 # INC 112 Basic Circuit Analysis Week 5 Thevenin’s Theorem.

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INC 112 Basic Circuit Analysis Week 5 Thevenin’s Theorem

Special Techniques Superposition Theorem Thevenin’s Theorem Norton’s Theorem Source Transformation

Linearity Characteristic If R L change its value, how will it effect the current and voltage across it?

I V V OC I SC For any circuit constructed from only linear components Not just RL, all resistors have this property. Voc = Voltage open-circuit Isc = Current short-circuit

Thevenin’s Theorem When we are interested in current and voltage across RL, we can simplify other parts in the circuit. Equivalent circuit

I V V OC I SC Voc = Voltage open-circuit Isc = Current short-circuit R = R equivalent Slope = 1/R

Thevenin’s Equivalent Circuit Thevenin’s equivalent circuit VTH = Voc (by removing RL and find the voltage difference between 2 pins) RTH (by looking into the opened connections that we remove RL, see how much resistance from the connections. If we see a voltage source, we short circuit. If we see a current source, we open circuit.)

Why do we need equivalent circuit? To analyze a circuit with several values of RL For circuit simplification (source transformation) To find RL that gives maximum power (maximum power transfer theorem)

Procedure 1. Remove RL from the circuit 2. Find voltage difference of the 2 opened connections. Let it equal VTH. 3.From step 2 find RTH by 3.1 short-circuit voltage sources 3.2 open-circuit current sources 3.3 Look into the 2 opened connections. Find equivalent resistance.

Example Find Thevenin’s equivalent circuit and find the current that passes through RL when RL = 1Ω

0V 10V 0V 6V Find VTH

Short voltage source RTH Find RTH

Thevenin’s equivalent circuit If RL = 1Ω, the current is

Example Find Thevenin’s equivalent circuit

Find VTH 0V 5V 0V 3V

Open circuit current source RTH Find RTH

Thevenin’s equivalent circuit

Example: Bridge circuit Find Thevenin’s equivalent circuit

Find VTH 0V 10V 8V 2V VTH = 8-2 = 6V

Find RTH RTH

Thevenin’s equivalent circuit

Special Techniques Superposition Theorem Thevenin’s Theorem Norton’s Theorem Source Transformation

I V V OC I SC For any point in linear circuit

Thevenin’s Equivalent Circuit

Norton’s Equivalent Circuit In= Isc from replacing RL with an electric wire (resistance = 0) and find the current Rn = RTH (by looking into the opened connections that we remove RL, see how much resistance from the connections. If we see a voltage source, we short circuit. If we see a current source, we open circuit.)

Example Find Norton’s equivalent circuit and find the current that passes through RL when RL = 1Ω

Find In Find R total Find I total Current divider

Short voltage source RTH Find Rn

Norton’s equivalent circuit If RL = 1Ω, the current is

Relationship Between Thevenin’s and Norton’s Circuit I V V OC I SC Slope = - 1/Rth

Norton’s equivalent circuit Thevenin’s equivalent circuit Same R value

Example Find Norton’s equivalent circuit

Find In Current divider

Open circuit current source RTH Find RTH

Norton’s equivalent circuit

Thevenin’s equivalent circuit Norton’s equivalent circuit 0.2 x 15 = 3

Equivalent Circuits with Dependent Sources We cannot find Rth in circuits with dependent sources using the total resistance method. But we can use

Example Find Thevenin and Norton’s equivalent circuit

Find Voc I1 I2 KVL loop1 KVL loop2

I1 I2 Solve equations I1 = 3.697mAI2 = 3.678mA

Find Isc I1 I2 I3 KVL loop1 KVL loop2 KVL loop3

Find Isc I1 I2 I3 I1 = 0.632mA I2 = 0.421mA I3 = -1.052 A Isc = I3 = -1.052 A

Thevenin’s equivalent circuit Norton’s equivalent circuit