Thévenin and Norton Equivalent Circuits ELEC 308 Elements of Electrical Engineering Dr. Ron Hayne Images Courtesy of Allan Hambley and Prentice-Hall

Equivalent Circuits  Two-terminal circuit Circuit that has any complex interconnection of resistances and sources Has ONLY two points that can be connected to other circuits  We will learn how to represent complex two- terminal circuits by simple equivalent circuits ELEC 3082

Thévenin Equivalent Circuits  Consists of voltage source in series with a resistance ELEC 3083

Circuit Parameters  The Thévenin source voltage is equal to the open-circuit voltage of the original network, or V t = v oc ELEC 3084

Circuit Parameters  The Thévenin short-circuit current is given by ELEC 3085

Circuit Parameters  The Thévenin resistance is given by  Thus, we can determine a Thévenin equivalent circuit simply by measuring the OPEN-CIRCUIT VOLTAGE and SHORT- CIRCUIT CURRENT ELEC 3086

Example 2.16 ELEC 3087

Exercise  Find the Thévenin equivalent circuit ELEC 3088

Norton Equivalent Circuits  Consist of independent CURRENT source in PARALLEL with a resistance ELEC 3089

Circuit Parameters  The Norton source current is equal to the short-circuit current of the original network, or I n = i sc ELEC 30810

Circuit Analysis Algorithm  Complete two of the following: Determine the open-circuit voltage (V t = v oc ). Determine the short-circuit current (I n = i sc ). Zero the sources and find the Thévenin resistance R t looking back into the terminals.  Use Ohm’s Law (V t =I n R t ) to compute the remaining parameter.  Draw one of the following: Thévenin equivalent circuit with independent VOLTAGE source V t in SERIES with R t Norton equivalent circuit with independent CURRENT source I n in PARALLEL with R t ELEC 30811

Exercise 2.29  Find the Norton equivalent circuit ELEC 30812

Maximum Power Transfer  Consider the two-terminal circuit and load resistance below. What value of R L would deliver maximum to the load resistance R L ? ELEC 30813

Maximum Power Transfer  The load resistance R L that absorbs the maximum power from a two-terminal circuit is equal to the Thévenin resistance, or R L =R t  The maximum power transferred to the load resistance is given by ELEC 30814

Example 2.21  Find the load resistance for max power transfer Find the max power ELEC 30815

Principle of Superposition  Suppose we have a circuit with MULTIPLE independent sources  We wish to determine a specific response (current or voltage) in the circuit  We can EASILY determine the response due to a SINGLE independent source (by zeroing out the other independent sources)  The SUPERPOSITION principle states that the total response is the SUM of the responses to each of the independent sources acting INDIVIDUALLY ELEC 30816

Superposition Illustration ELEC 30817

Strain Measurements ELEC 30818

Wheatstone Bridge  Circuit used to measure UNKNOWN resistances  Used by ME’s and CE’s to measure the resistances of strain gauges in experimental stress studies of machines and buildings ELEC 30819

Wheatstone Bridge ELEC 30820

Summary  Thevenin Equivalent Circuit  Norton Equivalent Circuit  Maximum Power Transfer  Superposition  Wheatstone Bridge ELEC 30821