Circuit Theorems 1

 Introduction  Linearity property  Superposition  Source transformations  Thevenin’s theorem  Norton’s theorem  Maximum power transfer Circuit Theorems2

Thevenin’s Theorem Thevenin’s Theorem  Thevenin’s theorem states that a linear two- terminal circuit can be replaced by an equivalent circuit consisting of a voltage source V Th in series with a resistor R Th where V Th is the open circuit voltage at the terminals and R Th is the input or equivalent resistance at the terminals when the independent source are turn off. Circuit Theorems3

Property of Linear Circuits Circuit Theorems4 i v v i Any two-terminal Linear Circuits + - V th I sc Slope=1/R th

Circuit Theorems5

How to Find Thevenin’s Voltage  Equivalent circuit: same voltage-current relation at the terminals.  Open circuit voltage at a-b Circuit Theorems6

How to Find Thevenin’s Resistance  Circuit Theorems7

CASE 1  If the network has no dependent sources: ●Turn off all independent source. ●R TH : can be obtained via simplification of either parallel or series connection seen from a-b Circuit Theorems8

CASE 2  If the network has dependent sources ●Turn off all independent sources. ●Apply a voltage source v o at a-b ●Alternatively, apply a current source i o at a-b Circuit Theorems9

 The Thevenin’s resistance may be negative, indicating that the circuit has ability providing power Circuit Theorems10

Simplified circuit Voltage divider Circuit Theorems11

Example 8  Find the Thevenin’s equivalent circuit of the circuit shown, to the left of the terminals a-b. Then find the current through R L for R L = 6, 16, and 36 . Circuit Theorems12

Find R th Circuit Theorems13

Find V th Circuit Theorems14

Norton’s Theorem  Norton’s theorem states that a linear two-terminal circuit can be replaced by equivalent circuit consisting of a current source I N in parallel with a resistor R N where I N is the short-circuit current through the terminals and R N is the input or equivalent resistance at the terminals when the independent source are turn off. Circuit Theorems15

Circuit Theorems16 v i V th -I N Slope=1/R N

How to Find Norton Current  Thevenin and Norton resistances are equal:  Short circuit current from a to b : Circuit Theorems17

Thevenin or Norton equivalent circuit :  The open circuit voltage v oc across terminals a and b  The short circuit current i sc at terminals a and b  The equivalent or input resistance R in at terminals a and b when all independent source are turn off. Circuit Theorems18

Example 11  Find the Norton equivalent circuit of the circuit shown. Circuit Theorems19

Example 11 Circuit Theorems20

Example 11 Circuit Theorems21

Example 11 Circuit Theorems22

Example 11 Circuit Theorems23

Maximum Power Transfer Circuit Theorems24

 Maximum power is transferred to the load when the load resistance equals the Thevenin resistance as seen the load (R L = R TH ). Circuit Theorems25

Circuit Theorems26

Example 13  Find the value of R L for maximum power transfer in the circuit shown. Find the maximum power. Circuit Theorems27

Example 13 Circuit Theorems28

Example 13 Circuit Theorems29

Summary Circuit Theorems30