Transistor As Amplifier

A transistor as an amplifier is a crucial electronic component used to boost weak signals. By using a small input signal to control a larger output, it plays a vital role in devices like radios, televisions, and audio systems. The transistor amplifies signals through its three layers—emitter, base, and collector—forming amplifier circuits. This makes transistors essential in devices like radios, televisions, and audio equipment. 

1.0Concept Of An Amplifier

It is a circuit that contains at least one transistor and is designed to increase the voltage, current, or power of an alternating signal. To amplify means to enlarge or magnify the input signal, with the output signal being a scaled-up version of the input.

2.0Amplifying Action Of Transistor

• As the base emitter junction of a transistor is forward biased,the depletion layer about this junction is much smaller than the depletion layer around the base-collector junction which is reverse biased.Thus the resistance REB of emitter base junction is much smaller than the resistance RBC of the collector base junction.

Power dissipation in the emitter base circuit,

$P_{EB}=I_E^2{R}_{EB}$

Power dissipation in the  base collector circuit,

$P_{BC}=I_C^2{R}_{BC}$

$I_E\approx I_C\text{and}{R}_{BC}\approx R_{EB}$

$P_{BC}\approx P_{EB}$

The power dissipated in the base-collector circuit is much higher than the power dissipated in the emitter base circuit or output power is much greater than the input power,This is the amplifying action of a transistor.

3.0Essential Concepts of Transistor For Amplification

• The collector current $I_C$ is almost equal to the emitter current $I_E$ But resistance offered by the emitter-base junction to the flow of current is small as it is forward biased.The resistance offered by the base-collector junction to the flow of current is large because this junction is reverse biased.
• Current is thus transferred from a low resistance circuit to a high resistance circuit,hence the name transistor which is the combination of words transfer and resistor.
• The base region of transistor is very thin and lightly doped.A thin and lightly doped base region contains a smaller number of majority charge carriers.This reduces the rate of of recombination of electrons and holes at the emitter base junction.Most (95-99% )of the majority charge carriers diffusing from emitter to base ,reach the collector.
• Thus the base current is small and the collector current is almost equal to the remitter current this results in the larger voltage and power gain of the transistor.
• In Voltage Amplifier,the input signal to be amplified is  superposed on a steady voltage $V_{EB}$ applied across the emitter-base junction.For a high voltage gain(the ratio of output voltage to the input voltage) the change in the collector current $\Delta I_C$ should be large as large as possible for a given change in the emitter-base voltage $\Delta V_{EB}$.

4.0Transistor As A common Emitter Amplifier

• The emitter is common between  to both input and output circuits.The emitter is forward biased by battery $V_{BB}$ and the collector current is reversed is reversed by battery $V_{CC}$ .This decrease the resistance Rin of the input circuit and increase the resistance $R_{Out}$ of the output circuit.
• The low a.c. input signal $V_i$ is superimposed on the forward biased $V_{BE}$ .A load resistance $R_L$ is connected between the collector and the d.c supply and the amplified output is obtained between the collector and the ground.
• When current $I_C$ flows in the output circuit ,the potential drop over  the load resistance is $I_C{R}_L$ .Hence the output voltage is 

$V_O=V_{CE}=V_{CC}-I_C{R}_L$

• When the input signal is fed to the base- emitter circuit the base -emitter voltage changes.This changes the emitter current $I_E$ and hence the collector current $I_C$.
• The output voltage $V_O$ varies in accordance with the above relation.These variation in the collector voltage appears as amplified Output.

5.0Phase Relationship Between Input And Output Signals

• When an a.c signal is fed to the input circuit, its positive half cycle increases the forward bias of the circuit which in turn increases the emitter current and hence the collector current.
• The increase in the collector current increases the potential difference across $R_L$, which makes the output voltage less positive or negative.
• So as the input signal goes through its positive half cycle, the amplified output signal goes through a negative half cycle. Similarly, as the input signal goes through its negative half cycle, the amplified output signal goes through its positive half cycle.
• In a Common Emitter Amplifier, the input and output voltages are in opposite phases 180 degrees.

6.0Basic Terms Used In Transistor

1.Transconductance:It is the ratio of the small change in the collector current to the small change in the emitter-base voltage.It is also called transfer conductance and having units (Siemen or mho).It depends on the geometry,doping levels,and the biasing of the transistor.

$g_m=\frac{\Delta I_C}{\Delta V_{BE}}$

2.a.c Current gain:It is the fraction of the small change in the collector current to the small change in base current when collector when collector-emitter voltage is kept constant.

${\beta }_{a.c}\text{ or }{A}_i={\left[\frac{\Delta I_C}{\Delta I_B}\right]}_{V_{CE}=\text{Constant}}$

3.d.c Current gain:It is the fraction of collector current to the base current when collector-emitter voltage is constant.

${\beta }_{d.c}={\left[\frac{I_C}{I_B}\right]}_{V_{CE}=\text{Constant}}$

4.a.c Voltage gain:It is the ratio of small change in output voltage to the small change in input voltage.

$A_v=\frac{\Delta V_{CE}}{\Delta V_{BE}}$

$\Delta V_{BE}=R_i\cdot \Delta I_B$

$\Delta V_{CE}=-R_o\cdot \Delta I_C$

Negative sign indicates that the input and the output voltage have a phase difference of 180 °.When the input voltage elevates, the output voltage decreases.

$A_v=-\frac{\Delta I_C}{\Delta I_B}\cdot \frac{R_o}{R_{in}}=-{\beta }_{a.c}\cdot \frac{R_o}{R_{in}}$

$A_v=A_i{A}_r$

Voltage gain= Current Gain ✕ Resistance Gain

5.a.c.Power gain:It is the ratio of the small change in output power to the small change in input power.

$\text{a.c Power gain}=\frac{\text{Change in output power}}{\text{Change in input power}}$

$A_p=\frac{(\Delta I_C{)}^2}{(\Delta I_B{)}^2}\cdot \frac{R_o}{R_i}={\beta }_{a.c}^2\cdot \frac{R_o}{R_i}$

The a.c power gain of a common emitter amplifier is much larger than that of a common base amplifier,it may be noted that the transistor is not generating any power.The energy for the higher a.c power at the output is supplied by the d.c battery.

Illustration-1.A transistor has a current amplification factor of 50.In a CE Amplifier circuit,the collector resistance is chosen as 5 and the input resistance is 1 .Calculate the output voltage if the input voltage is 0.01V.

Solution:

$A_v=\beta \frac{R_o}{R_i}$

$\frac{V_o}{V_i}=\beta \frac{R_C}{R_B}$

$V_o=\beta \frac{R_C}{R_B}{V}_i=\frac{50\times 5\times 10^3\times 0.01}{1\times 10^3}=2.5V$

Illustration-2.A silicon transistor has an input resistance of 665 ohms. When its base current changes by 15 µA, the collector current changes by 2 mA. This transistor is used in a common-emitter amplifier configuration with a load resistance of 5 kΩ. Calculate the current gain, transconductance, and voltage gain of the amplifier.

Solution:

1. Current gain

${\beta }_{a.c}=\frac{\Delta I_C}{\Delta I_B}=\frac{2\times 10^{-3}}{15\times 10^{-6}}=133$

2. Transconductance

$R_{in}=\frac{\Delta V_{BE}}{\Delta I_B}$

$\Delta V_{BE}=R_{in}\times \Delta I_B=665\times 15\times 10^{-6}V$

$g_m=\frac{\Delta I_C}{\Delta V_{BE}}=\frac{2\times 10^{-3}}{665\times 15\times 10^{-6}}=0.2{\Omega }^{-1}$

( C) Voltage gain

$A_v={\beta }_{ac}\times \frac{R_{out}}{R_{in}}=133\times \frac{5\times 10^3}{665}=1000$