EC8353 Electron Devices and Circuits

UNIT V FEEDBACK AMPLIFIERS AND OSCILLATORS

Advantages of negative feedback – voltage / current, series , Shunt
feedback –positive feedback – Condition for oscillations, phase
shift – Wien bridge, Hartley, Colpitts and Crystal oscillators.

By
Mr. R.Suresh , AP/RMDEEE
Ms.S.Karkuzhali , AP/RMDEEE
Feedback Amplifiers

1 - Desensitize The Gain

2 - Reduce Nonlinear Distortions

3 - Reduce The Effect of Noise

4 – Control The Input And Output Impedances

5 – Extend The Bandwidth Of The Amplifier

The General Feedback Structure

Basic structure of a feedback amplifier. To make it general, the figure shows signal flow as opposed to
voltages or currents (i.e., signals can be either current or voltage).

xi xo
Source  A Load
xs

xf
b

The open-loop amplifier has gain A  xo = A*xi

Output is fed back through a feedback network which produces a sample (xf) of the output (xo)  xf = bxo
Where b is called the feedback factor
The input to the amplifier is xi = xs – xf (the subtraction makes feedback negative)
Implicit to the above analysis is that neither the feedback block nor the load affect the amplifier’s gain (A).
This not generally true and so we will later see how to deal with it.
The overall gain (closed-loop gain) can be solved to be:

xo A
Af  
xs 1  Ab

Ab is called the loop gain 1+Ab is called the “amount of feedback”

Finding Loop Gain

Generally, we can find the loop gain with the following steps:

– Break the feedback loop anywhere (at the output in the ex. below)
– Zero out the input signal xs
– Apply a test signal to the input of the feedback circuit
– Solve for the resulting signal xo at the output
If xo is a voltage signal, xtst is a voltage and measure the open-circuit voltage
If xo is a current signal, xtst is a current and measure the short-circuit current
– The negative sign comes from the fact that we are apply negative feedback

x f  bxtst
xs=0 
xi
A xi  0  x f
xo  Axi   Ax f   bAxtst
xo
loop gain    bA
xf xtst
b
xo
xtst
Negative Feedback Properties

Negative feedback takes a sample of the output signal and applies it to

the input to get several desirable properties. In amplifiers, negative
feedback can be applied to get the following properties

–Desensitized gain – gain less sensitive to circuit component

variations

–Reduce nonlinear distortion – output proportional to input (constant

gain independent of signal level)

–Reduce effect of noise

–Control input and output impedances – by applying appropriate

feedback topologies

–Extend bandwidth of amplifier

These properties can be achieved by trading off gain

Gain Desensitivity
Feedback can be used to desensitize the closed-loop gain to variations in the
basic amplifier. Let’s see how.
Assume beta is constant. Taking differentials of the closed-loop gain equation
gives…
A dA
Af  dAf 
1  Ab 1  Ab 2
Divide by Af

dAf dA 1  Ab 1 dA
 
Af 1  Ab 2 A 1  Ab A

This result shows the effects of variations in A on Af is mitigated by the

feedback amount. 1+Abeta is also called the desensitivity amount
We will see through examples that feedback also affects the input and
resistance of the amplifier (increases Ri and decreases Ro by 1+Abeta factor)
Bandwidth Extension

Mentioned several times in the past that we can trade gain for bandwidth
Consider an amplifier with a high-frequency response characterized by a
single pole and the expression:
Apply negative feedback beta and the resulting closed-loop gain is:

As  
AM
1  s H

As  AM 1  AM b 
Af s   
1  bAs  1  s H 1  AM b 

•Notice that the midband gain reduces by (1+AMbeta) while the 3-dB roll-off
frequency increases by (1+AMbeta)
Basic Feedback Topologies
series-shunt
Depending on the input signal (voltage or current) to be
amplified and form of the output (voltage or current),amplifiers
can be classified into four categories. Depending on the
amplifier category, one of four types of feedback structures
should be used (series-shunt, series-series, shunt-shunt, or shunt-series
shunt-series) Voltage amplifier – voltage-controlled voltage
Source
Requires high input impedance, low output impedance
Use series-shunt feedback (voltage-voltage feedback)
Current amplifier – current-controlled current source series-series

Use shunt-series feedback (current-current feedback)

Transconductance amplifier – voltage-controlled current source
Use series-series feedback (current-voltage feedback)
Transimpedance amplifier – current-controlled voltage source
Use shunt-shunt feedback (voltage-current feedback)

shunt-shunt
Examples of the Four Types of Amplifiers
iOUT iOUT
RD RD

vOUT vOUT
vIN Vb vIN Vb

iIN iIN

Voltage Transimpedance Transconductance Current

Amp Amp Amp Amp

• Shown above are simple examples of the four types of amplifiers. Often, these
amplifiers alone do not have good performance (high output impedance, low
gain, etc.) and are augmented by additional amplifier stages (see below) or
different configurations (e.g., cascoding).
iOUT iOUT
RD RD RD RD

vOUT Vb vOUT v Vb
vIN IN

iIN iIN

lower Zout lower Zout higher gain higher gain

 Series-Shunt Feedback Amplifier
(Voltage-Voltage Feedback)

Samples the output voltage and returns a feedback

voltage signal
Ideal feedback network has infinite input
impedance and zero output resistance
Find the closed-loop gain and input resistance
The output resistance can be found by
applying a test voltage to the output
So, increases input resistance and reduces output
resistance  makes amplifier closer to ideal
VCVS
V f  bVo
Vi  Vs  V f
Vo  AVs  bVo 
Vo A
Af   Ro
Vs 1  bA Rof 
V  bAVi 1  bA
 Ri 1  Ab 
Vs V V
Rif   s  Ri s  Ri i
I i Vi Ri Vi Vi
The Series-Shunt Feedback Amplifier

The Ideal Situation

The series-shunt
feedback
amplifier:
(a) ideal structure;
(b) equivalent circuit.
Z o( s )
Z of( s )
1  A(s ) b (s )
Vo A
Af
Vs 1  Ab

Vs Vs Vs Vi  b  A  Vi
Rif Ri Ri
Ii Vi Vi Vi
Ri

Rif Ri  1  A  b 

Zif ( s ) Zi( s )   1  A ( s )  b ( s ) 
 Series-Series Feedback Amplifier
(Current-Voltage Feedback)
For a transconductance amplifier (voltage input, current
output), we must apply the appropriate feedback circuit
Sense the output current and feedback a voltage
signal. So, the feedback current is a
transimpedance block that converts the current
signal into a voltage.
To solve for the loop gain:
Break the feedback, short out the break in the current
sense and applying a test current Iout

To solve for Rif and Rof Gm ZL

Apply a test voltage Vtst across O and O’

Itst
I
A  o (also called Gm )
Vi Vf RF
I A I
Af  o  Loop Gain  Ab   out  Gm R f
Vs 1  Ab I tst

Vs Vi  V f Ri I i  bI o Ri I i  AbVi
Rif      Ri 1  Ab 
Ii Ii Ii Ii
Vtst I tst  AVi Ro I tst  AbI tst Ro
Rof     1  Ab Ro
I tst I tst I tst
 Shunt-Shunt Feedback Amplifier
(Voltage-Current Feedback

• When voltage-current FB is applied to a

transimpedance amplifier, output voltage is
sensed and current is subtracted from the
input
– The gain stage has some resistance
– The feedback stage is a transconductor
– Input and output resistances (Rif and
Rof) follow the same form as before
based on values for A and beta
Vo
A
Rif  Ri 1  Ab 
Ii
Vo
 bVo
I s  Ii  I f 
A Ro
Rof 
V
Af  o 
A 1  Ab 
I s 1  Ab
 Shunt-Series Feedback Amplifier
(Current-Current Feedback)

• A current-current FB circuit is used for

current amplifiers
– For the b circuit – input resistance
should be low and output resistance
be high
• A circuit example is shown
– RS and RF constitute the FB circuit
• RS should be small and RF large
– The same steps can be taken to Iout
RD
solve for A, Abeta, Af, Rif, and Rof
• Remember that both A and b
circuits are current controlled Iin

current sources
RF
RS
The General Feedback Structure

Exercise

A f  10 A  10
4 Amount_Feedback  20 log  1  A  b 
c)

R1 Amount_Feedback  60
a) b
R1  R2

b)
A Vs  1 Vo  A f  Vs Vo  10
Af d)
1  Ab

Vf  b  Vo Vf  0.999
b  1

given 4
Vi  Vs  Vf Vi  10  10

A
Af
1  Ab
4
e) A  0.8 10 A
A f  A f  9.998
1  Ab
b  Find  b  b  0.1

R1 R2 10  9.998
0.1 9  100  0.02
R1  R2 R1 10
Some Properties of Negative Feedback

Gain Desensitivity

A
Af
1 Ab

deriving

dA A
dAf dividing by Af
2 1 Ab
(1  A  b)

dAf 1 dA

Af (1  A  b ) A

The percentage change in Af (due to variations in some circuit parameter) is smaller than the
pecentage cahnge in A by the amount of feedback. For this reason the amount of feedback

1 Ab

is also known as the desensitivity factor.

Some Properties of Negative Feedback

Bandwidth Extension

High frequency response with a single pole

AM
A ( s)
s
1
H

AM denotes the midband gain andH the upper 3-dB frequency

A ( s)
Af ( s )
1  b  A ( s)

AM

 1 AMb 
Af ( s )
s
1

H  1  A M  b 
L
Hf 
H  1  A M  b  Lf
1  AM  b
Oscillator
Oscillator principle
• Oscillators are circuits that generate periodic signals.
• An oscillator converts DC power from power supply to
AC signals power spontaneously – without the need for
an AC input source (Note: Amplifiers convert DC
power into AC output power only if an external AC
input signal is present.)
• There are several approaches to design of oscillator
circuits. The approach to be discussed is related to the
feedback using amplifiers. A frequency-selective
feedback path around an amplifier is placed to return
part of the output signal to the amplifier input, which
results in a circuit called a linear oscillator that produces
an approximately sinusoidal output.
• Under proper conditions, the signal returned by the
feedback network has exactly the correct amplitude and
phase needed to sustain the output signal.
The Barkhausen Criterion I
• Typically, the feedback network is composed of passive lumped components
that determine the frequency of oscillation. So, the feedback is complex
transfer function, hence denoted as b( f )
• We can derive the requirements for oscillation as follows: initially, assume a
sinusoidal driving source with phasor Xin is present. But we are interested in
derive the conditions for which the output phasor Xout can be non-zero even
the input Xin is zero.

The output of the amplifier block can be wrtten as X out  A( f )[X in  b ( f )X out ]
A( f )
solve for X out, we obtain X out  X in
1  A( f ) b ( f )
If X in is zero, the only way t he the output can be nonzero is to have A( f ) b ( f )  1
• The above condition is know as Barkhausen Criterion.
The Barkhausen Criterion II
• The Barkhausen Criterion calls for two requirement for the loop gain .
First, the magnitude of the loop gain must be unity. Second, the phase
angle of the loop gain must be zero the frequency of oscillation. (e.g, if a
non-inverting amplifier is used, then the phase angle of must be
b( f )
zero. For a inverting amplifier, the phase angle should be 180)
• In real oscillator design, we usually design loop-gain magnitude slightly
larger than unity at the desired frequency of oscillation. Because a higher
gain magnitude results in oscillations that grow in amplitude with time,
eventually, the amplitude is clipped by the amplifier so that a constant-
amplitude oscillation results.
• On the other hand, if exact unity loop gain magnitude is designed, a slight
reduction in gain would result in oscillations that decays to zero.
• One important thing to note is that the initial input Xin is not needed, as
in real circuits noise and transient signals associated with circuit turning
on can always provide an initial signal that grows in amplitude as it
propagates around the loop (assuming loop gain is larger than unity).
 Contents:
• Introduction
• Classifications of Oscillators
• Circuit Analysis of a General Oscillator
• Hartley Oscilltor
• Colpitts Oscillator
• RC Phase shift Oscillator
• Wien Bridge Oscillator
• Crystal Oscillator
• Applications of Oscillators
 Objectives:
Different types of oscillators:
• An oscillator has a positive feedback with the loop gain infinite.
Feedback-type sinusoidal oscillators can be classified as
LC (inductor-capacitor) and RC (resistor-capacitor) oscillators.

 Tuned oscillator
 Hartley oscillator
 Colpitts oscillator
 Clapp oscillator
 Phase-shift oscillator
 Wien-bridge and
 Crystal oscillator
 INTRODUCTION:
• An oscillator is an electronic system.
• It comprises active and passive circuit elements and sinusoidal produces repetitive
waveforms at the output without the application of a direct external input signal to
the circuit.
• It converts the dc power from the source to ac power in the load. A rectifier circuit
converts ac to dc power, but an oscillator converts dc noise signal/power to its ac
equivalent.
• The general form of a harmonic oscillator is an electronic amplifier with the output
attached to a narrow-band electronic filter, and the output of the filter attached to
the input of the amplifier.
• The oscillator analysis is done in two methods—first by a general analysis,
considering all other circuits are the special form of a common generalized circuit
and second, using the individual circuit KVL analysis.
Difference between an amplifier and
an oscillator:
 CLASSIFICATIONS OF
OSCILLATORS:
• The classification of various oscillators is shown in Table .
 CIRCUIT ANALYSIS OF A
GENERAL OSCILLATOR:
 This section discusses the general oscillator circuit with a simple generalized
analysis using the transistor, as shown in Fig. .
 An impedance z1 is connected between the base B and the emitter E, an impedance
z2 is connected between the collector C and emitter E. To apply a positive feedback
z3 is connected between the collector and the base terminal.
 All the other different oscillators can be analyzed as a special case of the
generalized analysis of oscillator.
 CIRCUIT ANALYSIS OF A GENERAL
OSCILLATOR:
• The above generalized circuit of an oscillator is considered using a simple transistor-equivalent circuit
model. The current voltage expressions are expressed as follows:
CIRCUIT ANALYSIS OF A GENERAL OSCILLATOR:
CIRCUIT ANALYSIS OF A GENERAL
OSCILLATOR:
CIRCUIT ANALYSIS OF A GENERAL
OSCILLATOR:
CIRCUIT ANALYSIS OF A GENERAL
OSCILLATOR:
Hartley Oscillator:
Hartley Oscillator:
Colpitts Oscillator:
Colpitts Oscillator:
Colpitts Oscillator:
Phase-Shift Oscillator:
Phase-Shift Oscillator:
Phase-Shift Oscillator:
Phase-Shift Oscillator:
Phase-Shift Oscillator:
Phase-Shift Oscillator:
Wien-Bridge Oscillator:
Wien-Bridge Oscillator:
Wien-Bridge Oscillator:
Wien-Bridge Oscillator:
Wien-Bridge Oscillator:
 Wien-Bridge Oscillator:

• Advantages of Wien-Bridge Oscillator:

• 1. The frequency of oscillation can be easily varied just by changing RC network
• 2. High gain due to two-stage amplifier
• 3. Stability is high

• Disadvantages of Wien-Bridge Oscillator

• The main disadvantage of the Wien-bridge oscillator is that a high frequency of
oscillation cannot be generated.
 CRYSTAL OSCILLATOR:
• Crystal oscillator is most commonly used oscillator with high-frequency stability. They are
used for laboratory experiments, communication circuits and biomedical instruments. They
are usually, fixed frequency oscillators where stability and accuracy are the primary
considerations.
• In order to design a stable and accurate LC oscillator for the upper HF and higher frequencies
it is absolutely necessary to have a crystal control; hence, the reason for crystal oscillators.
• Crystal oscillators are oscillators where the primary frequency determining element is a
quartz crystal. Because of the inherent characteristics of the quartz crystal the crystal
oscillator may be held to extreme accuracy of frequency stability. Temperature
• compensation may be applied to crystal oscillators to improve thermal stability of the crystal
oscillator.
• The crystal size and cut determine the values of L, C, R and C'. The resistance R is the
friction of the vibrating crystal, capacitance C is the compliance, and inductance L is the
equivalent mass. The capacitance C' is the electrostatic capacitance between the mounted pair
of electrodes with the crystal as the dielectric.
Circuit Diagram of CRYSTAL OSCILLATOR:
Circuit Diagram of CRYSTAL OSCILLATOR:
Circuit Analysis of CRYSTAL OSCILLATOR:
APPLICATIONS OF OSCILLATORS:
 Oscillators are a common element of almost all electronic circuits. They are used in
various applications, and their use makes it possible for circuits and subsystems to perform
numerous useful functions.
 In oscillator circuits, oscillation usually builds up from zero when power is first
applied under linear circuit operation.
 The oscillator’s amplitude is kept from building up by limiting the amplifier
saturation and various non-linear effects.
 Oscillator design and simulation is a complicated process. It is also extremely
important and crucial to design a good and stable oscillator.
 Oscillators are commonly used in communication circuits. All the
communication circuits for different modulation techniques—AM, FM, PM—the use of an
oscillator is must.
 Oscillators are used as stable frequency sources in a variety of electronic
applications.
 Oscillator circuits are used in computer peripherals, counters, timers, calculators,
phase-locked loops, digital multi-metres, oscilloscopes, and numerous other applications.
 POINTS TO REMEMBER:
• 1. Oscillator converts dc to ac.
• 2. Oscillator has no input signal.
• 3. Oscillator behaviour is opposite to that of a rectifier.
• 4. The conditions and frequencies of oscillation are classified as:
IMPORTANT FORMULAE: