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Broadband characterization of conductor-backed coplanar waveguide using accurate on-wafer measurement techniques.

Broadband Characterization of Conductor-Backed Coplanar Waveguide Using Accurate On-Water Measurement Techniques [*]

Introduction

A conductor-backed coplanar waveguide (CBCPW), showin in Figure 1, is a useful transmission-line medium for monolithic microwave integrated circuit (MMIC) applications. Its transmission-line characteristics have been studied recently using quasi-static and full-wave analyses. [1,2,3] The full-wave analysis showed that the frequency dispersion of CPCPW is less severe compared to microstrip and coplanar waveguide. However, there is no experimental data reported to confirm the analysis.

In this paper, experimental results on the transmission-line characteristics of the CPCPW, including propagation constant and characteristic impedance, are presented. The test structures were fabricated on semi-insulating GaAs substrate and characterized using accurate on-wafer measurement techniques. The measured results agree very well with the theoretical calculations using a conformal mapping technique. However, at frequencies below a few GHz, the measurements show a rather strong skin effect, which is normally not considered by most of the analyses.

An uncertainty analysis was conducted to quantify the measurement errors. The phase uncertainty is dominated by probe position errors of approximately 10 [micrometer]. The magnitude uncertainty in the through-line measurement is dominated by the system erors.

Characterization Technique

In the past, many workers have used various measurement tecniques [4,5] to characterize transmission-line parameters of the propagation constant and of the characteristic impedance. For most cases, each technique was applied to obtain one parameter with a set of specially designed test patterns. In this paper, a simple technique was used that enables the simultaneous determination of both propagation constant and characteristic impedance.

The approach to the characterization is the direct transmission measurement. Two-port scattering parameters are measure by a vector network analyzer (VNA) integrated with an on-water probe station. The magnitude and phase of the S-parameters contain the necessary transmission-line characteristics. With precision calibration standards on wafer, the measured S-parameters are corrected to the probe tips with high accuracy. [6,7] The direct on-wafer measurement avoids the tedious de-embedding process required in the conventional test using coaxial test fixtures.

THe formulation can be found in Figure 2. A uniform transmission line can be characterized using a VNA to obtain two independent parameters, [S.sub.11](=[S.sub.22]) and [S.sub.21] (=[S.sub.12]). Since both [S.sub.11] and [S.sub.21] are complex numbers, the unknown characteristic impedance and propagation constant can be determined as complex quantities.

To simplify the formulation, the concept of even- and odd-mode excitations is applied. An evenmode is excited by applying two hyphothetical signals of equal magnitude and phase at both ports, as shown in Figure 2b. This arrangement hyphothetically places an ideal magnetic wall (open circuit) at the center between port 1 and port 2. The total signal [S.sub.e] leaving port 1 is, [S.sub.e] = [S.sub.11] + [S.sub.12] (1)

The signal also can be viewed as the reflected signal by the magnetic wall and can be expressed as, [S.sub.e] = zxoth[gamma]l-1/zcoth[gamma]l+1 where l = L/2 z = Z/[Z.sub.o]

Rearranged for the unknown parameters, Equation 2 becomes, zcoth [gamma]l = 1+[S.sub.e]/1-[S.sub.e] (3)

In a similar manner, assuming an odd-mode excitation, as shown in Figure 2c, will hyphothetically place an ideal electric wall (short circuit) at the center. The corresponding equations to Equations 1 and 3 are, respectively, [S.sub.o] = [S.sub.11] - [S.sub.12] (4) ztanh [gamma]l = 1+[S.sub.o]/1-[S.sub.o] (5)

From Equation 3 and 5, the transmission-line parameters easily can be obtained as, [z.sup.2] = (1+[S.sub.e]/1-[S.sub.e]) (1+[S.sub.o]/1-[S.sub.o]) (6) [tanh.sup.2] [gamma]l = (1+[S.sub.o]/1-[S.sub.o]) / (1+[S.sub.e]/1-[S.sub.e]) (7)

The characteristic impedance can be calculated without knowing the length of the test pattern, but the accuracy of the propagation constant is directly dependent on the line lenght L.

Test Pattern Preparation

The test patterns of the CBCPW were fabricated on a 100 [micrometer] thick GaAs substrate ([[Sigma].sub.r] = 12.9). The topside metal, forming the center conductor and coplanar ground, was evaporated gold of 1.5 [micrometer] thickness. The bottom metal was goldplated to a thickness of greater than 3 [micrometer]. Figure 3 shows two typical test patterns, a through-line structure for transmission-line characterization and a test structure for uncertainty analysis. The dimensions of the through lines are summarized in Table 1. To prevent the parallel-plate mode radiation, [8,9] many via holes have been placed to connect the coplanar ground to the bottom ground at 1 mm spacings. Every test pattern contains one pair of goldplated probe pads, 50 [micrometer] in size and spacings.

The accuracy of the through-line length has direct impact on the accuracy of the propagation constant. Therefore, it is important to determine the reference planes of the measurements for accurate measure of the line length. For this purpose, through lines of 1 mm, 2 mm and 3 mm lengths have been prepared. The same test patterns are used for parameter characterization as well.

Uncertainty Analysis

In the transmission-line characterization, the major uncertainty factors are probe contact repeatability and probe positioning. Several experiments have been designed to characterize these uncertainty factors. In one of these experiments two 50 [Omega] through lines were selected and their S-parameters were measured. The test was repeated 20 times by realigning and making probe contacts to the same test patterns without adjusting the spacing between the probes. Based on the through-phase measurements, the standard deviation of the probe contact repeatability was found to be 2.5 [micrometer]. This uncertainty contains the contributions due to the vector network analyzer's system noise, two-foot long flexible cables and other imperfections.

The contact repeatability is frequently presented in the form shown in Figure 4. It is the difference in dB between the S-parameters of the through line measured repeatedly and a reference data set saved in the memory of the network analyzer system. This graph presents the contact repeatability as a function of frequency. Assuming the contact difference causes only the phase shift, the maximum contact error can be calculated to be 6.2 + 0.5 [micrometer]. If the contact error is random with uniform distribution, the variance should be 3.1 [micrometer], which is in good agreement with the first study.

Another experiment was designed to determine the probe positioning uncertainty using the short-circuited CBCPW shown in Figure 2b. Because of the total reflection, the phase of [S.sub.11] and [S.sub.22] measurement contains the information on probe position with respect to the probe pads. The previously mentioned test was repeated to form a database. The analysis showed a standard deviation of 10 [micrometer] for each individual probe. This uncertainty contains the probe-positioning error, in addition to the probe contact and other system uncertainties. It is now obvious that the probe positioning error is the dominant factor. Since during the test the spacing between the probes was not adjusted, the uncertainty of probe 1 and probe 2 should be correlated, that is, the probe positioning error should be removed from the parameter of (360 - < [S.sub.11] - < [S.sub.22]. It has been verified that the standard deviation of this parameter is reduced to 5 [mu]m, closer to the through-phase measurement. This also confirms that the system uncertainty of the vector network analyzer in [S.sub.11] is higher than that in < [S.sub.21]. [10]

Determining the Reference Plane

To help determine the reference plane of the measurement, test patterns consisting of uniform transmission lines of 1, 2, and 3 mm in length have been designed. The line lengths do not include the probe pads that are necessary for the test. In theory, only two data points are needed to determine the reference plane on the probe pads. However, the uncertainty in the calculation is the sum of the uncertainties in each individual measurement. With three data points, the accuracy of the reference plane improves significantly.

The described approach is shown in Figure 5. The reference offset X/2 is defined with respect to the edge of the through line. At selected frequencies, the effective di-electric constants of the through lines were calculated for varying reference locations. Since the same reference error has larger effect on shorter lines, the change in the 1 mm line calculation presents a sharper slope than that for the 2 and 3 mm lines. The reference offset accurately is determined where the three curves meet. In the present case, the reference offset is 55 [mu]m from the edge of the through line.

Results

From the through-line measurements, the propagation constant and characteistic impedance of the transmission line can be calculated. The measurements of the through lines defined in Table 1 have been analyzed. The calculated characteristic impedance also is listed in Table 1 for comparison. The theoretical values of the impedance were calculated using a closed-form expression derived by conformal mapping. [2] The measured impedances are lower than the theoretical values and the difference increases as the gap width decreases. This is because zero metal-thickness was assumed in the theory. The metal thickness has more effect on the lines with narrower gaps. A correction factor for the thickness effect [11] may be applied for the width and gap correction,

[Delta] = 1.25t x 1 + ln(2/t)/[pi]

With this correction, the theoretical values are lower than the measurements, which indicates that Equation 8 overestimates the thickness effect.

The effective dielectric constant and attenuation constant of the lines are calculated using Equations 6 and 7. The results are presented in Figures 6, 7, and 8, respectively, for lines A, B and C as a function of frequency. The theoretical values of the effective dielectric constant and characteristic impedance are calculated by quasi-static conformal mapping techniques. [2] The theoretical attenuation constant is calculated using the incremental inductance rule, applying Equation 8 for thickness correction. The measurement is very accurate up to 20 GHz. Beyond 20 GHz, the measurement accuracy is degraded by coupling between test patterns and radiation due to discontinuities. Around 25 GHz, the 2mm long test patterns approach half wavelength and one of the denominators becomes very small. Since the parameters are calculated by cancelling two small numbers, the measurement uncertainties will cause an enlarged error to the calculation, as is shown by the impedance and attenuation constants. Nevertheless, the broadband data allows an intelligent judgment to be made in order to smooth the data. In general, the measurements are in good agreement with the theory.

For the CBCPW lines, the full-wave analysis [1] showed that the effective dielectric constant is slightly dispersive and increasing as a function of frequency. However, the measurement shows that the frequency dispersion behaves contrary in that the effective dielectric constant decreases as the frequency increases, especially at low frequencies. This effect becomes more obvious as the conductor width is reduced. Similar behavior also is observed in the characteristic impedance. This phenomenon can be explained by the skin effect due to finite conductivity and finite thickness of the gold metal. The measured attenuation constant increases with frequency, following a [square root of f] rule. The measurement agrees very well with the theory for line A, but not as well for line B. For line C, the discrepancy becomes rather obvious. This is because the thickness correction factor in Equation 8 fails to consider the effect from the gap width.

The elevated CBCPW structure, shown in Figure 9, will reduce current crowding at the edge and raise the impedance level. A structure with the dimensions shown in figure 9 has been fabricated and tested. The measured results are shown in Figure 10, which clearly shows the improvement in the insertion loss of the structure. According to the measurement, the characteristic impedance of the transmission line is 59 [omega].

Based on the uncertainty analysis, the measured effective dielectric constant has been determined with 2 percent accuracy. For the attenuation constant measurement, the uncertainty is dominated by the system [S.sub.21] magnitude uncertainty of 0.04 dB and 0.06 and dB at 8 and 18 GHz, respectively. [10]

Conclusion

The transmission-line characteristics of the conductor-backed coplanar waveguide has been experimentally studied. With the aid of precision on-wafer calibration standards, direct on-water S-parameter measurement techniques yield accurate results. An uncertainty analysis was conducted to quantify the measurement errors. The dominating phase uncertainty is caused by probe positioning errors of 10 [mu]m. The magnitude uncertainty in the through-line measurement is dominated by the system errors. Measured characteristic impedance, effective dielectric constant and attenuation constant are in good agreement with the theory.

References

[1] Y.C. Shih and T. Itoh, "Analysis of conductor-backed Coplanar Waveguide," Electronics Lett., vol. 18, No. 12, June 10, 1982, pp. 538-540.

[2] G. Ghione and C. Naldi, "Parameters of Coplanar Waveguides with Lower Ground Plane," Electronics Lett., Vol. 19, No. 18, September 1983, pp. 734-35.

[3] D.A. Rowe and B.Y. Lao, "Numerical Analysis of Shielded Coplanar Waveguide," IEEE Trans. Microwave Theory Tech., Vol. MTT-31, November 1983, pp. 911-15.

[4] P. Troughton, "Measurement Techniques in Microstrip," Electronics Lett., Vol. 5, No. 2, 1969, pp. 25-26.

[5] T. Edwards and R. Owens, "2 to 18 GHz Dispersion Measurement on 10 to 100 Ohm Microstrip Lines on Sapphire," IEEE Trans. Microwave Theory Tech., Vol. MTT-24, No. 8, 1976, pp. 506-513.

[6] E.W. Strid, "26 GHz Wafer Probing for MMIC Development and Manufacture," Microwave Journal, August 1986, pp. 71-82.

[7] K. Jones and E. Strid, "Verify Wafer-Probe Reference Planes for MMIC Testing," Microwaves & RF, April 1988, pp. 145-154.

[8] R.W. Jackson, "Considerations in the Use of Coplanar Waveguide for mm-Wave Integrated Circuits," IEEE Trans. Microwave Theory Tech., Vol. MTT-34, December 1986, pp. 1450-56.

[9] H. Shigesawa, M. Tsuji and A.A. Oliner, "Conductor-backed Slot Line and Coplanar Waveguide: Dangers and Full-wave Analysis," IEEE-MTT Intl, Microwave Symposium Digest, G-2, New york, May 25-27, 1988, pp. 199-202.

[10] B. Donecker, "Determining the Measurement Accuracy of the HP 8510 Microwave Network Analyzer," RF & Microwave Measurement Symposium, Hewlett Packard.

[11] I.J. Bahl and R. Garg, "Simple and Accurate Formulas for Microstrip with Finite Strip Thickness," Proc. IEEE, Vol. 65, November 1977, pp. 1611-12.

[*] Invited paper

Yi-Chi Shih received his PhD in electrical engineering from the University of Texas in 1982. From September 1982 to April 1984, he was an adjunct professor at the Naval Postgraduate School in the Electrical Engineering Department. From April 1984 to May 1986, he was a member of the technical staff at Hughes Aircraft Co.'s Microwave Products Division. From May 1986 to May 1987, he was the technical director of mm-Wave Technologies Inc. From May 1987 to November 1987, he was an independent technical consultant. Since November 1987, he has been a scientist at Hughes Aircraft Co.'s Microwave Products Division. His research interests include application of numerical techniques to electromagnetic field problems, computer-aided design of microwave nd mm-wave components, device modeling and the development of MIC and MMIC circuits.
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Author:Shih, Yi-Chi
Publication:Microwave Journal
Date:Apr 1, 1991
Words:2516
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