion give rise in the inverse transform to “echopulse” pairs which have the same envelope function as

the undistorted output pulse Mg(t − Tp), but which are

displaced symmetrically around Mg(t − Tp) by integral

multiples of a factor k which defines the “periodicity” of

the frequency-domain variations (ref. 9); that factor is Tp

for the variations caused by multiple reflections and

PPWG propagation and is therefore d dependent.

Uncorrected phase dispersion in the interconnecting

waveguide, transition, and horn also introduces nonlinearity to Φ(ω)—unrelated to Tp—which must be

largely eliminated either in hardware or software. When

the phase curvature that results from uncorrected dispersion exceeds approximately a radian at the band edges

of Φ(ω), relative to midband, the time response becomes

noticeably smeared, the side-lobe levels increase, and

side-lobe symmetry and null depth are reduced, as illustrated in figures 8 and 9. It will be shown that odd-order

dispersion produces a fixed-time shift of the envelope

peak. These effects did not discernibly degrade the accuracy of time-domain measurements when the total residual dispersion did not exceed a radian; however,

dispersion on the order of 4 to 5 rad significantly

degraded measurement accuracy.

In a physically realizable, time-invariant linear system, variations in M(ω) are accompanied by variations in

Φ(ω). Both variations contribute to time response; their

combined effect is to reduce one echo pulse and increase

the other. The side lobes of the echo-pulse envelopes

interact with the main lobe of the primary pulse to
5

produce a sum response in which both the amplitude and

position of the envelope peak can vary, relative to the

primary pulse alone (ref. 9). The PPWG propagation was

consistently observed to affect Γ(ω, d) much more

strongly than could be attributed solely to Z-axis multiple

reflections and is therefore the largest contributor to sidelobe interference and measurement error.

A previous study (ref. 9) of the effects of small variations in M(ω) and Φ(ω) on the time response revealed

that variations in M(ω) do not produce time shift, but

variations in Φ(ω) can. An approximate time response

for a frequency-response function having M(ω) = 1 and

(8)

can be derived symbolically when ∆Φ < 1. The basic

form of the result depends on whether the variation term

in equation (8) has even or odd symmetry over ∆ω with

respect to midband (ω1 + ω2)/2 and that symmetry

changes when ω0Tp changes by π/2, as illustrated in figure 10. With even symmetry ω0Tp = (2n + 1)(π/2), and

(9)

The echo-pulse and primary-pulse carriers are

orthogonal, and the two echo pulses have a combined

envelope function that has even symmetry about t = Tp.

Therefore, the root-squared sum envelope function of

f (t) has even symmetry about t = Tp, and there is no time

shift.

With odd symmetry ω0TP = mπ and

(10)

The envelope functions of the echo and primary

pulses add directly because they have inphase carriers.

Figure 11 shows the pulse orientations with m even and

∆ωTp/2 = 3π. At t = Tp the combined echo-pulse envelope function changes sign and adds to the primary-pulse

envelope on the high side of Tp and subtracts on the low

side, producing a positive time shift of the sum-process

envelope. When Tp is increased so that ∆ωTp/2=4π, the

Φ ω T

p () ω , Tp – ∆Φ ωTp = + sin ( )

f ( )t 2∆f Sinc

∆ω t T

p ( ) –

2 ---------------------------- ω0 t T

p = cos [ ] ( ) –

( ) –1 m ∆Φ

2

--------     Sinc ∆ωt

2

---------    







+

Sinc

∆ω t 2T

p ( ) –

2 ------------------------------- 





ω0 t T

p

+ sin [ ] ( ) –

f ( )t 2∆f Sinc

∆ω t T

p ( ) –

2 = ----------------------------

( ) –1 m + 1 ∆Φ

2

--------     Sinc ∆ωt

2

---------    







+

Sinc

∆ω t 2T

p ( ) –

2 ------------------------------- 





– ω0 t T

p cos [ ] ( ) –

time shift is negative. Time shift can be quantified by

representing the three components of the envelope function in equation (10) as Taylor series approximations

about t = Tp, carrying terms only through the second

order. The resulting quadratic approximation for f (t) has

a maximum at

(11)

where n is the order of the echo-pulse zero crossing at

t = Tp.

When ∆ωTp/2 = (2n + 1)π/2, the echo pulses have

local extremes at t = Tp; time shift is zero but the sumpulse amplitude has a local extreme value. The extremes

of the amplitude and position errors alternate and follow

a downward trend as Tp increases.

In summary, as Tp = 2d/c changes, the measurement

error exhibits compound periodicity as the parameters

that control the relative orientation of the primary and

echo-pulse lobes ∆ωTp/2, and the phase difference

between the primary and echo-pulse carriers ω0Tp

change by 2π. Increasing ∆ω causes the measurement

error to follow a downward trend. These are the same

general conclusions that were drawn earlier for the frequency-domain approach.

Time-domain measurements were affected less by

trough ripple than frequency-domain measurements

were. This difference probably occurs because the variations in Γ(ω) that are produced by trough ripple change

rapidly with ω and are widely dispersed in the timedomain transformation; relatively little interference is

contributed to the critical region that contains the main

lobe of the primary pulse.

Reduction of PPWG Effects

Any measure that can reduce PPWG disturbances

without significantly affecting the primary Z-axis reflection reduces the periodic variations of Φ(ω) from linear,

the resulting time-shift of the time-domain sum pulse,

and therefore the measurement error. Two effective

methods for reducing PP effects were found. First, adding a slight curvature to one of the surfaces can corrupt

the PP geometry sufficiently to completely squelch

PPWG propagation—with negligible reduction of the

primary response. This suppression was demonstrated

with a 25.4-cm (10-in.) square PP fixture operating at

16 ± 2 GHz that was modified to have a curvature radius

of 58.4 cm (23 in.) on the reflecting plate. For any value

of d, there was a circular locus in the X-Y plane along

which the plate spacing d would satisfy equation (3) and

squelch propagation.

t

M Tp ( ) –1 n 12∆Φ

nπ∆ω ≈ + --------------
6

Secondly, a 10-mm (0.04-in.) layer of commercially

available magnetic absorber on the ground plane was

used to negate substantially the electrical effect of the

ground plane. This absorber consists of lossy mu-metal

particles suspended in Rutile and also is available in a

paint-on medium (ref. 10). Measurements with several

different test fixtures operating in the 14- to 26-GHz

region showed that applying this material around the

horn aperture reduced the secondary pulse by 6 to 14 dB

while reducing the primary pulse amplitude only 0.2 dB.

When the aperture plane reflection, in V0 figure 2, is

negligibly small or when VES is used, distancemeasurement error was observed to be closely proportional to V2/V1. A ring of magnetic absorber that covered

the ground plane to about 6λ beyond the perimeter of a

5λ horn effectively suppressed PPWG contributions to

Γ(ω, d), leaving only Z-axis local and multiple reflections to corrupt the measurement. These tests were not

extensive; even less absorber coverage might adequately

suppress PPWG propagation.

Test Results

The results of time-domain delay measurements

using an HP 8510C as a reflectometer and a precision PP

fixture having 36λ square plates fed by a 5λ circular horn

are shown in figure 12. The local reflection was about

35 dB below the incident wave and 20 dB below the primary reflection; VES was therefore of little benefit. With

10-mm (0.04-in.) magnetic absorber over the ground

plane (using 801 points across a 4-GHz span), deviations

of the measured “round-trip” time delay from a straight

line of slope 0.067 ns/cm (0.1693 ns/in.) were no more

than ±3 ps for plate spacings between 0 and 38 cm

(15 in.)—a 1-way distance-measurement error of less

than 0.051 cm (0.02 in.). Removal of the absorber

increased that error fivefold.

These results were obtained without using nonuniform windowing for side-lobe suppression. Windowing drastically increased measurement error below some

minimum value of pulse separation and plate spacing

(ref. 11). With a 4-GHz span, the HP 8510C “normal”

window increased measurement error for plate separations less than 8.26 cm (3.25 in.) but reduced error appreciably for larger separations. This effect was interpreted

to be a consequence of the pulse broadening which

accompanies windowing. Windowing becomes detrimental when the “broadened” main lobes of the signal

and interference pulses interact with each other.

Conclusions

The accuracy of microwave reflectometer measurements of the distance between conductive parallel plates

is reduced by parallel-plate-waveguide (PPWG) propagation in the parallel-plate (PP) channels perpendicular

to the measurement axis. These additional propagation

channels influence Γ(ω, d) and distance measurements

derived from it. A simple radiating system modification

which can suppress parallel-plate propagation is the addition of a thin layer of lossy mu-metal “magnetic

absorber” to the antenna ground plane. With this modification, a measurement accuracy of 0.025 cm (0.01 in.)

was obtained using an HP 8510C as a time-domain

reflectometer.

The time-domain processing approach was superior to a representative frequency-domain phasemeasurement approach because of (a) less susceptibility

to the trough ripple that is produced by edge reflections

in a PP environment, (b) immunity to phase capture, and

(c) the applicability of vector error subtraction. Time did

not permit a thorough evaluation of the comparative

performance of the two approaches in the absence of

PPWG propagation; however, both approaches benefited

directly from increasing the operating bandwidth ∆ω.

NASA Langley Research Center

Hampton, VA 23681-0001

August 11, 1995

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Measurements. Microw. & RF, vol. 33, no. 9, Sept. 1994,

pp. 108–110.
8

Figure 1. Waveguide-fed, parallel-plate system.

Figure 2. Local, primary, and secondary reflections in a PP reflectometer.

d

X

Y

Horn input

port

Ground plane

Target plate

Z

V0

V1

V2

V0,

 local reflection

V1, primary reflection

V2, secondary reflection

Incident

wave
9

Figure 3. Characteristic behavior of Γ(ω0, d) in an ideal parallel-plate system.

Figure 4. Effect of antenna ground-plane removal on the reflection coefficient magnitude.

Φ(ω0,d/λ)

2π

4π

6π

0

d/λ

0

8π

10π

1.0

Γ(ω0,d) = M(ω0,d/λ)

.5 2.0 1.0 1.5 2.5

0

–5

–10

–15

–20

–25

–30

0 2 4 6 8 10 12 14 16 18 20

Plate separation, cm

M(ω0,d),

d

B

Frequency: 24 GHz

Conical horn, dia = 2.74 cm

Phase curvature: 115°

Plate size: 46 × 46 cm

Without ground plane

Far-field boundary, 2(dia.)2/λ
10

Figure 5. Comparison of PPWG and multiple-reflection signatures.

1.0

.5

0

1.5 2.0

Magnitude

PPWG

30

10

0

1.5 2.0

Phase error, deg

PPWG

20

–10

–20

–30

Multiple reflections

Multiple reflections

V1/V0 = 0.5

V2/V1 = 0.33

df/c = d/λ

df/c = d/λ

V1/V0 = 0.5

V2/V1 = 0.33
11

Figure 6. Smith-chart plot of Γ(ω, d0) between critical points, with linear phase term extracted.

Start frequency 14.800 GHz

Stop frequency 15.800 GHz
12

(a) Magnitude response.

Figure 7. “Trough ripple” effects.

Start frequency 14.965 GHz

Stop frequency 15.570 GHz

1.0

0 f

M(ω,d0)

.5
13

(b) Phase response with linear phase term extracted.

Figure 7. Continued.

Start frequency 14.800 GHz

Stop frequency 15.800 GHz

Φ

M(ω,d0), deg

0

45

90

45

90

135

180 f
14

(c) Phase delay response with linear phase term extracted.

Figure 7. Concluded.

Start frequency 14.800 GHz

Stop frequency 15.800 GHz

Phase delay, ns

0

10

20

30

–10

–20

–30

–60

–40

–50

f
15

Figure 8. Measured time response (without linear phase or dispersion removal); d = 25.9 cm (10.2 in.). Envelope magnitude, mV

.2

.3

.4

.5

.1

0

–1 0123456 789

Time, ns

Primary

response
16

Figure 9. Measured time response with linear phase and dispersion extracted; d = 25.9 cm (10.2 in.). Envelope magnitude, mV

.2

.3

.4

.5

.1

0

–1 0 1 2 3 4 5 6 7 8 9

Time, ns

Primary

response
17

Figure 10. Illustrations of the components of the phase function Φ(ω,Tp) = −ωTp + ∆Φ sinωTp as Tp is varied.

–2π

–4π

ω0

Tp1

0

–2π

–4π

ω0

Tp2 > Tp1

0

–6π

–2π

–4π

ω0

Tp3 > Tp2

0

–6π

ω

ω

ω

∆ω

∆ω

∆ω

Φ(ω, Tp2), rad

Φ(ω, Tp1), rad

Φ(ω, Tp3), rad
18

Figure 11. Echo-pulse side-lobe interference producing a positive time shift.

2∆f

Tp 2Tp

0

t

Lagging echo pulse

Primary pulse

Leading echo pulse
19

Figure 12. Delay measurements on a parallel-plate test fixture using an HP 8510C as a reflectometer.

3.25

3.10

Plate-to-plate spacing, in.

Plate-to-plate spacing, cm

Measured round-trip time delay, nsec

Uniform window

3.0 3.5

3.20

3.30

3.35

3.40

3.15

Magnetic absorber

on ground plane

No absorber

2.0

56789

2.5


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November 1995 Technical Memorandum

Reflectometer Distance Measurement Between Parallel Conductive Plates

WU 538-04-11

Chase P. Hearn and Robert T. Neece

L-17466

NASA TM-4694

This report presents an analytic and experimental investigation of the measurement problem in which a reflectometer is used to determine the distance to a target that is a highly conductive surface parallel to the reflectometer

antenna ground plane. These parallel surfaces constitute a waveguide (WG) which can contribute parasitic perturbations that seriously degrade the accuracy of the measurements. Two distinct parallel-plate-waveguide (PPWG)

phenomena are described, and their effects on both frequency and time-domain reflectometers are considered.

The time-domain processing approach was found to be superior to a representative frequency-domain phasemeasurement approach because of less susceptibility to perturbations produced by edge reflections and immunity

to phase capture. Experimental results are presented which show that a simple radiating system modification can

suppress parallel-plate (PP) propagation. The addition of a thin layer of lossy mu-metal “magnetic absorber” to the

antenna ground plane allowed a measurement accuracy of 0.025 cm (0.01 in.) when a vector network analyzer

(VNA) is used as a time-domain reflectometer.

Microwave reflectometer distance measurement 20

A03

NASA Langley Research Center

Hampton, VA 23681-0001

National Aeronautics and Space Administration

Washington, DC 20546-0001

Unclassified–Unlimited

Subject Category 32

Availability: NASA CASI (301) 621-0390

Unclassified Unclassified Unclassified