Dr inż. Agnieszka Wardzińska Room: 105 Polanka cygnus.et.put.poznan.pl/~award Advisor hours: Monday: Wednesday:

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 E x is arbitrary taken voltage source between the open connection points, and I x 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 E T ) and equivalent series impedance (Thevenin’s impedance Z T ) 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 J N ) with an impedance (Norton’s impedance Z N ) 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