1. TECHNIQUES OF DC CIRCUIT ANALYSIS: SKEE 1023
Application to operational amplifier circuit
SKEE 1023

2. Operational amplifier: Integrated circuit consisting several transistors and resistors normally used for analog circuit design.
Offset null(5)
Positive supply Vcc+ (7)
Inverting input (2) −
Output (6) +
Non-inverting input (3)
Negative supply Vcc− (4)
Offset null(1)

3. An op-amp can be modeled by a very good voltage amplifier circuit
Operational amplifier: Integrated circuit consisting several transistors and resistors normally used for analog circuit design.
How can we analyse circuit containing op-amps (consistings of hundreds of transistors and resistors!) using the knowledge that we have so far?
The answer is modeling !
An op-amp can be modeled by a very good voltage amplifier circuit
Later we’ll see that the analysis is even simplified when we assumed an ideal op-amp.

4. An op-amp can be modeled by a very good voltage amplifier circuit
vo = Avd = A(v2 - v1)
vo - output voltage with respect to ground
A - open loop gain
v1 - inverting input voltage with respect to ground
v2 - non-inverting input voltage with respect to ground
Avd + − Ro Ri vd v1 v2 v0
An op-amp can be modeled by a very good voltage amplifier circuit

5. An op-amp can be modeled by a very good voltage amplifier circuit
vo = Avd = A(v2 - v1)
vo - output voltage with respect to ground
A - open loop gain
v1 - inverting input voltage with respect to ground
v2 - non-inverting input voltage with respect to ground
Avd + − Ro Ri vd v1 v2 v0 vo
Positive saturation
Vcc
-Vcc/A
Vcc/A vd
Negative saturation
-Vcc

6. Let’s look at a practical circuit: Unity gain buffer
Vcc + − + − + − Vs
In drawing op-amp circuits, we normally do not include power supplies + vo −
Vcc − +

7. Let’s look at a practical circuit: Unity gain buffer+ − + − Vs
In drawing op-amp circuits, we normally do not include power supplies + vo −

8. Let’s look at a practical circuit: Unity gain buffer
Vs = iRi + iRo + Aovin
Using KVL, we can write:
Vo = iRo + Aovin i
Vin = iRi + − +
vin − Ro Ri + − Vs + −
Aovin + vo −
For Ri >> Ro
For Ao>>1
Whenever vin 0 , Aovin increases until vin=0 and hence the current cease to flow.

9. Modeling of an ideal op-amp
1. In previous analysis we have assumed Ri>>Ro
In practical op-amps it is true that Ri >> Ro and for ideal op-amp we will assume Ri → and Ro → 0
2. In previous analysis we have assumed Ao>> 1
In practical op-amps it is true that Ao>> 1 and for ideal op-amp we will assume Ao →
As a result of 1 and 2, when analysing an op-amp circuit with feedback, we will assume that:
i. i1 = 0, and i2 = 0
ii. v2 –v1 = 0

10. Let’s look back at the buffer circuit using ideal op-amp
Since vo is tied to v1 and in ideal op-amp v1=v2, it is obvious that vo = Vs (as we have seen before) + − Vs v2 v1 vo

11. Eg.2 (PP 5.2)
Find the closed-loop gain vo/vs. Determine current i when vs = 2V

12. OP AMP circuits
In SKEE1023, we will study some of the important op amp circuits:
Inverting amplifier
Non-inverting amplifier
Summing amplifier
Difference amplifier
You should :
Know how (not memorize!) to derive the input-output relationship (Gain = vo/vi))
Able to identify the circuit correctly

13. Inverting Amplifier
Reverses the polarity of a signal while amplifying it
Since i1 = i2, and v1 = v2 = 0

14. Non-inverting Amplifier
Maintains the polarity of a signal while amplifying it
Since i1 = i2, and v1 = v2 = vi

15. Summing Amplifier
Output is the inverted, scaled sum of the voltages applied to the input
KCL at node a gives: i = i1 + i2 + i3
And, since v+ = v- = 0

16. Difference Amplifier
Output is proportional to the difference between the two inputs voltages
Using voltage division rule,
With va = vb, applying KCL at the inverting input,

17. Difference Amplifier
Output is proportional to the difference between the two inputs voltages
It can be shown that: If