1. Lecture 3 Operational Amplifiers—Non-ideal behavior1

2. Goals Study non-ideal op amp behavior.
Demonstrate circuit analysis techniques for non-ideal op amps.
Understand frequency response limitations of op amp circuits. 2

3. Difference Amplifier Assume an ideal op-amp
vi2 = 0
v+ = 0 = v-, vo(1) = -R2.vi1 (inverting amplifier) R1
Vi1 = 0
V+ = R4. vi2, vo(2) = (1+ R2/R1) . R4.vi2
R3 + R R3+R4
non-inverting amplifier
vo = vo(1) + vo(2)
= (1+ R2). R4 vi R2.Vi1
R1 R3 + R R1
Assume an ideal op-amp
Use the superposition theory

4. Difference Amplifiers
In order to provide equal gain for both inputs
vo = -R2/R1 (v1 – v2)
(1 + R2 ) . R = R2
R1 R3 + R R1
R4/R3 = R2/R Balance Condition

5. Difference Amplifier For R2= R1
Also called a differential subtractor, amplifies difference between input signals.
Rin2 is series combination of R1 and R2 because i+ is zero.
For v2=0, Rin1= R1, as the circuit reduces to an inverting amplifier.
For general case, i1 is a function of both v1 and v2. 5

6. Difference Amplifier Define vo = Ad vid + Acmvicm
vid = v1 – v2 differential input voltage
vicm = (v1 + v2)/ Common-mode input voltage
vicm, and vid are another
representation for the inputs
vo = Ad vid Acmvicm
Differential
gain
Common-mode
gain
For the ideal case,
vo = -R2/R1(v1 – v2) = (-R2/R1).vid + 0
Ad = -R2/R1, and Acm = 0
If balance condition is not satisfied, (R4/R3≠ R2/R1) Then Acm ≠ 0

7. Difference Amplifier FOM

8. Integrator Since ic= is
Voltage at the circuit’s output at time t is given by the initial capacitor voltage integral of the input signal from start of integration interval, here, t=0.
Integration of an input step signal results in a ramp at the output.
Feedback resistor R2 in the inverting amplifier is replaced by capacitor C.
The circuit uses frequency-dependent feedback. 8

9. Differentiator Since iR= is
Input resistor R1 in the inverting amplifier is replaced by capacitor C.
Derivative operation emphasizes high-frequency components of input signal, hence is less often used than the integrator.
Output is scaled version of derivative of input voltage. 9

10. Operational Amplifier Complete Model
Represented by:
A= open-circuit voltage gain
vid = (v+-v-) = differential input signal voltage
Rid = amplifier input resistance
Ro = amplifier output resistance 3

11. Non-ideal Operational Amplifier
Various error terms arise in practical operational amplifiers due to non-ideal behavior.
Some of the non-ideal characteristics include:
√ Finite open-loop gain that causes gain error
Nonzero output resistance
Finite input resistance
Finite CMRR
Common-mode input resistance
√ DC error sources
√ Output voltage and current limits 11

12. Finite Open-loop Gain vo = A (v+ - v-) = A.vin |v+ - v- | > 0 V-
+VS V- - V
Vin = V+ - V- o S V- V+ i + V+ - A V + in
-VS
vo = A (v+ - v-) = A.vin
|v+ - v- | > 0
Example 1, Inverting Amplifier 12

13. 13

14. DC Error Sources: Input-Offset Voltage
vo=A(v+-v-), if v+ = v-
Then vo = 0 (Ideal case)
For real op-amp an input dc offset exists that can saturates the output.
We can bring the output back to zero by applying an external voltage equal in magnitude but opposite in direction to the offset voltage 14

15. Finding the error in the output voltage produced by the offset (vos)
Consider only the offset voltage.
i.e set any input signal to zero
Voe = output error due to vos
If an input signal is connected to R1
Total output =
FOR LF351, vos = 5mV (typical)
Desired output
error 15

16. DC Error Sources: Input-Offset Voltage (Example)
Output voltage is given by
Actual sign of VOS is unknown as only upper bound is given.
Note: Offset voltage of most IC op amps can be manually adjusted by adding a potentiometer as shown.
Problem: Find quiescent dc voltage at output.
Given data: R1 =1.2 kW, R2 = 99 kW,
Assumptions: Ideal op amp except for nonzero offset voltage. 16

17. DC Error Sources: Input-Bias and Offset Currents
Bias currents IB1 and IB2 ( base currents in BJTs or gate currents in MOSFETs or JFETs) are similar in value with directions depending on internal amplifier circuit type + - IB
Ios/2
IB2
IB1
Ideal -opamp
Equivalent circuit model
Sign of offset current is unknown as only upper bound is given. 17

18. DC Error Sources: Input-Bias and Offset Currents
In inverting amplifier shown, IB1 shorted out by ground connection. Since,inverting input is at virtual ground, amplifier output is forced to supply IB2 through R2 . i1
Set vin=0, v- = v+ = 0 (virtual gnd)
i1=0, i2=IB2
This poses a limitation on the value of R2 18

19. Numerical Example 19

20. DC Error Sources: Input-Bias and Offset Currents - Bias Current Compensation
By superposition, if
Since, offset current is typically 5.10 times smaller than individual bias currents, dc output voltage error can be reduced by using bias compensation.
Bias current compensation resistor RB is used in series with non-inverting input. Output due to IB1 alone is 20

21. DC Error Sources: Input-Bias and Offset Currents - Errors in Integrator
At t=0, reset switch is opened, circuit starts integrating its own offset voltage and bias current. Using superposition analysis,
Output becomes ramp with slope determined by VOS and IB2 and saturates at one of the power supplies.
At t<0, reset switch is closed, circuit becomes a voltage-follower, 21