Download Electrical circuits wyklad 3

Dr inż. Agnieszka Wardzińska
Room: 105 Polanka
[email protected]
cygnus.et.put.poznan.pl/~award
Advisor hours:
Monday: 9.30-10.15
Wednesday: 10.15-11.00
Thevenin’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 load we 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 series
impedance (Thevenin’s impedance ZT ) are in complex domain.
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:
and U from the Ohm’s law:
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 source equivalencies.
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
in DC but in complex domain