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=== Unknown variables ===
=== Unknown variables ===
There are twenty-four unknown variables. The locations (and directions in the case of currents) are labeled on the circuit diagram.
There are twenty-four unknown variables. The locations (and directions in the case of currents) are labeled on the circuit diagram. All unknowns are assumed to be of the form
: <math>X(t) = X_0 e^{i \omega t} + X_1</math>,
where <math>X_0</math> gives the amplitude of oscillation, or the AC component, and <math>X_1</math> gives the DC offset.
* Node voltages: <math>V_1</math>, <math>V_2</math>, <math>V_3</math>, <math>V_4</math>, <math>V_5</math>, <math>V_7</math>, <math>V_{out}</math>
* Node voltages: <math>V_1</math>, <math>V_2</math>, <math>V_3</math>, <math>V_4</math>, <math>V_5</math>, <math>V_7</math>, <math>V_{out}</math>
** Note: there is no <math>V_6</math> on this circuit; it was a redundant variable with <math>V_c</math>.
** Note: there is no <math>V_6</math> on this circuit; it was a redundant variable with <math>V_c</math>.
| RE || emitter resistance || 0.37<math>\Omega</math> || 1<math>\Omega</math>
| RE || emitter resistance || 0.37<math>\Omega</math> || 1<math>\Omega</math>
|}
|}
== Equations ==
There are five categories of equations, which give a set of twenty-four equations in total. Two categories of equations are non-linear and need to be linearized to solve this system as a linear model using matrices.
=== Resistor voltage drop ===
The resistor voltage drop equations all take the form
: <math>\Delta V = IR</math>
or
: <math>V_\alpha - IR = V_\beta</math>.