Download Unit 4 Network Theorems II 1. Thevenin`s theorem

Unit 4
Network Theorems II
1. Thevenin’s theorem
The main objective of Thevenin’s theorem is to reduce some portion of a circuit to an
equivalent source and a single element. This reduced equivalent circuit connected tothe
remaining part of the circuit will allow us to find the desired current or voltage. Thevenin’s
theorem is based on circuit equivalence. A circuit equivalent to another circuit exhibits
identical characteristics at identical terminals.
Figure 1 A Linear two terminal network
Figure 2 The Thevenin’s equivalent circuit
According to Thevenin’s theorem, the linear circuit of Fig. 3.30 can be replaced by the one
shown in Fig.1 (The load resistor may be a single resistor or another circuit). The circuit to
the left of the terminals x-y in Fig.1 is known as the Thevenin’s equivalent circuit.
The Thevenin’s theorem may be stated as follows:
A linear two–terminal circuit can be replaced by an equivalent circuit consisting of a
voltage source Vt in series with a resistor Rt, Where Vt is the open–circuit voltage at the
terminals and Rt is the input or equivalent resistance at the terminals when the
independent sources are turned off or Rt is the ratio of open–circuit voltage to the short–
circuit current at the terminal pair.
Action plan for using Thevenin’s theorem :
1. Divide the original circuit into circuit A and circuit B.
In general, circuit B is the load which may be linear or non-linear. Circuit is the balance of
the original network exclusive of load and must be linear. In general, circuit may contain
independent sources, dependent sources and resistors or other linear elements.
2. Separate the circuit from circuit A & B.
3. Replace circuit A with its Thevenin’s equivalent.
4. Reconnect circuit B and determine the variable of interest (e.g. current or voltage).
Procedure for finding Rt:
Three different types of circuits may be encountered in determining the resistance, Rt
(i) If the circuit contains only independent sources and resistors, deactivate the sources and
find Rt by circuit reduction technique. Independent current sources are deactivated by
opening them while independent voltage sources are deactivated by shorting them.
(ii) If the circuit contains resistors, dependent and independent sources, follow the
instructions described below:
(a) Determine the open circuit voltage voc with the sources activated.
(b) Find the short circuit current isc when a short circuit is applied to the terminals a-b
(c) Rt = voc/ isc
(iii) If the circuit contains resistors and only dependent sources, then
(a) v0c = 0 (since there is no energy source)
(b) Connect 1A current source to terminals a- b and determine vab.
(c) Rt = v0c/ 1