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Operational Amplifiers
A brief introduction
2/1/2005
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Op-Amp Introduction
• Need exists for a circuit element that can perform:
– Add, subtract, multiply, divide, differentiate, integrate
• Evolved from Analog Computers
• Op-Amp properties
– Single building block which can be assembled into above
functions by adding passive components (R,L,C)
– Inexpensive (used in high volume)
– Compact
• Op-Amp analysis
• Use assumptions of “Ideal Op-Amp” to allow low frequency
performance to be approximated
• Typically have near ideal characteristics but frequency
response of an integrator (G(s) = 1/ts). (Otherwise, the
high bandwidth would be impossibly difficult to manage.)
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Ideal Op-Amp Assumptions
+Vsupply
+
• Differential function
• Vout = A•DV
• Infinite
DV
• Intrinsic gain: A = 
• Input impedance: Zin = 
• Bandwidth: Vout  f(w)
Zin
A Zout
Vout
-
• Zero
-Vsupply
• Input offset voltage: Vio = 0 for Vout+ Vio= A•DV
• Input impedance: Zout = 0
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Rf
Inverting Amplifier
• Consider the circuit
configuration to the right
Vin  VRin  DV  VRb
+Vsupply
Rin
iin_op-amp
DV
Vin
ib
+
Vout
Rb
Vout  VR f  DV  VRb
-Vsupply
iRin  iR f  iin _ opamp
• Assuming intrinsic gain of the op-amp is very large
for the frequency of interest: DVA  Vout
– Vout is finite and typically within +15 to -15 V implying DV is
very small
• Assuming ib is very small given the intrinsic input
impedance is very large, Vb must be very small
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Inverting Amplifier
Vin  VRin
Vout  VR f
VRin

VR f
Rf
Vout

Vin
Rin
Rin
Rf
Vin
Vout
iRin  iR f

Rin
Rf
• Amplifier performance is a function of external
components only for ideal assumptions
• Input and output impedances of the amplifier can be
calculated as approximately:
Z in  Rin
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Z out 
Z out _ intrinsic

1  A Rin

Rin  R f

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



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Non-Inverting Amplifier
Rin
Vin  VRin  DV  VRb
Vout  VR f  VRb
iR f  ib  iRb
+
DV
Vin
ib
Vout  VR f  Vin
Vout
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-Vsupply
Vin  VRb
iR f  iRb
+Vsupply
VR f
Rf

Rb
VRb
Rb
VR f  Vin
 Rf
 Vin
 Vin  Vin 1 
Rb
 Rb
Rf
Vout
Rf
Rf
Rb



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Vout  R f
 1 
Vin  Rb



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Non-Inverting Amplifier
• Input and output impedances can be calculated as
approximately:

 Rin
Z in  Z in _ intrinsic1  A
R R

f
 in

Z out 
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



Z out _ intrinsic

 Rin
1  A
R R

f
 in





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