optimization-physics-contractAvailable
Electrical Circuit
Defines optimization applicability and derivative ownership for Electrical Circuit.
Reference contract
| Field | Value | Description |
|---|---|---|
| kind | Electrical Circuit | — |
| namespace | cir | — |
| status | certified | — |
| visible | true | — |
| optimizationContract | 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| — |
| governingEquations | [{"description":"KCL rows are augmented with branch-current unknowns for voltage sources, inductors, controlled sources, ports, and ideal op-amp constraints.","differentiability":"exact-ad","editor":null,"entityDimension":"global","latex":"\\mathbf C(\\mathbf p)\\dot{\\mathbf x}+\\mathbf g(\\mathbf x,\\mathbf p,\\mathbf u,t)=\\mathbf 0","mathml":"<math display=\"block\"><mrow><mi>C</mi><mover><mi>x</mi><mo>.</mo></mover><mo>+</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>0</mn></mrow></math>","name":"Modified nodal analysis","readOnly":true,"section":"governing-equation"},{"description":"Finite open-loop gain, unity-gain bandwidth, and output resistance are assembled as a dynamic MNA branch.","differentiability":"exact-ad","editor":null,"entityDimension":"global","latex":"\\tau\\dot v_o+v_o-A_0(v_+-v_-)-R_o i_o=0,\\quad\\tau=\\frac{A_0}{2\\pi f_u}","mathml":"<math display=\"block\"><mrow><mi>tau</mi><mover><msub><mi>v</mi><mi>o</mi></msub><mo>.</mo></mover><mo>+</mo><msub><mi>v</mi><mi>o</mi></msub><mo>-</mo><msub><mi>A</mi><mn>0</mn></msub><mo>(</mo><msub><mi>v</mi><mo>+</mo></msub><mo>-</mo><msub><mi>v</mi><mo>-</mo></msub><mo>)</mo><mo>-</mo><msub><mi>R</mi><mi>o</mi></msub><msub><mi>i</mi><mi>o</mi></msub><mo>=</mo><mn>0</mn></mrow></math>","name":"Single-pole op-amp macro model","readOnly":true,"section":"governing-equation"},{"description":"Diodes and smooth switches require an explicit complete MNA operating point. Their incremental conductance and switch control transconductance are stamped exactly.","differentiability":"exact-ad","editor":null,"entityDimension":"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","readOnly":true,"section":"governing-equation"}] | — |
The runtime provider, evidence fixture, derivative channels, geometric modes, objective symbols, reductions, contribution bindings, and governing equations are generated from the physics catalog.