Electrical Circuits
Dr inż. Agnieszka Wardzińska
Room: 105 Polanka
agnieszka.wardzinska@put.poznan.pl
cygnus.et.put.poznan.pl/~award
Advisor hours: Monday: 9.30-10.15 Wednesday: 10.15-11.00Thevenin’s Theorem (DC)
Thevenin’s Theorem states that any linear circuit (linear
fragment of a circuit) can be replaced by an equivalent
circuit. The equivalent circuit consist with a single voltage
source and series resistance conected to the load, as shown
below.
To calculate the U and I on the loadwe need to create Thevenin’s source and attache
load resistor between the two open points of the equivalent circuit. The voltage U and the current I can be calculated from voltage divider circuit formulas:
Thevenin’s Theorem (DC)
To calculate the equivalent voltage source (Thevenin’s voltage ET ),
we need to
remove the load from the original circuit and calculate the voltage across the open connection points where the load resistor used to be. To calculate the equivalent series resistance (Thevenin’s
resistance RT ) we need to calculate the resistance of the circuit from the nodes where we calculate the Thevenin’s voltage. If the circuit contain only independent sources to do it we remove all
sources in the original circuit (voltage sources shorted and current sources open) and calculate total resistance between the open
connection points. If the circuit contain dependent sources we need to calculate resistance without removing them. Then we remove only independens sources, and and calculate total resistance as:
where Ex is arbitrary taken voltage source between the open connection points, and Ix is a current going from the source.
Thevenin’s Theorem (AC)
The equivalent circuit for the AC
circuit consist with a single
voltage source and series
impedance conected to the load
(in general the impedance), as
shown below. It is analog as for
DC circuit, but all elements,
voltages and currents have in
general complex form.
To calculate the U and I on the load we need to create Thevenin’s source and
attache load impedance between the two open points of the equivalent circuit. The current I takes then the form:
The equivalent voltage source (Thevenin’s voltage ET ) and equivalent
Norton’s Theorem (DC)
The Norton’s Theorem is equivalent to Thevenin’s Theorem. It states that the linear circuit (linear fragment of a
circuit) can be replaced by a current source (Norton’s current source JN)
with a resistance (Norton’s resistance RN) conected parallel to the source.
The load is connected also parallel to the Norton’s current source.
To calculate the I through the load we can use the current divider circuit:
Norton’s Theorem (DC)
The Norton’s resistance we calculate as the
Thevenin’s resistance (see above). To
calculate the equivalent current source , we
need to remove the load from the original
circuit and shorten the connection points
where the load resistor used to be and
calculate the current through the short.
The Norton’s and Thevenin’s circuit are
equivalent and we can converse one of them
to the second using a voltage and current
Norton’s Theorem (AC)
Similar as for Thevenin’s Theorem for AC circuit we can calculate the current equivalent source (Norton’s current source JN) with an impedance (Norton’s impedance ZN) conected
parallel to the source.
To calculate the I through the load we can use the current divider circuit
and U from the Ohm’s law:
The Norton’s resistance and the equivalent current source we calculate as described
