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| * <math>V_5</math>: <math>I_6 = I_5 + h_3</math> | | * <math>V_5</math>: <math>I_6 = I_5 + h_3</math> |
| * <math>V_7</math>: <math>I_7 = I_t + k_e</math> | | * <math>V_7</math>: <math>I_7 = I_t + k_e</math> |
− | * <math>T_1</math>: <math>I_b + j_c = j_e</math> | + | * <math>T_1</math>: <math>j_b + j_c = j_e</math> |
| * <math>T_2</math>: <math>k_e = k_b + k_c</math> | | * <math>T_2</math>: <math>k_e = k_b + k_c</math> |
| + | |
| + | === Capacitors === |
| + | |
| + | Capacitors relate current and voltage according to the equation |
| + | : <math>I = C \frac{dV}{dt}</math>. |
| + | As stated above, the unknown voltages and currents are assumed to be of the form |
| + | : <math>X(t) = X_0 e^{i \omega t} + X_1</math> |
| + | so the capacitor equation can be linearized as |
| + | : <math>I = i \omega C V</math> |
| + | where <math>\omega = 2 \pi f</math>. This equation works for both AC and DC cases, because in the DC case the derivative on the voltage eliminates any DC bias for the current, but <math>\omega = 0</math> so the equation still holds. There is one such equation for each capacitor. |
| + | |
| + | * <math>C_1</math>: <math>h_1 = i \omega C_1 V_1</math> |
| + | * <math>C_2</math>: <math>h_2 = i \omega C_2 {V_2 - V_3)</math> |
| + | * <math>C_3</math>: <math>h_3 = i \omega C_3 V_5</math> |
| + | * <math>C_5</math>: <math>I_t = i \omega C_5 (V_7 - V_{out})</math> |