"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10

Complex Feedback Networks
3-8
Break the circuit at point X–Y, stand on the terminals looking into R 4, and calculate the
Thevenin equivalent voltage as shown in Equation 3–15. The Thevenin equivalent impedance
is calculated in Equation 3–16.
V TH V OUT
R TH R 3 R 4
R 4
R 3 R 4
(3–15)
(3–16)
Replace the output circuit with the Thevenin equivalent circuit as shown in Figure 5–8,
and calculate the gain with the aid of the inverting gain equation as shown in Equation
3–17.
VIN
_
a
+
Figure 3–8. Thevenin’s Theorem Applied to T Network
R1
R2
Substituting the Thevenin equivalents into Equation 3–17 yields Equation 3–18.
V OUT
V IN
VTH
VIN R2 RTH R1 R 2 R TH
R 1
Algebraic manipulation yields Equation 3–19.
V OUT
V IN
RTH
VTH
R3 R4
R4 R2 R3 R 4
R1 R 2 R 3 R 2 R 3
R 4
R 1
R3 R4 R4 (3–17)
(3–18)
(3–19)
Specifications for the circuit you are required to build are an inverting amplifier with an
input resistance of 10 k (R G = 10 k), a gain of 100, and a feedback resistance of 20 K or
less. The inverting op amp circuit can not meet these specifications because R F must
equal 1000 k. Inserting a T network with R 2 = R 4 = 10 k and R 3 = 485 k approximately
meets the specifications.