Why Extract Equivalent Circuit Models?
Measured S-parameter files (.s2p, .s1p) capture the complete electrical behavior of a component but are not directly usable in circuit simulators as simple element values. An equivalent circuit model — a network of R, L, C elements — is compact, physical, and works across simulators and design tools. Model extraction fits element values to match the measured S-parameters.
General Model Extraction Workflow
- Measure: Obtain accurate S-parameters of the component (de-embedded from fixture)
- Topologize: Choose a circuit topology based on the component's physical structure
- Fit: Optimize element values to minimize error between model and measured S-params
- Validate: Compare model vs. measured over the full frequency range
Common Equivalent Circuit Topologies
| Component | Topology | Key Elements |
|---|---|---|
| Chip inductor | Series RLC + shunt C | L_s, R_s, C_s, C_shunt |
| Chip capacitor | Series LC + shunt R | C_s, L_s (ESL), R_s (ESR) |
| SMD resistor | R + series L + shunt C | R, L_lead, C_shunt |
| Bond wire | Series L + R | L_wire, R_wire |
| Via | Series L, shunt C | L_via, C_pad |
Chip Inductor Model Example
A chip inductor near self-resonance needs at minimum a π-model:
Port1 ─── R_s ─── L_s ─── Port2
| |
C_p C_p
| |
GND GND
Element starting values:
- L_s: nominal inductance from datasheet (e.g., 10 nH)
- R_s: DC resistance + skin effect (start with DCR × (1 + 0.01×√f_GHz))
- C_p: back-calculate from SRF: C_p = 1/(4π² × f_SRF² × L_s)
Optimization Metric
Minimize the S-parameter error function:
Error = Σᵢ [ w_S11·|S11_meas(fᵢ) − S11_model(fᵢ)|²
+ w_S21·|S21_meas(fᵢ) − S21_model(fᵢ)|² ]
Use different weights w_S11, w_S21 to prioritize matching quality or passband performance.
Using RF View in the Validation Step
After extraction, generate S-parameter data from the equivalent circuit model (using SPICE or Qucs), save as .s2p, and load both the measured and model files in RF View simultaneously. Overlay S11 and S21 plots to visually verify model accuracy across frequency. Good models typically agree to within 0.5 dB in magnitude and 5° in phase across the valid frequency range.