Page 1 of 2
ECET 231 – Circuit Analysis I
Network Theorems
(Adapted from Course Textbook)
Superposition Theorem
The total current through or voltage across a resistor or branch may be determined by summing
the effects due to each source independently.
1. Remove all sources except the one being analyzed by replacing voltage sources with a short
circuit (wire) and current sources with an open circuit.
2. Perform the analysis with each source alone and add the resulting voltages, currents.
3. The superposition theorem does not apply to power dissipated by resistors. To calculate
power, either the current or voltage for a given resistor must first be found by superposition.
The power may then be determined using a conventional method involving the voltage or
current.
Thevenin’s Theorem
Any linear, bilateral network may be reduced to a simplified two-terminal circuit consisting of a
single voltage source in series with a single resistor.
1. Remove the load from the circuit.
2. Label the resulting two terminals (a and b, for example).
3. Set all sources in the circuit to zero by replacing voltage sources with short circuits and
current sources with open circuits.
4. Determine the Thevenin equivalent resistance, RTh, by calculating the total resistance as
seen between the two terminals, a and b.
5. Replace the sources that were removed in step 3 and determine the open-circuit voltage
between the terminals a and b. If the circuit has more than one source, this may require use
of the superposition theorem to determine the open circuit voltage due to each source
separately and then determine the combined effect. The resulting open-circuit voltage will be
the Thevenin voltage, ETh.
6. Draw the Thevenin equivalent circuit using the resistance determined in Step 4 and the
voltage determined in step 5.
7. Reconnect the load from the circuit. The Thevenin equivalent may now be used to analyze
the voltage across and current through the load.
Page 2 of 2
Norton’s Theorem
Any linear, bilateral network may be reduced to a simplified two-terminal circuit consisting of a
single current source in parallel with a single resistor.
1. Remove the load from the circuit.
2. Label the resulting two terminals (a and b, for example).
3. Set all sources in the circuit to zero by replacing voltage sources with short circuits and
current sources with open circuits.
4. Determine the Norton equivalent resistance, RN, by calculating the total resistance as seen
between the two terminals, a and b.
5. Replace the sources that were removed in step 3 and determine the current that would occur
in a short connected between the terminals a and b. If the circuit has more than one source,
this may require use of the superposition theorem to determine the short circuit current due to
each source separately and then determine the combined effect. The resulting short-circuit
current will be the Norton current, IN.
6. Draw the Norton equivalent circuit using the resistance determined in Step 4 and the current
determined in step 5.
7. Reconnect the load from the circuit. The Norton equivalent may now be used to analyze the
voltage across and current through the load.
Maximum Power Transfer Theorem
A load resistance will receive maximum power from a circuit when the resistance of the load is
equal to the Thevenin (Norton) resistance looking back at the circuit.