EE 301 AC Thvenin and Max Power Transfer

EE 301 AC Thèvenin and Max Power Transfer

Learning Objectives n n n Apply Thèvenin’s Theorem to AC circuits Explain under what

Thévenin’s theorem for AC n n ETh is the open circuit voltage at the

Determining ETh n Review Remove the load (open-circuit) and measure the resulting voltage. Eth

Determining ZTh n With the load disconnected, turn off all independent sources. ¨ Voltage

Applying Thévenin equivalent n Once ETh and ZTh have been found, the original circuit

Example Problem 1 Convert the source below into a Thévenin equivalent and determine the

Example Problem 2 Convert the source below into a Thévenin equivalent. ZLOAD

Example Problem 3 Convert the source below into a Thévenin equivalent and determine the

Conjugates n The conjugate of C is written as C*, which has the same

Review Maximum power transfer theorem n Maximum power is transferred to the load when

Max Power Transfer in AC Circuits n In AC circuits, max power transfer occurs

Max Power Transfer in AC Circuits n Since RLD=RTH, and the reactances cancel out,

Max Power Transfer in AC Circuits n n #1 Mistake with AC Max Power

Example Problem 4 Determine the load ZLOAD that will allow maximum power to be

Example Problem 5 Determine the load ZLD that will allow maximum power to be

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EE 301 AC Thèvenin and Max Power Transfer

Learning Objectives n n n Apply Thèvenin’s Theorem to AC circuits Explain under what conditions a source transfers maximum power to a load Determine the value of load impedance for which maximum power is transferred from the circuit

Thévenin’s theorem for AC n n ETh is the open circuit voltage at the terminals, ZTh is the input or equivalent resistance at the terminals when the independent sources are turned off.

Determining ETh n Review Remove the load (open-circuit) and measure the resulting voltage. Eth = open ckt voltage

Determining ZTh n With the load disconnected, turn off all independent sources. ¨ Voltage sources – 0 V is equivalent to a short-circuit. ¨ Current sources – 0 A is equivalent to a open-circuit. n ZTh is the equivalent resistance looking into the “dead” circuit through terminals a-b. Zth

Applying Thévenin equivalent n Once ETh and ZTh have been found, the original circuit is replaced by its equivalent and solving for ILD and VLD becomes trivial.

Example Problem 1 Convert the source below into a Thévenin equivalent and determine the current through load Zab.

Example Problem 2 Convert the source below into a Thévenin equivalent. ZLOAD

Example Problem 3 Convert the source below into a Thévenin equivalent and determine the power dissipated by the load.

Conjugates n The conjugate of C is written as C*, which has the same real value but the opposite imaginary part: Review

Review Maximum power transfer theorem n Maximum power is transferred to the load when RLD = RTh.

Max Power Transfer in AC Circuits n In AC circuits, max power transfer occurs when load impedance (ZL) is the complex conjugate of the Thévinin equivalent impedance (ZTh). n This means the load has a capacitor if the Thèvenin impedance includes an inductor XLD cancels out XTH! n

Max Power Transfer in AC Circuits n Since RLD=RTH, and the reactances cancel out, the resulting PMAX equation is the same as with DC!

Max Power Transfer in AC Circuits n n #1 Mistake with AC Max Power is not using the REAL value of resistance when calculating Pmax Transform ZTH into rectangular form to determine RTH X

Example Problem 4 Determine the load ZLOAD that will allow maximum power to be delivered to the load the circuit below. Find the power dissipated by the load.

Example Problem 5 Determine the load ZLD that will allow maximum power to be delivered to the load the circuit below. Frequency is 191. 15 Hz. Find the maximum power. What will happen to power if the frequency is changed to 95. 575?