B sc i cbcs unit 4

E1 BSc I CBCS Unit 4
AMPLIFIERS AND OSCILLATORS

AMPLIFIER: An amplifier is an electronic device or circuit which
is used to increase the magnitude of the signal applied to its
input
*Transistor Amplifiers:
*Voltage Amplifiers:
*Current Amplifiers:
*Power Amplifiers:Class A,Class B and Class C power Amps.
*Audio Frequency Amplifiers (A.F.
*Intermediate Frequency Amplifiers (I.F. ...
*Radio Frequency Amplifiers (R.F. ...
*Ultrasonic Amplifiers: ...
*Wideband Amplifiers:

Analysis of Common Emitter Amplifier using h-parameters

Figure 1(a) shows the circuit of a common emitter (CE)
amplifier using self-bias and load resistor R0 capacitively
coupled to the collector. Figure 1(b) gives the a.c. equivalent
circuit. Here we have eliminated the biasing circuit consisting
of R1, R2, Re and Cz.The R1 – R2 combination is equivalent to
resistance Rb (= R1 || R2) between base and ground. It is
assumed that Rb is large in comparison with the input
resistance of the amplifier between base and ground and
hence Rb is neglected in the equivalent circuit. Similarly, the
reactance of capacitor Cz is so small at the lowest operating
frequency that Cz effectively bypasses all a.c. components.

Hence Re-Cz combination is also excluded from the a.c.
equivalent circuit. In most of the amplifiers, the a.c. output
voltage developed across Rc is capacitively coupled to the
next stage through the capacitor Cb and R0 is the effective
impedance in the output circuit. Value of capacitor Cb is
chosen so large that its reactance at the operating frequency
is small and may be neglected. Then for a.c. operation, R0
comes in parallel with Rc and effective load resistance RL = RC
|| RO. This results in the simple a.c. equivalent circuit of
Figure 1(b).

Analysis: For the purpose of analysis, we replace the transistor
by its small signal two generator h-parameter model. This
results in the equivalent circuit of Figure 2. We assume
sinusoidal input. Hence in the equivalent circuit of Figure 2, we
have used rms value of voltages and currents namely Ib, Vb, Ic
and Vc.

Current Gain or Current Amplification:
Current gain is defined as the ratio of the load current I1
to the input current Ib. Thus,
Current Gain AI = IL/Ib=-Ic/Ib …..(1)
But from figure 2, Ic = hfe.Ib+ hoe.Vc ..(2)
Also Vc = IL.RL = -Ic.RL …..(3)
Combining Equation (2) and (3) we get,
Ic = hfe.Ib – hoe.Ic.RL or (1+hoe.RL)Ic = hfe.Ib
Hence current gain AI = - Ic/Ib = - hfe/(1+hoe.RL) …(4)

Input Impedance Ri:
This is the impedance between the input terminals B and E looking
into the amplifier as shown in Figure 2 and is, therefore, given by,
Ri = Vb/Ib} ……(5)
From figure 2 Vb = hie.Ib + hre.Vc …..(6)
But Vc = -Ic.RL = AI.Ib.RL …..(7)
Substituting the value of Vc from Equation (7) into Equation (6) we get,
Vb = hie + hre.AI.Ib.RL …..(8)
Hence input impedance Ri = Vb/Ib = hie + hre.AI.RL …..(9)
= hie – (hfe.hre)/ (hoe+YL) …..(10)
Where YL = 1/RL
From Equation (10) we find that the input impedance Ri is also a
function of load resistance RL.

Voltage Gain or Voltage Amplification:
It is the ratio of the output voltage Vc to the input voltage Vb. Thus,
Voltage Gain Av = Vc/Vb = - Ic RL/Ib Ri = AI.RL/Ri …..(11)
Output Admittance Y0: It is the ratio of the output current Ic to the output
voltage Vc with Vs = 0. Hence Y0 = Ic/Vc with VS = 0 ……(12)
On substituting the value of Ic from Equation (2) into Equation (12) we get,
Y0 =( hfe .Ib)/Vc + hoe …..(13) But with Vs = 0, Figure 2 gives (Rs + hie) Ib + hre
Vc = 0 Or Ib/Vc = - hre /(hie+Rs) ……(14)
Combining Equation (13) and (14) we get, Y0 = hoe-(hfe hre)/ (hie+Rs) ……(15)
Equation (15) shows that the output admittance Y0 is a function of source
resistance Rs. It source impedance is purely resistive, then the output impedance
Y0 is real i.e. purely conductive. Output impedance R0 = 1/Y0 ..(16)
In the calculation of Y0, RL has been considered external to the amplifier. If we
include RL in parallel with R0, we get the output terminal impedance Zt given by,
Z = R0.RL/R0 + RL …..(17)

Overall Voltage Gain Considering Rs:
Source voltage Vs applied at the input of an amplifier results in voltage
Vb between bae and emitter terminals (input terminals) of the
transistor and voltage Vc at the output. Then the overall voltage gain
considering the source resistance is given by AVS = Vc/Vs =
(Vc/Vb).Vb/Vs = AV. Vb/Vs …(18)
Figure 3(a) given the driven voltage source Vs with source resistance Rs
in series. This form of equivalent circuit for the energy source known
as Thevenin’s equivalent source. This energy source then drives the
amplifier represented by its input resistance Ri.
Then Vb = (Vs.Ri)/(Ri+Rs) ……(19)
Hence overall voltage gain AVS = Av. Ri/(Ri + Rs) …..(20)
If Rs=0,then AVS=AV. Thus, AV forms a special care of AVS with Rs = 0.

Overall Current Gain Considering Rs:We may replace the voltage
source Vs with series source resistance Rs by what is known as the
Norton’s equivalent source shown in Figure 3(b), consisting of current
source Is with source resistance Rs in shunt. This current source drives
the amplifier resulting in Ib at the input terminals of the amplifier and
current IL through the load impedance. Then the overall current gain
AIs is given by: AIs = IL/Is = -IC/Ib.Ib/Is = AI.Ib/Is …(21)

From Figure 3(b), Ib = Is.Rs/Rs+Ri …..(22)
Hence overall current gain AIS = AI .Rs / Rs + Ri …..(23)
From Equations (20) and Equation (23) we get, AVS = AIS.Ri/Rs …(24)
Equation (24) is true provided that the voltage source Vs and the current source
Is have the same source resistance Rs.
Power Gain Ap:From the circuit of Figure 2, the average power delivered to the
load imprudence RL is given by:
PL = |VC||IC cos theta| ……..(25)
Where theta is the phase angle between VC and IL. ……(26)
If load impedance is purely resistive, then cos theta = 1 and Equation (26)
reduce to: PL = VC.IL = -VC.IC …..(27)
The input power at input port is, Pi = Vb.Ib …..(28)
The power gain AP is the ratio of power PL delivered to the load to the input
power at the input port. Thus,
AP = PL/Pi = -VC.IC/Vb.Ib} = AV. AI = AI^2.RL/Ri …..(29)

Table 1 gives the above derivations in tabular from. The
expression for AV, AVS and AIS do not involve h-parameters,
while expression for AI, Ri and Y0 involves the h-parameters.
These expressions may be used for CB and CC configurations
also, of course, on using corresponding h-parameters.
Table 1: Result of small single analysis of low frequency ce
amplifier
AI = -hfe/1+hoe.RL AV = AI^2.RL/Ri
Ri = hie + hre AI.RL AVS.(AVRi/Ri + Rs)
Y0 = hoe-hre hfe/hie+Rs =1/ Z0=1/R0 AIS = AI Rs/Ri + Rs

RC Coupling Amplifier:
The resistance-capacitance coupling is, in short termed as RC coupling. This is
the mostly used coupling technique in amplifiers.
Construction of a Two-stage RC Coupled Amplifier:
The constructional details of a two-stage RC coupled transistor amplifier circuit
are as follows. The two stage amplifier circuit has two transistors, connected in
CE configuration and a common power supply VCC is used. The potential divider
network R1 and R2 and the resistor Re form the biasing and stabilization
network. The emitter by-pass capacitor Ce offers a low reactance path to the
signal.The resistor RL is used as a load impedance. The input capacitor Cin
present at the initial stage of the amplifier couples AC signal to the base of the
transistor. The capacitor CC is the coupling capacitor that connects two stages
and prevents DC interference between the stages and controls the shift of
operating point. The figure below shows the circuit diagram of RC coupled
amplifier.

Operation of RC Coupled Amplifier
When an AC input signal is applied to the base of first transistor, it gets amplified
and appears at the collector load RL which is then passed through the coupling
capacitor CC to the next stage. This becomes the input of the next stage, whose
amplified output again appears across its collector load. Thus the signal is
amplified in stage by stage action.

The important point that has to be noted here is that the total gain is
less than the product of the gains of individual stages. This is because
when a second stage is made to follow the first stage, the effective
load resistance of the first stage is reduced due to the shunting effect
of the input resistance of the second stage. Hence, in a multistage
amplifier, only the gain of the last stage remains unchanged.
As we consider a two stage amplifier here, the output phase is same
as input. Because the phase reversal is done two times by the two
stage CE configured amplifier circuit.
Frequency Response of RC Coupled Amplifier
Frequency response curve is a graph that indicates the relationship
between voltage gain and function of frequency. The frequency
response of a RC coupled amplifier is as shown in the following graph.

From the above graph, it is understood that the frequency rolls off
or decreases for the frequencies below 50Hz and for the
frequencies above 20 KHz. whereas the voltage gain for the range of
frequencies between 50Hz and 20 KHz is constant. We know that,

XC=1/2πfc , It means that the capacitive reactance is inversely proportional to
the frequency.At Low frequencies (i.e. below 50 Hz)
The capacitive reactance is inversely proportional to the frequency. At low
frequencies, the reactance is quite high. The reactance of input capacitor Cin
and the coupling capacitor CC are so high that only small part of the input signal
is allowed. The reactance of the emitter by pass capacitor CE is also very high
during low frequencies. Hence it cannot shunt the emitter resistance effectively.
With all these factors, the voltage gain rolls off at low frequencies.
At High frequencies (i.e. above 20 KHz)
Again considering the same point, we know that the capacitive reactance is low
at high frequencies. So, a capacitor behaves as a short circuit, at high
frequencies. As a result of this, the loading effect of the next stage increases,
which reduces the voltage gain. Along with this, as the capacitance of emitter
diode decreases, it increases the base current of the transistor due to which the
current gain (β) reduces. Hence the voltage gain rolls off at high frequencies.

At low frequencies the RC Coupled Amplifier works as RC high pass
filter and the gain increases with frequency.At some lower input
Signal frequency , the magnitude of gain is 𝐴 =Amax/ [1 + (
𝑓𝐿
𝑓
)˄2.
At Lower Cut off frequency f=fL=1/2πRC , then A=Amax./ 2 Amax.=3
dB Lower cut off frequency point.
Similarly, at higher input signal frequencies , amplifier works as RC
low pass filter , magnitude of gain given by A=Amax. / [1 + (
𝑓
𝑓𝐻
)˄2 .
At higher cut off f=fH =1/2πRC , gain equals A=Amax./ 2=0.707Amax.
=3dB higher cut off frequency point. The difference fH - fL=BW . In
which gain remains constant.

At Mid-frequencies (i.e. 50 Hz to 20 KHz)
The voltage gain of the capacitors is maintained constant in this range
of frequencies, as shown in figure. If the frequency increases, the
reactance of the capacitor CC decreases which tends to increase the
gain. But this lower capacitance reactive increases the loading effect of
the next stage by which there is a reduction in gain.
Due to these two factors, the gain is maintained constant.
Advantages of RC Coupled Amplifier
The following are the advantages of RC coupled amplifier.
The frequency response of RC amplifier provides constant gain over a wide
frequency range, hence most suitable for audio applications.
The circuit is simple and has lower cost because it employs resistors and
capacitors which are cheap.
It becomes more compact with the upgrading technology.

Disadvantages of RC Coupled Amplifier
The following are the disadvantages of RC coupled amplifier.
The voltage and power gain are low because of the effective load
resistance.
They become noisy with age.
Due to poor impedance matching, power transfer will be low.
Applications of RC Coupled Amplifier
The following are the applications of RC coupled amplifier.
They have excellent audio fidelity over a wide range of frequency.
Widely used as Voltage amplifiers
Due to poor impedance matching, RC coupling is rarely used in the
final stages.

Power Amplifiers :
The Power amplifiers amplify the power level of the
signal. This amplification is done in the last stage in
audio applications. The applications related to radio
frequencies employ radio power amplifiers. But the
operating point of a transistor, plays a very important
role in determining the efficiency of the amplifier. The
main classification is done based on this mode of
operation.
The classification is done based on their frequencies
and also based on their mode of operation.

Classification Based on Mode of Operation: On the basis of the
mode of operation, i.e., the portion of the input cycle during which
collector current flows, the power amplifiers may be classified as
follows.
Class A Power amplifier − When the collector current flows at all
times during the full cycle of signal, the power amplifier is known as
class A power amplifier.
Class B Power amplifier − When the collector current flows only
during the positive half cycle of the input signal, the power amplifier
is known as class B power amplifier.
Class C Power amplifier − When the collector current flows for less
than half cycle of the input signal, the power amplifier is known as
class C power amplifier.

There forms another amplifier called Class AB amplifier, if we
combine the class A and class B amplifiers so as to utilize the
advantages of both.
Before going into the details of these amplifiers, let us have a
look at the important terms that have to be considered to
determine the efficiency of an amplifier.
Terms Considering Performance
The primary objective of a power amplifier is to obtain
maximum output power. In order to achieve this, the
important factors to be considered are collector efficiency,
power dissipation capability and distortion. Let us go through
them in detail.

Collector Efficiency : This explains how well an amplifier
converts DC power to AC power. When the DC supply is given
by the battery but no AC signal input is given, the collector
output at such a condition is observed as collector efficiency.
The collector efficiency η is defined as the ratio of average a.c
power output to average d.c power in put to transistor
For example, if the battery supplies 15W and AC output power
is 3W. Then the transistor efficiency will be 20%.
The main aim of a power amplifier is to obtain maximum
collector efficiency. Hence the higher the value of collector
efficiency, the efficient the amplifier will be.

Power Dissipation Capacity: Every transistor gets heated up during
its operation. As a power transistor handles large currents, it gets
more heated up. This heat increases the temperature of the
transistor, which alters the operating point of the transistor.
So, in order to maintain the operating point stability, the
temperature of the transistor has to be kept in permissible limits. For
this, the heat produced has to be dissipated. Such a capacity is called
as Power dissipation capability.
Power dissipation capability can be defined as the ability of a power
transistor to dissipate the heat developed in it. Metal cases called
heat sinks are used in order to dissipate the heat produced in power
transistors.

Distortion is defined as the change of output wave shape from the
input wave shape of the amplifier. An amplifier that has lesser
distortion, produces a better output and hence considered efficient.
A Class A power amplifier is one in which the output current flows for
the entire cycle of the AC input supply. Hence the complete signal
present at the input is amplified at the output.
The operating point of this amplifier is present in the linear region. It
is so selected that the current flows for the entire ac input cycle. The
below figure explains the selection of operating point.
The output characteristics with operating point Q is shown in the
figure above. Here (Ic)Q and (Vce)Q represent no signal collector
current and voltage between collector and emitter respectively.

Advantages of Class A Amplifiers
The advantages of Class A power amplifier are as follows −
The current flows for complete input cycle
It can amplify small signals
The output is same as input
No distortion is present
Disadvantages of Class A Amplifiers
The advantages of Class A power amplifier are as follows −
Low power output
Low collector efficiency

When the collector current flows only during the positive half
cycle of the input signal, the power amplifier is known as class
B power amplifier.
Class B Operation
The biasing of the transistor in class B operation is in such a
way that at zero signal condition, there will be no collector
current. The operating point is selected to be at collector cut
off voltage. So, when the signal is applied, only the positive
half cycle is amplified at the output.
The figure below shows the input and output waveforms
during class B operation.

When the signal is applied, the circuit is forward biased for the
positive half cycle of the input and hence the collector current flows.
But during the negative half cycle of the input, the circuit is reverse
biased and the collector current will be absent. Hence only the
positive half cycle is amplified at the output.
Advantages The advantages of Complementary symmetry push pull class B
amplifier are as follows. As there is no need of center tapped transformers, the
weight and cost are reduced. Equal and opposite input signal voltages are not
required.
Disadvantages The disadvantages of Complementary symmetry push pull class
B amplifier are as follows.
It is difficult to get a pair of transistors (NPN and PNP) that have similar
characteristics.
We require both positive and negative supply voltages.

class AB is a combination of class A and class B type of amplifiers. As
class A has the problem of low efficiency and class B has distortion
problem, this class AB is emerged to eliminate these two problems, by
utilizing the advantages of both the classes.

Class C Power Amplifier
When the collector current flows for less than half cycle of the
input signal, the power amplifier is known as class C power
amplifier.
The efficiency of class C amplifier is high while linearity is poor.
The conduction angle for class C is less than 180o. It is
generally around 90o, which means the transistor remains idle
for more than half of the input signal. So, the output current
will be delivered for less time compared to the application of
input signal.
The following figure shows the operating point and output of a
class C amplifier.

This kind of biasing gives a much improved efficiency of
around 80% to the amplifier, but introduces heavy
distortion in the output signal. Using the class C
amplifier, the pulses produced at its output can be
converted to complete sine wave of a particular
frequency by using LC circuits in its collector circuit.

Amplifiers -Feedback:
The noise level in the amplifier circuits can be
considerably reduced by using negative feedback done
by injecting a fraction of output in phase opposition to
the input signal.
Principle of Feedback Amplifier: A feedback amplifier
generally consists of two parts. They are the amplifier
and the feedback circuit. The feedback circuit usually
consists of resistors. The concept of feedback amplifier
can be understood from the following figure.

From the above figure, the gain of the amplifier is
represented as A. the gain of the amplifier is the ratio of
output voltage Vo to the input voltage Vi. the feedback
network extracts a voltage Vf = β Vo from the output Vo of
the amplifier.

This voltage is added for positive feedback and subtracted for negative feedback,
from the signal voltage Vs. Now,
Vi= Vs+Vf=Vs+βVo i.e : Vi=Vs−Vf= Vs−βVo
The quantity β = Vf/Vo is called as feedback ratio or feedback fraction.
Let us consider the case of negative feedback. The output Vo must be equal to
the input voltage (Vs - βVo) multiplied by the gain A of the amplifier. Hence,
(Vs−βVo)A=Vo Or AVs−AβVo=Vo Or AVs=Vo(1+Aβ) Therefore, Vo/Vs=A/1+Aβ
Let Af be the overall gain (gain with the feedback) of the amplifier. This is defined
as the ratio of output voltage Vo to the applied signal voltage Vs, i.e., Af=Output
voltage/ Input signal voltage=Vo/Vs So, from the above two equations, we can
understand that,The equation of gain of the feedback amplifier, with negative
feedback is given by Af=A/1+Aβ
The equation of gain of the feedback amplifier, with positive feedback is given by
Af=A/1−Aβ
These are the standard equations to calculate the gain of feedback amplifiers.

Types of Feedbacks :The process of injecting a fraction of output energy of some
device back to the input is known as Feedback. It has been found that feedback
is very useful in reducing noise and making the amplifier operation stable.
Depending upon whether the feedback signal aids or opposes the input signal,
there are two types of feedbacks used.
Positive Feedback :The feedback in which the feedback energy i.e., either
voltage or current is in phase with the input signal and thus aids it is called as
Positive feedback.Both the input signal and feedback signal introduces a phase
shift of 180o thus making a 360o resultant phase shift around the loop, to be
finally in phase with the input signal.Though the positive feedback increases the
gain of the amplifier, it has the disadvantages such as Increasing distortion ,
Instability .It is because of these disadvantages the positive feedback is not
recommended for the amplifiers. If the positive feedback is sufficiently large, it
leads to oscillations, by which oscillator circuits are formed. This concept will be
discussed in OSCILLATORS tutorial.

Negative Feedback : The feedback in which the feedback energy i.e., either
voltage or current is out of phase with the input and thus opposes it, is called as
negative feedback. In negative feedback, the amplifier introduces a phase shift
of 180o into the circuit while the feedback network is so designed that it
produces no phase shift or zero phase shift. Thus the resultant feedback voltage
Vf is 180o out of phase with the input signal Vin.Though the gain of negative
feedback amplifier is reduced, there are many advantages of negative feedback
such as Stability of gain is improved,
Reduction in distortion
Reduction in noise
Increase in input impedance
Decrease in output impedance
Increase in the range of uniform application
It is because of these advantages negative feedback is frequently employed in
amplifiers.

Amplifiers Negative Feedback :
There are two main types of negative feedback circuits. They are −Negative
Voltage Feedback , Negative Current Feedback
Negative Voltage Feedback : In this method, the voltage feedback to the input of
amplifier is proportional to the output voltage. This is further classified into two
types − Voltage-series feedback , Voltage-shunt feedback
Negative Current Feedback : In this method, the voltage feedback to the input
of amplifier is proportional to the output current. This is further classified into
two types. Current-series feedback , Current-shunt feedback
Let us have a brief idea on all of them.
Voltage-Series Feedback : In the voltage series feedback circuit, a fraction of the
output voltage is applied in series with the input voltage through the feedback
circuit. This is also known as shunt-driven series-fed feedback, i.e., a parallel-
series circuit.The following figure shows the block diagram of voltage series
feedback, by which it is evident that the feedback circuit is placed in shunt with
the output but in series with the input.

As the feedback circuit is connected in shunt with the output, the
output impedance is decreased and due to the series connection with
the input, the input impedance is increased.

Voltage-Shunt Feedback : In the voltage shunt feedback
circuit, a fraction of the output voltage is applied in parallel
with the input voltage through the feedback network. This is
also known as shunt-driven shunt-fed feedback i.e., a parallel-
parallel proto type. The below figure shows the block diagram
of voltage shunt feedback, by which it is evident that the
feedback circuit is placed in shunt with the output and also
with the input.

As the feedback circuit is connected in shunt with the output and the input as
well, both the output impedance and the input impedance are decreased.
Current-Series Feedback
In the current series feedback circuit, a fraction of the output voltage is applied
in series with the input voltage through the feedback circuit. This is also known
as series-driven series-fed feedback i.e., a series-series circuit.
The following figure shows the block diagram of current series feedback, by
which it is evident that the feedback circuit is placed in series with the output
and also with the input.

As the feedback circuit is connected in series with the output and the input as
well, both the output impedance and the input impedance are increased.
Current-Shunt Feedback
In the current shunt feedback circuit, a fraction of the output voltage is applied
in series with the input voltage through the feedback circuit. This is also known
as series-driven shunt-fed feedback i.e., a series-parallel circuit.
The below figure shows the block diagram of current shunt feedback, by which
it is evident that the feedback circuit is placed in series with the output but in
parallel with the input.

As the feedback circuit is connected in series with the output, the
output impedance is increased and due to the parallel connection
with the input, the input impedance is decreased.
Let us now tabulate the amplifier characteristics that get affected by
different types of negative feedbacks.
CharacteristicsTypes of Feedback
Voltage-Series Voltage-Shunt Current-Series Current-Shunt
Voltage Gain Decreases Decreases Decreases Decreases
Bandwidth Increases Increases Increases Increases
Input resistance Increases Decreases Increases Decreases
Output resistance Decreases Decreases Increases Increases
Harmonic distortion Decreases Decreases Decreases Decreases
Noise Decreases Decreases Decreases Decreases

Advantages and disadvantages of negative feedback amplifier
The negative feedback reduces noise.
It has highly stabilized gain.
It can control step response of amplifier.
It has less harmonic distortion.
It has less amplitude distortion.
It has less phase distortion.
Input and output impedances can be modified as desired.
It can increase or decrease output impedances.
The disadvantage is poor performance in higher frequency. The feedback force
the output to follow the input but there is delay between all the stages of the
amplifier. This delay impose a limit on the frequency. The worst case is a
frequency where half a wave is equal to the delay.

Advantages of Positive Feedback: i) Voltage gain
increases. ii) No phase shift is provided. iii) Feedback
signal and input signal are in phase. iv) Input and
Output voltage increases.
Disadvantages of Positive Feedback: i) Stability
becomes poor as feedback increases. ii) Noise increases
with feedback. iii) Bandwidth decreases. iv) Input
impedance decreases.

Emitter Follower: Emitter follower circuit has a prominent place in feedback
amplifiers. Emitter follower is a case of negative current feedback circuit. This is
mostly used as a last stage amplifier in signal generator circuits.
The important features of Emitter Follower are −It has high input impedance
It has low output impedance , It is ideal circuit for impedance matching
All these ideal features allow many applications for the emitter follower circuit.
This is a current amplifier circuit that has no voltage gain.
Construction : The constructional details of an emitter follower circuit are
nearly similar to a normal amplifier. The main difference is that the load RL is
absent at the collector terminal, but present at the emitter terminal of the
circuit. Thus the output is taken from the emitter terminal instead of collector
terminal.
The biasing is provided either by base resistor method or by potential divider
method. The following figure shows the circuit diagram of an Emitter Follower.

Operation : The input signal voltage applied between base and emitter,
develops an output voltage Vo across RE, which is in the emitter section.
Therefore,
Vo=IERE The whole of this output current is applied to the input through
feedback. Hence, Vf=Vo
As the output voltage developed across RL is proportional to the emitter
current, this emitter follower circuit is a current feedback circuit. Hence,
β=Vf /Vo=1
It is also noted that the input signal voltage to the transistor (= Vi) is equal to
the difference of Vs and Vo i.e.,
Vi=Vs−Vo Hence the feedback is negative.
Characteristics :The major characteristics of the emitter follower are as follows
No voltage gain. In fact, the voltage gain is nearly 1.
Relatively high current gain and power gain.High input impedance and low
output impedance. Input and output ac voltages are in phase.

Voltage Gain of Emitter Follower
As the Emitter Follower circuit is a prominent one, let us try to get the
equation for the voltage gain of an emitter follower circuit. Our Emitter
Follower circuit looks as follows −

If an AC equivalent circuit of the above circuit is drawn, it would look
like the below one, as the emitter by pass capacitor is absent.

The AC resistance rE of the emitter circuit is given by rE=r′E+RE
Where r′E=25mV / IE
In order to find the voltage gain of the amplifier, the above figure can
be replaced by the following figure.

Note that input voltage is applied across the ac resistance of
the emitter circuit i.e., (r’E + RE). Assuming the emitter diode
to be ideal, the output voltage Vout will be Vout=ieRE Input
voltage Vin will be Vin=ie(r′e+RE)
Therefore, the Voltage Gain of emitter follower is
AV=VoutVin=ieREie(r′e+RE)=RE(r′e+RE) Or AV=RE(r′e+RE)
In most practical applications, RE≫r′e
So, AV ≈ 1. In practice, the voltage gain of an emitter follower
is between 0.8 and 0.999.

Sinusoidal Oscillators:
An oscillator is an electronic circuit that produces a periodic signal. If
the oscillator produces sinusoidal oscillations, it is called as a
sinusoidal oscillator. It converts the input energy from a DC source
into an AC output energy of a periodic signal. This periodic signal will
be having a specific frequency and amplitude.
The block diagram of a sinusoidal oscillator is shown in the following
figure −`

The above figure mainly consists of two blocks: an amplifier and a
feedback network.The feedback network takes a part of the output of
amplifier as an input to it and produces a voltage signal. This voltage
signal is applied as an input to the amplifier.
The block diagram of a sinusoidal oscillator shown above produces
sinusoidal oscillations, when the following two conditions are
satisfied −
The loop gain Avβ of the above block diagram of sinusoidal oscillator
must be greater than or equal to unity. Here, Av and β are the gain of
amplifier and gain of the feedback network, respectively.
The total phase shift around the loop of the above block diagram of a
sinusoidal oscillator must be either 00 or 3600.
The above two conditions together are called as Barkhausen criteria.

Oscillators Theory: The main statement of the oscillator is that the
oscillation is achieved through positive feedback which generates the
output signal without input signal. Also, the voltage gain of the
amplifier increases with the increase in the amount of positive
feedback.In order to understand this concept, let us consider a non-
inverting amplifier with a voltage gain ‘A’ and a positive feedback
network with feedback gain of β as shown in figure.

Let us assume that a sinusoidal input signal Vs is applied at the
input. Since the amplifier is non-inverting, the output signal Vo
is in phase with Vs. A feedback network feeds the part of Vo to
the input and the amount Vo fed back depends on the
feedback network gain β.
No phase shift is introduced by this feedback network and
hence the feedback voltage or signal Vf is in phase with Vs. A
feedback is said to be positive when the phase of the feedback
signal is same as that of the input signal.
The open loop gain ‘A’ of the amplifier is the ratio of output
voltage to the input voltage, i.e.,

A = Vo/Vi By considering the effect of feedback, the ratio of net output voltage
Vo and input supply Vs called as a closed loop gain Af (gain with feedback).
Af = Vo/Vs
Since the feedback is positive, the input to the amplifier is generated by adding
Vf to the Vs,
Vi = Vs + Vf
Depends on the feedback gain β, the value of the feedback voltage is varied,
i.e., Vf = β Vo
Substituting in the above equation, Vi = Vs + β Vo i.e. Vs = Vi – β Vo
Then the gain becomes Af = Vo/ (Vi – β Vo)
By dividing both numerator and denominator by Vi, we get
Af = (Vo / Vi)/ (1 – β) (Vo / Vi)
Af = A/ (1- A β) since A = Vo/Vi

Where Aβ is the loop gain and if Aβ = 1, then Af becomes infinity. From the above
expression, it is clear that even without external input (Vs = 0), the circuit can
generate the output just by feeding a part of the output as its own input.
And also closed loop gain increases with increase in amount of positive feedback
gain. The oscillation rate or frequency depends on amplifier or feedback network
or both.
Barkhausen Criterion or Conditions for Oscillation
The circuit will oscillate when two conditions, called as Barkhausen’s criteria are
met. These two conditions are 1. The loop gain must be unity or greater
2. The feedback signal feeding back at the input must be phase shifted by 360
degrees (which is same as zero degrees). In most of the circuits, an inverting
amplifier is used to produce 180 degrees phase shift and additional 180 degrees
phase shift is provided by the feedback network.
At only one particular frequency, a tuned inductor-capacitor (LC circuit) circuit
provides this 180 degrees phase shift.

Let us know how these conditions can be achieved. Consider the same circuit
which we have taken in oscillator theory. The amplifier is a basic inverting
amplifier and it produces a phase shift of 180 degrees between input and
output.The input to be applied to the amplifier is derived from the output Vo by
the feedback network. Since the output is out of phase with Vi.
So the feedback network must ensure a phase shift of 180 degrees while feeding
the output to the input. This is nothing but ensuring positive feedback.

Let us consider that a fictitious voltage, Vi is applied at the input of
amplifier, then
Vo = A Vi
The amount of feedback voltage is decided by the feedback network
gain, then
Vf = – β Vo
This negative sign indicates 180 degrees phase shift.
Substituting Vo in above equation, we get
Vf = – A β Vi
In oscillator, the feedback output must drive the amplifier, hence Vf
must act as Vi. For achieving this term – A β in the above expression
should be 1, i.e., Vf = Vs when – A β = 1.
This condition is called as Barkhausen criterion for oscillation.

Therefore, A β = -1 + j0. This means that the magnitude of A
β (modulus of A β) is equal to 1. In addition to the
magnitude, the phase of the Vs must be same as Vi. In order
to perform this, feedback network should introduce a phase
shift of 180 degrees in addition to phase shift (180 degrees)
introduced by the amplifier. So the total phase shift around
the loop is 360 degrees. Thus, under these conditions the
oscillator can oscillate or produce the waveform without
applying any input (that’s why we have considered as
fictitious voltage).
It is important to know that how the oscillator starts to
oscillate even without input signal in practice?

The oscillator starts generating oscillations by amplifying the
noise voltage which is always present. This noise voltage is
result of the movement of free electrons under the influence
of room temperature.
This noise voltage is not exactly in sinusoidal due to
saturation conditions of practical circuit. However, this nose
signal will be sinusoidal when A β value is close to one.
In practice modulus of A β is made greater than 1 initially, to
amplify the small noise voltage. Later the circuit itself adjust
to get modulus of A β is equal to one and with a phase shift
of 360 degrees.

Sustained Oscillations
Sustained oscillations are nothing but oscillations which oscillate with
constant amplitude and frequency. Based on the Barkhausen criterion
sustained oscillations are produced when the magnitude of loop gain
or modulus of A β is equal to one and total phase shift around the loop
is 0 degrees or 360 ensuring positive feedback.

Growing Type of Oscillations
If modulus of A β or the magnitude of loop gain is greater than unity
and total phase shift around the loop is 0 or 360 degrees, then the
oscillations produced by the oscillator are of growing type. The below
figure shows the oscillator output with increasing amplitude of
oscillations.

Exponentially Decaying Oscillations: If modulus of A β or the
magnitude of loop gain is less than unity and total phase shift around
the loop is 0 or 360 degrees, then the amplitude of the oscillations
decreases exponentially and finally these oscillations will cease.

Classification of oscillators
The oscillators are classified into several types based
on various factors like nature of waveform, range of
frequency, the parameters used, etc. The following is
a broad classification of oscillators.
1.Phase shift oscillator
2.Wein bridge oscillator
3.Colpitts oscillator

Phase Shift Oscillators: One of the important features of an
oscillator is that the feedback energy applied should be in
correct phase to the tank circuit. The oscillator circuits
discussed so far has employed inductor (L) and capacitor (C)
combination, in the tank circuit or frequency determining
circuit.
We have observed that the LC combination in oscillators
provide 180o phase shift and transistor in CE configuration
provide 180° phase shift to make a total of 360o phase shift
so that it would make a zero difference in phase.
Drawbacks of LC circuits

Though they have few applications, the LC circuits have few
drawbacks such as
Frequency instability
Waveform is poor
Cannot be used for low frequencies
Inductors are bulky and expensive
We have another type of oscillator circuits, which are made by
replacing the inductors with resistors. By doing so, the
frequency stability is improved and a good quality waveform
is obtained. These oscillators can also produce lower
frequencies. As well, the circuit becomes neither bulky nor
expensive.

All the drawbacks of LC oscillator circuits are thus
eliminated in RC oscillator circuits. Hence the need for RC
oscillator circuits arise. These are also called as Phase–shift
Oscillators.
Principle of Phase-shift oscillators:
We know that the output voltage of an RC circuit for a
sinewave input leads the input voltage. The phase angle by
which it leads is determined by the value of RC components
used in the circuit. The following circuit diagram shows a
single section of an RC network

The output voltage V1’ across the resistor R leads the input voltage
applied input V1 by some phase angle ɸo. If R were reduced to zero,
V1’ will lead the V1 by 90o i.e., ɸo = 90o.
However, adjusting R to zero would be impracticable, because it would
lead to no voltage across R. Therefore, in practice, R is varied to such a
value that makes V1’ to lead V1 by 60o. The following circuit diagram
shows the three sections of the RC network.

Each section produces a phase shift of 60o. Consequently, a total
phase shift of 180o is produced, i.e., voltage V2 leads the voltage V1
by 180o.
Phase-shift Oscillator Circuit
The oscillator circuit that produces a sine wave using a phase-shift
network is called as a Phase-shift oscillator circuit. The constructional
details and operation of a phase-shift oscillator circuit are as given
below.

Construction: The phase-shift oscillator circuit consists of a single
transistor amplifier section and a RC phase-shift network. The phase
shift network in this circuit, consists of three RC sections. At the
resonant frequency fo, the phase shift in each RC section is 60o so
that the total phase shift produced by RC network is 180o.
The following circuit diagram mentioned below shows the
arrangement of an RC phase-shift oscillator.
The frequency of oscillations is given by
Fo =1/(2πRC√6)
Where
R1=R2=R3=R
C1=C2=C3=C

Operation
The circuit when switched ON oscillates at the resonant frequency fo.
The output Eo of the amplifier is fed back to RC feedback network.
This network produces a phase shift of 180o and a voltage Ei appears
at its output. This voltage is applied to the transistor amplifier.
The feedback applied will be
m=Ei/Eo
The feedback is in correct phase, whereas the transistor amplifier,
which is in CE configuration, produces a 180o phase shift. The phase
shift produced by network and the transistor add to form a phase
shift around the entire loop which is 360o.
Advantages
The advantages of RC phase shift oscillator are as follows −

Advantages
The advantages of RC phase shift oscillator are as follows −
It does not require transformers or inductors.
It can be used to produce very low frequencies.
The circuit provides good frequency stability.
Disadvantages
The disadvantages of RC phase shift oscillator are as follows −
Starting the oscillations is difficult as the feedback is small.
The output produced is small.

Wien Bridge Oscillator
Another type of popular audio frequency oscillator is the Wien
bridge oscillator circuit. This is mostly used because of its important
features. This circuit is free from the circuit fluctuations and the
ambient temperature.
The main advantage of this oscillator is that the frequency can be
varied in the range of 10Hz to about 1MHz whereas in RC oscillators,
the frequency is not varied
Construction: The circuit construction of Wien bridge oscillator can
be explained as below. It is a two-stage amplifier with RC bridge
circuit. The bridge circuit has the arms R1C1, R3, R2C2 and the
tungsten lamp Lp. Resistance R3 and the lamp Lp are used to
stabilize the amplitude of the output.

The following circuit diagram shows the arrangement of a Wien bridge
oscillator.

The transistor T1 serves as an oscillator and an amplifier
while the other transistor T2 serves as an inverter. The
inverter operation provides a phase shift of 180o. This circuit
provides positive feedback through R1C1, C2R2 to the
transistor T1 and negative feedback through the voltage
divider to the input of transistor T2.
The frequency of oscillations is determined by the series
element R1C1 and parallel element R2C2 of the bridge.
f=1/2π√(R1C1R2C2)
If R1 = R2 and C1 = C2 = C
Then, f=1/2πRC

Now, we can simplify the above circuit as follows −

The oscillator consists of two stages of RC coupled amplifier
and a feedback network. The voltage across the parallel
combination of R and C is fed to the input of amplifier 1. The
net phase shift through the two amplifiers is zero.
The usual idea of connecting the output of amplifier 2 to
amplifier 1 to provide signal regeneration for oscillator is not
applicable here as the amplifier 1 will amplify signals over a
wide range of frequencies and hence direct coupling would
result in poor frequency stability. By adding Wien bridge
feedback network, the oscillator becomes sensitive to a
particular frequency and hence frequency stability is
achieved.

Operation: When the circuit is switched ON, the bridge circuit
produces oscillations of the frequency stated above. The two
transistors produce a total phase shift of 360o so that proper
positive feedback is ensured. The negative feedback in the
circuit ensures constant output. This is achieved by
temperature sensitive tungsten lamp Lp. Its resistance
increases with current. If the amplitude of the output
increases, more current is produced and more negative
feedback is achieved. Due to this, the output would return to
the original value. Whereas, if the output tends to decrease,
reverse action would take place.

Advantages: The advantages of Wien bridge oscillator are as follows
The circuit provides good frequency stability.
It provides constant output.
The operation of circuit is quite easy.
The overall gain is high because of two transistors.
The frequency of oscillations can be changed easily.
The amplitude stability of the output voltage can be maintained
more accurately, by replacing R2 with a thermistor.
Disadvantages:
The disadvantages of Wien bridge oscillator are as follows −
The circuit cannot generate very high frequencies.
Two transistors and number of components are required for the
circuit construction.

Colpitts Oscillator
A Colpitts oscillator looks just like the Hartley oscillator
but the inductors and capacitors are replaced with each
other in the tank circuit. The constructional details and
operation of a colpitts oscillator are as discussed below.
Construction:
Let us first take a look at the circuit diagram of a Colpitts
oscillator.

The resistors R1, R2 and Re provide necessary bias condition for
the circuit. The capacitor Ce provides a.c. ground thereby
providing any signal degeneration. This also provides
temperature stabilization.
The capacitors Cc and Cb are employed to block d.c. and to
provide an a.c. path. The radio frequency choke (R.F.C) offers
very high impedance to high frequency currents which means it
shorts for d.c. and opens for a.c. Hence it provides d.c. load for
collector and keeps a.c. currents out of d.c. supply source.
Tank Circuit: The frequency determining network is a parallel
resonant circuit which consists of variable capacitors C1 and C2
along with an inductor L. The junction of C1 and C2 are earthed.

The capacitor C1 has its one end connected to base via Cc and
the other to emitter via Ce. the voltage developed across C1
provides the regenerative feedback required for the sustained
oscillations.
Operation: When the collector supply is given, a transient
current is produced in the oscillatory or tank circuit. The
oscillatory current in the tank circuit produces a.c. voltage
across C1 which are applied to the base emitter junction and
appear in the amplified form in the collector circuit and
supply losses to the tank circuit.

If terminal 1 is at positive potential with respect to terminal
3 at any instant, then terminal 2 will be at negative potential
with respect to 3 at that instant because terminal 3 is
grounded. Therefore, points 1 and 2 are out of phase by
180o.
As the CE configured transistor provides 180o phase shift, it
makes 360o phase shift between the input and output
voltages. Hence, feedback is properly phased to produce
continuous Undamped oscillations. When the loop gain |βA|
of the amplifier is greater than one, oscillations are
sustained in the circuit.

Frequency
The equation for frequency of Colpitts oscillator is given as
f=1/2π 𝐿. 𝐶𝑇
CT is the total capacitance of C1 and C2 connected in series.
1/CT=(1/C1)+(1/C2)
CT=(C1.C2)/(C1+C2)
Advantages: The advantages of Colpitts oscillator are as
follows − Colpitts oscillator can generate sinusoidal signals of
very high frequencies.
It can withstand high and low temperatures.
The frequency stability is high.

Frequency can be varied by using both the variable
capacitors.
Less number of components are sufficient.
The amplitude of the output remains constant over a
fixed frequency range.
The Colpitts oscillator is designed to eliminate the
disadvantages of Hartley oscillator and is known to
have no specific disadvantages. Hence there are many
applications of a colpitts oscillator.

Applications
The applications of Colpitts oscillator are as follows −
Colpitts oscillator can be used as High frequency
sinewave generator.
This can be used as a temperature sensor with some
associated circuitry.
Mostly used as a local oscillator in radio receivers.
It is also used as R.F. Oscillator.
It is also used in Mobile applications.
It has got many other commercial applications.

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