1. Basics of Operational Amplifiers
CHAPTER 9
Basics of
Operational
Amplifiers

2. OBJECTIVES Describe and Analyze: Op-Amp Basics Feedback
Inverting Amplifiers
Non-Inverting Amplifiers
Comparators
Troubleshooting

3. Introduction Op-Amps have: Differential Inputs: (+) & (-)
High “Open Loop” Gain: AOL > 100,000
(Open-loop means without feedback. More on that later.)
High Input Impedance: Zin > 1 Meg
Low Output Impedance: Zout  0

4. Introduction Some Facts about Op-Amps:
Op-amps are the most commonly used linear ICs.
An IC package can have 1, 2, 4, or more op-amps.
Op-amps come in many varieties based on parameters such as bandwidth, cost, and transistor type (BJT, JFET, MOSFET).

5. Op-Amp Basics Analysis can be based on two approximations:
No current flows into or out of the input pins
The voltage across the input pins is zero

6. The front-end of an Op-Amp is a differential amplifier
Op-Amp Basics
The front-end of an Op-Amp is a differential amplifier

7. Simplest circuit, illustrates use of negative feedback
Voltage Follower
Simplest circuit, illustrates use of negative feedback

8. Non-Inverting Amplifier
Av = 1 + (Rf / Ri)

9. Non-Inverting Amp Gain equation derived as follows:
Vin applied to (+) input means V(+) = Vin
zero difference across inputs implies V(-) = V(+)
V(-) = V(+) implies V(-) = Vin
Iin = 0 implies V(-) = Vin = [Ri / (Ri + Rf)]  Vout
which leads to Vin / Vout = Ri / (Ri + Rf)
which leads to Vout / Vin = Av = (Ri + Rf) / Ri
which is the same as Av = 1 + Rf / Ri

10. Non-Inverting Amp An example calculation:
Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k
Find voltage at (-) input
Av = 1 + Rf / Ri = k / 5k = = 3
Vout = Av  Vin = 3  1V = 3 Volts DC
V(-) = V(+) = 1 Volt DC

11. Negative feedback reduces gain to a useable value

12. Negative Feedback
Besides setting the gain, negative feedback provides performance improvements such as:
Makes Zin higher
Makes Zout lower
Increases the usable bandwidth
Reduces distortion in the op-amp

13. It looks complicated, but actually it’s not
Negative Feedback
It looks complicated, but actually it’s not

14. Negative Feedback We can analyze negative feedback as follows:
Some of the output is fed back to the input:
Vfb = B  Vout where 0 < B < 1
The signal that gets to the op-amp is the applied input plus the feedback:
Vx = Vin + Vfb = Vin + B  Vout
But the output is the open-loop gain of the op-amp times the signal that gets to the input:
Vout = AOL  Vx = AOL  (Vin + B  Vout)
Now we can find closed-loop gain: ACL = Vout / Vin
as we will see on the next slide.

15. Negative Feedback Start with Vout = AOL  (Vin + B  Vout)
Then Vout = AOL  Vin + AOL  B  Vout
Then Vout – B  AOL  Vout = AOL  Vin
Then (1 - B  AOL )  Vout = AOL  Vin
Then Vout = [AOL / (1 - B  AOL ) ]  Vin
Then Vout / Vin = ACL = AOL / (1 - B  AOL )
Where ACL is the closed-loop gain
Now, if B  AOL >> 1 (which is usually the case)
then ACL  1 / B where B is set by a resistor ratio.

16. The Inverting Amplifier
Av = - (Rf / Ri) where minus means 180O phase shift

17. The Inverting Amp Gain equation derived as follows:
Vin applied to (-) input through Ri
zero difference across inputs implies V(-) = V(+)
(+) input grounded implies V(-)  0
(-) input is a “virtual ground”
which leads to Iin = Vin / Ri and If = Vout / Rf
no current into (-) input implies If = Iin
so Vout / Rf = Vin / Rin and Vout / Vin = Rf / Rin
If Vin makes Iin flow in, Vout must make If flow out.
So Vout has opposite polarity of Vin: Av = -Rf / Ri

18. The Inverting Amp An example calculation:
Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k
Av = - Rf / Ri = - (10k / 5k) = - 2
Vout = Av  Vin = -2  1V = -2 Volts DC

19. Very small V between inputs gives a binary output
Comparators
Very small V between inputs gives a binary output

20. Comparators Some Facts about Comparators:
Comparator output is high or low depending on which input has the higher voltage applied to it.
An open-loop op-amp can be used as a comparator.
Open-loop op-amps go into saturation, and they take a relatively long time to get out of saturation.
The output can “chatter” (oscillate high / low) when inputs are equal. Chatter can be cured with hysteresis.
There are ICs designed to be comparators. They are better at the job than op-amps.

21. Troubleshooting Check the power rails: +VCC and –VCC
Check if the output is in saturation (usually, saturation is not a good thing).
Check the input voltages, knowing that voltage across inputs is supposed to be virtually zero.
Check that polarity (phase) of output is the same as input for a non-inverting amplifier.
Check that polarity (phase) of output is the opposite input for an inverting amplifier.
Check signal levels based on gains (look at the resistor ratios of the feedback loops).