1. Chapter 5 OUTLINE Op-Amp from 2-Port Blocks
Op-Amp Model and its Idealization
Negative Feedback for Stability
Components around Op-Amp define the Circuit Function
EE40, Fall Prof. White

2. The Operational Amplifier
The operational amplifier (“op amp”) is a basic building block used in analog circuits.
Its behavior is modeled using a dependent source.
When combined with resistors, capacitors, and inductors, it can perform various useful functions:
amplification/scaling of an input signal
sign changing (inversion) of an input signal
addition of multiple input signals
subtraction of one input signal from another
integration (over time) of an input signal
differentiation (with respect to time) of an input signal
analog filtering
nonlinear functions like exponential, log, sqrt, etc
Isolate input from output; allow cascading

3. High Quality Dependent Source In an Amplifier
V0 depends only on input (V+  V-) +  A V+ V V0
Differential Amplifier
AMPLIFIER SYMBOL +  V0
AV1 V1 Ri
Circuit Model in linear region
AMPLIFIER MODEL
See the utility of this: this Model when used correctly mimics the behavior of an amplifier but omits the complication of the many many transistors and other components.

4. 3 signal terminals: 2 inputs and 1 output
Op Amp Terminals
3 signal terminals: 2 inputs and 1 output
IC op amps have 2 additional terminals for DC power supplies
Common-mode signal= (v1+v2)/2
Differential signal = v1-v2
V +
positive power supply
Inverting input v2 - +
v0 output
Non-inverting input v1
V –
negative power supply

5. Model for Internal Operation
A is differential gain or open loop gain
Ideal op amp
Common mode gain = 0
Circuit Model + i1 v1 Ro io Ri vo i2 v2 + – _
A(v1–v2)

6. Model and Feedback _ Negative feedback Circuit Model Positive feedback
connecting the output port to the negative input (port 2)
Positive feedback
connecting the output port to the positive input (port 1)
Input impedance: R looking into the input terminals
Output impedance: Impedance in series with the output terminals
Circuit Model v1 v2 Ri + – Ro vo
A(v1–v2) i1 i2 io _

7. Op-Amp and Use of Feedback
A very high-gain differential amplifier can function in an extremely linear fashion as an operational amplifier by using negative feedback. +  V0
AV1 - V1 Ri R2
Circuit Model R1
VIN R2 R1 - + V0
VIN
Summing Point
Negative feedback  Stabilizes the output
Hambley Example pp. 644 for Power Steering
We can show that that for A   and Ri  ,
Stable, finite, and independent of the properties of the OP AMP !

8. Summing-Point Constraint
Check if under negative feedback
Small vi result in large vo
Output vo is connected to the inverting input to reduce vi
Resulting in vi=0
Summing-point constraint
v1= v2
i1 = i2 =0
Virtual short circuit
Not only voltage drop is 0 (which is short circuit), input current is 0
This is different from short circuit, hence called “virtual” short circuit.

9. Ideal Op-Amp Analysis Technique
Applies only when Negative Feedback is present in circuit!
Assumption 1: The potential between the op-amp input terminals, v(+) – v(-), equals zero.
No Potential Difference
Assumption 2: The currents flowing into the op-amp’s two input terminals both equal zero.
No Currents R2 R1 - + V0
VIN
EXAMPLE

10. Ideal Op-Analysis: Non-Inverting Amplifier
Yes Negative Feedback is present in this circuit!
Assumption 1: The potential between the op-amp input terminals, v(+) – v(-), equals zero.
Assumption 2: The currents flowing into the op-amp’s two input terminals both equal zero.
KCL with currents in only two branches R2 R1 - + V0
VIN
EXAMPLE
VIN appears here
Non-inverting Amplifier

11. Non-Inverting Amplifier
Ideal voltage amplifier v0 + _ v2
vin + - RL 2 R2 R1

12. Ideal Op-Amp Analysis: Inverting Amplifier
Yes Negative Feedback is present in circuit!
Only two currents for KCL
Voltage is VR
Inverting Amplifier with reference voltage

13. Negative feedback  checked Use summing-point constraint
Inverting Amplifier
Negative feedback  checked
Use summing-point constraint R2 2 R1 i v2 _ + v0
vin + - v1 RL
Ideal voltage source – independent of load resistor

14. Voltage Follower + _
vin - RL v2 v0

15. Example 1 v1 v2
vin + - R RL v0 2 _ i1 i2 i5 i3 i4
Switch is open

16. Example 1 Switch is closed R 2 R _ + R RL v2 v0 v1 vin + - i5 i4 i2 i3

17. Example 2 Design an analog front end circuit to an instrument system +
Requires to work with 3 full-scale of input signals (by manual switch): V
For each input range, the output needs to be V
The input resistance is 1MW + _
vin R2 R1 RL v2 v0 2 b a c vb va v1

18. Example 2 (cont’d)

19. Summing Amplifier v1 R1 - + R0 - + v2 R2 _ + v0 - + v3 R3

20. Difference Amplifier R2 v1 R1 _ + v0 - + - + R3 v2 R4

21. What is the difference between:
Integrator
Want
What is the difference between: R + - C V0
vin

22. Differentiator
Want _ +
vin - R v0 C

23. Bridge Amplifier vx
R0(1+e) R0 _ + v0
vin + - Ra Ra vx

24. Application: Digital-to-Analog Conversion
A DAC can be used to convert the digital representation
of an audio signal into an analog voltage that is then
used to drive speakers -- so that you can hear it!
Binary
Analog
number
output
(volts)
0 1 .5
“Weighted-adder D/A converter”
0 1 0 1
0 1 1
0 1 0
1.5 2
4-Bit D/A 8V - + V0 5K
80K
40K
20K
10K S1
+ - S3 S2 S4
0 1
1 0 1
2.5 3
3.5 4
1 0
0 1
1 0 1 1
4.5 5
5.5 6
6.5 7
7.5
S1 closed if LSB =1
S " if next bit = 1
S " if " " = 1
S " if MSB = 1
(Transistors are used as electronic switches)
MSB
LSB

25. Characteristic of 4-Bit DAC8 7 6 5
Analog Output (V) 4 3 2 1 2 4 6 8 10 12 14 16
0000
0001
1111
1000
0100
Digital Input

26. Nonlinear Opamp Circuits
Start reading through online notes: “Introduction to nonlinear circuit analysis”.
Outline:
Differences between positive and negative feedback.
Oscillator circuit.