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Thevenin's theorem states that a linear two-terminal AC circuit can be replaced by an equivalent circuit consisting of a voltage source Vrh in series with an impedance Zth, where this the open-circuit voltage at the terminals and Zth is the input or equivalent impedance at the terminals when the independent sources are turned off Circuit B1 shown in Figure B1 is used for this lab practical. It is also used to illustrate how Vrh and Zth are calculated. In this case, 'a' and 'b' are two terminals and Z is the load impedance. The inductor has inductance L with internal resistance R. R R1 (Inductor) R2 R3 ZL Vs -2.0° (V) f = 4000 Hz Figure Bl: Circuit B1 Based on Thevenin's theorem, Circuit Bl has an equivalent circuit, namely Circuit B2, shown in Figure B2. The following steps can be used to calculate Vrh and Zmh. • Disconnect Z from Circuit Bl; Calculate the voltage Vab between two terminals 'a' and 'b'; • Vrh = Vabi Short the voltage source Vs (or set Vs to zero); Calculate the impedance Zs between 'a' and 'b' (with Z disconnected); Zn = Zab

Znh VTI ZE Figure B2: Circuit B2 The maximum average power transfer theorem states that for maximum average power transfer, the load impedance Z must be equal to the complex conjugate of the Thevenin impedance Znh, i.e., z =ZX 1. Calculation for the Thevenin equivalent circuit. a. Use the following values for Circuit Bl: • Ri = 472; • R2 = 10002; • R3 = 50002; • C= 100 nF; • L=22 mH with internal resistance R=68 2. b. Calculate Vth and Zh of Circuit Bl for its Thevenin equivalent circuit as shown in Circuit B2. c. Fill in Table Bl with your results. Hints: • Vth may be calculated by nodal analysis. Vrh may also be calculated by using the principle of voltage division twice as shown below: R (jol + R)+ R)||(R, +1/( j~C)) (jol+R)+R; R +(joL+R)+R;)||(R, +1/(joC))) • ZT, may be calculated as follows: Z= R; ||(R+ joL+(R || (R, +1/(joC)))). 2. Calculation for the maximum power transfer. a. Determine the value of Z, for the maximum power transfer. b. Your calculation for Z, should show that Z, is capacitive, i.e., Im(Z.)<0. Hence, Z, can be expressed as Z, = R, +1/(joc) where R, is the equivalent load resistor and C, is the equivalent load capacitor. Determine the value of C for the maximum power transfer in this case. c. Fill in Table Bl with your results. Hints: • Z, EZ Z has been calculated above. The imaginary part of Z, can be used to determine C, i.e., Im(Z. )=(-1)/(@C.). NB: Your pre-work (Table Bl) must be included in your lab report (Section 3).

Table Bl Calculated results for the Thevenin equivalent circuit and maximum power transfer V.V. Z® (V) Please include the amplitude and phase of V Th. Zτη (Ω) Z(92) C. (F) Details of your calculation: Please include major steps (e.g., formulas) for your calculation of Vrh, Zth and C