Antenna phase pattern measurements at millimeter wave frequencies using the differential phase method with only one power meter

International Journal of Infrared and Millimeter Waves, Pot 1J, No. 9, 1994

ANTENNA PHASE PATTERN MEASUREMENTS AT MILLIMETER WAVE FREQUENCIES

USING THE DIFFERENTIAL PHASE METHOD WITH ONLY ONE POWER METER

Juha Mallat, Arto Lehto, and Jussi Tuovinen

Radio Laboratory, Helsinki University o f Technology Otakaari 5 A, FIN-02150 Espoo, Finland

Received June 28, 1994

Abstract

The differential phase measurement method has been improved to need the use of only one power meter instead of three power meters. This enables accurate antenna phase pattern measurements with a simplified set-up, accompanied by the reduction in cost. All advantages of the differential phase measurement method are still also available, e.g. there is no need to phase lock oscillators or to use rotary joints. The measurement results for an antenna at 110 GHz are presented. A good agreement with earlier data was obtained.

Key words: antenna measurements, phase pattern, phase center

Introduction

The measurement of antenna phase patterns at millimeter waves frequencies was simplified by the introduction of the differential phase method [1]. In this method, the AUT (antenna under test) is trans- mitting and is rotated. The receiver has two channels so that there is an angle c~ between the antennas seen from the AUT. The phase center position and phase pattern of the AUT are easily calculated from the measured phase difference versus the angle of rotation of the AUT. The method is always applicable when the phase pattern is symmetric over the angle of + a / 2 from the boresight. The differential phase method is suitable for making accurate measurements since it avoids many of the problems present in conventional measurement methods. In the differential method the measurement set-up is relatively simple. There is no need for rotary joints or flexible cables. Another benefit is that

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1498 Mallat et al.

phase locking of the oscillators (transmitter and the LO of receiver) is not necessary.

The phase difference has been measured either by using an antenna measurement receiver [1] or by using three power meters [2] (see Fig. 1). Now, this method has been developed to the ultimate stage, requi- ring the use of only a single power meter. The calibration factors of the three power meter method are not needed. In addition, the cost reduction in the measurement apparatus is significant. The accuracy of phase information retrieval is equal or better when compared to the results obtained earlier. Possible sources of error have been considered by simulating, for example, the effects due to different measurement distances.

The differential phase method with a set-up using an antenna me- asurement receiver has been described in detail in reference [1] which also presents the geometry related to the measurement method. In re- ference [2] the improved method using three power meters is described. Much of the information available in these references has been left out from the following presentation in order to focus on new development.

CH 1 AUT !

ANTENNA RECEIVER LO MEASUREMENT

KECEIVER

a)

AUT

b)

RECEIVER

Figure 1: Earlier configurations for the differential phase method: a) with the antenna measurement receiver, and b) with three power meters.

Phase Pattern Measurements 1499

Measurement method

In the differential phase method, the phase pattern of the AUT is determined by measuring the phase difference of two signals at several discrete AUT rotation angle values. The measurement is made with an angle interval equal to a which is defined in Fig. 2. The phase pattern can then be calculated by summing cumulatively the phase difference values. The simpliest way to determine the phase differences is by using the amplitude data only. Earlier this was done by calculating the phase difference from the powers received in the two measurement channels and the power resulting from a vector sum of the signal fields. This required the use of three power meters and three power dividers with the two receiving antennas. The field amplitudes are calculated from the powers and the phase difference is determined from

Cd=180°- -a rccos E12 + E2 2 -- E3 2

2E1 E2 (1)

where E1 and E2 are the signal field amplitudes and E3 is the sum field amplitude [2]. Any difference in the electrical lengths and the phase from the receiving antennas to the third power meter would add another factor to the equation, but this factor will cancel out in the final analysis. In the new differential phase method with only one power meter, the measurement of the three signal power values is still required and the phase information is retrieved quite similarly as earlier. However, the calibration factors necessary with using three separate power meters are avoided. The need for only one power meter is a significant advantage in many respects.

The use of a single power meter is made possible by using the measu- rement set-up in the form shown in Fig. 2. The AUT is receiving the signals coming from two transmitting antennas. The power of the sum of the fields coming from the two antennas is measured with the power meter P. Also the powers due to both fields separately are measured.

S O U R C E [ < ~ - - . . . ~ . <-~zz x REcErvER ~ POWER ~ ~ I'~ ~

~ , ~ ~ DIVIDER a ~ l" 0 AUT / ~ POWER

PHASE METER

SHIFTER

Fi.gure 2: Measurement set-up for the differential phase measurements using one power meter.

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This can easily be done by blocking the signal from one transmitting antenna with an absorber while measuring the signal from the other antenna. The superheterodyne receiver shown in Fig. 2 will enhance the dynamic range of the measurement system, although in principle the power meter alone can be used. This is especially true at microwave frequencies where more transmitting power is easily available.

The measurement results give phase differences versus the angle of rotation. The phase pattern is calculated by cumulatively summing the differences from the measured pattern [1, 2]. The phase difference data at angles near boresight may directly be used to determine for the AUT the z-direction distance of the apparent phase center from the axis of rotation. This Az distance defines the position of the phase center for symmetrical antennas. The phase center has typically a fre- quency dependent location behind the aperture of the antenna. Thus a rotation axis in the center of the aperture may be chosen for the first measurements in order to avoid any ambiguity. The apparent phase center has been called the on-axis phase center in a study of various phase center definitions [3]. The phase center and the phase pattern are used, for example, in the design of antenna systems.

Measurement results

The method has been demonstrated by making a measurement with a corrugated horn antenna at 110 GHz. The phase pattern of the an- tenna is known from earlier measurements and theoretical calculations [1, 2]. Similarly as earlier, an angle of a = 5 ° was used in the set-up. As a separation of 56 mm could be arranged for the 20 dB pyramidal horns used in the transmitter, the distance to the AUT became 642 mm. The relatively small measurement distance helped to reduce considerably the amount of absorber material needed to suppress reflections in the set-up and in the surrounding laboratory environment.

A millimeter wave spectrum analyzer was used as the receiver and the power meter. A Gunn-oscillator supplied the measurement signal which was divided to two channels by using a power splitter. The measurement accuracy and convenience was improved by adding an isolator as well as an adjustable phase shifter and an attenuator be- fore the transmitter horns. Signal blockers were made from absorber material, and in the measurement they were used right in front of the transmitter horns when required.

The measured phase difference pattern using the new method with only one power meter is shown in Fig. 3 together with earlier data. All data groups have been normalized to give a phase difference ~ba = 0* at the boresight 0 = 0 °. The new result agrees well with the theoretical calculation. The agreement is also good with the measurement made

Phase Pattern Measurements 1501

80 T

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. v,,, i i i ~ i i i J

Z

m r~

N -20 . . . . . . . . . . . . . . . . . . . i ........................... i .......................... i ........................

i :. i

-40 . . . . . . . . . . . . i ................... T ....... ~ ............... ;:;

i : 1

-SO - 3 0 - 2 0 - 1 0 0 10 20 80

ANGLE [deg]

Figure 3: The phase difference Ca(0) of the 110 GHz corrugated horn in the E-plane: measured with one power meter (o), with three power meters (o and x), and with the antenna measurement receiver (- -); calculated (--) .

by using a Scientific Atlanta receiver and with two measurements (with and without t ransmitter phase locking) made by using the three power meter differential phase method. A small correction (as discussed in the error analysis) could have been made to the new data, thus getting an even better agreement.

Discussion of errors and optimization

The measured phase difference pattern (and subsequently the phase pattern to be retrieved) may have errors due to many sources. Yet only some of the sources are inherently related to the differential phase method. Additionally the method avoids many error sources occuring in other methods, such as the errors coming from flexible cables and rotary joints.

Significant sources of error are room reflections, inaccurate positio- ning of the axis of rotation, and too short a measurement distance. Frequency drift, noise in the receiver, inaccurate positioning of the transmitter, and inaccuracy in the rotation angle values are usually sources of only minor errors. Typical sources of error to the met-

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hod described in this paper are reflections from the absorber blockers, transmission through or around the blockers, crosstalk between the channels, inaccuracy in directing the transmitter horns to the AUT, amplitude instability in the transmitter, and nonlinearity in the power meter. Many of the error sources have been considered earlier in detail in [1, 2] and the discussion is omitted here.

Some sources of error in the measurement were studied by computer simulations. The antennas were simulated by using equivalent sources which resulted in good approximations of the real aperture fields and far-field patterns. The measuring distance and the inaccuracy in direc- ting the transmitter antennas were found to contribute to some small errors in the result. The errors also depend on the antenna radiation patterns which were tested by varying the aperture dimensions in the simulation.

Ideally the two transmitter antennas should be distant isotropic sources which would cause many drawbacks in practice. The test me- asurement set-up had two similar horn antennas which were from the AUT at a distance of rt~st equal to 235 × wavelength or 58 x the aper- ture diameter of the AUT. In one computer simulation the transmitter antennas were first replaced by isotropic sources which were then mo- ved towards infinity. For isotropic sources at rt~st and at 10 × rt~,t, the difference in the distance Az of the calculated phase centers was less than 0.1 mm. Some simulations were made considering the horn an- tennas vs. isotropic sources at equal distance. The simulations showed that for small differences in parameter values the correction for Az was approximately proportional to a factor

KA, = w 2 ( ¢ - a ) l r , (2)

where w is the transmitter antenna aperture width in the measurement plane, ¢ is the angle between the boresight directions of the transmitter antennas, and r is the measurement distance between the transmitter antennas and the AUT. (The aperture diameter of the AUT, if not a constant, could be added to the formula as a parameter similar to w).

The phase difference results for the new method were obtained with a measurement distance smaller than used in earlier measurements. Based on the simulations, a small correction could be made to the new results, leading to an almost perfect agreement with earlier theoretical and experimental data. The calculated correction is equivalent to a change of -0.5 mm in Az. The correction comes from the fact that the transmitter antennas were parallel in the set-up, resulting in ¢ = 0 °. The value of the correction is directly related only to the set-up and antennas of the demonstration measurement but it may be useful for calculating an error estimate in any different set-up.

Phase Pattern Measurements 1503

The error in A~ is accompanied by small deformations in the phase difference pat tern . If the correction due to the difference in Az is applied all over the phase difference pat tern , the errors decrease consi- derably near boresight. According to simulation results, the max imum uncorrected and corrected absolute values of error in the case of the test measurement are at [0[ < 20 ° about 2 ° and 0.3 °, respectively. This can be seen in Fig. 4.

The errors due to any inaccuracy in the field ampli tudes depend on the ratio of the ampli tudes as well as on the ~bd-value in the me- asurement points. An uncerta inty of 1 % in all measured field amp- li tudes results in a m i n i m u m uncerta inty of about 1 ° at ~bd ~ 120 °. The uncer ta inty peaks near ~ba = 0 ° or 180 ° and increases additionally approximately proport ionally to EI/E~ (or to E2/E1 if E2 > El) .

The test measurement was optimized by initially sett ing ~bd to about 90* with a phase shifter in the set-up. Additionally the field ampli tudes at boresight were adjusted with a variable a t tenuator to be approxima- tely equal. The uncer ta inty in the measured phase difference pat tern was es t imated to be less than 1 °. A suitable selection of Az (by chan- ging the place of the rotat ion axis) would help to minimize the ~ba-range needed, leading to an improved accuracy. Then, if required, the results t ransformed to e.g. Az = 0 m m could easily be calculated by using the relations in [2].

] . -~

/ i ",q t t ~ / i

t~ ! ..... ! . . . . . . . . . ~2 . . . . . . . . J o n v - -- - ;~ ~ .......... ~ ........ -" T J

- 1 1 - - - - - / - - - - 4 . . . . . . . ~ . . . . . . . . . . . . ~ . . . . " - , j . . . . . . . ! .............. ~ -I

I , i :, i / I i , ' i : i I

".330 -20 - I 0 0 I 0 20 30

ANGLE [deg]

Figure 4: The simulated error in the phase difference versus rotation angle in the test measurement set-up: uncorrected (--) , and corrected based on Eq. 2 (- -).

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The inaccuracy in Ax (which is the x-distance between the apparent phase center and the AUT axis of rotation in the set-up) is a minor error source if compared to Az uncertainty. This is due to the fact that the measurement method is very insensitive to Ax. In the test measurement, the axis of rotation was positioned to the center of the AUT aperture with an estimated uncertainty of 0.1 mm. The uncer- tainty with respect to Ax is equivalent to a fraction of a degree in Cd uncertainty.

As required by the measurement method, small absorber blockers were made to be used directly in front of the transmitter antennas. Unwanted signal reflection and transmission associated with these blockers will cause errors in field amplitudes E1 and E2. An uncer- tainty of less than 0.3 % is estimated for the amplitudes by taking into account the reflection level of the blockers with the isolation and the losses in the set-up. Similarly an amplitude uncertainty of less than 0.3 % is estimated to be due to the unwanted transmission which is 50 dB lower than the actual t ransmitted signal. Isolators and attenuators can be used in the measurement set-up in order to reduce the channel crosstalk if it comes from the reflections in the blockers.

The opt imum value of angle a depends on many factors which must be evaluated separately for each measurement application. A small value provides many data points to the phase pattern and also leads to a good accuracy in view of the error analysis.

Simply a power meter without a receiver front-end can be used in the measurement. However, the dynamic range limits the accuracy of the measurement. Consider a possible measurement situation at 110 GHz: a 50 mW oscillator in the transmitter, a receiving power meter with an effective noise level of - 4 0 dBm, the AUT and transmitter horns with gains of 20 dB and a measurement distance of 0.5 m. In this case a dynamic range of about 20 dB is available for the measurement near the center of the beam. Thus, in practice, a receiver front-end must probably be used to increase the sensitivity and the dynamic range. A receiver with a noise figure of F = 10 dB can be used to provide a dynamic range of about 60 dB which should be sufficient for most measurements. The dynamic range will be somewhat reduced by the amplitude pattern of the AUT at off-boresight directions.

In principle, it is possible to exchange the places of the transmitter and the receiver in the set-up shown in Fig. 2. In some situations it may be advantageous to have the AUT as the transmitt ing antenna bfor example if the transmitter part of the set-up is very small and can

e easily rotated).

Phase Pattern Measurements 1505

Comparison to earlier configurations of the method

References [1] and [2] describe the earlier configurations of the diffe- rential phase measurement method. In comparison to them, the imp- roved method described in this paper uses only one power meter as the detector which is a benefit. The earlier configurations use an antenna measurement receiver or three power meters which result in a more expensive set-up. In addition, they require a two-channel receiver to be used instead of a single-channel receiver. ~The input to the antenna measurement receiver or the power meters is ~rom the IF outputs of the front-end channels.) The method with three power meters also requires two calibration factors, which may decrease the accuracy. If a set-up without receiver front-ends is used, the dynamic range of the method with one power meter is 3 dB better than the dynamic range of the method with three power meters. This comes from the fact that there is one power division less in the former. On the other hand, the use of absorber blockers in the method with one power meter may someti- mes prove to be an inconvenience. The basic accuracy of the method with one power meter is estimated to be equal or better in comparison to the accuracies of the earlier configurations of the differential phase measurement method.

Conclusion

The differential phase method configured for requiring only one po- wer meter is presented. The method provides a possibility to accura- tely retrieve the phase pattern of millimeter wave antennas by making only power measurements with very simple equipment. The results of a demonstration measurement agree well with earlier theoretical and experimental data. Some possible sources of error were studied by simulations. A formula was presented for correcting for example the effect of too short a measurement distance.

Acknowledgement

The authors thank Prof. A. R£is£nen for useful advice. This work has been financed by the Academy of Finland and partially supported by grants from Emil Aaltonen Foundation, Jenny and Antti Wihuri Foundation, and Foundation of Technology.

References

[1] Tuovinen, J., Lehto, A., R~is~nen, A.: Phase measurements of milhmetre wave antennas at 105 GHz-190 GHz with a novel differential phase method, 1991, IEE Proceedings-H, Vol. 138, No. 2, pp. 114-120.

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[2] Lehto, A., Tuovinen, J., Boric, O., R£is£nen, A.: Accurate milli- meter wave antenna phase pattern measurements using the differential phase method with three power meters, 1992, IEEE Transactions on Antennas and Propagation, Vol. 40, No. 7, pp. 851-853.

[3] Wylde, J. R., Martin, D. H.: Ganssian beam-mode analysis and phase-centers of corrugated horns, 1993, IEEE Transactions on Micro- wave Theory and Techniques, Vol. 41, No. 10, pp. 1691-1699.