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There is one such equation per node, and each node already is labeled on the above diagram by the voltage at that point; thus there is one equation per voltage. Additionally, each transistor acts as a node.
There is one such equation per node, and each node already is labeled on the above diagram by the voltage at that point; thus there is one equation per voltage. Additionally, each transistor acts as a node.
* <math>V_1</math>: <math>I_1 = I_{in} + h_1</math>
* V<sub>1</sub>: I<sub>1</sub> = I<sub>in</sub> + h<sub>1</sub>
* <math>V_2</math>: <math>I_{in} = I_2 + h_2</math>
* V<sub>2</sub>: I<sub>in</sub> = I<sub>2</sub> + h<sub>2</sub>
* <math>V_3</math>: <math>I_3 + h_2 = I_4 + j_b</math>
* V<sub>3</sub>: I<sub>3</sub> + h<sub>2</sub> = I<sub>4</sub> + j<sub>b</sub>
* <math>V_4</math>: <math>I_5 + k_b = I_3 + j_c</math>
* V<sub>4</sub>: I<sub>5</sub> + k<sub>b</sub> = I<sub>3</sub> + j<sub>c</sub>
* <math>V_5</math>: <math>I_6 = I_5 + h_3</math>
* V<sub>5</sub>: I<sub>6</sub> = I<sub>5</sub> + h<sub>3</sub>
* <math>V_7</math>: <math>I_7 = I_t + k_e</math>
* V<sub>7</sub>: I<sub>7</sub> = I<sub>t</sub> + k<sub>e</sub>
* <math>T_1</math>: <math>j_b + j_c = j_e</math>
* T<sub>1</sub>: j<sub>b</sub> + j<sub>c</sub> = j<sub>e</sub>
* <math>T_2</math>: <math>k_e = k_b + k_c</math>
* T<sub>2</sub>: k<sub>e</sub> = k<sub>b</sub> + k<sub>c</sub>
=== Capacitors ===
=== Capacitors ===
: <math>I = C \frac{dV}{dt}</math>.
: <math>I = C \frac{dV}{dt}</math>.
As stated above, the unknown voltages and currents are assumed to be of the form
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>
: <math>X(t) = X_0 e^{i \omega t} + X_1\,\!</math>
so the capacitor equation can be linearized as
so the capacitor equation can be linearized as
: <math>I = i \omega C V</math>
: <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.
where ω = 2πf. 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 &3969; = 0 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_1</math>: <math>h_1 = i \omega C_1 V_1</math>