What are the different methods of solving circuits with dependent sources?

Node Voltage Method (Modified Nodal Analysis):

Convert the dependent sources into equivalent expressions using the controlling variables (usually voltages across or currents through certain elements).

Apply the node voltage method to solve the circuit as you would for circuits with only independent sources.

Mesh Current Method (Modified Mesh Analysis):

Convert the dependent sources into equivalent expressions using the controlling variables (usually voltages across or currents through certain elements).

Apply the mesh current method to solve the circuit as you would for circuits with only independent sources.

Superposition Theorem:

Use the superposition theorem to solve the circuit step-by-step by considering one dependent source at a time, treating all others as if they were turned off.

Combine the individual results to get the final solution.

Source Transformation:

Convert dependent sources into independent sources and resistors using source transformation techniques.

Solve the transformed circuit using regular methods for circuits with only independent sources.

Transform the solution back to the original circuit.

Thevenin or Norton Equivalent Circuits:

Convert the circuit with dependent sources into its Thevenin or Norton equivalent circuit using methods like source transformation.

Analyze the equivalent circuit using standard techniques.

Use the results to find the solution for the original circuit.

Nodal Admittance Matrix (Y-parameters):

Express the circuit using nodal admittance matrix (Y-matrix) and include the effects of dependent sources.

Solve for the node voltages using matrix methods.

Loop Analysis with Dependent Sources:

Use loop analysis (Kirchhoff's voltage law) while considering the effects of dependent sources.

Apply loop equations to find the unknown variables.

The choice of method depends on the complexity and structure of the circuit. Some methods may be more suitable for certain types of circuits, while others may be more convenient in different situations. As always, understanding the properties and characteristics of dependent sources is crucial to effectively solving circuits that involve them.