1. Introduction Equivalent circuit model of op-amp
a voltage controlled voltage
source with very high gain.
five terminals four ports
active element.
In+Ip+Ic++Ic-+Io=0
Equivalent circuit model of op-amp
Vi=Vp-Vn.
Ri is the input resistance
Ro is the output resistance
Vo=AVi=A(Vp-Vn)

2. How to use it in circuits?
Voltage Transfer Curve
In reality A, Ri are finite and Ro>0
The output is limited by power source
For a 741 op-amp powered with VCC= +10V and VEE= -10V, Vo will saturate
(reach the maximum output voltage range) at about ±10 V.
With an A=200,000V/V saturation occurs with an input differential
voltage of 10/200,000 = 50μV, a very small voltage.
How to use it in circuits?

3. Negative Feedback

4. Ideal op-amp model Ideal op-amp conditions:
Ip=In=0 No current into the terminals
Ri=∞ Infinite input resistance
Ro= Zero output resistance
A ∞ Infinite open loop gain
Ip=In=0 and Ri=∞ makes no power demands on the input signal
source. Ro=0 makes the output voltage independent of the load .
Even though the ideal op-amp model deviates much from the real
op-amps, the ideal conditions in the ideal op-amp model are very
useful in the design and analysis of circuits.

5. Fundamental Amplifier Configurations
(a) Inverting amplifier
(b) Non-inverting amplifier
(c) Differential amplifier
(d) Summing amplifier

6. Ideal op-amp conditions:
Inverting Amplifier— Ideal op-amp circuit analysis
Ideal op-amp conditions:
Ip=In=0 No current into the terminals
Ri=∞ Infinite input resistance
Ro= Zero output resistance
A ∞ Infinite open loop gain

7. Ideal op-amp conditions:
Non-Inverting Amplifier: Ideal op-amp circuit analysis
Ideal op-amp conditions:
Ip=In=0 No current into the terminals
Ri=∞ Infinite input resistance
Ro= Zero output resistance
A ∞ Infinite open loop gain

8. The Voltage Follower
Purpose ?

9. Inverting Amplifier — Effect of Finite Open-Loop Gain
The current through R1 is now
Considering I1=I2, the output voltage Vo can thus be determined from

10. Inverting Amplifier — Effect of Finite Open-Loop Gain
Let’s consider an inverting amplifier design
with R1=10kΩ and R2=100kΩ. In this case,
the ideal voltage gain is -10. By assuming
that A ranges in values from 1,000 V/V to
10,000,000V/V, Table I shows the real gain
and the resulting deviation in % from the ideal case

11. Non-Inverting Amplifier — Effect of Finite Open-Loop Gain
Since In=Ip=0, we have I1=I2 and therefore
Since the voltage Vi = Vp-Vn
= Vin-Vn, the output voltage
is given by

12. Differential Amplifier: Ideal op-amp circuit analysis
The output voltage is
In order to obtain Vout=0 when Vin1=Vin2 only if
System is linear and so we may
apply superposition
Which holds only if
The contribution of the signal
Vin2 to the output is
The output voltage is now
The contribution of the signal
Vin1 to the output is

13. Real Op-Amp Frequency Response
Real Op amps have a frequency dependant open loop gain
Where

14. If the open loop bandwidth is so small, how can the op amp be useful?
Real Op-Amp Frequency Response
If the open loop bandwidth is so small,
how can the op amp be useful?

15. Real Op-Amp Frequency Response
Closed loop band width:

16. Real Op-Amp Frequency Response

17. Real Op-Amp Frequency Response
Closed loop band width: