1. Operational Amplifiers
Week of 13th October 2008

2. The concept of negative feedback
Harold Black thought of the concept of negative feedback during a ferry ride on 6 August 1927

3. What is negative feedback

4. Amplifier possibilities
The input can be a voltage.
The input can be a current.
The output can be a voltage.
The output can be a current.
The total number of combinations is four.

5. Four types of negative feedback
Voltage-controlled voltage source (VCVS) (ideal voltage amplifier)
Current-controlled voltage source (ICVS) (transresistance amplifier)
Voltage-controlled current source (VCIS) (transconductance amplifier)
Current-controlled current source (ICIS) (ideal current amplifier)

7. Converters VCIS and ICVS amplifiers can be viewed as converters.
The VCIS is often called a voltage-to-current converter.
The ICVS is often called a current-to-voltage converter.

8. VCVS equivalent circuit
Low zout
High zin
vin
vout
AVvin
The input impedance is very high and
the output impedance is very low. It
approaches the ideal voltage amplifier.

9. ICVS equivalent circuit
Low zout
iin
Low zin
vout
rmiin
The input impedance is very low and
the output impedance is very low.
It is well suited for converting a current
into a voltage (rm is the transresistance).

10. VCIS equivalent circuit
iout
High zout
High zin
vin
gmvin
The input impedance is very high and
the output impedance is very high. It
is well suited for converting a voltage
into a current (gm is the transconductance).

11. ICIS equivalent circuit
iin
iout
High zout
Low zin
Aiiin
The input impedance is very low and
the output impedance is very high. It
approaches the ideal current amplifier.

12. VCVS voltage gain
Loop gain is the voltage gain of the forward and feedback paths
Loop gain is very large
Closed-loop voltage gain is ultrastable
Gain depends on characteristics of external resistors

13. The noninverting circuit is a VCVS amplifier.1 B = Rf R1
vout
vin Rf
The feedback fraction B = v2
vout v2 R1
AV(CL) =
AVOL
1 +AVOLB 1 B @
The term AVOLB is called the loop gain
and is normally much greater than 1.

14. The loop gain is usually very large which provides:
Gain stability
Low distortion
Low offsets
Near ideal input impedance
Near ideal output impedance

15. Input impedance of the noninverting amplifier
vout
vin Rf
zin(CL) = (1+AVOLB)Rin RCM R1
(RCM > 100 MW for a 741)
Rin = the open-loop input resistance of the op amp
RCM = the common-mode input resistance of the op amp

16. VCVS negative feedback
Has a curative effect on the flaws of an amplifier
Stabilizes voltage gain
Increases input impedance
Decreases output impedance
Decreases harmonic distortion

17. Output impedance of the noninverting amplifier
vout
vin Rf
zout(CL) =
Rout
1 + AVOLB R1
(Rout = 75 W for a 741)
Rout = the open-loop output resistance of the op amp

18. Distortion A sine wave has only one frequency called the fundamental.
An amplifier with distortion adds energy at new frequencies called harmonics.
Total harmonic distortion (THD) is the percentage of harmonic voltage in the output signal.
THD = (Total harmonic voltage/fundamental voltage) x 100%