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S-Parameters... Circuit Analysis and Design WHAT ARE "S" PARAMETERS? "S" parameters are measured so easily that obtaining accurate "S" parameters are reflection and transmission coefficients, phase information is no longer a problem. Measurements like elec- familiar concepts to RF and microwave designers. Transmission co- trical length or dielectric coefficient can be determined readily from efficients are commonly called gains or attenuations; reflection co- the phase of a transmission coefficient. Phase is the difference be- efficients are directly related to VSWR's and impedances. tween only knowing a VSWR and knowing the exact impedance. VSWR's have been useful in calculating mismatch uncertainty, but Conceptually they are like "h," "y," or "z" parameters because they describe the inputs and outputs of a black box. The inputs and when components are characterized with "s" parameters there is no outputs are in terms of power for "s" parameters, while they are mismatch uncertainty. The mismatch error can be precisely calcu- voltages and currents for "h," "y," and "z" parameters. Using the lated. convention that "a" is a signal into a port and "b" is a signal out of a port, the figure below will help to explain "s" parameters. Easy To Measure Two-port "s" parameters are easy to measure at high frequencies TEST DEVICE because the device under test is terminated in the characteristic impedance of the measuring system. The characteristic impedance i termination has the following advantages: s S2| s22 i i " S|2 1 1. The termination is accurate at high frequencies ... it is 02 possible to build an accurate characteristic impedance load. "Open" or "short" terminations are required to determine "h," "y," or "z" In this figure, "a" and "b" are the square roots of power; (a,)J is parameters, but lead inductance and capacitance make these termi- 2 nations unrealistic at high frequencies. the power incident at port 1, and (b2) is the power leaving port 2. The diagram shows the relationship between the "s" parameters 2. No tuning is required to terminate a device in the characteristic and the "a's" and "b's." For example, a signal a, is partially re- impedance . positioning an "open" or "short" at the terminals of flected at port 1 and the rest of the signal is transmitted through a test device requires precision tuning. A "short" is placed at the the device and out of port 2. The fraction of a, that is reflected at end of a transmission line, and the line length is precisely varied un- port 1 is Sn, and the fraction of a, that is transmitted is s, . Simi- ( til an "open" or "short" is reflected to the device terminals. On the larly, the fraction of a that is reflected at port 2 is $32, and the z other hand, if a characteristic impedance load is placed at the end fraction 5u is transmitted. of the line, the device will see the characteristic impedance regard- The signal bi leaving port 1 is the sum of the fraction of a, that was reflected at port 1 and the fraction of a? that was transmitted less of line length. from port 2. 3. Broadband swept frequency measurements are possible . Thus, the outputs can be related to the inputs by the equations: because the device will remain terminated in the characteristic im- bi = SM 3, -f Su 3i pedance as frequency changes. However, a carefully reflected "open" j = Si. a, -f s» a2 or "short" will move away from the device terminals as frequency When ai = 0, and when a, = 0, is changed, and will need to be "tuned-in" at each frequency. b, b, b, Sn — a, ', Su —' a, - ai 4. The termination enhances stability ... it provides a resistive The setup below shows how s and Su are measured. termination that stabilizes many negative resistance devices, which u might otherwise tend to oscillate. An advantage due to the inherent nature of "s" parameters is: 50il TRANSMISSION LINE 50iiTRANSMISSION LINE 5. Different devices can be measured with one setup . probes 0,-* ZSOURCE=50iii TEST -b, do not have to be located right at the test device. Requiring probes ESOfl DEVICE to be located at the test device imposes severe limitations on the RF SOURCE (?y) b,— — Q2=0 TERMINATION > i i setup's ability to adapt to different types of devices. Port 1 is driven and aj is made zero by terminating the 50 n Easy To Use transmission line coming out of port 2 in its characteristic 50 ^ Quicker, more accurate microwave design is possible with "s" impedance. This termination ensures that none of the transmitted parameters. When a Smith Chart is laid over a polar display of s,, signal, bj, will be reflected toward the test device. or s», the input or output impedance is read directly. If a swept- Similarly, the setup for measuring s,j and sn is: frequency source is used, the display becomes a graph of input or output impedance versus frequency. Likewise, CW or swept-frequency displays of gain or attenuation can be made. 50 a TRANSMISSION LINE 5011 TRANSMISSION LINE "S" parameter design techniques have been used for some time. son The Smith Chart and "s" parameters are used to optimize matching TERMINATION networks and to design transistor amplifiers. Amplifiers can be de- TERMINATION signed for maximum gain, or for a specific gain over a given fre- RF SOURCE quency range. Amplifier stability can be investigated, and oscillators can be designed. These techniques are explained in the literature listed at the If the usual "h," "y," or "z" parameters are desired, they can be bottom of this page. Free copies can be obtained from your local calculated readily from the "s" parameters. Electronic computers Hewlett-Packard Sales Representative. and calculators make these conversions especially easy. References: 1. "Transistor Parameter Measurements," Application Note 77-1, February WHY "S" PARAMETERS 1, 1967. 2. "Scattering Parameters Speed Design of High Frequency Transistor Cir- Total Information cuits," by Fritz Weinert, Electronics, September 5, 1966. "S" parameters are vector quantities; they give magnitude and 3. "S" Parameter Techniques for Faster, More Accurate Network Design," phase information. Most measurements of microwave components, by Dick Anderson, Hewlett-Packard Journal, February 1967. 4. "Two Port Power Flow Analysis Using Generalized Scattering Param- like attenuation, gain, and VSWR, have historically been measured eters," by George Bodway, Microwave Journal, May 1967. only in terms of magnitude. Why? Mainly because it was too difficult 5. "Quick Amplifier Design with Scattering Parameters," by William H. to obtain both phase and magnitude information. Froehner, Electronics, October 16, 1967. S-Parameters .... Circuit Analysis and Design APPLICATION NOTE 95 A Collection of Articles Describing S-Parameter Circuit Design and Analysis SEPTEMBER 1968 INTRODUCTION THE STATE OF HIGH-FREQUENCY CIRCUIT DESIGN The designer of high-frequency circuits can now do in hours what formerly took weeks or months. For a longtime there has been no simple, accurate way to characterize high-frequency circuit components. Now, in a matter of minutes, the frequency response of the inputs and outputs of a device can be measured as s parameters. As shown in some of the articles in this application note, an amplifier circuit can be completely designed on a Smith Chart with s-parameter data. Circuit de- sign is greatly accelerated by using small computers or calculators to solve lengthy vector design equations. This leads to some creative man-machine interactions where the designer can "tweek" his circuit via the computer and see how its response is affected The computer can search through hundreds of thousands of possible designs and select the best one. An even more powerful approach that makes one's imagination run away with itself is to combine the measuring equip- ment and the computer as in the HP 8541A. Theoret- ically, one could plug in a transistor, specify the type of circuit to be designed, and get a readout of the op- timal design. This note consists primarily of a collection of recent articles describing the s-parameter design of high- frequency circuits. Following the articles is a brief section describing the rather straightforward technique of measuring s parameters. Many useful design equations and techniques are contained in this litera- ture, and amplifier design, stability, and high-fre- quency transistor characterization are fully discussed. TABLE OF CONTENTS Section Page Microwave Transistor Characterization 1-1 !! Scattering Parameters Speed Design of High Frequency Transistor Circuits 2-1 Ml S-Parameter Techniques for Faster, More Accurate Network Design 3-1 Combine S Parameters with Time Sharing 4-1 V Quick Amplifier Design with Scattering Parameters 5-1 \ i Two-Port Flow Analysis Using Generalized Scattering Parameters 6-1 VII Circuit Design and Characterization of Transistors by Means of Three-Port Scattering Parameters. 7-1 APPENDIX A-l iii SECTION I MICROWAVE TRANSISTOR CHARACTERIZATION Julius Lange describes the parameters he feels are most important for characterizing microwave tran- sistors. These include the two-port s parameters, MSG (maximum stable gain), Gmax (maximum tuned or maximum available gain), K (Rollett's stability factor), and U (unilateral gain). The test setups used for measuring these parameters are described and a transistor fixture for Tl-line transistors plus a slide screw tuner designed by Lange are shown. Thearticle concludes with equations relating y parameters, h parameters, MSG, Gmax, K, and U to the two-port s parameters. Introduction 1-1 S Parameter Measurements 1-2 Gain and Stability Measurements 1-5 MSG (Maximum Stable Gain) 1-6 GMAX (Maximum Available Gain) 1-6 K (Rollett's Stability Factor 1-6 U (Unilateral Gain - Mason Invariant) 1-7 Test Fixtures. 1-8 Special S Parameter Relationships 1-12 Tr.XAS INSTRUMENTS INCORPORATED COMPONENTS GROUP MICROWAVE TRANSISTOR CHARACTERIZATION INCLUDING S-PARAMETERS* by Julius Lange A.
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