Scattering Analysis of a Millimeter-Wave Scalar Network Analyzer

This paper presents the results of a scattering analysis of a millimeter-wa~e scalar network analyzer system. The results clearly indlcate the way in which the individual system components contribute to calibration and measurement efror. procedures which minimize the caEbration error for waveguide measurement systems are deseribed, and the residuaf measurement uncertainty is quantified in a way which establishes the tightest possible bound on the measurement error.

I. INTRODUCTION o VER THE PAST several years, there has been considerable progress in the development of millimeterwave components and systems. The development activity in the millimeter-wave bands has resulted in a demand for measurement systems. At microwave frequencies, both scalar and vector network analyzer systems have been available for some time. These network measurement systems are commercially available' from several sources and have reached an advanced level of sophistication with regard to accuracy and automation.
They are coaxial based and their performance is generally well understood. At millimeter-wave frequencies, the situation is far less satisfactory. Until recently, an individual with the need to make millimeter-wave network measurements faced the task of creating his own measurement system. Now, scalar millimeter-wave analyzer systems are available commercially from at least one source, so progress has been made with regard to hardware availability. However, millimeter-wave measurement systems are normally waveguide-based and it is difficult to determine the performance of these systems through reference to the existing literature on microwave systems.
The best source of information on the performance of microwave scalar network analyzer systems appears to be the literature available from the various manufacturers (see [1], for example). Such literature, however; tends to be slanted toward the use of particular equipment and emphasizes the use of coaxial components. Althougtt many of the measurement system performance principles are independent of whether the hardware is coax or waveguide, it was found that the performance of a millinieter-wave scalar network analyzer could not be satisfactorily explained using results as they appear in the existing literature. Manuscript received June 6, 1983;revised September 6, 1983. This work was supported in part by the Navaf Postgraduate School Foundation Research Progrmn.
The author is with the Department of Electncaf Engineering, Naval Postgraduate School, Monterey, CA 93943.
The work described in this paper was motivated by the need to answer questions which arose during the development of an automated 60-90-GHz waveguide-based scalar network analyzer system. The questions related to system calibration and measurement uncertainties and their relationship to the characteristics of the individual components used to construct the system. Hence, the analyzer system was modeled as a multiport network and its response was determined through analysis using S-parameters, The pur- H.

A. System Description
A scalar millimeter-wave network analyzer consists of a signal source, directional couplers and detectors to sample incident and scattered waves, and a receiver to process the detector signals and display the results. If automated, the system kill also have a computer which is interfaced with the signal source and receiver via a control bus. A typical system diagram is shown in Fig. 1. The objective is to use the measurement system to determine the insertion loss IL and return loss RL of a device under test (DUT). With the DUT in the forward direction (port A driven), the return loss at port A and the insertion loss from port A to port B are related to the scattering coefficients of the DUT by RLA = -10log10 lS~uT12 (la) which the magnitudes of the scattering coefficients of the DUT may be determined.
A more detailed diagram of the measurement system couplers is shown in Fig. 2. The three couplers will be referred to as the R, A, and B couplers since they provide samples of the incident (reference) signal, the signal scattered from port A of the DUT, and the signal scattered from port B of the DUT, respectively.
The square-law detectors at coupler ports 3,4, and 6 provide output signals directly proportional to the RF-signal power scattered to these three ports. The return loss is determined from the ratio VA/ V~, while insertion loss is found from the ratio v'~\ V~. In an ideal system, these ratios would provide the desired quantities IL and RL directly. In practice, however, the results are corrupted by component imperfections. This makes it necessa~first to calibrate the system and then to accept some uncertainty when a measurement is made. The analysis which follows will identify the errors introduced by system component imperfections.
It further indicates how calibration uncertainty may be eliminated and how measurement uncertainty may be quantified.

B. Return-Loss Measurement Ana&sis
Return loss is given by (la) and (lc), which may be rewritten in the form RL~= -10loglOP;/P: where P; is the power scattered from port k of the DUT, and P; is the power incident on port k of the DUT.
Samples of the incident and scattered waves are coupled to ports R and A, where they are applied to the square-law detectors which produce output voltages V~and VA, respectively. We are interested in the ratio of these voltages which may be expressed as (VA/VJR) = const (G~,l/G~,l) where GTq, = power delivered to port q power available from source p " As shown in Appendices A and B, the ratio of detector voltages may be expressed in terms of the scattering coeffi- cients of the reflectometer bridge as where a 2 is a constant, and I'iD is the input reflection coefficient of the DUT and where it has been assumed that lS22rm] <<1. Further, it should be recognized that IS,II = 1 and that [Sdl /SA2 I <<1 will be approximately equal to the directivity of the A coupler. However, the coupler directivity will always be an upper bound for ISA1/SQ21.
Before making an insertion-loss measurement, the system must be calibrated so that the O-dB return-loss reference level is known. Equation (4) which means that the correct RL reference level may be precisely located. We may also calculated (vA/vR)':: -(vA\vR)'$ mm 'n = IS'*+ 8 (7b) 2(v JvR)% avg and this will be useful in evaluating the residual uncertainty when a measurement is made. &_ I is the equivalent of source mismatch, and it is determined from (7b) with uncertainty no greater than the A coupler directivity (see (6)).
The previous results have been derived assuming that a perfect sliding short is used to calibrate the system. If the short is Iossy, then its reflection coefficient will have a magnitude less than unit y. The return-loss reference level in this case will be in error by an amount equal to the loss in decibels. For example, if the sliding short produces VSWR = 20, then Irl = 0.905 and the reference level will be 0.86 dB too low. All subsequent measurements referenced to this level would be in error by the same amount.
Since waveguide losses increase dramatically in the millimeter-wave bands, this source of error should not be neglected. Now suppose that a DUT is connected to port 2 of the A coupler. In this case, we have no control ,over the phase of the reflection from the input port of the DUT and we obtain @h'vRk% = &+&r +~s22r: This may be written as The constants Cl and C2 lie in the interval [-1, 1] and depend upon the phases of the directivity and equivalent source mismatch error signal components relative to the signal reflected from the input of the DUT. Clearly, directivity and equivalent source mismatch error cause an uncertainty in the measurement of the DUT input-reflection coefficient. This uncertain y will vary with frequency and is dependent upon II',*I as well. As shown by (7b), 1S22 I may be found with small uncertainty at each measurement frequency during calibration. lS41/S42 I is not generally known as a function of frequency but is bounded from above by the coupler directivity D, which is specified by the manufacturer. Thus, we may express the detector voltage ratios in the form where the worst case uncertainty AI'in is given by The calibration and measurement data acquisition and the computation of measurement uncertainty as described above may be accomplished easily with an automated measurement system. During calibration, it is necessary to move a sliding short through a distance of at least one half a guide wavelength N, so that the phase of the reflected signal varies through a full 360 degrees, An appropriate calibration algorithm would be one which searches for and stores the maximum and minimum values of (VA/ VR) at each desired frequency as the short is moved a distance X/2 at the lowest frequency in perhaps 10 steps. After acquiring the DUT reflection data, an undistorted graph of return loss versus frequency with error bars may be gener:  (9) where SI is the isolator VSWR (maximum), and SC is the coupler VSWR (maximum). Thus, measurement uncertainty may be minimized by using an isolator and the A coupler with the lowest possible upper bound on VSWR.
There are two remaining observations which are worthy of comment. The first relates to the reflection coefficients r~~and r~q of the R and A coupler detectors. Although these reflection coefficients enter into the determination of the gains G~,, and G~,,, the final result is independent of detector VSWR. At any fixed frequency, the effects of detector VSWR are the same during both calibration and measurement and thus disappear through cancellation of the factor a which appears in both (4)  where I'~is the reflection coefficient of the load terminating the DUT. To evaluate the return loss (see (l)), lSl~uT I is required.
Equation (10) shows that Iri~I = lS~uTl only if 11'~1= O. Therefore, the best possible load should be placed on port B of the DUT when measuring lri~I at port A, and vice versa. If the DUT is terminated in the B coupler so that return-loss and insertion-loss data may be simultaneously acquired and displayed, then the B coupler VSWR will cause additional uncertain y in ISl~uT 1. Therefore, to achieve the lowest uncertainty, the unexcited port of the DUT should be terminated in a waveguide matched load.
Such a load has a VSWR, which is significantly lower than that of a directional coupler. Additionally, if a sliding load is used, the error due to load reflection may be averaged out in the same way that the equivalent source mismatch error is averaged out during the return-loss calibration procedure (see (5), (7)).

C. Insertion-Loss Measurement Analysis
Insertion loss is given by (lb) where Pq-is the power scattered from port q of the DUT, and P: is the power incident on port k of the DUT. All ports are terminated in the load impedance 20, except port k which is driven by a source with impedance 2.. For this measurement, the network is terminated in the B coupler and samples of the incident and scattered waves are coupled to ports R and B, respectively. The square-law detectors at these ports produce output voltages V~and V~. The ratio of these voltages is given by Using (15), (17), and (18), we find that the worst case uncertainty is +0.32 dB without isolators, while with isolators it is reduced to +0.21 dB. If the A coupler is removed from the system, then the equivalent source mismatch is reduced to Ir,'! <0.2. The worst case uncertainty in the location of the O-dB reference level for insertion-loss mea-surements is correspondingly reduced to +0.15 dB, assuming an isolator is used ahead of the B coupler detector.
, The uncertainty may be bounded more tightly if during the insertion-loss calibration run the return loss of the B coupler is measured. This will establish the value of lr~l.
During the return-loss calibration run, the value of ISzzI is found. Thus, lr(l < I$z I+ Clr~d I when the A coupler coupler is in the system (C is the power coupling factor). If the A coupler is removed from the system Ir;ls (sl-l)/(sl+l).
For either situation, the calibration uncertainty% 3,,0(1+Iwo is reduced since Ir: I is known from direct measurement at each frequency of interest. Now suppose that a DUT is placed between the A and B couplers. We then obtain III.

IQSULTS
The analytical results presented in the previous sections have been verified experimentally using an automated measurement system covering the 60-90-GHz band. The major components of the measurement system are a solid-state

A. Fixed Short
The return loss of a fixed waveguide short is of interest because the correct value of the return loss is known to be precisely O dB. It may thus be used to check the performance of the measurement system. The center curve in Fig.   3 shows the measured return loss for a WR (12) waveguide short. Notice that the return loss oscillates about the correct value of O dB as the frequency is varied. This oscillation is caused by the interference between the signal reflected from the short and the error signal component due to equivalent source mismatch. This represents a worst case situation since the reflection coefficient of the short is lrl = 1. For a load of unknown return loss, it is this error which introduces uncertainty into the measurement. The upper and lower curves in Fig. 3 bound the measurement uncertainty.
The correct value of return loss, O dB in this case, should always be between these two curves. It can be seen that this is generally the case, although there are several points where the upper bound dips a few tenths of a decibel below the O-dB level. This small error is consistent with our use of 10 positions of the sliding short for, calibration.
The error results from the failure of the calibration algorithm to determine ISZ2I precisely. The error may be reduced by using more positions of the sliding short. Also evident in Fig. 3 is the variation of the uncer- tainty with frequency. Here, the uncertainty is less near the edges of the band than it is at the center. Thus, the uncertainty near the edges of the band has been reduced considerably relative to the bound computed using the worst case equivalent source VSWR.

B. Detector Mount
A second example of a return-loss measurement is shown in Fig. 4 which presents the data obtained for a detector. The measured return loss is in the range 20-40 dB over the frequency band 60-70 GHz. At this level, the source mismatch is less important than the A coupler directivity error. Since the A coupler directivity was >40 dB (D < 0.01) in our system, there is considerable uncertainty if the measured return loss is in the vicinity of 40 dB. This can be seen clearly in Fig. 3.

C. Through Section
The insertion loss of a through section is of interest because the correct value of the insertion loss is known to be O dB. It may therefore be used to check measurement system performance in the same manner as with the short. The measured return loss of a through section is shown in Fig. 5 along with the bounds on uncertainty.
The measured insertion loss is within~0.3 dB of the correct value (O dB) over the 60-90-GHz frequency range shown in the figure. The correct value of insertion loss also lies within the computed range of uncertainty delineated by the curves above and below the curve of measured insertion loss except at 61 GHz. At this frequency, a drop in the measured insertion loss has pulled the upper bound on the uncertainty below the O-dB level to -0.1 dB. This anomaly is believed due to a small change in the output power level of the source between calibration and measurement at that frequency. Overall, insertion loss uncertainty is seen to be considerably less than was the case for return-loss measurements. This is in agreement with the results predicted by the model.

D. Calibrated Attenuator
As a last example, Fig. 6 shows the measured insertion loss of a WR (12) calibrated variable attenuator over the 60-90-GHz band. This attenuator was supplied from the manufacturer with a calibration curve at 75 GHz, and the micrometer was set accordingly for 10 dB of attenuation. The measured insertion loss varied~2.5 dB over the frequency band, but was indeed measured to be 9.74 +0.3 dB at 75 GHz.

CONCLUSIONS
This paper has presented a scattering analysis of a waveguide-based millimeter-wave scalar network analyzer system. The results of this analysis clearly indicate the relationship between system component specifications and the performance of the entire measurement system. These results may be summarized as follows.
1) The use of a (perfect) waveguide sliding short permits the correct O-dB return-loss reference level to be found precisely. Losses in the short will cause an error equal to the decibel value of the losses in the short.
2) The use of a sliding short permits the equivalent source mismatch ISZ2I to be determined.
3 If 1ow-VSWR isolators are placed ahead of high-VSWR detectors, the system insertion-loss measurement uncertainty will be reduced. The uncertainty may be reduced further if the A coupler is removed from the system when insertion loss is measured. 11) lr~l and lr~l may be reduced by using E-H tuners at spot frequencies to achieve higher accuracy. Mechanical tuners cannot be used in an automatic system, however, since retuning is necessary at each frequency.
12) The use of unnecessary components (such as waveguide switches) should be avoided since they will degrade system performance.
13) The use of a computer to control instruments and graph results is very desirable. Distortion due to source leveling and detector flatness can be removed and error limits can be computed and displayed.
The methods that are proposed here for determining measurements uncertainty result in the tightest possible bounds on the error. Calibration and measurement data are used to achieve this. Simple use of component specifi-cations alone would result in considerably looser bounds on error.
The model discussed in this paper does not account for instrumentation errors. Errors of this type may occur due to the following: 1) signal source harmonics; 2) changes in signal source frequency or output power level between calibration and measurement; 3) non-square law operation of detectors; 4) nonlinear amplification of detected signals. These are errors that will depend upon the specific hardware implementation of the measurement system, but they should not be overlooked, particularly since millimeterwave hardware is not yet mature.
Overall, the results presented here should bring the important features of measurement system response more clearly into view. The analysis should therefore be useful to those individuals concerned with scalar measurement of millimeter-wave network scattering coefficients.
APPENDIX A

RETURN-LOSS ANALYSIS
With reference to Fig. 2, the R coupler, A coupler, and isolator will be considered as a 4-port network. The behavior of this network may be determined from the network scattering equations. It will be assumed that Sld = Slz = S3A = S32 = O since these coefficients produce terms which are small in comparison to those retained. Likewise, S43 = O and will be neglected.