S-Parameter to Z-Parameter Converter

S-parameters (scattering parameters) describe a 2-port network in terms of reflected and transmitted power waves relative to a reference impedance Z0, the standard way RF and microwave networks are measured and specified. Z-parameters (impedance parameters) describe the same network in terms of absolute voltage and current relationships in ohms, more directly useful for series-connected circuit analysis.

First compute D = (1 minus S11)(1 minus S22) minus S12*S21 using complex arithmetic. Then Z11 = Z0*[(1+S11)(1-S22)+S12*S21]/D, Z12 = Z0*2*S12/D, Z21 = Z0*2*S21/D, and Z22 = Z0*[(1-S11)(1+S22)+S12*S21]/D. Every term is a complex number, so the conversion requires complex addition, subtraction, multiplication, and division throughout, not just the real parts.

Network analyzers and RF datasheets almost always report S-parameters as a magnitude (typically 0 to 1 for a passive network) and a phase angle in degrees, since that directly reflects how the reflected or transmitted wave was measured. This calculator accepts that native format and converts internally to rectangular (real and imaginary) form before running the complex arithmetic.

Z0 is the impedance against which S-parameters are defined, almost always 50 ohms in RF and microwave systems, though 75 ohms is common in video and cable TV work. Because the S-to-Z conversion formula scales every Z-parameter by Z0, entering the wrong reference impedance produces Z-parameters that do not match the actual network, even if the S-parameter magnitudes and phases themselves are correct.

Z12 differing from Z21 (and correspondingly S12 differing from S21) means the network is non-reciprocal, it behaves differently depending on which port the signal enters from. Amplifiers, isolators, and circulators are all non-reciprocal by design. Passive, non-magnetic components like cables, filters, and attenuators are reciprocal, so their measured S12 and S21 (and converted Z12, Z21) should be equal or very nearly so.

A singular conversion means the denominator D = (1-S11)(1-S22) - S12*S21 is numerically zero (or extremely close to it) for the entered S-parameters, making the Z-parameter conversion mathematically undefined. This is rare for physically realistic measured data and usually indicates an entry error or an S-parameter set describing a network at an unusual operating condition.

Yes, in principle, using the inverse formula (normalizing Z by Z0 and applying the standard Z-to-S relations), though that direction is not what this calculator computes. This calculator is scoped specifically to the S-to-Z direction, matching how measured network analyzer data (which is naturally in S-parameter form) most often needs to be converted for further analysis.

No. A unilateral network (for example, an ideal isolator or a simplified amplifier model) can have S12 = 0 while still producing valid, finite Z-parameters, as long as the denominator D stays nonzero. Setting a magnitude input to exactly 0 is a valid, supported input.

Magnitude and phase for each Z-parameter mirrors how the S-parameter inputs were entered, letting you compare an input reflection coefficient's phase against the resulting impedance's phase directly. The step-by-step working section additionally shows every result in rectangular (real plus imaginary) form for anyone who needs that representation instead.

RF and microwave engineers commonly measure a component (a filter, a matching network, an amplifier stage) on a vector network analyzer, which naturally outputs S-parameters, then convert to Z-parameters to combine that component's model with other series-connected elements in a larger circuit simulation, since impedance parameters add directly for series topologies in a way S-parameters do not.