--- title: "h-parameters versus S-parameters" subject: "RF and Microwave Engineering" chapter: 3 key: "semester_7/rf_and_microwave_engineering:h-parameters-vs-s-parameters" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/h-parameters-vs-s-parameters site: BCT Engineering --- # h-parameters versus S-parameters RF and Microwave Engineering · Chapter 3: RF and Microwave Network Theory and Analysis - Asked in: 2080 Chaitra, 5+5 marks - Video: [Scattering Parameters | Why S Parameters in Microwave measurement? | Calculation of S Parameters](https://www.youtube.com/watch?v=-PZQm_404Js) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/h-parameters-vs-s-parameters - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-3 ## Question Compare h-parameters with S-parameter. Using a two-port network describe 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. ## Answer #### 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 ```text a1 -> -> b2 o-----------+-------+-----------o port 1 | [S] | port 2 o-----------+-------+-----------o <- b1 <- a2 ``` At port *n*, with line impedance Z0: ```text 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: ```text | 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What do h-parameters and S-parameters relate respectively? A. Waves; voltages and currents B. Voltages and currents; incident and reflected waves C. Power; impedance D. Both use incident and reflected waves Answer: B. h-parameters are hybrid mixes of V and I for low frequency. S-parameters relate incident and reflected waves for RF and microwave. (Key point: Variables used) 2. Which is the measurement condition for S-parameters? A. Output shorted or input open B. All other ports matched to Z0 C. All ports open-circuited D. All ports shorted Answer: B. h-parameters need V2 = 0 or I1 = 0, whereas S-parameters need matched terminations. (Key point: Measurement condition) 3. S21 of a two-port is defined as A. b1/a1 with a2 = 0 B. b2/a1 with a2 = 0 C. b1/a2 with a1 = 0 D. b2/a2 with a1 = 0 Answer: B. S21 is the forward transmission coefficient, the output wave b2 divided by input wave a1 with the output matched. (Key point: S21 meaning) 4. A transistor has |S21| = 3 with matched ports. Its forward power gain is A. 3 (4.77 dB) B. 9 (9.54 dB) C. 6 (7.8 dB) D. 1.73 (2.4 dB) Answer: B. Power gain is |S21|^2 = 9, which is 9.54 dB. 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