III. Feedback and Operational Amplifiers
1. Basic concept of feedback
2. Operational amplifiers
3. Basic Op-Amp circuits

Inverting amplifier

Noninverting amplifier

Differential and summing amplifiers

Integrator and differentiator

Comparator
1. Basic concept of feedback
Feedback has become a well-known concept. It has entered the general vocabulary.
Negative feedback is the process of coupling the output back to the input in such a
way as to cancel some of the input.
Positive feedback is the process of coupling the output back to the input in such a way
as to increase the input. This causes oscillation sometimes intentionally. Very often the
oscillations are not desired but surprisingly easy excited.
Compensation means the prevention of unwanted oscillation.
2. Operational amplifiers
Universal symbol of the op-amp is shown in Fig. 1. Fig.2 shows a mini-DIP (Dual-In line
Package) and Fig. 3 shows the pin connections.
Fig. 1. Universal symbol of operational amplifier.
Fig. 2. Mini-DIP integrated circuit.
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Fig. 3. The 411 pin connections.

Op-amps have two inputs and a single output.

(+) and (-) are noninverting and inverting inputs respectively, and they concern relative
phase of output signal with respect to input signal; are the same for (+) input and are
opposite for (-) input.

Inside the IC (Integrated Circuit) there are transistors, resistors and capacitors. For
instance inside the 411 from Fig. 2 and Fig. 3 there is 24 transistors, 11 resistors and 1
capacitor.

The dot shows the corner from which we begin counting the pin numbers.

Offset-null terminals are for external correction of small asymmetry, which is
unavoidable in manufacturing process. Producers always give precise advice how to
perform this correction.

Op-amps have very big gain factor and are devoted for work with external feedback.
An open-loop input-output characteristic is shown in Fig. 4.
Vout
Vcc(+)
Vin
Vcc(-)
Fig. 4. Open loop input output characteristic of an op-amp.
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The golden rules
i.
The op-amp voltage gain is so high that a fraction of milivolt between the input
terminals causes that the output swing over its full range, form Vcc(+) to Vcc(-).
ii.
The inputs draw almost no current (very, very small, for instance 0.1nA=0.1*10-9A)
iii.
The output (with external feedback) attempts to make zero the voltage difference
between inputs.
3. Basic Op-Amps circuits

Inverting amplifier
The circuit is shown in Fig. 5.
R2
_
intput
R1
A
+
output
B
Fig.5. Inverting amplifier.
Point B is at ground, so the point A is also (see iii). This point A is called virtual ground.
The voltage across R 1 is Vin and the voltage across R 2 is Vout, therefore: Vout / R 2  Vin / R1 .
Voltage gain of the inverting amplifier is G  
R2
.
R1
Input impedance Z in  R1 because point A is at ground level. It is usually about a couple of
k. It is rather small value and small input impedance is an undesired feature of inverting
amplifier. The output impedance is a couple of ohms.

Noninverting amplifier
The circuit is shown in Fig. 6.
Fig. 6. Noninverting amplifier.
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The analysis is:
VA comes from a voltage divider: VA  Vout
R1
R1  R 2
Accordingly to (iii) Vin  VA
Voltage gain of the noninverting amplifier is: G 
Vout R1  R 2
R

1 2
Vin
R1
R1
The input impedance is infinite (about 1012 or more). The output impedance is a couple of
ohms.

Differential and summing amplifiers
The circuit in Fig. 7 is a differential amplifier with voltage gain G 
R2
. This circuit requires
R1
precise matching the resistors to achieve exact output value.
Fig. 7. Classic differential amplifier.
A summing amplifier is in Fig. 8. It is just a variation of the inverting amplifier. Point X is a
virtual ground, so the input current is i 
V1 V2 V3 1


 V1  V2  V3  . Therefore the output is
R R
R R
Vout  i * R  (V1  V2  V3 ) .
Fig. 8. An example of summing amplifier.
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
Integrator and differentiator
Op-amps allow making nearly perfect integrators. An example is shown in Fig. 9.
Fig. 9. Integrator.
Input current
Vin
flows through C and because the (-) input is virtual ground the same current
R
flows from the output, therefore:
dV
Vin
1
 C out and Vout 
 Vin dt .
R
dt
RC
Differentiators are similar to integrators, but with R and C reversed as Fig. 10 shows.
R
_
intput
C
+
output
Fig. 10. Differentiator.
Since the inverting input is at ground, the change of input voltage produces a current
iC

dV in
dV
and produces the output voltage Vout  i * R  RC in .
dt
dt
Comparator
It is very common to want to know which of two signals is larger, or to know when a given
signal exceeds a fixed, desired value. A device, which compares two values, is called
comparator. The simplest form of comparator is a high-gain differential amplifier made with
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an op-amp (it is not forbidden to design it from individual transistors, but what for?). It is
shown in Fig. 11.
V1
_
+
Voutput
V2
Fig. 11. Comparator.
The op-amp goes to positive or negative saturation according to the difference between both
the inputs. Because the voltage gain is typically 105-6 therefore just a fraction of milivot
between two inputs will cause the output to be saturated:
()
V1  V2  0  Vout  VCC
()
V1  V2  0  Vout  VCC
Although an ordinary op-amp can be used as a comparator (and very often it is) there are
special integrated circuits intended for use as comparators. The special chips are designed for
very fast response. They are compared with self-explanatory parameter called propagation
delay versus input overdrive.
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