July 2011 

NASA/TM-2011-217162 

Methods to Determine the Deformation of the 

IRVE Hypersonic Inflatable Aerodynamic 

Decelerator 

William R. Young 

Langley Research Center, Hampton, Virginia 
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July 2011 

NASA/TM-2011-217162 

Methods to Determine the Deformation of the 

IRVE Hypersonic Inflatable Aerodynamic 

Decelerator 

William R. Young 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 
Table of Contents 

1. Introduction ......................................................................................................... 3 

2. Radio Frequency Reflectometer Distance Measuring System ............................................... 4 

3. Some Methods for Measuring Phase Difference ............................................................... 4 

3.1. The Phase Detector .......................................................................................... 4 

3.2. Phase Determination from Zero Crossings of Sine waves .............................................. 9 

3.3. Six Port Probe Method ..................................................................................... 12 

4. Some Methods to Determine Range Which Use Phase ...................................................... 13 

4.1. Resonant Targets ........................................................................................... 13 

4.2. Radio Frequency Identification (RFID) ................................................................. 15 

5. Measurement Error Considerations ............................................................................ 16 

5.1. The Error Vector ........................................................................................... 16 

5.2. Directional Coupler Leakage ............................................................................. 19 

5.3. The Radar Equation ........................................................................................ 20 

5.4. Ratio of Leaked to Reflected Power ..................................................................... 21 

5.5. Connector Mismatch and Scatter ......................................................................... 22 

5.6. Importance of Approximately Equal Amplitude ...................................................... 23 

6. The Method of Choice, Frequency Doubling Target ........................................................ 23 

7. Concluding Remarks ............................................................................................. 25 

References ............................................................................................................. 28 
2

Abstract 

Small resonant targets used in conjunction with a microwave 

reflectometer to determine the deformation of the Hypersonic 

Inflatable Aerodynamic Decelerator (HIAD) during reentry is 

investigated. The reflectometer measures the distance to the 

targets and from this the HIAD deformation is determined. The 

HIAD is used by the Inflatable Reentry Vehicle Experiment 

(IRVE) which investigates the use of inflatable heat shields for 

atmospheric reentry. After several different microwave 

reflectometer systems were analyzed and compared it was 

determined that the most desirable for this application is the 

Frequency Doubling Target method. 
3

1. Introduction 

The Inflatable Reentry Vehicle Experiment (IRVE) requires a method to measure the deformation and 

motion of the Hypersonic Inflatable Aerodynamic Decelerator (HIAD) during reentry. It has been 

proposed that passive resonant targets of the, split ring resonator or other resonator types be placed in 

strategic locations on the back side of the decelerator next to the heat shield. These targets would be used 

in a radio frequency continuous wave reflectometry distance measuring system which would frequently 

(about 100 times per second) measure the distance from the surface antenna mounted on the center 

column to each target and hence characterize the motion of the IRVE Hypersonic Inflatable 

Aerodynamic Decelerator. See Figure 1. This approach is simple in concept and requires that a way be 

found to differentiate or identify each target separately from all other targets. It is believed that target 

differentiation or identification problems can be solved by using either a resonant target or an active or 

transponder target. However, it should be noted the active transponder target increases system 

complexity. This paper attempts to explain the basic principles of radio frequency continuous wave 

reflectometry and examine several different refinements of this overall approach such as the resonant 

target and harmonic generating approaches. Examined here are several other candidate approaches with 

improved target differentiation or identification. Some use active targets. 

 

Surface

Antenna

Target

Figure 1. The Hypersonic Inflatable Aerodynamic Decelerator (HIAD) 
4

2. Radio Frequency Reflectometer Distance Measuring System 

All of the methods discussed use radio frequency reflectometer distance measurement techniques and 

measure distance change to the target by determining the phase change of the reflected signal relative to 

the transmitted signal. To explain or illustrate this, let: 

F= frequency of the radio frequency signal used to measure the distance to the target 

L =the distance from the transmit antenna to the target. 

λ= the wavelength of the signal. 

ΔL= the change in distance to the target. 

ΔØ= the change in phase corresponding to the change in distance to the target. 

C= the speed of light. 

The signal travels at the speed of light C; hence λ is given by λ=C/F. Since there are 360 phase degrees in 

a wavelength, the change in signal path length is related to signal phase change by the ratio 360/λ. For 

example, if the path length changes by one fourth λ, then the signal phase changes by 90 degrees. The 

total distance traveled by the radio frequency signal to and from the target is 2L. If the distance to the 

target changes by ΔL then the path length changes by 2ΔL and the reflected signal phase change relative 

to the transmitted signal is given by 

ΔØ = 2ΔL(360)/λ = ΔL(720)/λ. 

Solving for the change in distance to the target gives 

ΔL = λΔØ/720. 

Or in terms of frequency instead of wavelength 

ΔL = CΔØ/720F. 

Radio frequency reflectometry distance measurement becomes measurement of the change in phase of the 

reflected signal relative to the transmitted signal. 

Ambiguity will result in the determination of ΔL if ΔØ is equal to or greater than 360 degrees. Knowing 

the maximum change in L makes it possible to choose a frequency or wavelength which will keep ΔØ 

smaller than 360 degrees. 

3. Some Methods for Measuring Phase Difference 

3.1. The Phase Detector 

The phase detector discussed and described here is also known as, and has the same circuit as, a double 

balanced mixer. Figure 2 shows the circuit configuration of this type phase detector. When used as a 

phase detector, this three port device or circuit compares two coherent RF signals applied to two of the 

ports and a voltage proportional to the phase difference between these signals appears at the third port. 

This output voltage varies sinusoidally with the phase difference between the two RF signals. Figure 3 

shows a plot of phase difference between the RF1 and RF2 signals versus a percentage of the maximum 

output voltage. The region of the sine curve between vertical lines B and C gives an approximate linear 

relation between phase change and output voltage. This is also true of the sine curve between lines D and 

E and between lines F and G. These linear regions represent approximately one fourth of a cycle or a 90 
5

RF 1

Input

RF 2

Input

Output Voltage

Proportional to

Phase Difference

Figure 2. Phase detector circuit. 

 

100

80

60

40

20

0

-20

-40

-60

-80

-100

λ/4

90°

π/2

λ/4

90°

π/2

λ/4

90°

π/2

A B C D E F G

70.7%

-70.7%

Percent of max Value

90 270 450

Figure 3. Phase detector output voltage vs phase difference. 

degree phase difference. This type of phase detector has an ambiguity problem. Without additional 

information, it cannot be determined exactly which portion of the sine curve is being indicated. It should 

also be noted that the maximum phase output voltage is dependent on the amplitude of the weaker of the 
6

two applied RF signals. A way must be found for the two RF inputs to be maintained at constant 

amplitude for accurate phase measurements. One of the two RF inputs is usually from a reference 

oscillator and will usually have constant amplitude. A limiting amplifier is often used to keep the other 

RF signal at constant amplitude [Mini-Circuits].

 

 

P hase

Detec tor

P ower

Divider

Os cillator

Volt

Meter

C able L ength

C hanger or

C able S tretcher

Figure 4. Phase detector demonstration circuit. 

Figure 4 shows a block diagram of a phase detector demonstration circuit which uses the phase detector 

described above. In this arrangement, the signal from the oscillator is divided into two paths by a power 

divider. In one path the signal is fed directly to the phase detector circuit. The other path goes through a 

cable length changer, also called a cable stretcher. The cable stretcher changes the physical length of the 

cable between the power divider and the phase detector. Changing the length of a cable changes the 

phase at the phase detector port. As explained earlier, increasing the path length by one wave length 

changes the signal phase by 360 degrees or the phase changes in proportion to the path length change 

whether in a cable or in free space. The change in output voltage of the phase detector resulting from the 

phase differences of the two RF input signals is displayed by the volt meter. This output voltage changes 

as the cable length is changed by the cable stretcher. 

 
7

 

2 Way

P ower

Divider

Os cillator

Volt

Meter

Volt

Meter

P ower

Divider

P ower

Divider

90 ° P hase

S hifter

P hase

Detec tors

C able L eng th

C hanger or

C able S tretcher

Figure 5. Dual phase detector demonstration circuit. 

Figure 5 shows a dual phase detector demonstration circuit which provides a way to eliminate some of the 

ambiguity with this type phase detector. A second phase detector is added with one of its ports fed by a 

signal which has had its phase shifted by 90 degrees. The outputs of these two phase detectors are 

compared in figure 6, where they appear as sine and cosine curves, since shifting a sine curve backward 

by 90 degrees gives a cosine curve. The top sine curve represents the output of the top phase detector in 

Figure 5, and the bottom cosine curve represents the output of the bottom phase detector. In Figure 6, 

notice that between vertical lines A and B the sine curve is nonlinear while the cosine curve is linear. The 

nearly linear regions are shown in red. Between lines B and C the sine curve is linear while the cosine 

curve is nonlinear. As we continue from left to right down the sine and cosine curves, notice how the 

regions of linearity and nonlinearity alternate between curves so that either one or the other is in a linear 

region. Notice also that when a curve is in a nonlinear region and its polarity is positive, the other curve 

in the linear region is on a positive slope and vice versa. 
8

 

A B C D E F G H

100

80

60

40

20

0

-20

-40

-60

-80

-100

100

80

60

40

20

0

-20

-40

-60

-80

-100 

Figure 6. Linear regions of a sine curve. 

 

60 Degrees 120 Degrees

300 Degrees

60 Degree Shift

120 Degree Shift

300 Degree Shift

Figure 7. Phase shifted sine waves. 
9

 

A

C

B

D

Figure 8. Sine curve zero crossing pulses. 

 

3.2. Phase Determination from Zero Crossings of Sine waves 

This method determines the phase difference between the transmitted and reflected signals by measuring 

the time interval between either the positive going zero crossings or the negative going zero crossings of 

the sine waves of two RF signals. Figure 7 illustrates how the zero crossings of sine curves relate to 

phase difference between sine curves. The phase difference is proportional to the time interval between 

zero crossings. 

Amplifying a sine wave in a linear amplifier then clipping its amplitude with a limiter circuit converts the 

sine wave signal into a square wave. The zero crossing points of the sine and square waves will have the 

same locations. Converting the sine wave to a square wave does not change the time locations of the zero 

crossings. This is shown by signals A and B in Figure 8. Passing the square wave through a 

resistor/capacitor (RC) high pass filter produces a train of narrow pulses shown as C in Figure 8. Each 

pulse of this pulse train has a sharp leading edge aligned precisely with the zero crossings of the sine 

wave. Notice the positive going zero crossings of the square wave can be distinguished from negative 

going zero crossings by the polarity of these pulses. Normally only the positive going pulses are used and 

the negative going pulses are eliminated from the waveform with a diode clamp circuit, resulting in the 

pulse train shown as D in Figure 8. 

If positive going zero crossing pulse trains are generated for both the reference or transmitted signal and 

the reflected signal, the positive going pulses of both trains can be compared to find the time between 

zero crossings of the two signals and from this, the phase difference can be determined. Figure 9 shows a 

block diagram illustrating two ways to derive phase information from these narrow pulse trains. 

 
10

 

Bistable

Multivibrator

Limiting

Amplifier

RC High 

Pass

Filter

Volt

Meter

Frequency

Counter Transmitted

Signal

Reflected

Signal

Start

Stop

Set

Reset

Oscillator

Digital Phase

Difference

Output

Analog Phase

Difference Output

A B C

Waveform Type

Diode

Clamp

Circuit

D

Limiting

Amplifier

RC High 

Pass

Filter

A B C Diode

Clamp

Circuit

D

Figure 9. Zero crossing phase detector. 

The first method, illustrated in Figure 9 in the top part of the figure, uses a frequency counter the count of 

which is started by the zero crossing pulse of the reference or transmitted signal. The counter is then 

stopped and reset by the zero crossing pulse of the reflected signal. This frequency count registered by 

the counter will be proportional to the phase difference between the signals. Since this data is in digital 

form, an analogue to digital converter is not required for data downlink. 

The second method, illustrated in the bottom part of Figure 9, uses a bistable multivibrator which is set 

high by the transmitted signal zero crossing pulse and reset to zero by the reflected signal zero crossing 

pulse. This is illustrated in Figure 10 showing 120 degrees difference between transmitted and received 

signals. The bottom waveform in the figure shows the output of the bistable multivibrator. Additional 

signal processing would be required to convert this waveform to an analog voltage which in turn would 

require an analog to digital converter. Figures 11 and 12 illustrate the 210 degree and the 300 degree 

cases. Notice that in each case shown in Figures 10 through 12, the output pulse width of the 

multivibrator is proportional to the phase difference. 

The zero crossing phase detector has the advantage of full cycle measurement without ambiguity within 

the cycle. Again, if the counter output is used to determine the phase, an analog to digital converter is not 

required. 
11

 

120 Degrees

Multivibrator

Output Pulses

Zero 

Crossin

g

Pulses

Set Pulse Train

Reset Pulse Train

Figure 10. 120 degree analog output pulse train. 

 

210 Degree Shift

210 Degrees

Output 

Pulse Train

Set Pulse Train

Reset Pulse Train

Figure 11. 210 degree analog output pulse train. 
12

 

300 Degrees

300 Degree Shift

Figure 12. 300 degree analog output pulse train. 

3.3. Six Port Probe Method [Bilik] 

When a Radio Frequency (RF) signal is reflected from a target, the reflected wave interferes with the 

incident wave in a manner which depends on the phase of the incident wave when it contacts the target. 

A “standing wave” is created from the interference between the transmitted wave and the wave reflected. 

As explained earlier, the source antenna would be located in the center of the HIAD as shown in Figure 1. 

When a target moves relative to the source antenna the phase of the incident wave at the target changes. 

This changes the phase relationship between the transmitted and reflected waves causing a positional 

change in the location of the peaks and valleys of the standing wave. The change in the phase 

relationship between the transmitted and reflected signals can be determined from this change in the 

standing wave. 

A six port probe can indirectly measure the phase difference between the transmitted and reflected signals 

by determination of the change in the standing wave pattern. From this change in standing wave the 

phase change of the reflected wave relative to the transmitted wave is determined. From this change in 

phase the change in distance to the target is determined. The phase of the transmitted signal is taken as 

the reference. By measuring the phase change of the reflected signal relative to the phase of the 

transmitted signal the change in distance to the target can be determined. 

The six port probe is a system component with six terminals or ports. Two of the ports are the RF input 

and output ports. The remaining four ports are connected at sample points inside the device to sample the 

standing wave in four different locations. From this information the standing wave pattern can be defined 

mathematically. From the voltages at the four ports, a computer program determines the standing wave 

pattern from the locations of the peaks and nulls. 
13

 

4. Some Methods Which Use Phase to Determine Range 

4.1. Resonant Targets 

Figure 13 shows a block diagram of the configuration envisioned for a reflectometer to measure phase 

and hence distance to the targets using one of the phase detector circuits discussed above. A directional 

coupler separates the reflected signal from the transmitted signal, or the directional coupler separates the 

reflected signal from the standing wave. The reflected signal once separated from the transmitted signal 

passes through a limiting amplifier. Next it is fed to the phase detector which measures the phase of the 

reflected signal relative to the transmitted reference signal as previously explained. 

 

P ower

Divider

Amplifier

L imiter

C ontroller

C alibration

and

Data

R ecording

P hase

Detec tor

Antenna

P hase

f 1

f 2

f n

R esonant

T argets

S tepped

F requency

O s cillator

T o

T elemetry

P ower

Divider

Amplitude

Direc tional

C oupler

S ignal F rom

Antenna

R eflec ted

S ignal P ort

Figure 13. Ranging using a phase detector. 
14

 

Surface

Antenna

Target

X Axis

Figure 14. Output voltage change vs target position. 

 

This approach falls in the category of passive resonant targets. Each target is tuned to a different 

frequency, and reflects more energy when the frequency it receives is at its resonant frequency. A radio 

frequency signal, generated by a frequency synthesizer, is transmitted from an antenna located in the 

center of the HIAD to the targets (Figure 1). The frequency synthesizer rapidly steps through the 

different frequencies of the targets. While the synthesizer is tuned to the frequency of a target, a stronger 

signal comes from that target than any of the other targets, and this signal is reflected back to the antenna. 

Here the reflected signal is compared with the transmitted signal and from the change in the phase 

difference between the transmitted and reflected signals, the change in the distance to the target is 

determined. 

 

In Figure 14, the red sine wave superimposed on an image of the IRVE Aeroshell illustrates the change in 

voltage output of the phase detector as a function of target displacement. The target motion along the x 

axis of the sine wave causes a change in the output voltage of the phase detector. The magnitude of the 

sine wave (y axis direction) corresponds to the value of the phase detector output voltage caused by the x 

axis displacement. This voltage is proportional to the phase change. 
15

 

Power

Divider

Six Port

Probe

Antenna

f 1

f 2

f n

RF

Signal

Source

Isolator

Isolator

Termination

12 Bit

A/D

Calibration

Reference

Signal

Conditioners

To

Telemetry

Signal Reference Line

Conditioner

Diode

Detectors

Target ID

Resonant

Targets

Figure 15. Reflectometer distance measurement using the six port probe. 

Figure 15 illustrates one method for measuring range change using the six port probe. In this example 

resonant targets are again used. This method is similar to the phase detector method described above. As 

before, a radio frequency signal generated by a frequency synthesizer is used as the signal source. The six 

port probe does not require that the reflected signal be amplifier limited as is the case with the phase 

detector. However the six port probe requires computer computations to extract the phase change 

information from its four diode detector voltage outputs. 

4.2. Radio Frequency Identification (RFID) 

The targets could incorporate an RFID chip inside to provide target identification. Examples of these 

systems include Smart Card, “blink”, and E-ZPass. 

RFID Systems are based on radio frequency (RF) tags and RF readers. These tags contain a microchip 

with a small memory. Memory capacities of several tens of kilobits or more are possible. RFID systems 

may be divided in two main categories: passive and active. In passive systems a small antenna receives 

power from a nearby RF transmitter and captures enough energy to power the logic circuits in the tags. 

Active systems power the circuits in the tags with batteries, and can support more sophisticated 

electronics with more data storage capacity, data processing capabilities and / or interfaces to external 

sensors [Coca]. 

Having information as to the unique identification of a particular RFID modulated on its return signal 

carrier does not seem to provide a simple way to distinguish among the different targets [Nititin]. 

Existing systems can identify only one RFID target in the field at a time. A way must be found to use the 

subtle difference in the spectrum of each target to determine its unique contribution to the phase change. 

Multiple RFID transponders responding at once will add to the error vector in much the same way as 

scattering from nearby structures. This could add to the calibration problem. 
16

 

Error Vector

Phase angle of

Reflected Signal

Reflected Signal

Imaginary

Axis

Real Axis

Phase angle of 

Measured

Reflected Signal

Measured 

Reflected 

Signal

Figure 16. Error vector small relative to the reflected signal vector. 

5. Measurement Error Considerations 

5.1. The Error Vector 

The three phase measuring methods described above are subject to errors which are caused by the 

imperfections in the system components and the measurement environment. Some examples of these 

error sources are the antenna mismatch, the directional coupler leakage from the transmitted signal, 

reflections from objects other than the target (scatter) [Georgiadis], connector mismatch, etc. This is not a 

complete list of all the possible error sources contributing to the error vector, but these are the largest 

contributors. All of the individual error sources will add together vectorially and can be thought of as 

being lumped into a single error vector. Figure 16 shows how this error vector affects the measurement 

of the actual reflected signal. The real and imaginary axes represent the reference frame from which the 

amplitude and phase of the reflected signal are actually measured. From Figure 16 we see that the 

measured phase and amplitude differ from the actual phase and amplitude because of the error vector. 

Note the circle is centered on the start or tail of the reflected signal vector and not the origin of the 

coordinate system. This circle represents possible locations or values of the reflected signal vector when 

the error vector is fixed in both amplitude and phase and the amplitude of the reflected signal is fixed 

while the phase of the reflected signal is allowed to vary. As the phase of the reflected signal varies 

through 360 degrees this circle is generated. Actually the amplitude of the reflected signal vector will 

decrease in magnitude as the target moves away and a spiral rather than a circle would be drawn. To 

illustrate, two other same amplitude reflected signal vectors, shown in red, are drawn in the circle at 

different phase angles. 
17

Error Vector

Phase angle of

Reflected Signal

Reflected Signal

Measured Reflected Signal

Measured Phase Angle

Of Reflected Signal

Imaginary

Axis

Real Axis

Figure 17. Error vector slightly smaller than reflected signal vector. 

Figure 17 shows how as the size of the error vector relative to the size of the reflected signal vector 

increases, the measured values differ even more from their actual values as would be expected. 

Error Vector

Reflected

Signal

Phase angle of

Reflected Signal

Imaginary

Axis

Real Axis

Measured Reflected Signal

Maximum Phase Angle Change

of Measured Reflected Signal

Figure 18. Error vector larger than reflected signal vector. 
18

Figure 18 shows the condition when the error vector is larger than the reflected signal vector. For this 

case the origin of the coordinate system is outside the circle of the actual reflected signal vector. Notice 

when this occurs, the possible variation of the measured phase angle of the reflected signal is restricted to 

a value of less than 360 degrees. For the specific case illustrated in figure 18, the phase change of the 

reflected signal is limited to a maximum variation of about 90 degrees, while the actual phase angle could 

vary through a full 360 degrees. From this we see that serious errors can result unless the error vector is 

considered in the measurement. 

 

Error Vector

Reflected

Signal Phase angle of

Reflected Signal

Imaginary

Axis

Real Axis Measured Reflected Signal

Figure 19. Error vector much larger than reflected signal vector. 

Figure 19 shows the condition when the reflected signal is small compared to the error vector. This 

condition can occur when the return from the target is small perhaps because the range distance is great. 

From this illustration we can see that as the return from the target gets smaller the measured value for the 

reflected signal becomes the error vector [Rytting]. 

Before we can accurately determine the change in distance to the target (range) we must know the phase 

change of the reflected signal. Before we can know that we must know the magnitude and phase of the 

error vector. Modern network analyzers have built into their functionality a calibration procedure which 

measures the error vector associated with each type of measurement. Once determined the error vector is 

vectorially subtracted from the measured vector to give the desired vector. To accurately determine the 

range, a way must be found to determine the magnitude and phase of the error vector, a way to minimize 

it, or both. 
19

5.2. Directional Coupler Leakage 

A directional coupler is used in the resonant target method illustrated in Figure 13. Directional coupler 

leakage of the transmitted signal, antenna connector mismatch and reflections from objects other than the 

target (scatter), have been identified as the largest contributors to the error vector. Directional coupler 

leakage and antenna mismatch will be examined as to their contribution to the error vector and their 

potential to cause problems in determining the error vector and hence the calibration of the reflectometer. 

Scatter from objects other than the target will not be addressed because at this stage it is an unknown 

quantity and will probably be much less of a concern. 

In Figure 13 note that the signal reflected from the resonant target, which contains the target phase and 

distance information, is separated from the transmitted signal by the directional coupler located next to 

the antenna. The reflected signal leaves the directional coupler at its bottom terminal, which we will call 

the reflected signal port of the directional coupler. From here the reflected signal is fed to a power divider 

which is the first component of the phase measurement part of this method. It is an unfortunate fact that 

all directional couplers are imperfect and consequently will let some of the transmitted signal leak into the 

reflected signal port of the directional coupler. This leaked transmitted signal corrupts the desired 

reflected signal and introduces an error into the phase measurement. It adds to the error vector. 

Directivity is a figure of merit for a directional coupler. The directivity, given in negative dB in the table 

below, represents a ratio of the transmitted signal leaked into the reflected signal port to the transmitted 

signal passing through the directional coupler. The higher the directivity or the larger the negative 

number, the smaller the leakage of the transmit signal into the reflected signal port. 

The data in Table 1 below came from three different manufacturer’s data sheets and one manufacturer’s 

catalog. The directional couplers listed represent the ones with the best directivity listed for the 2.0 to 4.0 

GHz frequency range. Note the best directional coupler found has a directivity of -30 dB. 

Table 1. Directivity of Typical Directional Couplers. 

Manufacturer Model# or Series Frequency 

Range In GHz

Directivity 

In dB 

Directivity 

as ratio 

MITEQ CD-202-403-20S-R 2.0 to 4.0 -20 0.01 

MECA 780 2.0 to 4.0 -22 0.00631 

PULSAR C30-24-481/7N 2.0 to 4.0 -18 0.01585 

HP 797D 2.0 to 4.0 -30 0.0001 

Expressing directivity as a ratio we can write

 

t

l

P

P

 (1) 

where 

  Directivity 

Pt  Transmitted signal power at the directional coupler terminal 

Pl  Transmitted power leaked into the reflected signal port. 
20

5.3. The Radar Equation 

Again referring to Figure 13, the ratio of the received reflected signal power from the targets at the 

antenna terminal relative to the transmitted signal power at the same antenna terminal, can be calculated 

using the radar equation which is 

  3 4

2 2

4 R

PG P t

r



   (2) 

where 

Pt  The transmitted signal power at the antenna terminal 

Pr  The received signal power at the antenna terminal 

  The wavelength of the microwave signal used by the radar 

G  The gain of the radar antenna for both transmit and receive 

  The effective radar cross section of the target 

R  The distance from the antenna to the target. 

From the radar equation we see that the ratio of received reflected power to transmitted power at the 

antenna input connection is given by 

 3 4

2 2

(4 ) R

G

P

P

t

r



   . (3) 

The above equation is used to calculate the ratio of reflected to transmitted power for various target sizes 

and antenna gains and the results are shown in Table 2 below. The HIAD of the vehicle in question has 

an inflated diameter of 3 meters. The range, R, to the targets is therefore 1.5 meters. The wavelength 

used for the calculations corresponded to a frequency of 2 GHz and the effective radar cross section of 

the target is assumed to be equal to the actual targer area. For convenience, we will call the ratio of 

received reflected power to transmitted power, as determined by the above equation, the Radar Ratio. 

From examining the data in Table 2 notice that the reflected power at the antenna terminal is very small 

relative to the transmitted power. The last row of Table 2 shows this to be true even for a large target and 

a high antenna gain factor. 
21

Table 2. Target Size and Antenna Gain Comparisons 

Antenna 

Gain 

Factor 

Target 

Area in 

Square 

Inches 

Target 

Area in 

Square 

Centimeters 

Target 

Area in 

Square 

Meters 

Receive To 

Transmit 

Power 

Ratio 

Receive 

To 

Transmit 

Power 

Ratio in 

dB 

 4 1 6.452 0.000645 2.309E-8 -76.366 

 4 1.5499 10.0 0.001 3.578E-8 -74.463 

 4 2 12.904 0.00129 4.618E-8 -73.356 

 4 4 25.808 0.00258 9.236E-8 -70.345 

 4 5 32.26 0.00323 1.154E-7 -69.376 

 4 8 51.616 0.00516 1.847E-7 -67.335 

 6 1 6.452 0.000645 5.195E-8 -72.844 

 6 1.5499 10.0 0.001 8.052E-8 -70.941 

 6 2 12.904 0.00129 1.039E-7 -69.834 

 6 4 25.808 0.00258 2.078E-7 -66.824 

 6 5 32.26 0.003226 2.598E-7 -65.854 

 6 8 51.616 0.005162 4.156E-7 -63.813 

 8 1 6.452 0.000645 9.236E-8 -70.345 

 8 1.5499 10.0 0.001 1.431E-7 -68.442 

 8 2 12.904 0.00129 1.847E-7 -67.335 

 8 4 25.808 0.00258 3.694E-7 -64.325 

 8 5 32.26 0.00323 4.618E-7 -63.356 

 8 8 51.616 0.00516 7.388E-7 -61.314 

5.4. Ratio of Leaked to Reflected Power 

The ratio of leaked transmitted power to reflected power is given by directional coupler directivity 

divided by the Radar Ratio. This can be shown as follows 

 

r

l

r

t

t

l

t

r

t

l

t

r P

P

P

P

P

P

P

P

P

P

P

P     (4) 

Note that the smaller the directivity ratio the smaller the amount of transmitted power that leaks into the 

reflected signal port to adversely affect the reflected signal. In Table 1 the best directional coupler listed 

has a directivity of -30 dB. This value and the above relationship were used to determine the ratio of 

leaked transmitted power to reflected signal power for various system parameters as tabulated in Table 3. 

Most of the information in Table 2 above is repeated below in Table 3. Two columns have been added for 

the ratio of leaked to reflected power in linear and dB form. The column for target area in square meters 

was eliminated to make room for the additional information. 
22

Table 3. Comparison of Leaked to Reflected Power. 

Antenna 

Gain 

Factor 

Target 

Area in 

Square 

Inches 

Target 

Area in 

Square 

Centimeters 

Receive To 

Transmit 

Power 

Ratio 

Receive 

To 

Transmit 

Power 

Ratio in 

dB 

Ratio of 

Leaked 

To 

Reflected 

Power in 

dB 

Ratio of 

Leaked 

To 

Reflected 

Power 

 4 1 6.452 2.309E-8 -76.366 46.366 43311 

 4 1.5499 10.0 3.578E-8 -74.463 44.463 27944 

 4 2 12.904 4.618E-8 -73.356 43.356 21656 

 4 4 25.808 9.236E-8 -70.345 40.345 10828 

 4 5 32.26 1.154E-7 -69.376 39.376 8662 

 4 8 51.616 1.847E-7 -67.335 37.335 5414 

 6 1 6.452 5.195E-8 -72.844 42.844 19249 

 6 1.5499 10.0 8.052E-8 -70.941 40.941 12420 

 6 2 12.904 1.039E-7 -69.834 39.834 9625 

 6 4 25.808 2.078E-7 -66.824 36.824 4812 

 6 5 32.26 2.598E-7 -65.854 35.854 3850 

 6 8 51.616 4.156E-7 -63.813 33.813 2406 

 8 1 6.452 9.236E-8 -70.345 40.345 10828 

 8 1.5499 10.0 1.431E-7 -68.442 38.442 6986 

 8 2 12.904 1.847E-7 -67.335 37.335 5414 

 8 4 25.808 3.694E-7 -64.325 34.325 2707 

 8 5 32.26 4.618E-7 -63.356 33.356 2166 

 8 8 51.616 7.388E-7 -61.314 31.314 1353 

The ratio of leaked to reflected power varies from 43,311 to 1 as the worst case to 1,353 to 1 for the best 

case which is found in the bottom row of Table 3. This means that even for the best case the leaked 

transmitted signal will be over 1,000 times greater than the reflected signal. To recover the reflected 

signal from the combined leaked signal and reflected signal, it will be necessary to somehow measure the 

leaked signal with no target present, and subtract this from the combined signals as a system calibration. 

In this situation the error vector is huge relative to the reflected signal vector. This means finding a small 

difference between two large numbers which requires great accuracy in both measurements. Calibration 

of the system will be difficult and suggests that a different approach should be used. 

5.5. Connector Mismatch and Scatter 

Connector mismatch at the antenna input terminal and at the output of the directional coupler will cause 

additional transmitted power to be leaked to the reflected signal port. The antenna mismatch and the 

mismatch at the directional coupler terminal can be analyzed in the same manner. Therefore we will only 

look at the consequences of antenna mismatch. If we let ρ = the reflection coefficient of the antenna input 

terminal, S = the resulting standing wave ratio, or SWR, and assume a very good antenna match with an 

SWR of 1.02:1 we can write 

 0.0099

2.02

0.02

1

1   

  S

S

 (5) 
23

The reflected power from the antenna mismatch is given by the relationship 

 2 Prm  Pt (6) 

Where 

Prm  The power reflected due to the antenna mismatch and 

Pt The transmitted signal power. 

0.000098 9.8 5 2    E  P

P

t

rm 

When we compare this value with the receive to transmit power ratios calculated with the radar equation 

and tabulated in the bottom row of Table 2 and Table 3, we see that the transmitted power reflected 

because of the antenna mismatch is more than 100 times larger than the reflected signal coming from the 

target. This mismatch signal adds to the directional coupled transmit power leakage and the size of the 

error vector. This mismatch signal component would be corrected for or subtracted out in the system 

calibration as described above. 

5.6. Importance of Approximately Equal Amplitude 

For proper operation all of the phase measuring devices discussed in this paper require the two phase 

coherent signals to have nearly the same amplitude. Consider the application shown in Figure 15 which 

uses a six port probe as the phase measuring device. In this case the phase change is determined from the 

change in the standing wave pattern. The Radar Ratios listed in Table 2 show how much larger the 

transmitted signal is than the signal reflected from the targets. This indicates that the standing wave 

created by the reflected wave as it interferes with the transmitted wave will be difficult to measure and to 

extract the necessary phase information. The case illustrated on the bottom line of Table 2, is probably 

the best case (easiest to measure) that can be expected. It shows the reflected signal to be 1,355,000 

(1/7.388E-7) times smaller than the transmitted signal. This means the six port probe must extract phase 

change information from a standing wave pattern with variations which are 0.00007388 percent of the 

overall wave amplitude. 

6. The Method of Choice, Frequency Doubling Target 

This approach, as illustrated in Figures 20 and 21, uses a radio frequency reflectometry phase shift 

distance measuring system. It differs from the other methods in that the target transmits back the second 

harmonic of the signal it receives. Figure 20 shows a functional block diagram of one of the targets and a 

drawing of the target configuration. The target has dipole receive and transmit antennas. The received 

signal is sent to a ceramic lowpass filter which keeps signals intended for other targets (all the other target 

frequencies) from being doubled in the frequency doubler and leaking back to the target receive antenna 

where these signals would be transmitted and interfere with other targets. Next it is sent to a frequency 

doubling circuit followed by a ceramic bandpass filter which is tuned to the second harmonic of the 

intended received signal for this target. The ceramic filter rejects all other harmonics of the received 

signal generated in the frequency doubler. The second harmonic is transmitted back to the reflectometer 
24

through another dipole antenna mounted orthogonally to the receive antenna. Figure 21 shows one 

possible configuration of the reflectometer ranging system for use with the frequency doubling target. 

 

Transmit 

Antenna

Receive 

Antenna

Target Block Diagram 

Target

Frequency

Doubler

Ceramic

Bandpass

Filter

Ceramic

Lowpass

Filter

Receive

Antenna

Transmit

Antenna

Figure 20. Harmonic generating target. 

 

Frequency

Synthesizer

Power

Splitter

Controller

And

Signal Processor

Frequency

Doubler

Six Port

Probe

One Of 32

Targets

Transmit 

Antenna

Receive 

Antenna

Power

Amplifier

Receiver

A to D

Converter

To TM

Down 

Link 

Ceramic

Filter

Power

Splitter

Figure 21. Ranging using harmonic generating target. 
25

Each target has a band pass ceramic filter tuned to a different frequency. Each target’s unique ceramic 

filter frequency enables the system to differentiate between targets because only the target whose 

frequency matches the frequency being transmitted at that instant will respond with the return of the 

second harmonic signal. In Figure 21 a harmonic generator like the one in the target generates a reference 

second harmonic signal in the reflectometer, which is phase coherent with the signal returned from the 

target. This phase coherent second harmonic reference signal is compared with the signal from the target 

to get the phase information for range. The controller steps the frequency synthesizer through the 

frequencies of all the targets in one interrogation cycle. 

The Frequency Doubling Target has a distinct advantage over the other ranging methods described here 

since it is not subject to any of the largest contributors to the error vector. The return signal does not pass 

through the transmit antenna and a directional coupler is not requited. This eliminates directional coupler 

leakage, antenna mismatch, and connector mismatch from the list of error sources. Scatter from the 

transmitted signal will be rejected by the frequency selectivity of the receiver so transmitted signal scatter 

will be eliminated as an error source also. 

A six port probe is shown in Figure 21 as the method for measuring phase difference between the second 

harmonic of the transmitted signal and the second harmonic signal coming from the target. Note that 

since the transmitted and received signals are separated from each other it is possible for the received 

signal to pass through a receiver as shown in Figure 21. The receiver is used to amplify the received 

signal until it has an amplitude nearly equal to that of the reference signal. When the amplitude of the 

received signal changes, the automatic gain control of the receiver readjusts the gain so that the received 

signal is at an optimum level to give maximum accuracy in the phase measurement whether the phase is 

measured using a six port probe or one of the other methods discussed above. 

One source of error unique to the frequency doubling target method is the presence of second harmonics 

transmitted along with the fundamental frequency. These harmonics are generated by any nonlinearity in 

the transmit system and will be exactly the same frequency as the signal coming from the harmonic 

generating target. This signal would be much like the leaked transmitted signal in the directional coupler. 

The addition of a band pass filter at the transmit antenna will suppress the undesired second harmonic 

signal and will control this source of error. 

Reduced error vector components and frequency selectivity of the targets for improved target identity 

makes this method the method of choice. 

 

7. Concluding Remarks 

As stated above, the Frequency Doubling Target is the method of choice because it is not subject to any of 

the largest contributors to the error vector. In addition the signal levels applied to the phase detector are 

at an optimum level for optimum phase detector preformance and accuracy. 

The zero crossing phase determination method has the advantages of full cycle measurement without 

ambiguity within the sine curve cycle. This gives it a clear advantage over the other methods. 
26

It has been implied that only phase needs to be measured to determine the range to the target. In order to 

determine the error vector and calibrate the measuring system by subtracting the error vector, it will be 

necessary to measure the amplitude of the measured reflected signal as well. Considerable developmental 

work will be required to develop a method to determine the error vector and hence calibrate the system. 

The operating frequency selection will be influenced by available spectrum and by optimization of the 

phase slope curve for minimum error while avoiding target position ambiguity. Figures 22, 23, and 24 

are plots of frequency versus wavelength. The maximum deflection of the aeroshell should be slightly 

less than λ/4. This requirement, the plots and the maximum expected aeroshell displacement or 

deformation make it possible to identify an operating frequency for optimum performance. 

 

 

 

Frequency in MHz vs Wavelength in Centimeters 

10

15

20

25

30

1000 1500 2000 2500 3000

Frequency in MHz

Wave length in Centimeters

Figure 22. Frequency vs wavelength for lower frequencies. 
27

 

Frequency in MHz vs Wavelength in Centimeters 

2

4

6

8

10

3000 5000 7000 9000 11000

Frequency in MHz

Wave length in Centimeters

Figure 23. Frequency vs wavelength for higher frequencies. 

 

 

Frequency in MHz vs Wavelength in Centimeters

1

10

100

1000

100 1000 10000

Frequency in MHz

Wave length in Centimeters Wavelength in Centimeters

Figure 24. Frequency vs wavelength on logarithmic scale. 
28

References: 

 [Mini-Circuits] Mini-Circuits Data sheet for model ZRPD-1+Phase Dector 

Minicircuits.com 

[Bilik] Vladimir Bilik, Six-Port Measurement Technique: Principles, Impact, Applications, Slovak 

University of Technology, Faculty of Electrical Engineering and Information Technology, Ilkovicova 3, 

SK-81219 Bratislava, Slovakia. E-mail bilikv@elf.stuba.sk 

[Coca] Eugen COCA1 , Valentin POPA2, Edvaluation of RFID Location Systrems University "Stefan 

cel Mare" of Suceava, Faculty of Electrical Engineering and Computer Science, 13, Universitatii Street, 

720229, Suceava, Romania, 1eugen.coca@usv.ro, 2valentin.popa@usv.ro 

[Nititin] Pavel V. Nikitin, Rene, Martinez, Shashi, Ramamurthy, Hunter, Leland, Gary Spiess, and 

K. V. S. Rao, Phase Based Spatial Identification of UHF RFID Tags, Intermec Technologies 

Corporation, 6001 36 th Ave W, Everett, WA, 98203, USA 

[Georgiadis] Apostolos Georgiadis, Gain, Phase Imbalance, and Phase Noise Effects on Error Vector 

Magnitude, IEEE Transactions on Vehicular Technology, Vol. 53, No. 2, March 2004 

[Rytting] Douglas Kent Rytting, Network Analyzer Accuracy Overview, Agilent Technologies, 1400 

Fountaingrove Parkway, Santa Rosa, CA 95403 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Methods to Determine the Deformation of the IRVE Hypersonic Inflatable

Aerodynamic Decelerator

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Young, William R.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

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14. ABSTRACT

Small resonant targets used in conjunction with a microwave reflectometer to determine the deformation of the Hypersonic

Inflatable Aerodynamic Decelerator (HIAD) during reentry are investigated. The reflectometer measures the distance to the

targets and from this the HIAD deformation is determined. The HIAD is used by the Inflatable Reentry Vehicle Experiment

(IRVE) which investigates the use of inflatable heat shields for atmospheric reentry. After several different microwave

reflectometer systems were analyzed and compared it was determined that the most desirable for this application is the

Frequency Doubling Target method.

15. SUBJECT TERMS

HIAD, IRVE, deformation, microwave, phase, reflectrometry, target

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