S-Parameters
Understanding S-Parameters
S-parameters are the foundation of microwave measurement and design. Every RF component datasheet includes S-parameter data, and every simulation tool uses S-parameter models. They were developed because traditional circuit parameters (Z, Y, h, ABCD) require open-circuit or short-circuit termination conditions that are impractical at microwave frequencies.
The Four Two-Port S-Parameters
- S11 (input reflection coefficient): The ratio of reflected wave to incident wave at port 1 when port 2 is terminated. Equivalent to return loss: RL = -20 log10(|S11|).
- S21 (forward transmission): The ratio of transmitted wave at port 2 to incident wave at port 1. For amplifiers, this is gain. For passive devices, this is insertion loss.
- S12 (reverse transmission): The ratio of transmitted wave at port 1 to incident wave at port 2. For amplifiers, this is reverse isolation.
- S22 (output reflection coefficient): The ratio of reflected wave to incident wave at port 2 when port 1 is terminated. Output return loss.
S-Parameter Measurement
S-parameters are measured using a vector network analyzer (VNA). The VNA sends a known signal into each port and measures the magnitude and phase of reflected and transmitted waves. Before measurement, the VNA must be calibrated using known standards (short, open, load, and through connections) to remove systematic errors from cables and connectors.
S-Parameter Formats
- Touchstone (.s2p) files: Industry-standard text format for exchanging S-parameter data. Includes frequency, magnitude/phase or real/imaginary for each parameter.
- Smith Chart display: S11 and S22 are commonly plotted on Smith Charts to visualize impedance behavior.
- Polar/rectangular: S21 can be displayed in magnitude/phase or real/imaginary format.
[b1] [S11 S12] [a1]
[b2] = [S21 S22] [a2]
where a = incident wave, b = reflected wave
Return loss = -20 × log10(|S11|) dB
Insertion loss = -20 × log10(|S21|) dB
Gain = 20 × log10(|S21|) dB
Isolation = -20 × log10(|S12|) dB
VSWR from S11:
VSWR = (1 + |S11|) / (1 - |S11|)
S-Parameter Quick Reference
| Parameter | Meaning | Ideal Passive | Ideal Amplifier |
|---|---|---|---|
| S11 | Input match | < -20 dB | < -10 dB |
| S21 | Forward gain/loss | ~0 dB (low loss) | +15 to +40 dB |
| S12 | Reverse isolation | = S21 (reciprocal) | < -30 dB |
| S22 | Output match | < -20 dB | < -10 dB |
Frequently Asked Questions
What are S-parameters used for?
S-parameters characterize how RF signals behave when entering and leaving a component. S11 tells you how well the input is matched (return loss). S21 tells you the gain or insertion loss. S12 shows reverse isolation. S22 shows output match. They are measured with a vector network analyzer and used throughout RF design and simulation.
What is a good S11 value?
S11 represents input return loss. Lower (more negative) is better. S11 of -10 dB means 10% of power is reflected (acceptable for amplifiers). S11 of -20 dB means 1% reflection (good for passive components). S11 of -30 dB means 0.1% reflection (excellent match).
What is the difference between S-parameters and Z-parameters?
S-parameters use matched terminations and measure wave ratios, making them practical at microwave frequencies. Z-parameters require open-circuit conditions, which create radiation and parasitic effects above a few hundred MHz. S-parameters can be mathematically converted to Z, Y, or ABCD parameters when needed.