Chapter 20
AC Network Theorems
Superposition Theorem• The voltage across (or current through) an
element is determined by summing the voltage (or current) due to each independent source.
• All sources other than the one being considered are eliminated.
• Replace current sources with opens.• Replace voltage sources with shorts.
Superposition Theorem
• A circuit may operate at more than one frequency at a time.
• Diode and transistor circuits will have both dc and ac sources.
• Superposition can still be applied.
Superposition Theorem
• The superposition theorem can be applied only to voltage and current.
• It cannot be used to solve for the total power dissipated by an element.
• This is because power is not a linear quantity, but instead follows a square-law relationship.
Thévenin’s Theorem• Thévenin’s theorem converts an ac circuit
into a single ac voltage source in series with an equivalent impedance.
• First, remove the element or elements across which the equivalent circuit is to be found.
• Label the two terminals.• Set all sources to zero - replace voltage
sources with shorts, current sources with opens.
Thévenin’s Theorem
• Calculate the Thévenin equivalent impedance.
• Replace the sources and determine the open-circuit voltage.
• If more than one source is involved, use superposition.
• Draw the resulting Thévenin equivalent circuit, including the portion removed.
Norton’s Theorem
• Norton’s theorem converts an ac network into an equivalent circuit consisting of a single current source and a parallel impedance.
• First, remove element or elements across which the Norton circuit is to be found.
• Label the terminals.• Set all sources to zero.
Norton’s Theorem
• Determine the Norton equivalent impedance.• Replace the sources and calculate the short-
circuit current.• Superposition may used for multiple sources.• Draw the resulting Norton circuit with
elements which were removed replaced.
Thévenin and Norton Circuits
• It is possible to find the Norton equivalent circuit from the Thévenin equivalent circuit.
• ZN = ZTh
• IN = ETh/ZTh
Thévenin’s and Norton’s Theorems
• If a circuit contains a dependent source which is controlled by an element outside the area of interest, the previous methods cannot be used to find the Thévenin or Norton circuit.
• If a circuit contains a dependent source controlled by an element in the circuit, other methods must be used.
Thevenin’s and Norton’s Theorems
• If a circuit has a dependent source which is controlled by an element in the circuit, use the following steps to determine the equivalent circuit.
• First, remove the branch across which the equivalent circuit is to be determined.
• Label the terminals.
Thevenin’s and Norton’s Theorems
• Calculate the open-circuit voltage. The dependent source cannot be set to zero.Its effects must be considered.
• Determine the short-circuit current.
• ZN = ZTh = ETh/IN• Draw the equivalent circuit, replacing the
removed branch.
Thevenin’s and Norton’s Theorems
• A circuit may have more than one independent source.
• It is necessary to determine the open-circuit voltage and short-circuit current due to each independent source.
• The effects of the dependent source must be considered simultaneously.
Maximum Power Transfer Theorem
• Maximum power will be delivered to a load when the load impedance is the complex conjugate of the Thévenin or Norton impedance.
• ZTh = 3 + j4 ZL = 3 - j4
• ZTh = 10 30° ZL = 10 -30°
Maximum Power Transfer Theorem
• If the Z is replaced by its complex conjugate, the maximum power will be
N
NNmax
Th
Thmax
Th
Th
R
ZIP
R
EP
RR
REP
L
LL
4
422
2
2
2
Relative Maximum Power
• If it is not possible to adjust the reactance part of a load, then a relative maximum power will be delivered.
• The load resistance has a value determined by
22ThTh XXRRL