S-Parameter Conversion Calculator Formula

Understand the math behind the s-parameter conversion calculator. Each variable explained with a worked example.

Formulas Used

S11 Linear Magnitude

s11_linear = pow(10, s11_db / 20)

S21 Linear Magnitude

s21_linear = pow(10, s21_db / 20)

S12 Linear Magnitude

s12_linear = pow(10, s12_db / 20)

S22 Linear Magnitude

s22_linear = pow(10, s22_db / 20)

VSWR at Port 1

vswr_port1 = (1 + pow(10, s11_db / 20)) / (1 - pow(10, s11_db / 20))

Insertion Loss

insertion_loss = abs(s21_db)

Variable	Description	Default
`s11_db`	S11 (Return Loss at Port 1)(dB)	-15
`s21_db`	S21 (Forward Gain/Insertion Loss)(dB)	-0.5
`s12_db`	S12 (Reverse Isolation)(dB)	-30
`s22_db`	S22 (Return Loss at Port 2)(dB)	-20

Scattering parameters describe how RF energy propagates through a network.

S11: Input return loss (reflection at port 1)

S21: Forward transmission (gain or insertion loss)

S12: Reverse transmission (isolation)

S22: Output return loss (reflection at port 2)

Linear = 10^(dB/20) (for voltage/amplitude)

dB = 20 x log10(Linear)

For passive devices, S21 is negative (loss). For amplifiers, S21 is positive (gain).

A filter with S11=-15 dB, S21=-0.5 dB, S12=-30 dB, S22=-20 dB.

s11_db = -15s21_db = -0.5s12_db = -30s22_db = -20

01S11 linear: 10^(-15/20) = 0.1778
02S21 linear: 10^(-0.5/20) = 0.9441
03S12 linear: 10^(-30/20) = 0.03162
04VSWR at port 1: (1+0.1778)/(1-0.1778) = 1.43
05Insertion loss: 0.5 dB

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