Norton's Theorem Dr. Holbert ECE201 Lect-14 1

Introduction Any Thevenin equivalent circuit is in turn equivalent to a current source in parallel with a resistor [source transformation]. A current source in parallel with a resistor is called a Norton equivalent circuit. Finding a Norton equivalent circuit requires essentially the same process as finding a Thevenin equivalent circuit. ECE201 Lect-14 2

Independent Sources Isc RTh Circuit with one or more independent sources Norton equivalent circuit ECE201 Lect-14 3

No Independent Sources RTh Circuit without independent sources Norton equivalent circuit ECE201 Lect-14 4

Finding the Norton Equivalent Circuits with independent sources: Find Voc and Isc Compute RTh Circuits without independent sources: Apply a test voltage (current) source Find resulting current (voltage) ECE201 Lect-14 5

Example: Strain Gauge Strain is the amount of deformation of a body due to an applied force-it is defined as the fractional change in length. Strain can be positive (tensile) or negative (compressive). One type of strain gauge is made of a foil grid on a thin backing. ECE201 Lect-14 6

A Strain Gauge Backing Foil The strain gauge’s resistance varies as a function of the strain: R = GF  R  is the strain, R is the nominal resistance, GF is the Gauge Factor ECE201 Lect-14 7

Typical values Measured strain values are typically fairly small-usually less than 10-3. GF is usually close to 2. Typical values for R are 120, 350, and 1000. A typical change in resistance is R = 2•10-3•120 = 0.24 ECE201 Lect-14 8

Measuring Small Changes in R To measure such small changes in resistance, the strain gauge is placed in a Wheatstone bridge circuit. The bridge circuit uses an excitation voltage source and produces a voltage that depends on R. ECE201 Lect-14 9

The Bridge Circuit R R+R + – – + Vex Vout R R ECE201 Lect-14 10

Norton Equivalent for Any  GF = 2 ECE201 Lect-14 11 11

Thevenin/Norton Analysis 1. Pick a good breaking point in the circuit (cannot split a dependent source and its control variable). 2. Thevenin: Compute the open circuit voltage, VOC. Norton: Compute the short circuit current, ISC. For case 3(b) both VOC=0 and ISC=0 [so skip step 2] ECE201 Lect-14 12

Thevenin/Norton Analysis 3. Compute the Thevenin equivalent resistance, RTh (or impedance, ZTh). (a) If there are only independent sources, then short circuit all the voltage sources and open circuit the current sources (just like superposition). (b) If there are only dependent sources, then must use a test voltage or current source in order to calculate RTh (or ZTh) = VTest/Itest (c) If there are both independent and dependent sources, then compute RTh (or ZTh) from VOC/ISC. ECE201 Lect-14 13

Only steps 2 & 4 differ from Thevenin & Norton! Thevenin/Norton Analysis 4. Thevenin: Replace circuit with VOC in series with RTh, ZTh. Norton: Replace circuit with ISC in parallel with RTh, ZTh. Note: for 3(b) the equivalent network is merely RTh (or ZTh), that is, no voltage (or current) source. Only steps 2 & 4 differ from Thevenin & Norton! ECE201 Lect-14 14

Class Examples Learning Extension E5.4 Learning Extension E8.15(c) ECE201 Lect-14 15