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Thevenin’s Theorem
V OUT
V TH
R 4
R TH
R 3
R 4
V R 2
R 1
R 2
R 4
R 1 R 2
R 1 R 2
R 3
R 4
(2–15)
The circuit analysis is done the hard way in Figure 2–10, so you can see the advantage
of using Thevenin’s Theorem. Two loop currents, I 1 and I 2 , are assigned to the circuit.
Then the loop Equations 2–16 and 2–17 are written.
R 3
V
I1
R 1
I 2
R 4
R 2
V OUT
Figure 2–10. Analysis Done the Hard Way
(2–16)
V I 1
R1 R 2
I2 R 2
(2–17)
I 2
R2 R 3
R 4
I1 R 2
Equation 2–17 is rewritten as Equation 2–18 and substituted into Equation 2–16 to obtain
Equation 2–19.
I 1
I 2
R 2
R 3
R 4
(2–18)
R 2
(2–19)
V I 2
R 2 R 3 R 4
R 2
R1 R 2
I2 R 2
The terms are rearranged in Equation 2–20. Ohm’s law is used to write Equation 2–21,
and the final substitutions are made in Equation 2–22.
I 2
V
(2–20)
R 2 R 3 R 4
R1 R
R 2
R2
2
(2–21)
V OUT
I 2
R 4
R
V OUT
V
4
R 2 R 3 R 4
R 1 R 2
(2–22)
R 2
R 2
This is a lot of extra work for no gain. Also, the answer is not in a usable form because
the voltage dividers are not recognizable, thus more algebra is required to get the answer
into usable form.
Review of Circuit Theory
2-7