M'L INST. OF STAND & TECH R.I.C.

UllOS M7tT13

N!ST

PUBLICATIONS

NisrUnited States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Technical Note 1398

Portable Calibrator for Across-the-Road

Radar Systems

Arthur R. Ondrejka

Robert T. Johnk

K

100

J5753

^0.1398

1998

NIST Technical Note 1398

Portable Calibrator for Across-the-Road

Radar Systems

Arthur R. Ondrejka

Robert T. Johnk

Electromagnetic Fields Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

May 1998

>!c.^'

Q

k

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'"TES

U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary

TECHNOLOGY ADMINISTRATION, Gary R. Bachula, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director
National Institute of Standards and Technology Technical Note

Natl. Inst. Stand. Technol., Tech. Note 1398, 40 pages (May 1998)

CODEN:NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1998

For sale by the Superintendent of Docunnents, U.S. Government Printing Office, Washington, DC 20402-9325
CONTENTS

1. INTRODUCTION 1

2. DESCRIPTION OF ACROSS-THE-ROAD RADAR SYSTEMS 5

3. DESCRIPTION OF CALIBRATOR 8

4. OPERATION AND DESIGN 9

5. SWITCH CONTROL SECTION CIRCUIT OPERATION AND DETAILS 13

6. LABORATORY TESTS ON THE CALIBRATOR 16

7. RECOMMENDED TESTS FOR ACROSS-THE-ROAD SYSTEMS 19

8. DESCRIPTION OF TESTS PERFORMED 20

9. CONCLUSIONS 23

10. REFERENCES 24

APPENDIX A. FOURIER ANALYSIS OF THE CALIBRATOR PERFORMANCE 26

APPENDIX B. REFLECTIVE PHASE SHIFTER DESIGN CONSIDERATIONS 30

111

PORTABLE CALIBRATOR FOR ACROSS-THE-ROAD RADAR SYSTEMS

Arthur R. Ondrejka and Robert T. Johnk

Electromagnetic Fields Division

National Institute of Standards and Technology

Boulder, Colorado 80303

The calibrator provides simulated radar reflections with a choice of target signatures,

such as automobile, truck, small vehicle like a motorcycle, and several trucks in close

proximity, to test those radars that have the ability to distinguish these targets. The

calibrator can also simulate a vehicle approaching or receding from the radar in order

to evaluate the radar's effectiveness in differentiating the direction oftarget motion.

This paper describes an inexpensive, easy-to-use electronic calibrator that can be used

to improve the credibility of across-the-road type radars. Such a device can detect

actual failures that generate erroneous speed readings. Regular documented use of the

calibrator can greatly facilitate the maintenance of across-the-road systems by

indicating faulty readings and trends in the radar operation, indicative of imminent

failure. A precision calibrator is necessary to determine that the radar instrumentation

is operating properly and that the computer algorithm results in displaying the correct speed.

Key Words: across, antenna, accuracy, beam width, calibrator, chirp, Doppler,

Fourier, photo, radar, switch, transmission, verification, uncertainty.

1. INTRODUCTION

An electronic calibrator for evaluating across-the-road radars has recently been designed and developed

by the Electromagnetic Fields Division at the NIST Boulder laboratories. The purpose of this calibrator is to provide a precision standard reference signal for the verification of radar units. This

type of radar has been used extensively in Europe since 1974 [1], but is only now being considered for

introduction into the United States. Even though modem across-the-road systems are basically a CW

Doppler radar, these systems are significantly different from the older, down-the-road radar guns,

which have to be aligned with the direction of motion of the moving target vehicle. Across-the-road

radar transmits energy into a very narrow beam that is positioned at an angle with respect to the road

The speed measurement occurs when a target vehicle passes through the radar beam. The fact that

measurements are no longer being taken with the target vehicle traveling parallel to the main radar

beam introduces problems into the speed measurement system that require a careful daily calibration to

1
Radar Beam Target Vehicle

Radar Antenna

Figure 1. The across-the-road radar concept.

guarantee the accuracy of an across-the-road system. This paper describes an electronic device that can be used for this purpose. The simple architecture of this calibrator makes possible low-cost mass

production using printed circuit board techniques.

Across-the-road radar systems have several advantages over the more familiar down-the-road systems.

Perhaps the most salient is the ability to provide positive identification of offending vehicles by

providing a license plate photograph of an offending vehicle. Also, across-the-road systems can be

operated in the automatic, unattended mode, thereby fi'eeing law enforcement personnel. Across-theroad systems can register up to 260 offenses per hour, a capability that cannot be matched by older

down-the-road radars or the newest state-of-the-art lidar systems [9]. Also, since the radar beam

energy is not directed down the road, detection by personal radar detectors is a much more diflScult. Thus, across-the-road systems possess stealth capabilities that conventional down-the-road systems

simply do not have [1]. A significant disadvantage of across-the-road radars is slightly reduced accuracy. When these radars

are used correctly, their speed accuracy is generally ±2 mph at 55 mph. A properly used down-theroad radar gun can determine vehicle speed to well within a ±1 mph uncertainty. Future requirements

may be as restrictive as +1, -2 mph at maximum speed (say 120 mph). However, the percent accuracy

is relatively constant at different speeds. A -2 mph error at 120 mph is a -1.7 percent error. This same percentage at 55 mph gives a -0.9 mph error. An error limit of +1, -2 mph is pushing the normal

capability of the radar system, so the radar will have to be calibrated often. We have designed our

calibrator to make this operation easy.

The concept of an across-the-road radar system is depicted in Figure 1, where the radar is placed at the

2
side of a thoroughfare and the radar main beam is aimed at an angle 9 with respect to the direction of

motion of traffic. A target vehicle traveling at highway speeds passes through the beam very quickly,

usually in less than a second. The radar system must make a correct measurement of the vehicle's

speed quickly, as well as compensate for both the error caused by the angle of the radar beam and the

variation in the Doppler-shifted frequency as the vehicle moves through the various angles of the beam.

This change or chirping of the Doppler frequency is called the cosine effect [1,2,3,4] since the

frequency is a fiinction of the cosine of the angle between the direction of target motion and the radar

beam.

The Doppler-shifted frequency is given by

/Doppler = fr^fd=fr ± ^^^cos(e),

3x108 (1)

where v (m/s) is the speed of the target vehicle, fr (Hz) is the transmitted frequency of the radar, U is the Doppler shift, that is, the difference between the Doppler-shifted frequency and the transmitting

1600

1500-

N

s 1400

>.u

B

0) 1300 S

O"

9t i

1200 u

V

a

a.o 1100

1000

900

200 300 Time (ms)

400 500

Figure 2. Calculated Doppler frequency from eq (1) for a spherical reflector passing

through an across the road radar beam at 20 mph. Note the upward chirp in the

Doppler shift indicates that the target is moving away from the radar.
frequency, and is the angle between the direction of the traffic flow and the main beam maximum.

The term 'T)oppler frequency" is sometimes used instead of Doppler shift in the literature. The plus

sign in Eq (1) denotes an approaching target with an upward Doppler shift, and a minus sign

corresponds to a downward Doppler shift due to a receding target. Equation (1) would be exactly true

if the target were a small reflector like a sphere with only one scattering center located at a point. The

change in Doppler frequency due to the cosine term in Eq (1) is depicted in Figure 2, where an upward

chirp for a receding target has been plotted. However, since all motor vehicles possess complex,

distributed geometries, as is depicted in Figure 3, various portions of a target vehicle will pass through

the main radar beam at different times resulting in a complicated spectrum of overlapping Doppler

chirps in rapid succession. This sequence of signals is unique for a given type of vehicle and is called

the vehicle's signature [1,5]. Figure 4 shows the complexity of the measured Doppler spectrum that was detected by an across-the-road system during actual field measurements obtained here at NIST.

The target vehicle was a pickup truck passing through a radar beam at 20 mph. Figure 5 shows the same data after averaging. The chirps correspond to the intervals of rapidly rising frequency, and there

are three distinct chirps visible. Across-the-road systems must process vehicle signatures that are far more complicated than those obtained for the older down-the-road systems. This makes it necessary to have a calibrator to establish their accuracy.

Target Vehicle

"^^

Target V

Additional

Scattering

Centers

Radar Beam

Scattering Center

Radar Antenna

Figure 3. Multiple scattering centers of a target vehicle.
1600

200 400 Time (ms)

600 800

Figure 4. Measured Doppler frequency spectrum for a small pickup truck passing

through a radar beam at 20 mph. The time interval for each measurement is 25 ms.

2. DESCRIPTION OF ACROSS-THE-ROAD RADAR SYSTEMS

The block diagram in Figure 6 shows that the across-the-road radar system is composed of a lowpower CW generator that transmits a continuous wave of microwave radar energy in one of three

microwave bands, an antenna to focus the energy into a narrow beam, a receiver that senses the

microwave energy that is reflected from the target vehicle and measures the Doppler shift between the

transmitted energy and the returned reflection, and a computer that processes the received signal to determine the speed of the target vehicle. An optional camera which can photograph the target just as

it emerges from the radar beam may be included [1,6]. Three microwave bands are allocated for the

operation of across-the-road radar systems Table 1 gives the band, the range of carrier frequencies,

and a representative range of the Doppler shifts for a vehicle speed of 55 mph, and when the carrier

frequency is exactly at the middle ofthe band [7].

The chirp frequencies are given as an example only. The exact range of frequencies must be calculated

for each radar carrier frequency using eq (1). The calibrator being described was designed for the Kband units, but an appropriate calibrator can be built for any radar band.

The radar antenna plays a vital role in the operation of an across-the-road radar system. The ftinction of
1600

300 400 Time (ms)

600 700 800

Figure 5. Weiglited averages of the measured Doppler spectrum for the same pickup

trucli. Each point is averaged over a 25 ms intreval.

the antenna is twofold: it enables the radar to discriminate spatially between various vehicles; it also

provides gain that boosts the reflected signal to a level that enables accurate and efficient processing.

Several different antenna t\'pes are used on these radar s\'stems; parabolic dish antennas, pyramidal

horn antennas, and slotted array types. WTiile horn and parabolic dishes are the most familiar types,

slotted arrays are conformal, rugged, and amenable to gain pattern adjustment [8].

The CW generator on across-the-road s\'stems is tvpicaUy a Gunn diode oscillator that generates

power on the order of 1 00 mW. These sources generate clean sinusoidal signals that are quite suitable

for use in CW Doppler radar applications [7,8], and the power is more than sufficient to obtain

accurate speed data for the short measurement distances that are involved.

Table 1. Doppler shifts for selected radar bands.

Band Carrier frequency range (GHz) Doppler frequency chirp (Hz)

X

K

Ka

10.50-10.55

24.10-24.25

33.40-36.00

1564-1667

3592-3828

5156-5495
cw

GENERATOR

24.10-24.25 GHz

I

MULTIPLEXER

HOMODYNE

RECEIVER

\,/

TARGET

VEHICLE

approaching

doppler

receding

doppler

DIGITAL

SIGNAL

PROCESSOR

DIGITAL

READOUT

Figure 6. Block diagram of an across-the-road radar system.

The most complex and expensive component of an across-the-road system is the receiver. It must not

only be capable of measuring the speed of the target vehicle but also must be able to discriminate

between vehicles that are approaching from those that are moving away from the antenna. For this purpose, the receiver must have the ability to determine whether the Doppler-shifted frequency is higher or lower than the transmitted signal, which requires a sophisticated filtering or a sideband

cancellation scheme [7,8]. Furthermore, since the speed limits for trucks are sometimes different than

automobiles, the radar must also be able to identify the type of vehicle in its beam. Such a capability is implemented by measuring the amount oftime that a selected target vehicle is in the radar beam.
3. DESCRIPTION OF CALIBRATOR

The operational concept of the NIST-developed calibrator is depicted in Figure 7. The calibrator

receives the transmitted radar signal and directs it to a switched passive delay line which, in turn,

modulates and reflects the signal back to the radar under test. The switching sequence is precisely

controlled so that the reflected signal is modulated in a manner that is very similar to that of a passing

vehicle. The reflective phase shifter circuit that is realized in this manner mimics a vehicle passing

through the radar beam and provides the basis for an accurate calibration standard. The reflective

switch principle resuhs in a one-port architecture that is simple and easy to implement using printedcircuit board techniques, suitable for low-cost mass production. Thus, it might very well be cost

effective and economical to incorporate a printed circuit version of the NIST calibrator into all operational across-the-road systems for on-site performance verification.

For actual radar system calibrations, the signal generated by the calibrator should cause the radar to read a speed of 55 mph for several categories of vehicles (cars, motorcycles, trucks) that are either

approaching or receding from the radar. Since the speed indicated in the readout on the radar unit

cannot be adjusted by the operator, the results ofthese tests are simply recorded for future reference. If

the speed readings are outside the error limits set by the user, the operator may add or subtract the

REFLECTIVE

TERMINATIONS

ANTENNA

ANTENNA

RADAR

UNIT

INCIDENT

WAVE

FREQ = f

SINGLE -POLE

N -posmoi

SWITCH

REFLECTED

WAVI

FREQ = f±f

r doppler

MATCHING

NETWORK

CW DOPPLER

RADAR SYSTEM

UNDER TEST SWITCH

CONTROLLER

RADAR CALIBRATOR

Figure 7. The NIST radar calibrator concept.

8
offset difference to the actual speed readings to correct the measurements in real traffic. This is tedious. Furthermore, the operator is warned that the unit may be marginal and approaching a

condition of more serious errors. Under these conditions, it is recommended that the radar unit be

returned to a service depot for repair and readjustment.

The calibrator, the details ofwhich are to be described, can be enclosed in a volume less than 1 5 cm on

a side and weighs less than 1 kg, including batteries. The operation of the NIST calibrator is straightforward. In use, it is placed in front of the radar unit and provides a synthetic reflected signal

each time a switch labeled "Calibrate" is depressed. It simulates a Doppler signal which is similar to

that produced by an actual target vehicle traveling at 55.0 mph ± 0.1 mph. It approximates the

information of the cosine variation in Doppler frequency and provides a selection of durations of the

signal to simulate a motorcycle, automobile, truck, or cluster of several vehicles. Furthermore, it can

shift the radar's microwave frequency up or down depending whether it is simulating an approaching or

receding vehicle.

The required horizontal beamwidth for an across-the-road radar is 5°. This is a measure of the

intensity ofthe radiated power density as a fiinction of angle from center of the radar beam (boresight).

For a 5° beamwidth, the power density in the beam decreases to half the boresight power at ±2.5°.

The pattern amplitude decreases to a small value at ±5°. The NIST-developed calibrator is designed to

chirp the entire ±5°, which is equivalent to sweeping from 53.0 mph to 56.5 mph, on the upward chirp.

There are two normal combinations for the calibrator: either the reflected microwave frequency can be

higher than the one transmitted by the radar, as if the target were approaching, and the frequency is swept (chirped) dovmward toward lower frequency, or else the reflected frequency is lower than the

radar, and the chirp is upward, as for a receding target, ff the radar is set to detect approaching targets

and the calibrator is set for the receding combination, the radar should reject the signal entirely.

The calibrator is intended to be used for six routine tests which are done at the speed measurement site before and after each day's use of the radar. Resuhs of these tests are usually recorded in the radar

operator's log for fiiture reference. These six tests include the Doppler audio test, speed calibration,

vehicle type discrimination, direction separation (approaching and receding vehicles), radar system

sensitivity, and EMI compatibility with the other electrical and/or electronic systems which might be

located in the radar vehicle.

4. OPERATION AND DESIGN

Figure 8 shows a typical calibrator with an exploded view showing the major components. A Teflon

radome covers the aperture of the microwave horn antenna and provides protection from the

environment without significantly impeding the microwave energy from the radar unit. An aluminum

shield around the antenna prevents radar energy from leaking past the antenna and interfering with the

operation of the control circuits. The printed circuit board mounted against the back wall of the

enclosure contains all the associated circuitry needed for operation of the calibrator.
Teflon Radome

"Calibrate"

Switch

Multi-Function Switch

1) Power & self calibration

2) Pulse duration and approaching & receding

Doppler

K-Band

Pyramidal

Horn

Antenna

Aluminum

Case

PC Board

with Logic &

Microwave

Circuitry \

Aluminum

Back Plate

Teflon

Radome

Figure 8. Drawing of the NIST calibrator with an exploded view.

10
A momentary switch (labeled "Calibrate") located near the handle on top of the calibrator initiates each

reflected signal. The switch located on the side ofthe box turns the power on and selects the particular

type of operation desired, that is, auto or truck, approaching or receding, and chirp upward or downward. Several other options include various self tests and radar diagnostics.

Figure 9 shows a detailed block diagram of the calibrator. The architecture of the calibrator consists of

two main functional units: the microwave switch section and the switch control section. The switch

section consists of an antenna, a single-pole five-position switch, and a matching network. The switch

control section contains low-frequency electronic circuitry that generates precisely controlled signals

which drive the switch to a number of prescribed sequences. The selection of a sequence is determined

by the particular test that is being performed on a given radar system.

Basically, the device is a modulated passive reflector. The CW microwave energy from the radar is received by the calibrator antenna, reflected from the open circuit end of the switched delay line, and

re-emitted toward the radar unit. The information carried by the reflected signal is determined by the

way the switch is sequenced. In each successive switch position, the delay line is a little longer so that

the microwave energy has fiarther to travel, giving a reflected signal which seems to be coming from an

object that is moving away from the radar. Eventually, the switch must return to its starting position,

but this simply moves the waveform backward by 360° v^th no noticeable interruption in the Doppler

shift. The overall eflfect is that of a continuously receding vehicle. Of course, the switch can be

sequenced in the reverse order giving the eflfect of an object approaching the radar. One complete

sequence of the switch generates one cycle of the Doppler frequency. The switch rate is continuously

increased or decreased in constant increments to simulate the desired chirp. A detailed mathematical

analysis ofthe calibrator operation is presented in Appendix A.

In the microwave section of the calibrator, only the antenna, switch, and delay lines operate at the

K-band frequencies, simplifying the microwave circuitry. For a commercial version, we anticipate that

these three components will be fabricated onto a single microwave printed circuit board substrate In our present breadboard, the antenna used is a K-band standard gain horn using a precision 2.92 mm

adapter. The switch is a commercially available single-pole, five-position, coaxial diode switch which was originally designed for use up to 18 GHz. As Figure 9 shows, the matching network consists of a shunt-connected tuning stub located at the switch input to lower its input VSWR at the operating

frequency of 24.15 GHz. The shunt stub consists of a coaxial tee connector to which is connected an open ended length of 0.141 in diameter coax line. This would probably not be necessary if the switch were designed for use at K-band. Since the switch is coaxial, we designed the delay lines from short

lengths of the same coaxial cable as the tuning stub. Unfortunately, the switch was manufactured with

SMA connectors on all ports, so all stubs had to follow suit, and because of the interacting eflfects of all the connectors, the whole combination had to be modeled on a linear microwave network simulator to optimize it properly. A single substrate commercial unit would be much simpler and very inexpensive.

Such an integrated microstrip architecture would be much easier to produce and it would perform

much better. The process and procedures for designing the microwave switch section is discussed in detail in Appendix B.

11
PYRAMIDAL

HORN

ANTENNA

OPEN-CIRCUIT

COAXIAL STUB

REFLECTIVE LOAD

(50 Q 0.1 41 "COAX)

(5 TOTAL)

OPEN-CIRCUIT 0.141"

COAXIAL STUB 50 Q

(MICROWAVE SECTION)

(CLOCK & LOGIC SECTTCDN)

DIRECTION

SELECTOR

upper / lower

sideband

COUNTER

/

MULTIPLEXER

START

CONTROL

LOGIC

I

RAMP

SELECTOR

DURATION

SELECTOR

CHIRP RAMP

GENERATOR

VOL AGE

CONTROLLED

CLOCK

SWITCH

DRIVER

Figure 9. NIST radar calibrator system block diagram.

12
5. SWITCH CONTROL SECTION CIRCUIT OPERATION AND DETAILS

The remaining circuits are necessary to drive the switch and are located on a separate circuit board.

This section contains clock circuits that provide the signals that step the switch and the precision ramp

voltage that sweeps the clock frequency upward or downward. The clock frequency and the ramp

voltage will drift for several minutes after the calibrator is turned. In order to stabilize these critical circuits and avoid the problems associated with drift, they are allowed to free run and generate a Doppler shift which is continuously being chirped first upward and then downward. This sequence is not interrupted by a request for an output. When the operator initiates a reflection sequence by

depressing the "Calibrate" switch, the logic circuit selects one ofthe ramps as directed by the operator.

The chirped clock signal activates a simple ring counter which can be stepped from low bit to high bit or vice versa. This determines in which direction the switch will be sequenced, as an approaching or receding target. This process generates either an upper or lower sideband with respect to the radar

carrier frequency and should not be confiised with chirping. The remaining circuitry is necessary to

trigger the logic sequence properiy.

The operator can select four durations for the simulated signal, 0.1 s, 0.25 s, 1.40 s, and 2.1 s. These

correspond roughly to length of time that various sized vehicles are actually in the radar beam if they

are traveling at 55 mph. These times simulate a motorcycle, an automobile, a truck, and a combination

ofvehicles that are too close to resolve. The first and last durations are often outside the capabilities of

the radar, which simply notifies the operator of an error condition and withholds a speed reading

output. Clearly, these are at best approximate times since the radar beam becomes wider at greater

distances and different automobiles have different lengths, both of which would affect the signal

duration.

The calibrator can then be set to synthesize the chirp variation due to a vehicle passing through the

radar beam either approaching or receding. At 55 mph and a 5° wide K-band radar beam centered at 20° to the line of approaching traffic, and for a carrier frequency of 24.175 GHz, we would expect the

Doppler shift to chirp downward from 3828 Hz to 3592 Hz. This is not a linear sweep but a curved

fiinction determined by the cosine ofthe angle (see Eq (1)) between the direction of the vehicle and the

direction of the radar beam. Often, radars make no use of the information in this curvature and

presume a linear sweep. The calibrator is corrected for the slight difference due to the curvature.

Figures 10 and 1 1 are schematics of the actual circuits used for our prototype system. Figure 10 shows

the system clock. It is adjusted to be five times the desired Doppler shift frequency, since our switch

requires five positions per cycle of Doppler. The frequency of the clock is modulated by a triangular

(ramp) waveform so that its frequency is alternately chirped upward and downward. The clock and

ramp generators are two halves of a CMOS TLC556I depicted in Figure 10. In each part, the output

square wave drives the RC timing circuit to produce the triangular ramp waveform. Rl-Cl controls

13
Chirp Modulated

19 kHz Clock

Chirp

Timing

Pulse

TLC556I

TIMER

IC

sw1a

gg p Resistors R1 - Duration Switch

Figure 10. Clock signal generator circuit.

14
the pulse duration and the sweep ramp voltage. R2-C2 controls the 19 kHz clock frequency R3

controls the amount of ramp voltage which is applied to the 19 kHz clock timer, therefore adjusting the

amount of frequency chirp that will be produced. Switches SW la, lb, and Ic, can be configured to

select any of the pulse durations given in Table A of which only the four mentioned previously are

actually used. Switches SW 2a and 2b select either the normal ramp modulation, or a high or low dc

voltage which will produce a constant Doppler shift equal to, respectively, the high or low frequency

limit of the chirp. The frequency of this unchirped signal can be measured using a precision counter,

and if there are errors, the low frequency can be adjusted using R2. The high frequency can be

adjusted using R3.

If the accuracy or stability of the clock and ramp circuitry is not adequate under all operating

conditions, such as extremes of operating temperature, the clock can be replaced with a crystalcontrolled device, and the ramp generator by a more precise digital circuit.

The Switch Driver in Figure 11 is a ring counter composed of a CD4015 dual shift register and

associated logic circuits. The two registers are clocked in opposite directions, and one of these is selected to produce the effect of approaching traffic and the other for receding traffic. A high bit is introduced into the register and propagates through all four cells. Each of these logic conditions

activates one position of the microwave switch. The fifth position of the switch is activated when all register cells are low (CD4002). The binary encoder was necessary only because the microwave

switch we selected required binary coded inputs. This circuit may not be necessary for other switches.

The microwave switch is a commercially available unit designed for use up to 1 8 GHz.

The remaining electronics in the lower portion of Figure 1 1 are logic control circuits. Since the clocks

are free running, a randomly timed request from the operator to initiate a signal will rarely occur at the

correct part of the clock cycle. In order to avoid generating a faulty signal, the circuit waits until it recognizes the end of the chirp cycle just before the correct one. Then the logic turns on the

microwave switch at the beginning of the desired chirp. The circuit shovm as Start Logic makes this selection.

The manual "Calibrate" switch, SW4, is normally in the reset position and the output from U26 is low.

The operator begins a Doppler chirp by moving the switch to the Trigger position. The pair of Schmitt

triggers form a switch debounce. If the chirp timing signal at SW5 is low (wrong chirp ramp in progress), the output of U19 goes high setting the flip-flop U23/24 high. U25 then waits for the chirp

timing signal to go high before allowing an output, and the timing cycle is correct. All later repetitions

ofthe chirp timing pulse are excluded from the output until flip flop U17/ 18 is reset by returning switch

SW4 to its Reset position.

If the chirp timing signal is already high (desired chirp ramp is in progress) when switch SW4 is triggered, taking an output from the ramp generator would produce only a portion of the ramp

Therefore, the logic waits until the previously described sequence takes place. The high input to U19

keeps its output low which retains the output of U23/24 low, and the logic output stays low. When the

chirp timing signal goes low, the output of U19 goes high, switching U23/24 output to high setting

15
Direction Control Switch <V- -< 8w3a,bo^3p

Binary Encoder CD4050

U9

SWITCH DRIVER 2N6660 Speaker

"Test 8W4

Reset "J40imU17

S ' Schmitt Triggers CO40106

From clock A"^ •"'^ signal generator 19kHz

Clock

'^3^

U20

START LOGIC

) 4001)0-' Switch

Driver U25 U26 Signal

J40m>--g4002)(>-^

U19 -^-5400^

H^-

Figure 11. Schematic diagram of the switch driver and control logic.

with U25 ready for the next high from the chirp timing logic. As soon as this high appears (correct

chirp ramp), the output of U25 goes low, turning the logic on and delivering the 19 kHz chirp to the

switch driver circuit.

6. LABORATORY TESTS ON THE CALIBRATOR

The spectral content of the reflected calibrator signal was obtained using the simple laboratory test setup of Figure 12. The test setup consisted of a CW microwave synthesizer, a 20 dB waveguide

directional coupler, a WR-42 waveguide pyramidal horn antenna, and a microwave spectrum analyzer.

This setup provides a direct measure of the signal content that is reflected by the calibrator and thereby an assessment of the calibrator performance. In this test, the calibrator was switched at a constant rate with an equal time allocated to each of the switch positions. In Figs. 13 and 14 the signal at the center of the spectrum analyzer trace is the radar transmitter output (carrier) which was chosen to have a 16
Microwave

Synthesizer

Spectrum

Analyzer

WR-42 Waveguide

Directional Coupler

(20 dB)

^

Horn

Antenna

>

NIST

Calibrator

Figure 12. Laboratory setup for the calibrator performance test.

-40

60 -

m

¥

3

O

a

(0

O -80

Q.

a

oQ

•uo

>-100

e

o

o

-120

Center Frequency = 24.099 999 2 GHz

I

I

I I I I

I

I M I I I I I I M I

I I I M I

I I I I

I

I I I I -5000-4000-3000-2000-1000 1000 2000 3000 4000 5000

A Frequency [Hz]

Figure 13. Measured spectrum obtained from the NIST calibrator for an increasing

phase sequnce with 1/Ts= 3620 Hz. Note that the dominant reflected spectral component

is 3620 Hz above the synthesizer transmitting frequency of 24.10 GHz.

17
frequency of 24.10 GHz. The signals that are located ±3620 Hz on either side of the carrier are the

Doppler-shifted sidebands produced by the calibrator. This is the correct Doppler shift for the original

simulated speed of 55 mph. If 65 mph would be a more appropriate speed, the correct Doppler shift would be 4670 Hz. The calibrator is set in the "test" mode where the chirp generator is de-activated,

and the output is a continuous signal. The upper curve (Figure 13) shows the resulting frequencies

when the calibrator is set to simulate an approaching vehicle. The dominant signal is the upper

sideband frequency which is clearly 20 dB greater than the reflected carrier. The undesired lower

sideband is suppressed 25 dB below the desired one. The lower curve (Figure 14) shows that the reverse is true when the calibrator is set for a receding vehicle.

The suppression of the undesired sideband is a ftinction of several parameters, but principally it is determined by the number of positions in the microwave switch. A Fourier series analysis of the

switched delay line signal indicates that a four-position switch would provide about 16 dB suppression,

which we decided would be inadequate. A five-position switch provided a significant improvement of

an additional 9 dB. A six-position sv/itch would involve higher cost with only slight performance

improvement over the five position switch. The five-position switch was chosen as the practical

compromise. A Fourier series analysis ofthe switch is presented in Appendix A.

-40 —I

-140

Center Frequency = 24.099 999 2 GHz

I I I I

I

I I I I I I I M I

I I I I 1 M I I

I

I I I I

I

I' M I

I M I I I I I M I -5000-4000-3000-2000-1000 1000 2000 3000 4000 5000

A Frequency [Hz]

Figure 14. Measured spectrum obtained from the NIST calibrator for an decreasing

phase sequnce with 1/Ts= 3620 Hz. Note that the dominant reflected spectral component

is 3620 Hz below the synthesizer transmitting frequency of 24.10 GHz.

18
The other parameters that should be considered are those that aflfect the amplitude of the reflected

signal. Therefore, the switch should be chosen to have a minimum change in input reflection

coefficient amplitude and insertion loss between switch positions.

7. RECOMMENDED TESTS FOR ACROSS-THE-ROAD SYSTEMS

These tests, classified as Field Calibrations, are intended to evaluate those parameters of an across-theroad radar system that have a direct and significant effect on the accuracy of the radar unit, and which

have the greatest possibility of changing fi-om day to day. It is recommended that they be performed

daily. Five tests can be performed simultaneously by this procedure: audio output, speed calibration,

direction sensing, radar sensitivity, and EMI susceptibility. Errors in the angle of the radar beam due to misalignment ofthe radar vehicle with the direction oftraffic can not be measured by this calibrator.

A Audio Output. An audio-fi"equency output ofthe Doppler shifl: is available on many commercially

available radar systems. This may be produced either by a calibrator or any vehicle passing through the

radar beam. During this test, the sound intensity can be adjusted to a level that can be heard

comfortably in normal traffic noise.

B Speed Calibration. The radar should be tested for correct speed reading before and after use in

traffic using the precision electronic calibrator. The ideal displayed speed for this calibrator is 55.0 mph.

C Direction Sensing. The direction sensing circuits should have at least 20 dB rejection of the

undesired direction compared to the desired one. This should be tested before and after use in a traffic condition. The speed test cycle is repeated using the electronic calibrator set to synthesize an approaching vehicle while the radar is set to detect a receding one. The radar should reject the signal

giving a reading of either mph or ERROR. The other combination of synthetic receding vehicle and

approaching direction in the radar can also be verified. D Radar Sensitivity. The radar's sensitivity is measured by the greatest distance over which it can make a correct speed measurement. This "initial detection range" can be tested daily as part of the

setup procedure using the electronic calibrator. The calibrator output is adjusted to a signal strength

which is small, but one which the radar should be able to measure accurately. The radar can be tested

fiirther by moving the calibrator fi"om its normal position of 2 m in fi'ont of the radar antenna to 6 m

This effectively reduces the reflected signal by about 10 dB, which is approaching a value that is too

small for the radar the measure. Success in measuring this signal indicates that the radar is fiinctioning

at maximum sensitivity. Failure in this test does not disqualify the radar, but may warn the operator to expect continued decrease in the radar's eflfectiveness.

E Susceptibility to Radiated EMI. The radar must continue to operate when exposed to the normal

fields that occur within the radar vehicle during operation of accessory equipment such as on-board or

19
personal transceivers. These tests can be done while the calibrator is positioned for testing the radar.

Each transmitter can be turned on for the duration of one calibrator test cycle. Clearly, the radar

should still read the correct speed. If problems occur, the test indicates that, first, the particular

transmitter should not be activated during radar operation, and second, that some type of maintenance

is required to avoid the problem in the fliture.

8. DESCRIPTION OF TESTS PERFORMED

A commercial radar unit was chosen to test the effectiveness of our calibrator. This radar operated in

the K band at a fixed fi"equency of 24. 1 5 GHz. It was composed of a control unit with a separate

microwave generator/antenna unit. The control unit contained the switches necessary for the operator

to direct the fiinctioning of the radar, such as whether it should sense automobiles or trucks,

approaching or receding, close or far. It also was used to input the information about the current speed

limits for autos and trucks. This unit contained the computer which calculated the speed of the target

fi^om the Doppler fi-equency, and determined when a violation occurred.

The generator/antenna unit produced the CW microwave signal, radiated it into a 5° wide beam, and

received the reflected signal. This unit also processed the signal to determine whether the target was

approaching or receding. The associated camera/flash unit was not included in the NIST tests.

The radar unit was set up in its standard configuration with its own internal calibrator connected

between the antenna unit and the radar unit. This internal calibrator injects a Doppler-shifl fi-equency

directly into the low-fi-equency audio section of the radar unit without passing through the antenna or any of the microwave circuitry. It has a constant (not chirped) Doppler fi-equency which simulates a

target vehicle traveling at 37 mph. This internal calibrator was activated many times during the tests and always gave the same response of 37 mph.

For these tests, the NIST calibrator was set to generate a Doppler signal appropriate for a speed of

55 mph. It was located directly in the beam of the radar under test, and 2 m away fi-om it. The

operator adjusted the calibrator controls for the proper test sequence, for example, truck approaching,

and activated the start switch. Within a few seconds, the calibrator produced the required reflected

signal and a speed reading appeared on the radar display. With both the calibrator and the radar preset to detect approaching trucks, for example, the radar should read 55 mph ± 1 mph. When the radar was

preset to detect any improper combination of vehicle and direction, it should have read either mph or ERROR.

There were several switch options on the fi-ont panel ofthe radar unit that are listed in Table 2.

There were several indicator lights on the radar fi-ont panel including a power on, a battery condition,

and a signal present. This last indicator remained lit only as long as a Doppler signal was being

presented to the radar. At power up, the radar made some critical self tests and proceeded only afl;er it had passed the tests.

20
Table 2. Switch options on the front of the radar unit.

Switch option Function a target approaching, receding, or both

b target automobile, truclc, or both

c automobile speed limit input

d truck speed limit input e radar range setting I or II f radar reset switch which sets the speed readout to 00 mph

g power switch

Table 3. Test results on a commercial across-the-road radar system,

Radar operational mode Pulse Signal Speed Offense

duration recorded? recorded recorded?

Mode 1: Calibrator receding - Radar

receding Automobile mode - Chirp up

Mode 2: Calibrator receding - Radar

receding Truck mode - Chirp up

0.1 s Yes No

0.25 s Yes 56 Yes

1.35 s Yes 56 No

2.00 s Yes 0- No

0.1 s Yes No

0.25 s Yes 56 No

1.35 s Yes 56 Yes

2.00 s Yes 0- No

Mode 3 : Calibrator approaching - Radar approaching Automobile mode - Chirp down

0.1 s Yes 54 Yes

0.25 s Yes 55 Yes

1.35 s Yes 55 Yes

2.00 s Yes 56 Yes

Mode 4: Calibrator approaching - Radar approaching Truck mode - Chirp

down

0.1s Yes 53 No

0.25 s Yes 55 No

1.35 s Yes 56 No

2.00 s Yes 56 No

21
We tested the radar for this power-on test and internal calibration with dl combinations of these switch

positions, and the unit passed all tests successfully. We then tested the radar for its ability to communicate with our calibrator, and discovered that its antenna was horizontally polarized. It communicated well with the calibrator located 1, 2, and 3 m in front of the radar antenna. There was

no communication when our calibrator was vertically polarized. We chose to continue the tests with a 2 m separation.

Using our calibrator, we tested the radar for accurate speed indication using all combinations of

front-panel switch positions and all calibrator options. The range switch was tested in both positions

for every combination of all the other radar switch options, but had no effect on the results. We

surmise that the calibrator had adequate signal output to activate the radar at any range sensitivity, and

these results will not be reported further.

The radar speed limits were set at 50 mph for both automobiles and trucks. A select few of these

results are given in Table 3 below. The uncertainty of our calibrator at 55 mph is less than ±1% at laboratory temperature.

Notice the difference between the approaching mode and the receding mode. Also, notice the readings

that appear as 0~ which indicate an error due to too long a pulse. This implies congested traffic where

the radar may make an incorrect evaluation of speed, and, in the receding mode, no offense is recorded.

All measurements, where the approaching/receding modes on the radar and the calibrator were

different, as, for example, having the approaching mode on the calibrator and receding mode on the

radar unit, or vice versa, resulted in no input signal, that is, no signal indicator, and no speed readings on the radar output. This was true for all combinations of switch options on the radar and calibrator.

This is an indicator of the quality of the calibrator's ability to reject the undesired sideband, which we

reported previously to be 25 dB. This is adequate for our purposes.

Now considering the calibration data in measurement set 1, the radar was set to track only

automobiles. The measured speed is 56 mph for chirp up. It appears that the data were taken at the

end of the pulse when the vehicle was farthest away from the radar unit. The radar interpreted the

0.25 s pulse as an automobile and registered an offense since the speed was in excess of the 50 mph

limit set into the radar. The radar also recorded no offense for the 1 .35 s pulse since it interpreted it as a truck and the 2.0 s pulse, both of which it was supposed to ignore.

Data set 2 shows similar results for the radar switched to the truck mode. Offenses were recorded for

the 1.35 s (truck) pulse, and the shorter pulses did not give an offense. Otherwise the error in the

measured speed is similar to the automobile mode.

When the radar was set for approaching traffic, several differences were apparent. First of all, the radar

did not wait until the end of the pulse to register its output. This implied to us that the radar was

reading the data toward the beginning of the pulse. Data set 3 shows that when the Doppler frequency was chirped from high to low, the output speed was high. In other words, the measurement was taken

22
early in the pulse when the vehicle was most distant. To confirm this conclusion, the calibrator was

switched to its diagnostic mode and the approaching sideband was chirped from low to high. This

combination is not found in normal radar use. The resulting speed reading was low, which confirmed

the early-time hypothesis. These results would be consistent with the data in the receding mode if the

manufacturer wanted to use only those data taken when the target vehicle was farther away from the

radar. It certainly eliminates most of the complex target signature by making use of only the simpler

reflection from the front or back ofthe vehicle and eliminating the complex reflections from the sides.

In the receding mode shown in data sets 1 and 2, since the radar took its data late in the reflection

sequence, it was able to sense the duration of the pulse, and therefore to determine the length of the

synthesized vehicle. With this information, the computer could properly assign the violation to either an auto or truck. In data set 3, since the measurements are concluding early in the reflection sequence,

the radar set seems to be ignoring the length of the pulse, and it is clearly not discriminating between

auto and truck reflections. A hazard in this procedure is that the radar is assigning a violation to all vehicle types. This is a serious system malflinction that was easily uncovered by the calibrator.

The synthesized truck data in set 4 resembles set 3 in that the speed reading is again being made at the

beginning of the chirp while the frequency is high, and the radar does not discriminate between vehicle

types. In this case, however, no violation is recorded for any pulse width. We propose that the radar

set is not measuring the reflected signal for a long enough time to sense a truck. Data set 4 supports

the claim that there is a serious malflinction in the radar unit and suggests that the set be returned to a

repair depot for flirther diagnosis.

The variations of ±1 mph seem insignificant, but the average of the speed over this waveform was

55 mph, so the radar should have read the correct 55 mph. If the total allowable error is chosen to be

+1,-2 mph, then the error budget is completely consumed by these inaccuracies and there is no margin

left for additional errors due to temperature effects, antenna misalignment, radar vehicle misalignment, or electromagnetic interference effects. Clearly, the radar unit would not meet this accuracy

requirement.

Occasional road testing of the radar with an actual calibrated target vehicle is desirable as a check of

the overall operation of the radar. Clearly, these tests should be done with a vehicle having a speedometer uncertainty less than 1 mph. These tests will help in assessing the errors that are not

evaluated by the calibrator, such as the effects of mechanical misalignment of the radar vehicle and the

variety ofvehicle signatures.

9. CONCLUSIONS

This paper describes an inexpensive, easy-to-use electronic calibrator that can be used to improve the

credibility of across-the-road type radars. It can warn the user of actual failures that may result in erroneous speed readings. Regular documented use of the calibrator can also indicate trends in the

operation ofthe radar that may suggest that a particular unit should be scheduled for maintenance, thus

23
avoiding the unexpected failure of a system and the expensive consequences ofthat uncertainty.

The test results on a commercial across-the-road system unit show the value of using the calibrator for

evaluations. Not only can the radar be tested for correct speed readout, but, often, the sources of the

errors can be diagnosed. This allows the testing laboratory to make more informed decisions about the

qualifications of a particular radar unit and, therefore, to better predict how the radar will fiinction in actual use. The calibrator is capable of more complex combinations of sideband and chirp that enhance

this diagnostic capability, but these are beyond the scope ofthis report.

The authors wish to express their appreciation to Brian Trayner of the National Health and

Transportation Safety Administration for flinding this work, and to Dr. George Leiberman for his vital contributions to the effective management ofthe project.

We are fiorther indebted to our division chief. Dr. Dennis Friday, our group leader. Dr. Motohisa

Kanda, and our readers, Manley Weidman, Nicholas Di Minco, Dr. Matt Young, and Dr. Caii

Stubenrauch. The accuracy of the material presented in this Tech Note, as well as its readability, have

benifited greatly from their suggestions.

11. REFERENCES

[1] Harry, R.; Amos, S.J.; and Pratt A.P.S.; An Examination of Doppler Radar Speedometers

Incorporating Photography. St. Albans, United Kingdom: Police Scientific Development Branch

(PSDB), 1991.

[2] Berger, F.B., "The Nature ofDoppler Velocity Measurement," IRE Transactions on Aeronautical

and Navigational Electronics, September 1957.

[3] Fisher, P.D., "Shortcomings of Radar Speed Measurement," IEEE Spectrum, December 1980,

pp. 28-31.

[4] Mennie, D., "Helping Speeders Beat the Radar Rap," IEEE Spectrum, August 1978, pp. 38-42.

[5] Rihaczek, A. W., Principles of High Resolution Radar. Los Altos, CA; Peninsula Publishers,

1985.

[6] Radar Equipmentfor the Measurement of the Speed of Vehicles, Organisation Internationale

de Metrologie Legale (OIML): Paris, 1991.

[7] Edde, B., Radar: Principles, Technology, and Applications. Englewood Cliffs, NJ: Prentice

Hall, 1993.

24
[8] Skolnik, ML, Introduction to Radar Systems. New York, NY: Mc Graw Hill, 1980.

[9] Bodard, P., "They Have Lasers, and We Captured One for a Test," Car and Driver Magazine,

April, 1992.

[10] Gabel, R.A., Roberts, R. G., Signals and Linear Systems. New York, NY: John Wiley and Sons,

1988.

[11] Dwight, H.B., Tables of Integrals and Other Mathematical Data. New York, NY: Macmillan

Publishing Co., 1961.

[12] Gupta, K.C., Garg, R., Chadha, R., Computer-Aided Design ofMicrowave Circuits. Norwood,

MA: Artech House, 1981.

[13] Engen, G.F., Microwave Circuit Theory and Foundations of Microwave Metrology. London,

UK: Peter Pereginus Ltd., 1992.

[14] Collin, R.E., Foundationsfor Microwave Engineering. New York, NY: McGraw Hill, 1966.

[15] Gupta, K.C., Garg, R., Microstrip Lines and Slotlines. Norwood, MA: Artech House, 1979.

[16] Johnk, C.T.A., Engineering Electromagnetic Fields and Waves. New York, NY: John Wiley

and Sons, 1988.

25
APPENDIX A

FOURIER ANALYSIS OF THE CALIBRATOR PERFORMANCE

This appendix presents the analysis of the signal that is reflected fi"om the calibrator when switched at a

constant rate. The signal is expanded in a complex exponential Fourier series representation [10], and

an analytical expression for the Fourier coeflBcients is developed. The expression facilitates the

understanding ofthe calibrator operation.

The transmitted CW signal from the radar under test can be represented in analytic form [5] as

- Si^Ae^'^'frt , (A.1)

where A is the complex amplitude and/ is the radar transmit frequency.

The signal that is reflected back to the radar under test is given by

Sr(t) = eJ"''^''[c + a(t)], (A.2)

where c is the complex amplitude due to scattering from both the calibrator and possibly other nearby

objects, and a(t) is the modulated component generated solely by the calibrator. It is the modulated

component a(t) which provides a suitable Doppler signature for the verification of radar performance.

If the calibrator is operated in the mode for which each of the N phase states has equal duration (no

chirping), and the switching sequence is repeated every 7^ seconds, the resulting modulated component

is given by

a(t) = Y(t)eJ^('^ ,

T(t) = An. (m-1)^ < ^^^77 N N

m = ],2,...,N,

(A.3)

26
where A,r, and 9rn are amplitude and phase values that are constant for each value of m. In order to achieve optimal calibrator performance, amplitude and phase shifts to be realized are given by

_ ±27mi

Am ~ ^' C7nj ~ '

(A.4)

m^ 1,2, ...,N,

where ^ is a constant. A positive sign in eq (A.4) denotes an increasing phase sequence (this simulates an approaching vehicle and a minus sign denotes a decreasing phase sequence (for a receding vehicle).

The calibrator functions most effectively when the amplitudes of each of the switch states are exactly

equal and the phase shifts increase or decrease in fractional increments of 2;Trad over the total number

of phase shift states, A^. In the case of the NIST unit N=5, so eq (A.4) yields an optimal increment of

271/5 rad or 72°.

In order to understand precisely how the calibrator fiinctions, the modulated term can be expanded in a complex exponential Fourier series as [10]

00 j27mt

a(t)^ Z dne~Y^, (A.5)

«=-oo

with

7 „ -jlTmt

dm = —\o^(^)e~j^ dt. (A.6)

Ts

From eqs (A.5) and (A.1), the modulated signal is periodic with period Ts with sidebands that are located on both sides of the carrier fi"equencyyr, at intervals corresponding to integer harmonics of the

fiindamental switching fi"equency 7/7!,. The complex amplitudes ofthese sidebands are given by [10]

Applying eqs. (A.3) and (A.5) to (A.6) yields

7 N-1 ^ ,.r j27ip 2nm ,^^^ d^-i- Ziy e^e-iT:"*PTs^N)a,. (A.7)

^ 5 p=0

Applying a suitable change of variable to the integral in eq (A.7) obtains the simplified result

7 N-l J2p^ .r,/M -Jll^ , ..«.

J s p=0

Equation (A. 8) is a product of a geometric series and a simple integral with an exponential integrand,

both of which can be readily evaluated. Using results tabulated in Dwight [11] yields after some

27
simplification

' m

j27mi

)e-W<^-'><'"-'>(e-^-l) N

-J2^ sin[7r(m-J)J

n

sin A(m- 1)1 N

(A.9)

m = 0,±l,±2,±3, ... .

Equation (A.9) is the final desired result for the complex sideband spectrum assuming a constant

amplitude taper and a stepwise increasing phase taper.

Equation (A.9) indicates that the three nonzero harmonics, closest to the carrier fi-equency of the radar

under test occur at fi-equencies oi fr+l/Ts, fr+(N+l)/Ts, fr-(N-l)/Ts, and the locations of these

fi'equencies are depicted in Figure 15. The dominant reflected signal component occurs at the first of

these fi'equencies, and it is shifl:ed above the radar carrier by the fiandamental switching fi^equency l/T^.

The two other harmonic components are removed fi"om the radar carrier fi-equency by (N-1) and

Upward Doppler

i Shift due to

Calibrator

Radar

i

-^

Operating

Frequency

\

I

i I

(N-1)

T s

f .(^ r T

Figure 15. Reflected signal spectrum with an increasing phase sequence.

28
(N+I) times the fundamental switching frequency.

The fact that all of the other sidebands between the fundamental and the (N-])th harmonic have zero amplitude is absolutely vital to the success of the switched reflector concept. For a suitable choice of

A^, the radar under test filters out all of the sidebands except for the fundamental at J/T^ which

effectively makes the switched reflector a single sideband modulator that shifts the frequency of the

radar under test up by an amount J/Ts, which simulates a vehicle approaching at a constant rate. If the

phase progression specified in eq (A. 4) is reversed, the sideband positions are transposed with respect

to the radar carrier frequency, and the calibrator shifts the reflected frequency dovm by J/Ts which

simulates a receding vehicle.

In the case of the NIST calibrator with N=5, the next higher harmonic of the fundamental switching

frequency is the fourth. If the fimdamental switching frequency is set to correspond to a Doppler shift of 55 mph for the radar under test, the next reflected component occurs at a Doppler shift corresponding to 220 mph, which will not be processed by commercial radar units. The selection of

N=5 in the NIST calibrator is therefore sufficient for the unit to function as a "virtual" single sideband

modulator for the evaluation of commercially available across-the-road radar systems

29
APPENDIX B

REFLECTIVE PHASE SHIFTER DESIGN CONSIDERATIONS

This appendix explains the design issues that are involved in obtaining a proper reflective phase shifter performance. The design equations are first introduced and discussed, and then general design

procedures and guidelines are given.

For a single-pole, N-position switch, the microwave performance at each switch position can be

represented in terms of two-port scattering parameters. Scattering parameters are highly usefial since

they can readily be measured using vector network analyzers. The measured data obtained is then

incorporated into a linear microwave network simulator for the purpose of assessing and optimizing

the calibrator performance [12].

bf = Sfiaf + Sfio"^

(B.I)

The switch in Figure 16 can be characterized in terms of its scattering parameters as

where /w^7,2,...,7V^ denotes the switch position, S denotes the network scattering parameters, and the

a,b terms are the incident and reflected wave variables at the switch ports. The coefficients Si] and S22 are the switch reflection coefficients obtained with a matched (50 CI) resistive load; S]2 and 821 are the

corresponding switch transmission coefficients, also obtained for a matched load [13]. Since PESf

diode microwave switches are linear and passive, reciprocity [14] demands that 812^821. If the Sparameters for the switch are known, the performance at port 1 can be determined for an arbitrary load

termination on port two. Assuming that the termination on port 2 has a complex reflection denoted by

Fl, the wave variables at port 2 ofthe switch are interrelated by

m — T^ m im

«2 = rf/7j. (B.2)

30
optional

input

matching

network

r

m

switch

optional

switch

matching

network

Figure 16. Microwave network representation of the switch section.

If eq (B. 1) is applied to eq (B.2) and the ratio is taken ofthe reflected to incident wave variables at port

1, we obtain the input reflection coeflBcient ofthe switch

b? _ P

m

switch

rim +

Qm rrin Y^m

(B.3)

The input reflection coeflBcient is a complicated Sanction of the switch scattering parameters and the

load reflection coeflBcient. The input reflection coeflBcient to the switch determines the magnitude and

phase ofthe signal that is reflected back to the radar under test.

The ftmctional dependence given in eq (B.3) can be simplified significantly through proper microwave

design. If the magnitudes of switch parameters Sn and S22 are small, or can be reduced by the use of

matching networks (see Figure 16); the switch reflection coeflBcient simplifies to

p m

switch (sf^r r- m

i T (B.4)

For a switch that has a good input and output match, the input reflection coeflBcient is a simple product

ofthe two-way switch transmission characteristics and the load reflection coeflBcient.

One viable approach to achieving a desired switch reflection phase at a given switch position is to place a length of open-circuit transmission line at the switch output. The desired phase can be synthesized by

simply adjusting the length of the line. If the switch is well matched, reflection phases over the entire

range of 0° to 360° can be realized. Thus combining open-circuit transmission lines and input/output

31
matching networks permit the synthesis of arbitrary phase sequences. Assuming that the magnitudes of

switch transmission parameters do not vary much from one switch position to the next (this should be

the case for any suitably designed switch), the desired switched reflector performance can readily be

achieved.

The reflection coeflficient at the input of an open-circuit section of coaxial transmission Une of length H"

is given by

Tl ^ e'-i^'- ,

(B.5)

eiine = ^ keff h"" ,

where kef is the effective wavenumber of the transmission Une section. In terms of the material

properties ofthe dielectric insulator ofthe coaxial line, the effective wavenumber is given by

keff = ^^fr 4f^0S0£r > (B-6)

where jUo= 4;t x 10'\ Sq^ 8.85 x 10'^^, and £> is the relative dielectric of the insulating medium, which

must be determined either by measurement or manufacturer-supplied data. Equation (B.5) is also valid

for printed-circuit microstrip transmission structures, but a formula given in [12] that accounts for

dispersion effects must be used in place of eq (B.6) to obtain suflBcient accuracy.

Equation (B.5) assumes a perfect open circuit, and fringing effects are ignored. Open-circuit coax and

microstrip lines have a fringing capacitance associated with them [15] that effectively lengthens the line, so if the line section lengths are computed from eq (B.6), the lengths will have to be made somewhat

shorter to obtain the correct phases. Making open-circuit microstrip and coaxial line sections shorter is straightforward and simple, and requires minimal time. The accurate computation of fringing effects is involved and is beyond the scope of this work. In the case of microstrip lines, empirical formulas can be found in [15]. Microstrip fringing effects derived from theory or measurement data are often

incorporated into commercially available microwave network simulators. If we use coaxial cable

sections, the input reflection phase that includes flinging effects can be directly measured with a vector

network analyzer without having to compute an additional correction.

Now the total reflection phase shift provided by the combination ofthe open-circuit Une and the switch

is given by

^ = Oline + dswitch > (^•'7)

where Oi,„e is the phase contribution given by eq (B.5), and 0sw,tch is the phase shift provided by the

measured transmission characteristics of the switch/matching networks combination. Equation (B.7)

indicates that once the switch transmission phase is known, the desired phase shift can be achieved by

32
simply superimposing the transmission phase contribution of an open circuit line section to that of the

switch.

The results ofthe discussion up to this point, along with the experience gained from the construction of

the NIST calibrator can be used to generate a systematic design procedure for the reflective phase

shifter portion ofthe radar calibrator. This procedure is summarized in the following steps;

1. Measure the two port S-parameters (magnitude and phase) of the switch at the radar frequency of

interest at all of the switch positions using a vector network analyzer or some other suitable

measurement system.

2. If the switch reflection coeflScient magnitudes \Sii\ or \S22\ are too large, the magnitude of the

offending parameter must be reduced using a matching network at the switch input (if \Si]\ is too large) or at the switch outputs if \S22\ is too large. There is no hard and fast rule for the determination of

unacceptable values of reflection coeflBcient magnitudes. Unacceptable levels can only be determined

by carrying out an analysis of the switch input reflection characteristics using eq (B.4) for a prescribed

set of phase shifts at each of the switch positions. There are a lot of possibilities for matching network

designs, and once again there is no hard and fast rule for the type of matching network that must be

used. In our calibrator, |»S'/;| was too large so the simple open-circuit shunt stub arrangement of Figure

9 was used on the switch input. This type of matching network can be designed either by incorporating

the measured switch S-parameter data into a computerized microwave network simulator, or by using

simple Smith chart design procedures that are extensively treated in Johnk [16].

3. After the switch has been matched, the lengths of the open-circuit line sections must be determined.

The first step of this procedure is to prescribe the required set of input reflection switch phase shifts that will be realized at the A'^ switch positions. Then the required line input phases must be found from

eq (B.7). The line phase shift requirements are then converted into realizable physical lengths using

eq (B.6), or, in a more direct fashion, by placing the open-circuit line sections on a vector network

analyzer and adjusting the line length until the required phase shift is obtained. The direct method of

obtaining required line phase shifts using a network analyzer was used with excellent results in the

construction ofthe NIST calibrator.

4. Once the open-circuit lines are installed on the switch outputs, the design and construction of the

calibrator is completed. At this point, the calibrator switch section performance must be verified by

measuring the calibrator input reflection phase characteristics at each of the N switch positions. The

relative phases from one switch position to the next should be consistent with eq (A. 4) of Appendix A

for optimal performance. If the results obtained in this step are satisfactory, the design of the

microwave portion ofthe calibrator is complete.

33

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