1. Operational Amplifier OpAmp

2. Overview Amplifier impedance The operational amplifier Ideal op-amp
Negative feedback
Applications
Amplifiers
Summing/ subtracting circuits

3. Impedances Why do we care about the input and output impedance?
Simplest "black box" amplifier model:
ROUT
VIN
RIN
AVIN
VOUT
The amplifier measures voltage across RIN, then generates a voltage which is larger by a factor A
This voltage generator, in series with the output resistance ROUT, is connected to the output port.
A should be a constant (i.e., gain is linear)

4. Impedances
Attach an input - a source voltage VS plus source impedance RS RS
ROUT
RIN
VOUT
VIN
AVIN VS
Note the voltage divider RS + RIN.
VIN=VS(RIN/(RIN+RS)
We want VIN = VS regardless of source impedance
So want RIN to be large.
Q: What would be the input impedance of an ‘ideal amplifier’?
 The ideal amplifier has an infinite input impedance

5. Impedances Attach a load - an output circuit with a resistance RLRS
ROUT
RIN RL
VIN
AVIN
VOUT VS
Note the voltage divider ROUT + RL.
VOUT=AVIN(RL/(RL+ROUT))
Want VOUT=AVIN regardless of load
We want ROUT to be small.
Q: What would be the output impedance of an ‘ideal amplifier’?
 The ideal amplifier has zero output impedance

6. Operational Amplifier
Integrated circuit containing ~20 transistors, multiple amplifier stages

7. Ideal Operational Amplifier
Operational amplifier (Op-amp) is made of many transistors,
diodes, resistors and capacitors in integrated circuit technology.
Ideal op-amp is characterized by:
Infinite input impedance
Infinite gain for differential input
Zero output impedance
Infinite frequency bandwidth

8. Operational Amplifier
An op amp is a high voltage gain, DC amplifier with high input impedance, low output impedance, and differential inputs.
Positive input at the non-inverting input produces positive output
Positive input at the inverting input produces negative output.

9. 741 Op Amp IC

10. A component-level diagram of the common 741 op-amp
A component-level diagram of the common 741 op-amp. Dotted lines outline: current mirrors (red); differential amplifier (blue); class A gain stage (magenta); voltage level shifter (green); output stage (cyan).

11. Operational Amplifier
IC Product
DIP-741
Dual op-amp 1458 device
Operational Amplifier

12. A small-scale integrated circuit, the 741 op-amp shares with most op-amps an internal structure consisting of three gain stages: 1. Differential amplifier (outlined blue) — provides high differential amplification (gain), with rejection of common-mode signal, low noise, high input impedance

13. 2. Voltage amplifier (outlined magenta) — provides high voltage gain, a single-pole frequency roll-off, and in turn drives the 3. Output amplifier (outlined cyan and green) — provides high current gain (low output impedance), along with output current limiting, and output short-circuit protection. Additionally, it contains current mirror (outlined red) bias circuitry and a gain-stabilization capacitor (30 pF).

14. Op Amp Equivalent Circuit
vd = v2 – v1
A is the open-loop voltage gain v2 v1
Voltage controlled voltage source

15. Operational Amplifier
Can model any amplifier as a "black-box" with a parallel input impedance Rin, and a voltage source with gain Av in series with an output impedance Rout.

16. Ideal op-amp Place a source and a load on the model+
vout RL RS
So the equivalent circuit of an ideal op-amp looks like this:
Infinite internal resistance Rin (so vin=vs).
Zero output resistance Rout (so vout=Avvin).
"A" very large
iin=0; no current flow into op-amp

17. Ideal vs. Real op-amps!

18. Symbols for Ideal and Real Op Amps
uA741
LM111
LM324

19. Ideal Vs Practical Op-Amp
Open Loop gain A 
105
Bandwidth BW
10-100Hz
Input Impedance Zin
>1M
Output Impedance Zout
0  
Output Voltage Vout
Depends only on Vd = (V+V)
Differential mode signal
Depends slightly on average input Vc = (V++V)/2 Common-Mode signal
CMRR
10-100dB
Ref:080114HKN
Operational Amplifier

20. Typical Op Amp Parameters
Variable
Typical Ranges
Ideal Values
Open-Loop Voltage Gain A
105 to 108 ∞
Input Resistance Ri
105 to 1013 W
∞ W
Output Resistance Ro
10 to 100 W
0 W
Supply Voltage
Vcc/V+
-Vcc/V-
5 to 30 V
-30V to 0V
N/A

21. Almost Ideal Op Amp Ri = ∞ W Ro = 0 W Usually, vd = 0V so v1 = v2
Therefore, i1 = i2 = 0A
Ro = 0 W
Usually, vd = 0V so v1 = v2
The op amp forces the voltage at the inverting input terminal to be equal to the voltage at the noninverting input terminal if there is some component connecting the output terminal to the inverting input terminal.
Rarely is the op amp limited to V- < vo < V+.
The output voltage is allowed to be as positive or as negative as needed to force vd = 0V.

22. Many Applications, e.g., Amplifiers Adders and subtractors
Integrators and differentiators
Clock generators
Active Filters
Digital-to-analog converters

23. Applications Audio amplifiers Instrumentation amplifiers
Speakers and microphone circuits in cell phones, computers, mpg players, boom boxes, etc.
Instrumentation amplifiers
Biomedical systems including heart monitors and oxygen sensors.
Power amplifiers
Analog computers
Combination of integrators, differentiators, summing amplifiers, and multipliers

24. Applications
Originally developed for use in analog computers:

25. Using op-amps Power the op-amp and apply a voltage
Works as an amplifier, but:
No flexibility (A~105-6)
Exact gain is unreliable (depends on chip, frequency and temp)
Saturates at very low input voltages (Max vout=power supply voltage)
To operate as an amp, v+-v-<VS/A=12/105 so v+≈v-
In the ideal case, when an op-amp is functioning properly in the active region, the voltage difference between the inverting and non-inverting inputs≈0

26. Voltage Transfer Characteristic
Range where we operate the op amp as an amplifier. vd

38. Inverting Apmlifier

40. Non-inverting amplifier

43. Noninverting Amplifier

44. When A is very large: >>1
Take A=106, R1=9R, R2=R
>>1
Gain now determined only by resistance ratio
Doesn’t depend on A, (or temperature, frequency, variations in fabrication)

45. Negative feedback:
How did we get to stable operation in the linear amplification region???
Feed a portion of the output signal back into the input (feeding it back into the inverting input = negative feedback)
This cancels most of the input
Maintains (very) small differential signal at input
Reduces the gain, but if the open loop gain is ~, who cares?
Good discussion of negative feedback here:

46. Why use Negative feedback?:
Helps to overcome distortion and non-linearity
Improves the frequency response
Makes properties predictable - independent of temperature, manufacturing differences or other properties of the opAmp
Circuit properties only depend upon the external feedback network and so can be easily controlled

47. Positive Feedback
When we flip the polarization of the op-amp as shown on the figure we will get a positive feedback that saturates the amplifier output.
This is not a good idea.

48. Negative vs. Positive Feedback
Familiar examples of negative feedback:
Thermostat controlling room temperature
Driver controlling direction of automobile
Pupil diameter adjustment to light intensity
Familiar examples of positive feedback:
Microphone “squawk” in sound system
Mechanical bi-stability in light switches
Fundamentally
pushes toward
stability
Fundamentally
pushes toward
instability or
bi-stability
EE 42/100 Fall 2005
Week 8, Prof. White

49. Operational Amplifier
Noninverting amplifier
Noninverting input with voltage divider
Less than unity gain
Voltage follower
Ref:080114HKN
Operational Amplifier

50. Operational Amplifier
Inverting Amplifier
Kirchhoff node equation at V+ yields,
Kirchhoff node equation at V yields,
Setting V+ = V– yields
Notice: The closed-loop gain Vo/Vin is dependent upon the ratio of two resistors, and is independent of the open-loop gain. This is caused by the use of feedback output voltage to subtract from the input voltage.
Ref:080114HKN
Operational Amplifier

51. Op amp circuit 1: Voltage follower
So vO=vIN
or, using equations
What's the gain of this circuit?

52. Op amp circuit 1: Voltage follower (unity buffer amplifier)
So vO=vIN
or, using equations
What's the application of this circuit?
Buffer
voltage gain = 1
input impedance=∞
output impedance=0
Useful interface between different circuits:
Has minimum effect on previous and next circuit in signal chain RS
ROUT
RIN RL
VIN
AVIN
VOUT VS

54. Voltage Follower
Special case of noninverting amplifier is a voltage follower
Since in the noninverting amplifier
vo = v1(1+ R2 /R1)
vo = v1
so when R2=0
=>

55. Op amp circuit 2: Inverting Amplifier
Signal and feedback resistor, connected to inverting (-) input.
v+=v- connected to ground
v+ grounded, so:

57. Op amp circuit 3: Summing Amplifier
Same as previous, but add more voltage sources

58. Operational Amplifier
Multiple Inputs
Kirchhoff node equation at V+ yields,
Kirchhoff node equation at V yields,
Setting V+ = V– yields
Ref:080114HKN
Operational Amplifier

59. Summing Amplifier CircuitRa ia if Rf Rb in va + – ib – + + vn – + vo – vb + – ic + vp –
superposition ! Rc vc + –
in = 0  ia + ib + ic = -if
vp = 0  vn = 0
EE 42/100 Fall 2005
Week 8, Prof. White

60. Summing Amplifier Applications
Applications - audio mixer
Adds signals from a number of waveforms
Can use unequal resistors to get a weighted sum
For example - could make a 4 bit binary - decimal converter
4 inputs, each of which is +1V or zero
Using input resistors of 10k (ones), 5k (twos), 2.5k (fours) and 1.25k (eights)

61. Another non-inverting amplifier
Feedback resistor still to inverting input, but no voltage source on inverting input (note change of current flow)
Input voltage to non-inverting input

63. Differential Amplifier (subtractor)
Useful terms:
if both inputs change together, this is a common-mode input change
if they change independently, this is a normal-mode change
A good differential amp has a high common-mode rejection ratio (CMMR)

64. Amplifies the difference in voltage between its inputs
Amplifies the difference in voltage between its inputs. The name "differential amplifier" must not be confused with the "differentiator”