S-Parameter Conversion Calculator Formula

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

Use the S-Parameter Conversion Calculator

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)

Variables

VariableDescriptionDefault
s11_dbS11 (Return Loss at Port 1)(dB)-15
s21_dbS21 (Forward Gain/Insertion Loss)(dB)-0.5
s12_dbS12 (Reverse Isolation)(dB)-30
s22_dbS22 (Return Loss at Port 2)(dB)-20

How It Works

Understanding S-Parameters

Scattering parameters describe how RF energy propagates through a network.

Parameter Meanings

  • 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)

    • Conversion

    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).

    Worked Example

    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
    1. 01S11 linear: 10^(-15/20) = 0.1778
    2. 02S21 linear: 10^(-0.5/20) = 0.9441
    3. 03S12 linear: 10^(-30/20) = 0.03162
    4. 04VSWR at port 1: (1+0.1778)/(1-0.1778) = 1.43
    5. 05Insertion loss: 0.5 dB

    Frequently Asked Questions

    What does negative S21 mean?

    For passive devices, S21 is negative (in dB) indicating insertion loss. For amplifiers, S21 is positive indicating gain.

    What is good S11 for an amplifier?

    S11 below -10 dB (VSWR < 2:1) is acceptable. Below -15 dB is good. Below -20 dB is excellent.

    How are S-parameters measured?

    Using a vector network analyzer (VNA) with calibrated test ports and known reference impedance (usually 50 ohms).

    Ready to run the numbers?

    Open S-Parameter Conversion Calculator