physics-equationAvailable
Nonlinear small-signal linearization
Diodes and smooth switches require an explicit complete MNA operating point. Their incremental conductance and switch control transconductance are stamped exactly.
Reference contract
| Field | Value | Description |
|---|---|---|
| differentiability | exact-ad | — |
| entity_dimension | global | — |
| latex | \left(\frac{\partial\mathbf g}{\partial\mathbf x}\bigg|_{\mathbf x_0}+i\omega\mathbf C\right)\widehat{\mathbf x}=-\frac{\partial\mathbf g}{\partial\mathbf u}\bigg|_{\mathbf x_0}\widehat{\mathbf u} | — |
| mathml | <math display="block"><mrow><mo>(</mo><msub><mi>g</mi><mi>x</mi></msub><mo>(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>)</mo><mo>+</mo><mi>i</mi><mi>omega</mi><mi>C</mi><mo>)</mo><mover><mi>x</mi><mo>^</mo></mover><mo>=</mo><mo>-</mo><msub><mi>g</mi><mi>u</mi></msub><mo>(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>)</mo><mover><mi>u</mi><mo>^</mo></mover></mrow></math> | — |
| name | Nonlinear small-signal linearization | — |
| section | governing-equation | — |
Diodes and smooth switches require an explicit complete MNA operating point. Their incremental conductance and switch control transconductance are stamped exactly.
Contract
| Property | Value |
|---|---|
| differentiability | exact-ad |
| entity_dimension | global |
| latex | \left(\frac{\partial\mathbf g}{\partial\mathbf x}\bigg|_{\mathbf x_0}+i\omega\mathbf C\right)\widehat{\mathbf x}=-\frac{\partial\mathbf g}{\partial\mathbf u}\bigg|_{\mathbf x_0}\widehat{\mathbf u} |
| mathml | <math display="block"><mrow><mo>(</mo><msub><mi>g</mi><mi>x</mi></msub><mo>(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>)</mo><mo>+</mo><mi>i</mi><mi>omega</mi><mi>C</mi><mo>)</mo><mover><mi>x</mi><mo>^</mo></mover><mo>=</mo><mo>-</mo><msub><mi>g</mi><mi>u</mi></msub><mo>(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>)</mo><mover><mi>u</mi><mo>^</mo></mover></mrow></math> |
| name | Nonlinear small-signal linearization |
| section | governing-equation |