Download Circuit Theorems

CIRCUIT THEOREMS
SUPERPOSITION THEOREM


If a circuit has two or more independent sources, the
value of the specific variable is determined by the
contribution of each independent source to the
variable and then add them up.
The superposition principle states that the
voltage across (or current through) an element in a
linear circuit is the algebraic sum of the voltages
across (or currents through) that element due to each
independent source acting alone.
STEPS TO APPLY SUPERPOSITION PRINCIPLE:
1) Turn off all independent sources except one source:
a) Current source  by ‘open’ circuit
b) Voltage source  by ‘short’ circuit
2) Find the output (voltage or current) due to that
active source using nodal or mesh analysis.
3) Repeat step 1 for each of the other independent
sources.
4) Find the total contribution by adding algebraically
all the contributions due to the independent
sources.
EXAMPLE:
EXAMPLE FOR PRACTICE:
EXAMPLE
EXAMPLE (CONT...)
EXAMPLE
EXAMPLE TO PRACTICE
THEVENIN’S THEOREM

Thevenin’s theorem states that a linear twoterminal circuit can be replaced by an equivalent
circuit consisting of a voltage source VTh in series
with a resistor RTh, where VTh is the open-circuit
voltage at the terminals and RTh is the input or
equivalent resistance at the terminals when the
independent sources are turned off.
EXAMPLE
FIND THE THEVENIN EQUIVALENT CIRCUIT
FOR THE FOLLOWING NETWROK
NORTON’STHEOREM

Norton’s theorem states that a linear twoterminal circuit can be replaced by an equivalent
circuit consisting of a current source IN in
parallel with a resistor RN, where IN is the shortcircuit current through the terminals and RN is
the input or equivalent resistance at the terminals
when the independent sources are turned off.
MAXIMUM POWER TRANSFER THEOREM

Maximum power is transferred to the load when
the load resistance equals the Thevenin
resistance as seen from the load (RL = RTh).
EQUATIONS OF MAXIMUM POWER
TRANSFER THEOREM
The maximum power transfer theorem states the
following:
“A load will receive maximum power from a linear
bilateral dc network when its total resistive value
is exactly equal to the Thévenin resistance of the
network as “seen” by the load.”
MILLMAN’S THEOREM



Through the application of Millman’s theorem, any number
of parallel voltage sources can be reduced to one.
In the following figure, the three voltage sources can be
reduced to one.
This would permit finding the current through or voltage
across RL without having to apply a method such as mesh
analysis, nodal analysis, superposition, and so on.
MILLMAN’S THEOREM



Step 1: Convert all voltage sources to current sources
Step 2: Combine parallel current sources and the conductance
Step 3: Convert the resulting current source to a voltage source,
and the desired single-source network is obtained
SUBSTITUTION THEOREM

If the voltage across and the current through any branch of a dc
bilateral network are known, this branch can be replaced by
any combination of elements that will maintain the same
voltage across and current through the chosen branch
RECIPROCITY THEOREM

The current I in any branch of a network, due to a single
voltage source E anywhere else in the network, will equal the
current through the branch in which the source was originally
located if the source is placed in the branch in which the current
I was originally measured.

Ref.
- Fundamentals of Electric Circuits (3rd Edition)
by Charles K. Alexander and Mathew N.O.Sadiku
