Lecture Chapter 4C
Thevenin 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.
2.
3.
4.
Find V open circuit
Find I short circuit
Vth = Voc
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-b
note 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
24
Option 2, Rth by Test Source
24
Circuits with only dependent sources are resistive.
MUST hook up external test source
Problem 2 Find the Thèvenin equivalent circuit at the terminals U-V.
(Rt = 9.74)
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 R
This 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
24
Option 2, Rth by Test Source
24
Circuits with only dependent sources are resistive.
MUST hook up external test source
Problem 2 Find the Thèvenin equivalent circuit at the terminals U-V.
(Rt = 9.74)
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 R
This 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)