King Saud University College of Engineering Electrical Engineering Department EE-205 Electrical Circuit Lab Experiment No. 4 Thevenin’s and Maximum Power Transfer Theorems In ac Circuits Objectives - To verify experimentally Thevenin’s and maximum power transfer theorems as applied to ac circuits. Material Required Resistors: Inductors: Capacitors: Equipment: 100 Ω ,1 k Ω , 3.3 k Ω , 10 k Ω , one decade resistance box. 17.5 mH inductor with iron core. Two 0.1 µ F, 0.47 µ F, 1 µ F, 4.7 µ F, 22 µ F. Multimeter, signal generator. Background I. Thevenin’s Theorem Thevenin’s theorem can be applied to ac circuits in the same manner as has been applied to dc circuits. To find the variable of interest, isolate the related branch from the circuit, short out all the independent voltage sources and open all the independent current sources (this can be done only in theory, not in practice) and calculate ZTH across the terminals in question. Then replace all sources and calculate ETH, which is the voltage across the terminals of question. Draw the Thevenin’s equivalent and replace the branch that has been isolated and find using basic rules the desired variable (voltage, or current etc.). See Fig.1 a Zth Active AC Circuit ZL Eth a + - ZL b b where a Active AC Circuit Eth = Vab b a + - & Zth Passive AC Circuit b Fig. 1: Thevenin's Theorem. 1 II. Maximum Power Transfer Theorem Maximum power transfer theorem in ac circuits states that the max power will be transferred to a load when the load impedance is the conjugate of the Thevenin’s impedance across the load terminals. See Fig.2 a Active AC Circuit ZL * ( for maximum power transfer ) = Z th b a Passive AC Circuit Zth b Fig. 2 Maximum power transfer theorem. 2 Procedure I: ١. Wire the circuit shown in Fig. 6a, and measure VR and IR. ٢. Isolate the (10 KΩ) resistor from the circuit and measure the voltage across the terminals (a-b). This voltage is ETH. ٣. Calculate ZTH by shorting the supply. ٤. Reconstruct the Thevenin’s equivalent circuit for the circuit of Fig.6-a by inserting the ETH and ZTH as shown in Fig.6-b and measure IR. and VR. Compare this with step (1). 96 mH 1 KΩ a ( With Iron Core ) + + 5V 1 KHz 3.3 KΩ VR - 10 KΩ a Zth IR + Eth VR - - b IR 10 KΩ b (b) (a) Fig. 6: Circuits for procedure I. Procedure II : ١. Construct the circuit of Fig.7. Set Rpot = R + RL 100 Ω a 17.5 mH V Potentiometer 5V 1 KHz b C ZL Fig. 7: Circuit for procedure II. ٢. Replace different capacitor combinations as shown in Table 1 and measure for each combination the V(a-b). ٣. Calculate ZTH for the circuit of Fig. 7 and record it in the rectangular form. ٤. Calculate ZL for each combination of capacitor and list the data in Table 1. ٥. Calculate the power transferred to the load using. P = V 2 ( a −b ) / R pot Repeat this for all combinations of capacitors and list this data in Table 1. 3 ٦. On a graph, plot P vs X C and locate the maximum power transfer on the graph what can you conclude about the maximum power transfer? Table 1 Combination of capacitors V(a-b) (V) Xc (Ω) ZL (Ω) P (mW) 0.1 µF 0.47 µF 0.57 µF 1 µF 1.1 µF 1.2 µF 1.47 µF 4.7 µF 22 µF 4