Question

How can you determine the Thevenin or Norton equivalent circuit of a network containing dependent sources?

Answer 1

Determining the Thevenin or Norton equivalent circuit of a network containing dependent sources follows the same general process as analyzing networks with independent sources. The key is to find the open-circuit voltage and the short-circuit current at the load terminals.

Here's a step-by-step guide to finding the Thevenin equivalent circuit:

Identify the Load Terminals: Determine which part of the network you want to simplify and consider it as the load terminals. Remove any elements connected across the load terminals to open the circuit.

Thevenin Equivalent Voltage (Vth):

For an independent source: Replace all the independent sources in the network (voltage sources and current sources) with their internal resistances turned off (replaced by short circuits for voltage sources and open circuits for current sources).
For a dependent source: Leave the dependent sources as they are since their values depend on the rest of the network.

Find the open-circuit voltage (Voc): Apply any necessary circuit analysis methods (e.g., nodal analysis, mesh analysis) to find the voltage at the load terminals with all other elements disconnected.

Thevenin Equivalent Resistance (Rth):

Turn off all the independent sources (replacing voltage sources with short circuits and current sources with open circuits) in the network.
Remove the load and calculate the total resistance seen from the load terminals. This can be done by replacing all the resistors with their internal resistances (if any).
The total resistance seen from the load terminals is the Thevenin equivalent resistance (Rth).

Construct the Thevenin Equivalent Circuit: Now that you have Vth and Rth, you can create the Thevenin equivalent circuit by connecting a voltage source (Vth) in series with a resistor (Rth) across the load terminals.

Finding the Norton equivalent circuit follows a similar process, but instead of an equivalent voltage source in series with an equivalent resistor, you will have an equivalent current source in parallel with an equivalent resistor.

Here's a summary of the steps to find the Norton equivalent circuit:

Identify the Load Terminals.

Norton Equivalent Current (In):

For an independent source: Replace all the independent sources in the network (voltage sources and current sources) with their internal resistances turned off (replaced by short circuits for voltage sources and open circuits for current sources).
For a dependent source: Leave the dependent sources as they are since their values depend on the rest of the network.

Find the short-circuit current (Isc): Apply any necessary circuit analysis methods to find the current flowing through the load terminals with all other elements replaced or disconnected.

Norton Equivalent Resistance (Rn):

Turn off all the independent sources (replacing voltage sources with short circuits and current sources with open circuits) in the network.
Remove the load and calculate the total resistance seen from the load terminals. This can be done by replacing all the resistors with their internal resistances (if any).
The total resistance seen from the load terminals is the Norton equivalent resistance (Rn).

Construct the Norton Equivalent Circuit: Now that you have In and Rn, you can create the Norton equivalent circuit by connecting a current source (In) in parallel with a resistor (Rn) at the load terminals.

Remember that when dealing with dependent sources, you may need to consider the relevant equations and expressions to account for their behavior in the simplified Thevenin or Norton equivalent circuit.