by Harley Berman
Scattering parameters, also known as s-parameters, are used to characterize the behavior of an RF component to varying input stimuli. With s-parameters, we can obtain useful information about a DUT such as insertion loss, return loss, and more, however, s-parameters only characterize single ended and unbalanced network performance. Although it is possible to use s-parameters to determine the insertion loss of a balanced device such as a balun from its single ended port to either of its balanced ports, conventional s-parameters tell us nothing about the balun’s response to common mode or differential signals. This is where mixed-mode scattering parameters come into play.
What Are Mixed Mode Scattering Parameters?
Mixed mode scattering parameters are a set of network parameters used to characterize differential circuits. For baluns, this means that the 0° and 180° ports are treated as a single 100Ω differential port and the single-ended common port remains the same 50Ω common port. The two-port mixed mode s-parameters of the balun are then characterized based on differential (d), common mode (c), or single-ended (s) signals (see above). For example: S12ds is the differential output response given a single ended input, which can be thought of as the differential insertion loss of the balun with a single ended input. The figures below show the insertion loss of the BAL-0003 plotted from both single ended s-parameters (S12) as well as mixed mode s-parameters (S12ds and S12cs).
The three plots above clearly show the utility of mixed mode scattering parameters because, although all three plots are of insertion loss, none of the plots are identical and each plot tells us something unique about the balun’s performance. We can see that the mixed mode insertion loss, S12ds, looks like the single ended insertion loss with a gain of 3dB across the band. This is because the single ended parameter describes insertion loss from a single ended input to a single ended output whereas S12ds describes the output as a 100Ω differential port, combining the output of the 0° and 180° ports. Since a balun is by nature a differential device, driving it with a common mode signal yields a very high insertion loss (S12cs above) due to the common mode rejection of the balun.
How Do I Obtain Mixed Mode Scattering Parameters?
Although it is possible for some VNAs to output mixed mode scattering parameters directly, I do not expect everybody to have a high performance VNA to take these measurements and after all, the onus is on us, the component seller, to provide this data. Recently at Marki Microwave, we have completed the process of updating all of our balun datasheets with these mixed mode parameters. I computed the mixed mode parameters by doing a mathematical transformation to the published s-parameter on the website. For information on how to compute this transformation you can read here, and here. On our datasheets, we define the mixed mode scattering parameters as follows:
S11dd: differential return loss of the differential port driven with a differential signal
S11dc: differential return loss of the differential port driven with a common signal
S12ds: insertion loss from a single ended input to a differential output
S11cc: common mode return loss of the differential port driven with a common signal
S11cd: common mode return loss of the differential port driven with a differential signal
S12cs: insertion loss from a single ended input to a common output
S22ss: single ended return loss
S21sd: insertion loss from a differential signal to single ended output
S21sc: insertion loss from a common signal to single ended output
Mixed Mode Scattering Parameter Summary
- Mixed mode s-parameters are used to characterize differential circuits
- Mixed mode s-parameters give more information about balanced devices than single ended s-parameters
- Mixed mode s-parameters characterize a devices behavior based on signaling type, not just relative powers using the format S(output port)(input port)(output mode)(input mode)