Unit 3 - Notes

CSE212 8 min read

Unit 3: Bipolar junction Transistors

1. Junction Transistor

A Bipolar Junction Transistor (BJT) is a three-terminal, three-layer, two-junction semiconductor device capable of amplifying or switching electrical signals. It is called "bipolar" because its operation relies on both types of charge carriers: electrons and holes.

Structure and Types

A BJT consists of three alternately doped semiconductor regions:

NPN Transistor: A thin layer of P-type semiconductor is sandwiched between two N-type regions.
PNP Transistor: A thin layer of N-type semiconductor is sandwiched between two P-type regions.

Transistor Terminals

Emitter (E): Heavily doped to inject a large number of charge carriers (electrons in NPN, holes in PNP) into the base. It has a moderate physical size.
Base (B): Very lightly doped and physically very thin. Its primary function is to pass most of the injected carriers from the emitter to the collector.
Collector (C): Moderately doped but physically the largest of the three regions to dissipate the heat generated during transistor operation. It collects the charge carriers coming from the base.

2. Operation of a BJT

For normal amplification purposes, a BJT is operated in the Active Region. In this region:

The Emitter-Base Junction (EBJ) is forward-biased.
The Collector-Base Junction (CBJ) is reverse-biased.

NPN Transistor Operation (Active Mode)

Forward Biasing of EBJ: The forward bias narrows the depletion region at the emitter-base junction. Electrons (majority carriers in the emitter) are injected into the P-type base.
Base Recombination: Because the base is lightly doped and very thin, only a small percentage (about 1-5%) of these electrons recombine with the holes in the base. This recombination constitutes the small base current ( $I_B$ ).
Collection at CBJ: The remaining electrons diffuse across the base and reach the depletion region of the reverse-biased Collector-Base junction. The electric field here sweeps these electrons into the collector region, constituting the collector current ( $I_C$ ).

Note: The operation of a PNP transistor is identical, but the roles of electrons and holes, as well as the voltage polarities, are reversed.

3. Transistor Current Components

In a BJT, the total emitter current ( $I_E$ ) is the sum of the base current ( $I_B$ ) and the collector current ( $I_C$ ).

$I_E = I_B + I_C$

Current Components Breakdown

Emitter Current ( $I_E$ ): Consists of majority carriers injected from the emitter to the base.
Base Current ( $I_B$ ): Composed of two minor components:
- Recombination current in the base.
- Injection of majority carriers from the base into the emitter (usually negligible due to heavy emitter doping).
Collector Current ( $I_C$ ): Consists of two components:
- $I_{C(majority)}$ : The carriers from the emitter that successfully crossed the base.
- $I_{CBO}$ (Collector-Base Leakage Current): Due to minority carriers crossing the reverse-biased CBJ. It is temperature-dependent.
$I_C = \alpha I_E + I_{CBO}$

Key Current Parameters

Alpha ( $\alpha$ - Common Base Current Gain): The ratio of collector current to emitter current. Typically ranges from 0.95 to 0.998.
$\alpha = \frac{I_C - I_{CBO}}{I_E} \approx \frac{I_C}{I_E}$
Beta ( $\beta$ - Common Emitter Current Gain): The ratio of collector current to base current. Typically ranges from 20 to 500.
$\beta = \frac{I_C}{I_B}$
Relationship between $\alpha$ and $\beta$ :
$\beta = \frac{\alpha}{1 - \alpha} \quad \text{and} \quad \alpha = \frac{\beta}{1 + \beta}$

4. CE, CB and CC Configurations of BJT

A BJT is a three-terminal device. To connect it in a two-port circuit (one input port, one output port), one terminal must be common to both input and output. This leads to three configurations.

4.1 Common Base (CB) Configuration

Common Terminal: Base is common to both input (Emitter) and output (Collector).
Input Characteristics: Plot of $I_E$ vs. $V_{BE}$ at constant $V_{CB}$ . Resembles a forward-biased diode curve. Input resistance is very low.
Output Characteristics: Plot of $I_C$ vs. $V_{CB}$ at constant $I_E$ . The curves are almost horizontal, showing that $I_C \approx I_E$ and is practically independent of $V_{CB}$ . Output resistance is very high.
Current Gain: Less than unity ( $\alpha < 1$ ).

4.2 Common Emitter (CE) Configuration

Common Terminal: Emitter is common to input (Base) and output (Collector).
Input Characteristics: Plot of $I_B$ vs. $V_{BE}$ at constant $V_{CE}$ . Input resistance is moderate (higher than CB, lower than CC).
Output Characteristics: Plot of $I_C$ vs. $V_{CE}$ at constant $I_B$ . Divided into three regions: Active, Saturation, and Cut-off.
Current Gain: Very high ( $\beta$ ).

4.3 Common Collector (CC) Configuration

Common Terminal: Collector is common to input (Base) and output (Emitter).
Alternative Name: Emitter Follower (because the output voltage at the emitter strictly follows the input voltage at the base).
Characteristics: High input resistance and very low output resistance.
Voltage Gain: Slightly less than unity ( $A_v \approx 1$ ). Current gain is high ( $\beta + 1$ ).

5. Comparisons of Transistor Amplifier Configurations

Characteristic	Common Base (CB)	Common Emitter (CE)	Common Collector (CC)
Input Resistance	Very Low ( $\approx 20 - 50 \Omega$ )	Moderate ( $\approx 1 - 2 k\Omega$ )	Very High ( $\approx 50 - 500 k\Omega$ )
Output Resistance	Very High ( $\approx 1 - 2 M\Omega$ )	Moderate ( $\approx 40 - 50 k\Omega$ )	Very Low ( $\approx 50 \Omega$ )
Current Gain ( $A_i$ )	Less than 1 ( $\alpha$ )	High ( $\beta$ , ~50 to 300)	High ( $\beta + 1$ )
Voltage Gain ( $A_v$ )	High	High	Less than 1 ( $\approx 1$ )
Phase Shift	$0^\circ$ (In-phase)	$180^\circ$ (Out-of-phase)	$0^\circ$ (In-phase)
Primary Application	High-frequency applications	Audio/General amplification	Impedance matching

6. BJT as an Amplifier

An amplifier increases the amplitude of a weak AC signal. The CE configuration is most commonly used for this purpose due to its high voltage and current gains.

Mechanism of Amplification

DC Biasing: The BJT is biased in the Active Region using external DC sources to establish a quiescent point (Q-point). This ensures the transistor remains in the active region throughout the entire cycle of the input AC signal.
Signal Superposition: A weak AC input signal is applied to the base. This causes small variations in the base-emitter voltage ( $v_{be}$ ).
Current Multiplication: Due to the transfer characteristics of the BJT, small variations in $v_{be}$ cause substantial changes in base current ( $i_b$ ), which in turn causes very large variations in the collector current ( $i_c = \beta \cdot i_b$ ).
Voltage Output: The fluctuating collector current flows through a load resistor ( $R_L$ ), producing a large amplified AC voltage ( $v_{out} = -i_c R_L$ ). The negative sign indicates a $180^\circ$ phase shift in the CE configuration.

7. Transistor as a Switch

When operating as a switch, the BJT is driven between two extreme regions: Cut-off and Saturation. It does not operate in the active region.

State 1: OFF State (Cut-off Region)

Biasing: Both EBJ and CBJ are reverse-biased.
Condition: Input base voltage is zero or negative ( $V_{BE} < 0.7V$ for Si).
Result: Base current $I_B = 0$ . Consequently, collector current $I_C = 0$ .
Behavior: The transistor acts as an open switch. The voltage across the collector-emitter terminals is equal to the supply voltage ( $V_{CE} = V_{CC}$ ).

State 2: ON State (Saturation Region)

Biasing: Both EBJ and CBJ are forward-biased.
Condition: A high input voltage is applied to the base, providing a large base current ( $I_B > I_{C(sat)} / \beta$ ).
Result: The collector current reaches its maximum possible value determined by the external load resistor ( $I_{C(sat)} \approx V_{CC} / R_L$ ).
Behavior: The transistor acts as a closed switch. The voltage drop across the transistor is minimal ( $V_{CE(sat)} \approx 0.2V$ ).

8. Transistor Switching Times

In reality, a transistor cannot switch instantly between the Cut-off and Saturation states due to the presence of internal junction capacitances and the time required for charge carriers to cross the base region.

Total Turn-On Time ( $t_{on}$ )

The time required for the transistor to transition from the OFF state to the ON state.
$t_{on} = t_d + t_r$

Delay Time ( $t_d$ ): The time required for the input base voltage to rise from its initial negative/zero value to the threshold voltage (about 0.7V), charging the emitter-base junction capacitance. $I_C$ reaches 10% of its maximum value.
Rise Time ( $t_r$ ): The time required for the collector current to rise from 10% to 90% of its maximum saturation value ( $I_{C(sat)}$ ).

Total Turn-Off Time ( $t_{off}$ )

The time required for the transistor to transition from the ON state to the OFF state.
$t_{off} = t_s + t_f$

Storage Time ( $t_s$ ): When the input drive is removed, the transistor remains in saturation for a brief period. This is the time required to remove or sweep out the excess minority charge carriers stored in the base region. During this time, $I_C$ drops from 100% to 90% of its saturation value.
Fall Time ( $t_f$ ): The time required for the collector current to fall from 90% to 10% of its maximum value. This corresponds to the discharging of the junction capacitances as the transistor fully enters cut-off.

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