Unit 1:

Amplifiers
 Differential Amplifier
 is a type of electronic amplifier that multiplies the difference between two
inputs by some constant factor (the differential gain).

 is the basic building block of operational amplifiers.

A Schematic Symbol of a
Differential Amplifier

where:
Vs+ and Vs_= supply voltages
A= amplifier gain
V = non-inverting input
+
V_ = inverting input
 Basic Differential Amplifier Circuit

Emitter Biased Circuits

Example page 651
Calculate the dc voltages and currents in the circuit below.
 AC Operation of the Circuit

• Separate input signals are

applied as Vi and Vi with
1 2

separate outputs resulting

as Vo and Vo
1 2

• To carry out AC analysis,

each transistor is replaced
by its ac equivalent.

AC Connection of differential amplifier

 Single-Ended AC Voltage Gain
To calculate single ended ac voltage gain Vo/Vi , apply signal to one input with
the other connected to ground. The AC equivalent of circuit is shown in figure.
Example page 654

Calculate the single-ended output voltage, V0 , in the circuit below.

1
Double-Ended AC Voltage Gain

AC Equivalent

Vo Rc
Ad  
Vd 2ri
Vd  Vi  Vi
1 2

where:
Ad= Differential Mode Gain
 Common-Mode Operation

Common-Mode Connection AC Circuit in Common-Mode Connection

Vo RC
AC  
Vi ri  2  1RE
Example page 656

Calculate the common-mode gain for the amplifier circuit shown below.

β1= β2=75
ri1= ri2 = ri =20kΩ
Block diagram of an Op amp
Pin diagram 741 Op amp
 Characteristics of an Ideal op-amp

 Infinite input impedance

 Infinite Voltage gain
 Zero output impedance
 Zero Offset voltage
 Infinite bandwidth
 Infinite Common Mode Rejection Ratio (CMMR)
 Infinite slew rate
 Inverting Amplifier
-is a constant gain amplifier circuit.
Example: 1 Page 685

If the circuit above has R1=100kΩ and Rf=500kΩ, what output voltage results
for an input of V1=2V?
Rf 500k
Vo   V1   (2V )  10V
R1 100k
Example : 2 Page 716
Determine the output voltage for a 741 op-amp shown below with a
sinusoidal input of 2.5 mV.
 Noninverting Amplifier
-is a constant gain amplifier circuit.
Example Page 686
If the circuit above has R1=100kΩ and Rf=500kΩ, what output voltage results
for an input of V1=2V?

Example page 716

Calculate the output voltage from the circuit below for an input of 120µV.

240kΩ

2.4kΩ +16V

-16V
 Multi-Stage Gains
When a number of stages are connected in series, the overall gain is the
product of the individual stage gains.

The total gain (3-stages) is given by:

A  A1 A 2 A 3

or
 R f  R f  R f 
A   1      
 R 1  R2  R3 
Example page 717
Calculate the output voltage using the multi-stage circuit shown below for
resistor components of value Rf=470kΩ, R1=4.3kΩ, R2=33kΩ and
R3=33kΩ for an input of 80µV.
Example page 717
Show the connection of an LM124 quad op-amp as a three-stage
amplifier with gains of +10, -18 and -27. Use 270-kΩ feedback resistor for
all three circuits. What output voltage will result for an input of 150µV?
Example page 718
Show the connection of three op-amp stages using an LM348 IC to
provide outputs that are 10, 20 and 50 times larger than the input. Use a
feedback resistor of Rf=500kΩ in all stages.
 Voltage Buffer/ Unity Follower
Any amplifier with no gain or loss is called a unity gain amplifier.
The advantages of using a unity gain amplifier:

• Very high input impedance

• Very low output impedance

Realistically these circuits

are designed using equal
resistors (R1 = Rf) to avoid
problems with offset
voltages.

V0 = V 1
Example

100kΩ 100Ω

100Ω 10Ω

+ vx -
3mA 1kΩ
5V
1MΩ 1MΩ
20kΩ
 Voltage Summing Amplifier
The summing amplifier is used to add the voltages.
Since the input resistance is very large V1=V2=0, therefore

The output is the sum of individual signals times the gain:

R R R 
Vo   f V1  f V2  f V3 
 R1 R2 R3 
Example Page 687

Calculate the output voltage of an op-amp summing amplifier for the following
sets of voltages and resistors. Use Rf=1MΩ in all cases.
(a) V1=1V, V2=2V, V3=3V, R1=500kΩ, R2=1MΩ, R3=1MΩ.
(b) V1=-2V, V2=3V, V3=1V, R1=200kΩ, R2=500kΩ, R3=1MΩ.
Example Page 720

Calculate the output voltage for the circuit of the figure below. The inputs
are V1= 50mV sin(1000t) and V2=10mV sin(3000t).

330kΩ

33kΩ +9V
4
11
10
10kΩ 741
5
6
-9V
Example

100kΩ
V1=0.1V
20kΩ

400kΩ
Vo
20kΩ 10kΩ
 Subtractor Amplifier
-is used to subtract two voltages.

R3 R2  R4 R
V2 Vo  V1  4 V2
R1  R3 R2 R2
if R1  R3 and R2  R4
Vo
V1
Vo  V1  V2

Rf  Rf  Rf 
Vo     V1  V2 
 R 
 R3  1  R2 
 Rf R f Rf 
Vo   V2  V1 
 R2 R3R1 
Example page 721
Determine the output for the circuit below with the components Rf=1 MΩ, R1=100kΩ,
R2=50kΩ and R3=500kΩ.
Example page 721
Determine the output voltage for the circuit shown below.

100kΩ 100kΩ

20kΩ 741 Vo
Vo

20kΩ
 Integrator Amplifier
-is used to produce a voltage output proportional to the product (multiplication)
of the input voltage and time
Input-output waveforms using square wave

Input-output waveforms using sine wave

1
vo (t )  
RC  v1(t )dt

1
fa  , gain limiting frequency
2RF C F
1
fb  , frequency at which the gain is 0dB
2R1C F
 Example 7-15 page 279

In the circuit of Figure 1, R1CF= 1 second and the input is a step (dc) voltage
as shown in Figure 2. Determine the output voltage and sketch it. Assume that
the op-amp is initially nulled.
Figure 2

Figure 1
 Differentiator Amplifier
-is used to produce a voltage output proportional to the input voltage's rate of change
-is used in waveshaping circuits to detect high frequency components in an input signal
and also as a rate-of-change detector in FM modulators.

dv1 (t )
vo (t )   RC
dt
1
fa  , frequency at which the gain is 0dB
2RF C1
1 1
fb   , gain limiting frequency Input-output waveforms
2R1C1 2RF C F
 Differentiator Amplifier
Time period, T ≥ RFC1
Steps in designing a workable Differentiator

1. Select fa equal to the highest frequency of the input signal to be differentiated.

Then, assuming a value of C1< 1µF, calculate the value of RF.

2. Choose fb=20fa and calculate the values of R1 and CF so that R1C1=RFCF.

Practical Differentiator Circuit

 Example 7-16 page 283

(a) Design a differentiator to differentiate an input signal that varies in frequency

from 10 Hz to about 1 kHz.
(b) If a sine wave of 1V peak at 1000 Hz is applied to the differentiator of part
(a), draw its output waveform.
 Peak Detector
Input Waveform

+V c c

7
2 D1
- 6 + -
R 3 Vo
+ +
Rom=R
4
D2
- C
-V e e RL=10k

+
V in
-

GND

Output Waveform

741 Pin Out

Diagram
 A conventional ac voltmeter cannot be used to measure the
non sinusoidal waveforms line sawtooth triangular, pulse
wave etc, because it is designed to measure rms value of a
sine wave.
 For proper operation:
 Charging Time Constant Discharging time constant
T
CRd  CRL  10T
10
 Rd is forward bias resistance of the diode
 RL is the load resistor
 R  protect opamp from excessive discharge current.
 Rom =R minimizes offset problems
 D2  prevents the op-amp from going into negative
saturation.
Precision Rectifier

“Precision” Half-wave rectifier

Precision Rectifier

Vi

“Precision” Full-wave rectifier

 INSTRUMENTATION AMPLIFIER
-is a differential op-amp circuit providing high input impedances with ease of
gain adjustment through the variation of a single resistor, Rgain.

This produces a voltage drop between points 3 and 4 equal to:

General Expression for overall voltage gain in the instrumentation amplifier

Example page 728
Calculate the output voltage expression for the instrumentation amplifier circuit
given below. Assume that all resistors are 5kΩ.
 Log Amplifier
A logarithmic amplifier has an output voltage that is proportional to the logarithm
of the input.

VBE = A log (Ic)

Logarithmic Amplifier circuit

 The capacitor across the npn transistor is used to reduce the ac gain.

 The diode protects the transistor against excessive reverse base-to-emitter voltage.

 Resistor R1 is determined by the inequality pair

Vi
R1  max

Ic
max

Vi
R1  max

input _ bias _ current _ of _ op _ amp

Example
Design a logarithmic amplifier, using the circuit below, having an input
voltage varying from 1 mV to 10 volts. Assume that the input bias current of
the op-amp (e.g., a 741) is 80 nA, and the maximum collector current is to
be 1 mA.
Anti Log Amplifier