Chapter 4
The Operational Amplifier
Ckts W/ Operational Amplifiers
•
Why Study OpAmps
At This Point?
1. OpAmps Are Very
Useful Electronic
Components
2. We Have Already Developed The Tools To
Analyze Practical OpAmps Circuits
3. The Linear Models for OpAmps Include
Dependent Sources
•
A PRACTICAL Application of Dependent Srcs
OpAmp Symbol & Model
• The Circuit Symbol
Is a Version of the Amplifier
TRIANGLE
 The Linear Model
• Typical Values
Ri : 105   1012 
OUTPUT RESISTANCE
RO : 1  50
A : 105  107
INPUT RESISTANCE
GAIN
Vo =
• -Vcc, when A(Vp-Vn)<-Vcc
• A(Vp-Vn),
when -Vcc< A(Vp-Vn)< +Vcc
• +Vcc, when A(Vp-Vn) >+Vcc
2 Ways of Using Op-Amps
• “Open Loop”: very high gain amplifier
– Useful for comparing 2 voltages
– Fixed gain, always at MAX OUTPUT!!
• “Closed Loop” with negative feedback
– Useful for amplifying, adding, subtracting,
differentiation and integration (using capacitors)
– Variable gain, controlled by resistor selection
“Open-Loop” examples
• Ideal Comparator and Transfer Characteristic
 “Zero-Cross” Detector → Heart of Solid State Relay Cnrtl
“Closed Loop” Example: Unity Gain Buffer
Op-Amp BUFFER GAIN
LM324
0.99999
LMC6492
0.9998
MAX4240
0.99995
 Controlling Variable = Vin  Ri I
 Solve For Buffer Gain
Vout

Vs 1 
1
Ri
RO  AO Ri
recall AO  
KVL :  Vs  Ri I  RO I  AOVin  0
KVL : - Vout  RO I  AOVin  0
 Thus The Amplification
V
AO    out  1
VS
Consequences for Vp-Vn
• Normally, A is 10,000 or more, so to avoid
saturation, abs(Vp-Vn) must be < Vcc/10000,
or, if Vcc = 20V, about 2 mV which is
negligible for most circuits
• With an Ideal Op-amp, A = infinity,
so Vp = Vn to avoid saturation
• Negative Feedback resistors “force” Vp = Vn
i.e. if Vp-Vn gets large, A(Vp-Vn) pulls
back toward zero (more on this later)
Terminal Characteristics for an ideal op amp in it’s Linear Range:
• Ip = In = 0
(very high input
resistance=1MOhm)
• Io can be very large
(coming from Vcc/-Vcc)
But…always remember Vcc/-Vcc limits…
if Vo saturates Vp does not = Vn !!!
Inverting Amplifier
Vo = -RfVs
Rs
When in linear
region
Inverting Amplifier
with Feedback Path broken
• Vo= -AVs
Saturation
(unless Vs<2mv)
Summing Amplifier
Vo = - Rf (Va + Vb + Vc)
Rs
(in linear region)
Non-Inverting Amplifier
Vo=(Rs+Rf) Vg
Rs
In linear region
Difference Amplifier
Vo= Rb (Vb – Va)
Ra
in linear region AND
IFF Ra/Rb = Rc/Rd
Common Mode Rejection Ratio
IF Ra/Rb =(1-e) Rc/Rc (e=very small)
CMMR = abs(1 + Rb/Ra)
e
Comparator, used in digital circuits
Application, the Flash
Converter
• Comparators quantize
Encoder converts to binary