Small-signal
A balanced measurement is a single-ended one seen through a change of basis. Pick which physical ports make each logical port and the page writes out every mixed-mode parameter in terms of the single-ended ones.
Which analyzer ports make up each logical port. The default, 1 and 3 in and 2 and 4 out, is an example pairing for a four-port network; the first port of a pair is its positive line.
The differential and common-mode waves of a pair are the difference and the sum of its two single-ended waves, each divided by √2 so that power is conserved. Collect those rows into T and the whole conversion is one similarity transform.
Written out with your port numbers, so they can be read straight off an analyzer's single-ended trace set. Enter the measured values on the analyzer, which does the conversion itself.
Both lines of a pair are assumed to share the per-line reference from the DUT card, which is what the analyzer's single-ended measurement uses. If the DUT is to be characterised at a different reference, renormalise the whole single-ended matrix first; the transform alone does not do that.
Order-of-magnitude only
| Item | Thumb | Why it matters |
|---|---|---|
| Balanced through path | Sdd21 ≈ S21 when the pair is symmetric | The differential gain is the single-ended gain, not 6 dB more; the extra 3 dB per side is in the reference impedance |
| Single-ended out of a pair | Ssd21 = (S21 − S23)/√2 | An ideal balun-free split reads −3.01 dB; that is the definition, not loss |
| Mode conversion | Sdc21, Scd21 below −30 dB is well balanced | Skew of 1 ps at 28 GHz converts about −21 dB; conversion is what radiates and what receives interference |
| Power between modes | |Sdd21|² + |Scd21|² = |S21|² for an ideal pair | What leaves the differential mode goes somewhere; a flat Sdd21 can hide a rising Scd21 |
| Common-mode reference | Zc = Z0/2, Zd = 2 Z0 | 25 Ω and 100 Ω for a 50 Ω analyzer; a return loss quoted without its mode is ambiguous |
Linear network, each single-ended port referenced to the same real impedance on both lines of a pair. The transform is exact under that condition and depends only on the port assignment, not on the DUT. It does not model a physical balun or a source that drives only the differential mode. A different common-mode termination can also change the differential response when mode conversion is present; use the full mixed-mode matrix and the actual termination.
Bockelman and Eisenstadt, "Combined differential and common-mode scattering parameters: theory and simulation", IEEE Trans. MTT 43(7), 1995.
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