Introduction • Thevenin’s Theorem is a very important and useful theorem. • It is a method for the reduction of a portion of a complex circuit into a simple one. • It reduces the need for repeated solutions of the same sets of equations. Thevenin’s Theorem V-I Characteristic of Thevenin Equivalent Thevenin Equivalent Circuit Any two-terminal linear network, composed of voltage sources, current sources, and resistors, can be replaced by an equivalent two-terminal network consisting of an independent voltage source in series with a resistor. Network of Sources and Resistors . RTh i a + v b . Arbitrary Network i VTh RTh i . a + .V v = VTh-RThi VTh v b . . a + v Th 0 .i i sc Arbitrary Network v b . 1 Finding VTh and RTh • RTh Open circuit across terminals Finding VTh and RTh – Cont’d . i a • + VTh i = 0, v = voc = vTh voc=VTh . v = 0, i = isc = - b . a Calculate the opencircuit voltage in the original network, voc voc . - VTh = voc b Thevenin Equivalent - Example Find the Thevenin equivalent with respect to terminals a,b. 25 V 20 Ω 4Ω . a 3A . b RTh = RTh . i a isc=VTh/RTh VTh vTh RTh Calculate the shortcircuit current in the original network, isc + Network of Sources and Resistors 5Ω Short circuit across terminals .b . a Network of Sources and Resistors voc isc isc . b Alternative Method of finding RTh -- for circuits containing only independent sources 1. Set all independent sources to zero 2. Find equivalent resistance Req of the dead circuit between the terminals Circuit with all independent sources set equal to zero . a Req . b RTh = Req 2 Alternative Method of finding RTh -- for circuits containing dependent sources 1. Set all independent sources to zero 2. Apply either a test voltage source v0 (or a test current source i0 ) to the terminals 3. Calculate i0 (or v0 ) v0 RTh = i0 Circuit with all independe nt sources set equal to zero Circuit with all independe nt sources set equal to zero .a .b Thevenin Equivalent - Example Find the Thevenin equivalent of the following circuit. If a 10Ω resistor is connected between the terminals, what current will flow in it? i0 v0 - + 3Ω 2i1 a o i1 10 A . 4Ω 6Ω a + v0 . - i0 o b b 3