Amplifiers Study Notes for Electrical Engineering

By Yash Bansal|Updated : August 5th, 2021

In this article, you will find the Study Notes on Amplifiers which will cover the topics such as Introduction, Amplifier Parameters,  Comparison between three configurations,  Multistage Amplifier, Feedback Amplifier and Circuits, Operational Amplifier and Circuits

In this article, you will find the Study Notes on Amplifiers which will cover the topics such as Introduction, Amplifier Parameters,  Comparison between three configurations,  Multistage Amplifier, Feedback Amplifier and Circuits, Operational Amplifier and Circuits

1. Introduction

  • An amplifier is used to increase the amplitude of a signal waveform, without changing other parameters of the waveform such as frequency or wave shape. 
  • There are many forms of electronic circuits classed as amplifiers, from Operational Amplifiers and Small Signal Amplifiers up to Large Signal and Power Amplifiers.
  • The classification of an amplifier depends on the size of the signal, large or small, its physical configuration and how it processes the input signal that is the relationship between input signal and the current flowing in the load.

An amplifier is an electronic circuit designed by using an active device like bipolar junction transistor (BJT), field effect transistor (FET), that changes, usually increases the amplitude of the input signal (usually voltage or current). The relationship between the input and the output signals of an amplifier is expressed as a function of input frequency, commonly known as transfer function of amplifier.

Based upon the value of signal variation, amplifier can be classified in two types

(i) Small signal Amplifier

(ii) Large signal Amplifier

1.1.  Small Signal Amplifier

In the AC signal, signal variation and peak change value is maximum with respect to DC value. Small signal Amplifier is defined as an amplifier in which signal variation is much smaller than the DC value.

From the characteristic curve of BJT, it can be seen that BJT is a nonlinear device. But in small signal amplifier BJT exhibits piece wise linearly or it simply behave as a linear element, that’s way small signal amplifier output signal will be distortion less. Small signal amplifier is used as voltage amplifier.

1.2.  Large signal Amplifier

In the ac amplifier in which signal variation is large or signal variation is comparable to dc value is known as large signal amplifier. Transistor behave as nonlinear element, in large signal amplifier due to which equal changes in base current do not produce proportional equal changes in collector current and output signal gets distorted. A large signal amplifier has large ac output current and voltage, and also it can supply greater ac output power to the load hence it is useful as power amplifier.

2. Amplifier Parameters

  • Gain (A):
    • It is a measure of the "Amplification" of an amplifier, i.e. how much it increases the amplitude of a signal.
    • It is the ratio of the output signal amplitude to the input signal amplitude.
    • Voltage gain = Amplitude of output voltage / Amplitude of input voltage.
    • Current gain = Amplitude of output current / Amplitude of input current.
    • Power gain = Signal power out / Signal power in.
  • Bandwidth:
    • An important piece of information that can be obtained from a frequency response curve is the Bandwidth of the amplifier.
    • This refers to the ‘band’ of frequencies for which the amplifier has a useful gain.
    • Outside this useful band, the gain of the amplifier is considered to be insufficient compared with the gain at the centre of the bandwidth.
    • Bandwidth specified for voltage amplifiers is the range of frequencies for which the amplifier’s gain is greater than 0.707 of the maximum gain. Alternatively, decibels are used to indicate the gain, the ratio of output to the input voltage.
  • Input Impedance:
    • The word impedance means opposition to AC current flow.
    • At 0 Hz, (that is, DC) impedance (symbol Z) is the same as resistance (R), but at frequencies other than 0Hz impedance and resistance are not the same.
    • The input impedance of an amplifier is the effective impedance between the input terminals.
    • Input Impedance is influenced by a number of factors including the frequency of the applied signal, the gain of the amplifier, any signal feedback used and even what is connected to the output of the amplifier.
  • Output Impedance:
    • It is not solely dependent on the actual components connected to the output of an amplifier.
    • It is an ‘apparent’ impedance and can best be demonstrated as being responsible for a fall in signal voltage at the output terminals of an amplifier when a current is drawn from the output terminals.
    • The more current drawn from the output terminals, the greater the reduction in output signal voltage.
    • The effect is that of an impedance or resistance in series with the output terminals.


3. Comparison between Three Transistor Configurations


4. Small-Signal variations

Consider the BJT circuit shown in figure 1. Various small signal parameters for the circuit is described below.

4.1 Collector Current and the transconductance

If a signal vbe is applied as shown in Figure 1, The total instantaneous base-emitter voltage vBE becomes

vBE = VBE + vbe

Instantaneous collector current becomes

Thus, the instantaneous collector current is composed of the dc bias value IC and a signal component iC. So, signal current in the collector is:

4.2.  Base Current and input Resistance at the Base

To determine the resistance seen by vbe, first evaluate the total base current iB using equation (V) as follows

The small signal input resistance between base and emitter, looking into the base, is denoted by rπ and is defined as

4.3.  Emitter Current and the input Resistance at the Emitter

Total Emitter current iE can be determined from equation (V) as

So, we have the signal current,

If we denote the small signal resistance between base and emitter, looking into the emitter, by re, it can be defined as


5. Small Signal Hybrid - Π Equivalent Circuit of BJT:

A bipolar junction transistor can be treated as a two-port network as shown in figure 2. Small time-varying signals is superimposed at Q-point. Since the sinusoidal signals are small, the slope at Q-point is treated as constant, which has the units of conductance. The inverse of this conductance is the small-signal resistance defined as rπ. The small-signal input base current is related to the small-signal input voltage by

vbe = ib rπ

where 1/rπ is equal to the slope of the iB – vBE curve. rπ can be found as given below,

(Note: The resistance rπ is called diffusion resistance or base-emitter input resistance. rπ is a function of Q-point parameters.)

While considering the output characteristics of bipolar transistor. Initially consider the case in which the output collector current is independent of the collector-emitter voltage, then the collector current is a function only of the base-emitter voltage. Then it can be written as,

Then term IS exp (VBE/VT) evaluated at Q-point is just the quiescent collector current. The term ICQ/VT is conductance. Since this conductance relates a current in the collector to a voltage in the B-E circuit, the parameter is called transconductance and is written as


Using these new parameters, a new simplified small-signal hybrid-π equivalent circuit can be developed for npn transistor, as shown in Figure 3(a).

The small-signal collector current is related to the small-signal base current as

and is called an incremental or ac common-emitter current gain.

It can be written as,

The small-signal equivalent circuit of bipolar transistor in Figure 3(b) uses this parameter.

Note: If rπ and gm is multiplied, then

6. Methodology to Analyse a BJT Amplifier:

In linear amplifier circuits, superposition theorem is applicable, means the ac and dc analysis can be performed separately. The analysis of the BJT amplifier proceeds as follow:

Step 1: Determine the dc operating point of the BJT and in particular the dc collector current Ic.

Step 2: Calculate the values of the small signal model parameter,

Step 3: Eliminate the dc sources by replacing each dc current source with an open circuit.

Step 4: Replace the BJT with one of its small signal equivalent circuit models. Although any one of the models can be used, one might be more convenient than the other for the particular circuit being analysed.

Step 5: Analyse the resulting circuit to determine the required quantities (eg. Voltage gain, input resistance etc.).


7. Basic Transistor Amplifier Configurations:

As it is already discussed, the bipolar transistor is a three-terminal device, so three basic single-transistor amplifier configurations can be formed, depending on which of the three transistor terminals is used as signal ground. These three basic configurations are appropriately called common emitter, common collector (emitter-follower) and common base. Which configuration or amplifier is used in any particular application depends on whether the input signal is voltage or current and whether the desired output signal is voltage or current. The characteristics of these three types of amplifiers will be determined to show the conditions under which each amplifier is most useful. Each of the three basic transistor amplifiers can be modelled as a two-port network in one of four configurations as shown Table 1.


8. Frequency Response of Common Emitter Amplifier: 

In common emitter amplifier circuit of figure 4(a) , it was assumed that the coupling capacitors Cc1 and Cc2 and the bypass capacitor CE were acting as perfect short circuits at the signal frequencies of interest, also there is neglected the internal capacitances of the BJT that is, Cπ and Cμ of the BJT high frequency model. It was assumed to be sufficiently small to act as open circuit at all signal frequency of interest. So, it is observed that the gain is almost constant over a wide frequency band, called the mid-band.

Figure 4(b) shows that the gain fall off at signal frequencies below and above the mid-band. The gain fall-off in the low frequency band is due to the fact that even though CC1, CC2 and CE are large capacitance, as the signal frequency is reduced their impedance increase and they no longer behave as short circuit. On the other hand, the gain falloff in the high frequency band as result of Cgs and Cgd, which though very small, their impedance at sufficiently high frequency decrease, thus they can no longer be considered as open circuits.

8.1 Cut-off Frequency

For a given circuit with equivalent resistance (Req) and equivalent capacitance (Ceq), the 3-dB cut-off frequency is given by

Thus, we calculate 3 dB frequencies due to CC1, CC2, CE as below.

  • The effect of CC1 is determined with CE and CC2 assumed to be acting as perfect short circuit as shown in figure 5(a). So,

9.Multistage Amplifier:

For most systems, a single transistor amplifier does not provide sufficient gain or bandwidth or will not have correct input or output impedance matching. The solution is to combine multiple stages of amplifiers.

In multistage amplifier, the output of first stage is fed as input to next stage as shown in figure 1. Such a connection is commonly referred as “Cascading”.

                                    Figure 6

Therefore, overall gain is the product of voltage gain of individual stages.


          AV = overall gain

          AV1 = voltage gain of 1st stage

          AV2 = voltage gain of 2nd stage


If there are ‘n’ number of stages, the product of voltage gains of those ‘n’ stages will be the overall gain of that multistage amplifier circuit.

10.Effect of Cascading on Bandwidth:

10.1.Identical Stages:

The lower cutoff frequency for the multi stage amplifier is given by :

and the upper cutoff frequency for multi-stage amplifier is given by:


n = no. of stages

Thus, bandwidth of multi-stage amplifier is

10.2.Non Identical Stages:

Here for every gain, separate bandwidth is present.

        Figure 2: Cascading of non identical stages

11.Types of Coupling and Comparison:

In a multistage amplifier the output of one stage makes the input of the next stage. Normally a network is used between two stages so that a minimum loss of voltage occurs when the signal passes through this network to the next stage. Also, the dc voltage at the output of one stage should not be permitted to go to the input of the next. Otherwise, the biasing of the next stage is disturbed.

The three couplings generally used are

i. RC coupling

ii. Transformer coupling

iii. direct coupling


R-C coupling



Direct Coupling

Frequency Response

Excellent in audio frequency range







Space & Weight




Impedance Matching

Not good




Voltage amplification

Power amplification

amplifying extremely low frequency


12.Popular Cascading Design:

12.1.Cascade Amplifier: (CE – CB configuration):

The cascade amplifier is combination of common-emitter and common-base amplifier. While the C-B amplifier is known for wider bandwidth than the C-E configuration, the low input impedance (10s of Ω) of C-B is a limitation for many applications. The solution is to precede the C-B stage by a low gain C-E stage which has moderately high input impedance (kΩs).

                                                 Figure 8

The key to understanding the wide bandwidth of the cascode configuration is the Miller effect.

 A common-base configuration is not subject to the Miller effect because the grounded base shields the collector signal from being fed back to the emitter input. Thus, a C-B amplifier has better high frequency response.

The way to reduce the common-emitter gain is to reduce the load resistance. The gain of a C-E amplifier is approximately RC/re. The collector load RC is the resistance of the emitter of the C-B stage loading the C-E state. CE gain amplifier gain is approximately Av = RC/re = 1. This Miller capacitance is Cmiller = Ccbo (1 – Av) = Ccbo (1 – (–1) = 2Ccbo.

We now have a moderately high input impedance C-E stage without suffering the Miller effect, but no C-E stage voltage gain. The C-B stage provides a high voltage gain. The total current gain of cascode is β as current gain of the C-E stage is 1 for the C-B is β.

Note-A cascode amplifier has a high gain, moderately high input impedance, a high output impedance, and a high bandwidth.

12.2. Darlington Pair [CC - CC]:

It consists of two emitter followers in cascaded mode. The overall gain is close to unity. The main advantage of Darlington amplifier is very large increase in input impedance and an equal decrease in output impedance.

           Figure 9

Following are the important characteristics of Darlington pair:

  • Extremely high input impedance.
  • Extremely high current gain.
  • Extremely low output impedance.

13. Feedback Amplifier:

The feedback-amplifier can be defined as an amplifier which has feedback lane that exists between output to input. In this type of amplifier, feedback is the limitation which calculates the sum of feedback given in the following amplifier. The feedback factor is the ratio of the feedback signal and the input signal.

        Figure 10: Basic Feedback Amplifier

13.1.Difference between Positive and Negative Feedback:

Positive feedback

Negative feedback

V0 = AVi

V0 = AVi

Vi = Vs + Vf

Vi = Vs – Vf

V0 = A(Vs + Vf)

V0 = A(Vs – Vf)

V0 = A(Vs + βV0)

V0 = A(Vs – βV0)

V0(1 – βA) = AVS

V0(1+ βA) = AVS


(1) Apf > A > Anf.

 Apf. = positive feedback gain

A = without feedback gain.

Anf = negative feedback gain. 

NOTE- Negative feedback theory is applied for stable system like Amplifier.

13.2.Effects of Negative Feedback:

Advantage of Negative Feedback Amplifier:

A. Stability of AC Gain

Suppose there is a small change in the internal resistance ‘re’ of an amplifier then the fractional change of gain with feedback is

Note- For a good stable system, sensitivity decreases and desensitivity increases means less sensitive to temperature and noise.

B. Increase in Input Impedance  :

C. Decrease in Output Impedance:

D. Increase in BW:

Lower cutoff frequency decreases

Upper cutoff frequency increases

13.3.Types of Negative Feedback Amplifier:

There are two main types of negative feedback circuits.

5.3.a. Negative Voltage Feedback

5.3.b Negative Current Feedback

a 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.

(i) Voltage Series Feedback

(ii) Voltage Shunt Feedback

b   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.

(i) Current Series Feedback

(ii) Current Shunt Feedback

Let’s have a brief description of all.

i) Voltage Series Feedback:

In voltage series feedback circuit, a fraction of the output voltage is applied in series with the input voltage through the feedback circuit.

The following figure shows the block diagram of voltage series feedback.

            Figure 6: Voltage Series Feedback

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. 

ii) Voltage Shunt Feedback

In voltage shunt feedback circuit, a fraction of output voltage is applied in parallel with the input voltage through the feedback network.

The below figure shows block diagram of voltage shunt feedback.

   Figure 7: Voltage Shunt Feedback

iii) Current Series Feedback:

In current series feedback, a fraction of the output voltage is applied in series with the input voltage through the feedback circuit.

The following figure shows the block diagram of current series feedback.

       Figure 8: Current Series Feedback

As the feedback current is connected in series with the output and the input as well, both the output impedance and the input impedance are increased.

iv) Current Shunt Feedback:

In current shunt feedback circuit, a fraction of output voltage is applied in series with the input voltage through the feedback circuit.

The below figure shows the block diagram of current shunt diagram by which it is evident that the feedback circuit is placed in series with the output but in parallel with the input.

  Figure 9: Current Shunt Feedback


14. Operational Amplifier

  • Op-Amp (Operational Amplifier) is a fundamental building block for handling analog electrical signals.
  • An operational amplifier is a high gain, differential, voltage amplifier.
  • OP AMP has two inputs called “+” and “-,” ( or VIN+ and VIN-) and a single output.
  • The output depends only on the difference of the voltage on the two inputs.
  • If the difference between the two input voltages is VIN , the output voltage is VOut, then VOut = ΔVIN GV; where Gv is the (voltage) gain.
  • The differential operation involves the use of opposite polarity inputs.
  • Common mode operation involves the use of the same polarity inputs.
  • Common-mode rejection compares the gain for differential inputs to that for common inputs.



  • An ideal op-amp is usually considered the following properties, and they are considered to hold for any input voltages:
    • Infinite open loop gain
    • Infinite bandwidth ( the frequency magnitude response is flat everywhere with zero phase shift)
    • Infinite input impedance
    • Zero input current (There is no leakage or bias current into the device)
    • Zero input offset voltage (when the input terminals are shorted, output is a virtual ground)
    • Infinite slew rate  (Rate of change of the output voltage is unbounded) and power bandwidth (full output voltage and currently available at all frequencies).
    • Zero output impedance (Rout = 0, and so output voltage does not vary with output current)
    • Zero noise
    • Infinite CMRR (Common mode rejection ratio)
    • Infinite Power supply rejection ratio for both power supply rails.
  • Properties of Op-Amp


  • Op-Amp Classification


15. Differential Operational Amplifier

  • A differential operational amplifier has inverting and non-inverting inputs with high input impedance and differential or open-loop gains between 1000 and 10 million.
  • When the inverting input is used with negative feedback due to R0, the closed loop gain is given by (-R0 / R1) and the input impedance is R1 the output impedance is the open loop output impedance divided by loop gain.



         Loop gain (dB) = Open loop gain (dB) – Closed loop gain (dB)

  • If a number of signals are connected to the inverting input, the output is proportional to the sum of the input signals, making possible the solution of linear algebraic and differential equations on an analog computer.
  • If the non-inverting input to a differential operational amplifier is used, the input impedance is increased to a value, 

         Rcm || (Ri × loop gain)

          where Rcm is the common mode impedance and Ri is the differential impedance.

  • One way to increase input impedance to an amplifier utilizing the inverting input is to reduce the feedback voltage by connecting a voltage divider at the output.
  • The voltage gain for a non-inverting input is: 
  • A true ideal differential amplifier the difference between two input voltages providing an output,


  • In practice, the output also consists of an error term that is due to the common-mode input voltage = (V1 + V2)/2.
  • The total output of a differential amplifier is:

Vcm16. Common Mode Rejection Ratio (CMRR)

  • The common mode rejection ratio is a figure of merit of a differential amplifier since it is the ratio of differential gain, Ad (the desired gain), to the common-mode gain AC.


  • Emitter-coupled differential amplifiers are the type of circuit used predominantly in ICs, because of the manufacturing ability to closely match components, and since the devices are so closely spaced their variations due to temperature tend to cancel, providing excellent DC coupling stability.
  • High values of CMRR are provided by large effective values of emitter resistance Re, in the emitter-coupled amplifier. This may be provided by a transistor or CRD to provide essentially a constant-current source in the emitter.


  • Ideal Voltage Transfer Curve: 
    • The graphic representation of the output equation is shown in the figure in which the output voltage V0 is plotted against differential input voltage Vd, keeping gain Ad constant.



17. Applications of Operational amplifiers

  • Inverting Amplifier
  • Non-inverting Amplifier
  • Differentiator
  • Differential Amplifier
  • Voltage follower
  • Selective inversion circuit
  • Current-to-voltage converter
  • Active rectifier
  • Integrator
  • Comparator
  • Filters
  • Voltage comparator
  • Signal Amplifier

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Ruchi kumari

Ruchi kumariAug 12, 2019

Lot of thanks

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