Chapter 20

	AC Network Theorems

Superposition Theorem

	Voltage across (or current through) an element
		Determined by summing voltage (or current) due to each independent source
	All sources (except dependent sources) other than the one being considered are eliminated

Superposition Theorem

	Replace current sources with opens
	Replace voltage sources with shorts

Superposition Theorem

	Circuit may operate at more than one frequency at a time
	Superposition is the only analysis method that can be used in this case
	Reactances must be recalculated for each different frequency

Superposition Theorem

	Diode and transistor circuits will have both dc and ac sources
	Superposition can still be applied

Superposition Theorem

	Superposition theorem can be applied only to voltage and current
	It cannot be used to solve for total power dissipated by an element
	Power is not a linear quantity
		Follows a square-law relationship

Superposition for Dependent Sources

	If controlling element is external to the circuit under consideration
		Method is the same as for independent sources

Superposition for Dependent Sources

	Simply remove sources one at a time and solve for desired voltage or current
	Combine the results

Superposition for Dependent Sources

	If the dependent source is controlled by an element located in the circuit
		Analysis is different
		Dependent source cannot be eliminated

Superposition for Dependent Sources

	Circuit must be analyzed by considering all effects simultaneously

Thévenin’s Theorem

	Converts an ac circuit into a single ac voltage source in series with an equivalent impedance
	First, identify and remove the element or elements across which the equivalent circuit is to be found

Thévenin’s Theorem

	Label two open 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  open-circuit voltage

Thévenin’s Theorem

	If more than one source is involved
		Superposition may be used
	Draw resulting Thévenin equivalent circuit
		Including the portion removed

Norton’s Theorem

	Converts an ac network into an equivalent circuit
		Consists of a single current source and a parallel impedance
	First, identify and remove the element or elements across which the Norton circuit is to be found

Norton’s Theorem

	Label the open terminals
	Set all sources to zero

Norton’s Theorem

	Determine Norton equivalent impedance
	Replace sources and calculate short-circuit current

Norton’s Theorem

	Superposition may be used for multiple sources
	Draw resulting Norton circuit
		Including portion removed

Thévenin and Norton Circuits

	Possible to find Norton equivalent circuit from Thévenin equivalent circuit
		Use source transformation method
	ZN = ZTh
	IN = ETh/ZTh

Thévenin’s and Norton’s Theorems

	If a circuit contains a dependent source controlled by an element outside the area of interest
		Previous methods can be used to find the Thévenin or Norton circuit

Thévenin’s and Norton’s Theorems

	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 controlled by an element in the circuit
		Use following steps to determine equivalent circuit

Thevenin’s and Norton’s Theorems

	First
		Identify and remove branch across equivalent circuit is to be determined
	Label the open terminals

Thevenin’s and Norton’s Theorems

	Calculate open-circuit voltage
		Dependent source cannot be set to zero
		Its effects must be considered
	Determine the short-circuit current

Thevenin’s and Norton’s Theorems

	ZN = ZTh = ETh/IN
	Draw 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

Thevenin’s and Norton’s Theorems

	Effects of dependent source must be considered simultaneously

Maximum Power Transfer Theorem

	Maximum power
		Delivered to a load when the load impedance is the complex conjugate of the Thévenin or Norton impedance

Maximum Power Transfer Theorem

	ZTh = 3W + j4W     ZL = ZTh*  = 3W - j4W
	ZTh = 10 WÐ30°    ZL = ZTh* = 10 WÐ-30°

Maximum Power Transfer Theorem

	If the ZL is the complex conjugate of ZTh or ZN

Relative Maximum Power

	If it is not possible to adjust reactance part of a load
		A relative maximum power will be delivered
	Load resistance has a value determined by