AE 242
Aerospace Measurements
Laboratory
Operational Amplifier
Integrated circuit many stages of matched transistor amplifiers
Very high gain differential amplifier
High input impedance and low output impedance
Initially designed for mathematical operations: multiplication, division, addition,
subtraction etc
v1 - voltage at non-inverting
input
v2 - voltage at inverting input
v - Output voltage
A – Open loop gain
All are measured wrt ground v A ( v1 v 2 )
Output is amplification of difference at input terminals
Operational Amplifier
Simple to use and understand as compared to transistors. Large
number of applications. Most popular is 741 (8 pin dip).
Can be used in many modes
• Differential
• Single ended
• Open loop
• Feed back
Operational Amplifier
Pin assignment
Generally in circuit diagram
connection are pointed to pin
number 2, 3, 4, 7 and 6.
Pin 2 & 3 are input
Pin 4 & 7 are power supply
Pin 6 is output
Pin 1 & 5 for offset null
Operational Amplifier
Common mode rejection ratio (CMRR): Ratio of common mode
differential voltage gain Ad to common mode voltage gain Acm.
Ad
CMRR
Acm
Generally Ad is very large compared to Acm and CMRR is a very large
number. Typically 90dB ~ 31.6 k Higher the number it is better. This
quality is important when the OpAmp is used in differential mode.
Helps in noise reduction. Generally noise is common to both the input
terminals and the applied signal is voltage difference at the input
terminals. For precision opamp it is as high as 120 dB.
dB 20 log10 x
dB 20 log10 x
dB values
Operational Amplifier
Large-signal voltage gain: Ratio of output voltage to difference of input
voltage. It is very high 20 k. It means that 0.05 mV differential voltage at
input will give one volt output.
Output voltage swing: This is the saturation voltage of output in positive
and negative range. This will always be less than supply voltage,
generally 1 to 2 volts. Opamp with rail to rail output are also available.
Output resistance : Equivalent resistance at output i.e. measured between
output terminal and ground. It is ~ 75 ohms.
Gain bandwidth product : The bandwidth of the op-amp when the
voltage gain is one. This can be obtained from open loop voltage gain
and frequency characteristics.
Slew rate : Maximum rate of change of output volt per second, important
for high frequency signal. V/ S This is a measure of how rapidly output
will change in response to input signal. Perfect square wave is not
possible.
Operational Amplifier
Bandwidth with feed back
Bandwidth of an amplifier is
defined as the band of
frequencies for which the gain
remain constant
f0 is break frequency (5 Hz)
fF = f0 (1 + AB)
fF is bandwidth with feed
back, B is feed back gain
Open loop gain versus frequency
Operational Amplifier
Ideal op-amp
• Infinite voltage gain
• Infinite input resistance - no loading on source
• Zero output resistance - so that output can
drive any number of devices
• Zero output voltage when input voltage is zero
• Infinite bandwidth
• Infinite CMRR
• Infinite slew rate
For practical opamps and practical use many of
the characteristic can be approximated to above
mentioned characteristics.
Equivalent circuit of an op-amp
Equivalent circuit is shown using input resistance, output resistance, and
open loop gain. Input resistance will load the source and output
resistance will drive the output.
Operational Amplifier
Ideal Voltage transfer curve : Output voltage cannot exceed the positive
and negative saturation voltages. Offset voltage is zero. Slope is
generally very large (almost vertical). Amplifies the difference in input
voltages not the individual voltages.
Operational Amplifier
Open-loop op-amp configuration
No connection between output and input
1 Differential amplifier
2 Inverting amplifier
3 Noninverting amplifier
Operational Amplifier
Non-inverting amplifier
Signal is applied to non-inverting (positive) terminal. Inverting terminal is
grounded.
v0 = A (v1 - v2) =A v1, where A is open loop gain
Output is in phase with input, it will
have same polarity as input.
In open loop configurations any
input signal of few milli volts will
saturate the output due to high
open loop gain
Operational Amplifier
v0
Difference input voltage ideally zero Opamp equation vid
A
A is very large and ideally infinite. Vid = 0
v1 = v2, inverting and non-inverting terminal are at same voltage
Golden rule 1 : opamp will work in such a way that it will drive the two
inputs to same level
Golden rule 2 : No current can flow into opamp
Using above two rules op-amp circuit analysis becomes easy.
Applicable for negative feedback
Operational Amplifier
Voltage series feed back - Noninverting amplifier
Input - noninverting terminal (positive)
Feedback - inverting terminal vo ?
v2 v f ?
Operational Amplifier
v
Closed loop voltage gain AF
0
v in
R1 v o
v o A ( v1 v 2 ) v1 v in v 2 vf
R1 R F
A(R1 R F ) v in
vo
R1 R F AR1
v0 A ( R 1 RF )
AF
vin R1 RF AR1
Exact gain, involves open loop
gain and generally not known
correctly
Operational Amplifier
v0 A ( R 1 RF )
Closed loop voltage gain AF Exact
vin R1 RF AR1
v0 RF
A is open loop gain AR1 >>R1 + RF AF 1 Ideal
vin R1
Gain is decide by two
resistance : R1 and RF
independent of open loop gain
As a general rule R1 and RF
should be less than 1 M
Operational Amplifier
v R1 1
Feedback gain B f AF
v o R1 RF B
v0 A ( R 1 RF ) v A(R1 RF ) /(R1 RF )
AF AF
0
vin R1 RF AR1 v (R1 RF ) /(R1 RF ) AR1 /(R1 RF )
in
A
AF Exact
1 AB
v 1
AF
0
Ideal
v B in
Operational Amplifier
Using Golden rule
R1
a) v1 = v2, b) No current flows in to opamp V2 V0
RF R1
V1 Vin V2
V0 R
1 F
Vin R1
Operational Amplifier
Input resistance with feed back
RiF = Ri (1+AB) B = 1/AF
It means that input resistance in feed back is (1+AB) times than open loop
input resistance Ri It means that input resistance increases.
Output resistance with feed back
RoF = Ro /(1+AB)
It means that output resistance in feed back is 1/(1+AB) times open loop
output resistance Ro It means that output resistance in feed back is much
smaller compared to open loop.
Operational Amplifier
Voltage follower
Lowest gain that can be obtained by a non-inverting amplifier is one, this
configuration is called voltage follower. Output will follow the input.
Output is exactly equal to input and input resistance is very high.
Used as isolator. Any system connected on right side will obtain power
from OpAmp. Power drawn from input will be almost zero, depends on
the input resistance of OpAmp.
