RF/LAB

Small-signal

Voltage & power gain

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.

Port topology

SourceZd1 DUTSdd21 LoadZd2 + + Vd1 Vd2 Differential reference impedance at both ports

Reference impedances

These are the reference impedances of the parameter you already have. If the analyzer measured in its own reference, enter that. Renormalising a measurement to different impedances needs the whole S-matrix, not the transmission term alone.

Result

Why the two differ

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.

Standard references

100 Ω differential, 50 Ω single-ended

TopologyParameterZ1Z2Voltage factorAdd to dB
Diff → DiffSdd21100 Ω100 Ω10.00 dB
Diff → SESsd21100 Ω50 Ω0.7071−3.01 dB
SE → DiffSds2150 Ω100 Ω1.414+3.01 dB

Model and limits

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.

Keysight: complex impedance and the Smith chart

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