- 2080 Chaitra · 5+5 marks
h-parameters versus S-parameters
Short answer
h-parameters use voltage/current with open/short terminations for low frequencies; S-parameters use incident/reflected waves with matched loads, safe for active devices, and work in waveguides. For a two-port, b1=S11 a1+S12 a2, b2=S21 a1+S22 a2, with a_n=V_n^+/√Z0, b_n=V_n^-/√Z0, yielding reflection and transmission coefficients when ports are terminated in Z0.
Compare h-parameters with S-parameter. Using a two-port network describe S-parameters.
Comparison of h-parameters and S-parameters
h-parameters (hybrid parameters) relate a mix of voltages and currents (V1, I2 in terms of I1, V2) and are used at low frequencies. S-parameters relate incident and reflected waves and are used at RF and microwave frequencies.
| Point | h-parameters | S-parameters |
|---|---|---|
| Variables | Voltage and current (V1, I1, V2, I2) | Incident and reflected waves (a, b) |
| Equations | V1 = h11·I1 + h12·V2; I2 = h21·I1 + h22·V2 | b1 = S11·a1 + S12·a2; b2 = S21·a1 + S22·a2 |
| Measurement condition | Output short (V2 = 0) or input open (I1 = 0) | All other ports matched to Z0 |
| Frequency range | Low frequency (audio, BJT models) | RF and microwave |
| Units | h11 in Ω, h22 in S, h12 and h21 unitless | All dimensionless (complex ratios) |
| Effect on active devices | Short/open can cause oscillation | Matched load keeps device stable |
| Use in waveguides | Not possible (V, I not unique) | Possible |
| Physical meaning | Input impedance, current gain, etc. | Reflection, transmission, power gain |
| Instrument | Multimeter, curve tracer | Vector network analyzer |
S-parameters of a two-port network
a1 -> -> b2
o-----------+-------+-----------o
port 1 | [S] | port 2
o-----------+-------+-----------o
<- b1 <- a2
At port n, with line impedance Z0:
an = Vn+/√Z0 = (Vn + Z0·In)/(2√Z0) (incident wave)
bn = Vn-/√Z0 = (Vn - Z0·In)/(2√Z0) (reflected wave)
The network relates them linearly:
| b1 | | S11 S12 | | a1 |
| b2 | = | S21 S22 | | a2 |
- S11 = b1/a1 (a2 = 0): input reflection coefficient, output terminated in Z0.
- S21 = b2/a1 (a2 = 0): forward transmission coefficient (gain or loss).
- S22 = b2/a2 (a1 = 0): output reflection coefficient, input terminated in Z0.
- S12 = b1/a2 (a1 = 0): reverse transmission coefficient (isolation).
Setting aₖ = 0 means port k is terminated in a matched load, so no wave is reflected back into the network.
Properties: reciprocal → S12 = S21; lossless → |S11|² + |S21|² = 1. Return loss = −20 log|S11| dB, insertion loss = −20 log|S21| dB, VSWR = (1 + |S11|)/(1 − |S11|).
Example: a transistor with |S21| = 3 has forward power gain |S21|² = 9 (9.54 dB) when both ports are matched to 50 Ω.
✓ Answer checked by Claude Opus 5.5 (high effort)
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