Lecture Chapter 4CThevenin Equivalent Circuits

Problem 1 Two measurements are made on the same "linear mystery circuit" as shown. What would be the measured current Im if the 50-ohm resistor is

replaced by a short circuit? ( 96 Amps)

Thevenin: simple model for complex circuit• To find Thevenin Equivalent at a terminal a-b:

1. Find V open circuit2. Find I short circuit3. Vth = Voc4. Rth = Voc/Isc

Vth = Voc = 30V; Rth = 120Ω

"Lookback" resistance• Another way to find Rth– Turn off all sources • Replace Voltage source with short• Replace Current source with open• Calculate Rab, equivalent resistance

Find Thevenin Eq at a-bnote how R4 does not affect Voc! [Vth=__Rth=8]

Problem 3 Find the Thèvenin equivalent circuit at the terminals A-B. Rt = 25Ω;Vt = 160V

Norton Equivalent• Norton vs Thevenin Equivalents – same at a-b

Thevenin and Norton Equivalents would be indistinguishable at a-b

• To find Norton Equivalent, find Thevenin, set In = Vth/Rth, and Rn = Rth

• this is the basis of the "source transform" method, which can help simplify circuits

Given Thevenin Equivalent, What is the Norton Equivalent?

Find Thevenin by "Source Transform"

Another Way to Look at Thevenin Equivalents

• All our circuit elements and laws are linear– Vs = 9V, Is = 10A, V=IR, sum of v= 0, sum of i=0

• We can model the V-I curve of any linear circuit– define equation of line: slope and a y-offset• Rth and Vth

Do Handouts Problem 1/2

More Thevenin Equivalents• Dependent Sources– Find Voc the same (use NV, MC, Source Xform, etc)– For Rth:• You can always find Isc, then Rth = Voc/Isc• OR Turn off Independent sources,

– hook up a “Test Voltage Source” Vt (not Vth!!)– Find current produced by test source It,

» Then Rth = Vt/It

Find Thevenin at a-b (Vth=8, Rth=1)• Option 1) Find Voc, Isc

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Option 2, Rth by Test Source

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Problem 2 Find the Thèvenin equivalent circuit at the terminals U-V.(Rt = 9.74)

Circuits with only dependent sources are resistive. MUST hook up external test source

One More (if time permits)

Do Handout problems 3 and 4

Max Power Transfer• Q: What is the most power we can deliver to

RL?

RL gets Max Power when RL = Rth

• Thevenin Eq of circuit in previous slide:

Example: Max power RL can get?

Find io by Superposition

• Fundamental theorem in physics, – applies to ccts too.

Superposition continued• Activate each source separately, add results

Handouts

1) (ans: 48V, 16 Ohms)

2) Find Thevenin Equivalent to left of 8 ohm RThis can be simplified with Source Xform, OR Solved with NV [72V, 4 Ohm]

3) Problem 1 Find the Thèvenin equivalent circuit at the terminals G-H.(Vth=12, Rth=34)

4) Problem 1 Find the Thèvenin equivalent circuit at the terminals S-T. Rt = 50Ω

Find Thevenin at a-b. Use "Lookback" to find Rth, Superposition to find Vth

Problem 2 Find the Thèvenin equivalent circuit to the left of the terminals A-B. (1V, 0 Ohm)

Find Thevenin at a-b (Vth=8, Rth=1)• Option 1) Find Voc, Isc

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Option 2, Rth by Test Source

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Problem 2 Find the Thèvenin equivalent circuit at the terminals U-V.(Rt = 9.74)

Circuits with only dependent sources are resistive. MUST hook up external test source

One More (if time permits)

Do Handout problems 3 and 4

Max Power Transfer• Q: What is the most power we can deliver to

RL?

RL gets Max Power when RL = Rth

• Thevenin Eq of circuit in previous slide:

Example: Max power RL can get?

Find io by Superposition

• Fundamental theorem in physics, – applies to ccts too.

Superposition continued• Activate each source separately, add results

Handouts

1) (ans: 48V, 16 Ohms)

2) Find Thevenin Equivalent to left of 8 ohm RThis can be simplified with Source Xform, OR Solved with NV [72V, 4 Ohm]

3) Problem 1 Find the Thèvenin equivalent circuit at the terminals G-H.(Vth=12, Rth=34)

4) Problem 1 Find the Thèvenin equivalent circuit at the terminals S-T. Rt = 50Ω

Find Thevenin at a-b. Use "Lookback" to find Rth, Superposition to find Vth

Problem 2 Find the Thèvenin equivalent circuit to the left of the terminals A-B. (1V, 0 Ohm)