Lesson 9: Thèvenin's theorem and Maximum Power Transfer

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Presentation transcript:

Lesson 9: Thèvenin's theorem and Maximum Power Transfer

Learning Objectives State and explain Thèvenin's theorem. List the procedure for determining the Thèvenin equivalence of an actual circuit from the standpoint of two terminals. Apply Thèvenin's Theorem to simplify a circuit for analysis.

Learning Objectives Analyze complex series-parallel circuits using thevenin’s theorem. Apply the Maximum Power Transfer theorem to solve appropriate problems.

Thévenin’s theorem Thévenin’s theorem greatly simplifies analysis of complex circuits by allowing us to replace all of the elements with a combination of just one voltage source and one resistor. Thévenin’s theorem provides a simplified circuit that provides the same response (voltage and current) at the load terminals. This allows the response to be easily determined for various load values.

Thévenin equivalent circuit Thévenin’s theorem A complex two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTh in series with a resistor RTh. original circuit Thévenin equivalent circuit

Thévenin equivalent circuit Thévenin’s theorem ETh is the open circuit voltage at the terminals, RTh is the input or equivalent resistance at the terminals when the sources are turned off. original circuit Thévenin equivalent circuit

Thévenin’s theorem 1. Remove your load and label your terminals a and b. 2. Solve for VTH. 3. Solve for RTH. 4. Draw your new equivalent circuit.

Thévenin’s theorem 1. To convert to a Thévenin circuit, first identify and remove load from circuit and Label resulting open terminals.

Thévenin’s theorem  

Thévenin’s theorem  

“Turning off” sources 3. “Turning off” a source means setting its value equal to zero. Voltage sources – 0 V is equivalent to a short-circuit. Current sources – 0 A is equivalent to a open-circuit. Voltage sources become short-circuits Current sources become open-circuits

Thévenin’s theorem With the load disconnected, turn off all source. RTh is the equivalent resistance looking into the “dead” circuit through terminals a-b. Rth

Thévenin’s theorem 3. Set all sources to zero, and calculate RTh .

Applying Thévenin equivalent 4. Now REDRAW the circuit showing the Thèvenin equivalent with the load installed..

Applying Thévenin equivalent Repetitive solutions for various load resistances now becomes easy with the transformed circuit.

1. Remove your load and label your terminals a and b. 2. Solve for VTH. 3. Solve for RTH. 4. Draw your new equivalent circuit. Example Problem 1 Find the Thévenin equivalent circuit external to RLD. Determine ILD when RLD=2.5 Ω.

1. Remove your load and label your terminals a and b. 2. Solve for VTH. 3. Solve for RTH. 4. Draw your new equivalent circuit. Example Problem 2 Find the Thévenin equivalent circuit external to RLD and determine ILD.

MAX POWER TRANSFER In some applications, the purpose of a circuit is to provide maximum power to a load. Some examples: Stereo amplifiers Radio transmitters Communications equipment Our question is: If you have a system, what load should you connect to the system in order that the load receives the maximum power that the system can deliver?

Maximizing PLD How might we determine RLD such that PLD is maximized?

Maximum power transfer theorem Maximum power is transferred to the load when the load resistance equals the Thévenin resistance as seen from the load (RLD = RTh). When RLD = RTh, the source and load are said to be matched.

Maximizing PLD As RLD increases, a higher percentage of the total power is dissipated in the load resistor. But since the total resistance is increasing, the total current is dropping, and a point is reached where the total power dissipated by the entire circuit starts dropping.

Maximum power The power delivered when RLD = RTh is BE CAREFUL!!! Note that this is not true if RLD  RTh

MAXIMUM POWER TRANSFER THEOREM The total power delivered by a supply such as ETh is absorbed by both the Thévenin equivalent resistance and the load resistance. Any power delivered by the source that does not get to the load is lost to the Thévenin resistance.

Example Problem 3 Find the Thévenin equivalent circuit to the left of terminals a-b. Calculate the maximum power transfer to the load if RLD=RTH Determine the power dissipated by RLD for load resistances of 2 and 6.

Efficiency When maximum power is delivered to RLD, the efficiency is a mere 50%.

Efficiency Communication Circuits and Amplifiers: Max Power Transfer Is More Desirable Than High Efficiency Power Transmission (115 VAC 60 Hz Power ): High Efficiency Is More Desirable Than Max Power Transfer Load Resistance Kept Much Larger Than Internal Resistance Of Voltage Source

Example Problem 4 Find the value of R so that RLD=RTH Calculate the maximum power dissipated by RLD

Additional Example Problems

1. Remove your load and label your terminals a and b. 2. Solve for VTH. 3. Solve for RTH. 4. Draw your new equivalent circuit. Example Problem 1 Find the Thévenin equivalent circuit external to RLD. Determine ILD when RLD=6 Ω

1. Remove your load and label your terminals a and b. 2. Solve for VTH. 3. Solve for RTH. 4. Draw your new equivalent circuit. Example Problem 4 Find the Thévenin equivalent circuit to the left of terminals a-b. Find the current through RLD with RL = 2, 4, and 6 . Determine the power dissipated by RLD for each resistance.