Small-signal
A transmission parameter is a wave ratio. Its magnitude squared is a power ratio whatever the port impedances are, but the voltage ratio carries a square root of impedance with it.
Differential in, differential out
These are the reference impedances of the parameter you already have, which are the source and load terminations it assumes. For a raw measurement on 50 Ω analyzer ports, use 100 Ω differential and 50 Ω single-ended. The voltage factor is one only when the input and output references are equal; differential-to-single-ended gives 1/√2, and single-ended-to-differential gives √2. After port-impedance conversion on the analyzer, enter the converted references and use the converted S11 below. Renormalising needs the whole S-matrix, so it is done on the analyzer, not here.
The gain above is referred to the incident wave, which equals the input terminal voltage only when the input is matched. Enter the input reflection to also get the gain referred to the terminal; it needs the phase as well as the magnitude, because the two differ by 1 + S11.
Each travelling wave is normalised by the square root of its port's reference impedance. That normalisation is the whole reason a voltage ratio and a power ratio separate.
With port 2 terminated in its own reference impedance there is no reflected wave, so the total output voltage equals the outgoing wave. With a source of impedance Z1, the incident wave equals half the source electromotive force, which is also the actual input voltage when the input is matched.
The power ratio has no such factor, because the normalisation cancels when you square the magnitude. That is the asymmetry in one line.
If you need the gain referred to the actual terminal voltage at the input rather than to the incident wave, the input reflection enters as well. The two forms agree when the input is matched.
100 Ω differential, 50 Ω single-ended
| Topology | S-param | Z1 | Z2 | Voltage factor | Add to dB |
|---|---|---|---|---|---|
| Diff → Diff | Sdd21 | 100 Ω | 100 Ω | 1 | 0.00 dB |
| Diff → SE | Ssd21 | 100 Ω | 50 Ω | 0.7071 | −3.01 dB |
| SE → Diff | Sds21 | 50 Ω | 100 Ω | 1.414 | +3.01 dB |
| SE → SE | S21 | 50 Ω | 50 Ω | 1 | 0.00 dB |
Small-signal linear two-port, real positive reference impedances, each port terminated in its own reference. A differential port behaves as an ordinary port with its own differential reference impedance; that impedance is twice the per-line value only when the two lines are uncoupled. A real coupled pair has a differential impedance of twice its odd-mode impedance, which is lower.
The conversion depends only on the ratio of the two reference impedances, so it is a fixed offset for a given topology, not a frequency-dependent correction. It does not describe a DUT terminated in something other than its reference impedance, and it says nothing about compression or distortion, which depend on the load the device physically sees.
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