Unit 2: Bipolar Junction Transistor (BJT) - Subjective Questions

A Bipolar Junction Transistor (BJT) is a three-terminal device with two PN junctions formed by three doped regions: Emitter (E), Base (B), and Collector (C).

NPN Transistor:

• Consists of a thin P-type base sandwiched between two N-type regions.
• Majority carriers are electrons.
• For active operation: Emitter-Base junction is forward biased, Collector-Base junction is reverse biased.
• Electrons flow from emitter to collector; conventional current flows from collector to emitter.

PNP Transistor:

• Consists of a thin N-type base between two P-type regions.
• Majority carriers are holes.
• For active operation: Emitter-Base junction is forward biased, Collector-Base junction is reverse biased (with reversed supply polarity compared to NPN).
• Holes flow from emitter to collector.

Key Differences:

NPN transistors are more commonly used because electrons have higher mobility, giving better performance.

In a BJT operating in the active region, several current components exist due to carrier flow across the junctions.

Current Components (for NPN):

• (Emitter current): Total current entering from the emitter, consisting mainly of electrons injected into the base.
• (Base current): Small current due to recombination of carriers in the base and hole injection.
• (Collector current): Current collected at the collector, comprising:
  • Injected carriers reaching the collector
  • Reverse saturation current (leakage)

Fundamental Relationship:

By Kirchhoff's current law:

Current Transfer Ratio (Common Base):

Including leakage:

Common Emitter relation:

Also:

These equations describe how a small base current controls a large collector current, giving the transistor its amplifying action.

Definition of (Common Base current gain):

It is the ratio of collector current to emitter current. Its value is close to 1 (typically 0.95–0.99).

Definition of (Common Emitter current gain):

It is the ratio of collector current to base current. Its value is typically 20–500.

Derivation of Relationship:

Start with:

Since , we have .

Substituting:

Therefore:

Result:

This shows that as , becomes very large.

In the Common Base (CB) configuration, the base is common to both input and output. Input is applied between emitter and base; output is taken between collector and base.

Input Characteristics: ( vs at constant )

• Resembles a forward-biased diode curve.
• increases exponentially once exceeds the cut-in voltage ( V for Si).
• Input resistance is low (few tens of ohms).
• For higher , the curve shifts slightly left (Early effect).

Output Characteristics: ( vs at constant )

• Three regions are visible:
  • Active region: , nearly constant, independent of .
  • Saturation region: Occurs for small/negative ; drops rapidly.
  • Cut-off region: When , only leakage current flows.
• Output resistance is very high.

Key Features of CB:

• Current gain
• Voltage gain: high
• Low input resistance, high output resistance
• Used in high-frequency applications.

In the Common Emitter (CE) configuration, the emitter is common to both input and output. Input is applied between base and emitter; output taken between collector and emitter.

Input Characteristics: ( vs at constant )

• Similar to a forward-biased diode curve.
• increases with after cut-in voltage.
• Input resistance is moderate (higher than CB, few hundred ohms to kΩ).
• Higher shifts the curve rightward.

Output Characteristics: ( vs at constant )

• Three regions:
  • Active region: , curves are nearly flat but slope upward slightly (due to Early effect).
  • Saturation region: Low ( V); both junctions forward biased, rises steeply.
  • Cut-off region: ; small leakage current flows.

Key Features of CE:

• Current gain is high
• Voltage gain: high
• Power gain: highest among all configurations
• Phase inversion of between input and output
• Most widely used configuration for amplification.

Early Effect, also called base-width modulation, refers to the variation in the effective width of the base region as the reverse bias voltage across the collector-base junction () changes.

Cause:

• As (or ) increases, the reverse bias on the collector-base junction increases.
• This widens the depletion region at the collector-base junction.
• The depletion region extends into the base, reducing the effective base width ().

Consequences:

• Reduced recombination: With a narrower base, fewer carriers recombine, so more reach the collector.
• Increase in : Collector current increases slightly with increasing even at constant . This gives the output characteristics a small upward slope instead of being perfectly flat.
• Increase in : Current gain increases as base width decreases.
• Punch-through: At very high voltages, the base width may reduce to zero, causing device breakdown.

Early Voltage ():
When output characteristic lines are extrapolated backward, they meet the voltage axis at a point (the Early voltage), typically 50–100 V.

Output resistance:

A higher Early voltage means the transistor behaves more like an ideal current source.

The three basic transistor configurations differ significantly in their electrical characteristics.

Summary:

• CB: Good for high-frequency work due to low input capacitance.
• CE: Best all-round amplifier with high power gain; most commonly used.
• CC (Emitter Follower): Voltage gain ≈ 1, used as a buffer for impedance matching between high-impedance source and low-impedance load.

A BJT operates in three main regions depending on the biasing of its two junctions (Emitter-Base junction, EBJ and Collector-Base junction, CBJ).

1. Cut-off Region:

• Biasing: EBJ reverse biased, CBJ reverse biased.
• Both junctions off; transistor acts as an open switch.
• (only small leakage current flows).
• .
• Used in switching (OFF state).

2. Active Region:

• Biasing: EBJ forward biased, CBJ reverse biased.
• Transistor acts as an amplifier.
• (linear relationship).
• Collector current is controlled by base current.
• Used in analog amplification.

3. Saturation Region:

• Biasing: EBJ forward biased, CBJ forward biased.
• Transistor acts as a closed switch.
• is maximum and no longer controlled by .
• V.
• Used in switching (ON state).

Summary Table:

A transistor can be modeled as a two-port network with an input port and an output port. The hybrid (h) parameters are widely used because they are convenient to measure for BJTs.

Two-Port Representation:

• Input port: voltage , current
• Output port: voltage , current

Defining Equations:

For CE configuration (, , , ):

• (Input impedance): — measured with output short-circuited. Units: ohms.

• (Reverse voltage gain): — measured with input open-circuited. Dimensionless.

• (Forward current gain): — measured with output short-circuited. Dimensionless (equals ).

• (Output admittance): — measured with input open-circuited. Units: siemens (mho).

Why 'hybrid'? Because the parameters have mixed dimensions (ohms, siemens, and dimensionless).

h-Parameter Equivalent Circuit (CE):

The hybrid model represents the transistor using the two defining equations:

Circuit description:

• Input side: A resistance in series with a voltage source (dependent on output voltage).

• Output side: A current source in parallel with a conductance .

  i_b → h_ie i_c → o---/\/---+---o o---+-------+---o			v_be (h_re·v_ce) (h_fe·i_b) (1/h_oe) v_ce

  o---------+---o o---+-------+---o

Current Gain (): with load resistance

Output current . With :

Input Impedance ():

Using ... substituting :

These expressions allow complete small-signal analysis of the amplifier.

DC Load Line:
The DC load line is a straight line drawn on the output characteristics of a transistor that represents all possible combinations of and for a given circuit with fixed and load resistance .

Derivation: Applying KVL to the output (collector) circuit of a CE amplifier:

This is a linear equation. To draw it, find two points:

• Saturation point (Y-intercept): Set :
  

• Cut-off point (X-intercept): Set :
  

Joining these two points gives the DC load line.

Q-Point (Quiescent/Operating Point):

• The Q-point is the intersection of the DC load line with the output characteristic curve corresponding to the operating base current .
• It defines the DC operating conditions (, ) with no AC signal applied.

Importance of Q-point placement:

• For faithful amplification, the Q-point should be at the center of the load line (active region).
• If Q is too close to saturation or cut-off, the output signal gets clipped (distortion).

The load line and Q-point together determine the maximum symmetrical output swing.

Need for Biasing:
Biasing establishes proper DC operating conditions (the Q-point) so that the transistor operates in the active region for faithful amplification. Without proper biasing:

• The transistor may enter cut-off or saturation.
• The output signal will be distorted or clipped.

Objectives of Biasing:

• Set the Q-point in the middle of the active region.
• Ensure the Q-point remains stable against variations in temperature and transistor parameters.
• Provide proper input/output signal conditions.

Stability Factor ():
The collector current is sensitive to changes in (reverse saturation current), , and . The stability factor measures how much changes with these parameters.

Definition (w.r.t. ):

General expression:

Interpretation:

• A lower value of means better stability (ideal ).
• Practical circuits aim for small .

Why Stabilization is Required:

• doubles for every rise in temperature.
• varies from device to device and with temperature.
• decreases ~2.5 mV/°C.
• These variations shift the Q-point, possibly causing thermal runaway. Stabilization circuits (e.g., voltage-divider bias with emitter resistor) counteract these effects.

Fixed Bias Circuit:
In the fixed bias configuration, the base is connected to through a single resistor .

Base circuit KVL:

Since is independent of :

General Stability Factor Formula:

Substituting :

Comment on Stability:

• For a typical transistor with , .
• This is a very high value, indicating poor stability.
• Any change in is amplified ~101 times in .
• Also, since depends on , and varies with temperature and device, the Q-point shifts significantly.

Conclusion: The fixed bias circuit is simple but offers poor thermal stability, making it unsuitable where stable operation is required. Voltage-divider bias is preferred instead.

Voltage-Divider Bias Circuit:
This circuit uses two resistors and forming a voltage divider across to set a fixed base voltage, along with an emitter resistor for stabilization.

Circuit Analysis (using Thevenin's theorem):

Thevenin voltage:

Thevenin resistance:

Applying KVL to base-emitter loop:

Since and if is small:
(when is small)

Key Observation: is nearly independent of , depending mainly on stable resistor values and supply voltage.

Stability Factor:

For , (excellent stability).

Why Most Widely Used:

• Excellent Q-point stability independent of variations.
• Uses a single power supply.
• provides negative feedback counteracting temperature effects.
• The emitter resistor prevents thermal runaway.

This makes voltage-divider bias the preferred choice for linear amplifier design.

Both load lines are used to analyze transistor amplifier operation, but they apply under different signal conditions.

DC Load Line:

• Drawn considering only DC resistances in the collector circuit.
• Equation:
• Represents the operating path when no AC signal is applied.
• Determines the Q-point.

AC Load Line:

• Drawn considering AC resistances (coupling capacitors short-circuit and load appears in parallel).
• AC load resistance:
• Passes through the same Q-point but with a steeper slope.
• Represents the operating path when an AC signal is applied.

Comparison Table:

Significance:

• The AC load line determines the actual maximum output voltage swing without distortion.
• Since , the AC load line is steeper, giving a smaller allowable voltage swing than the DC line would suggest.
• Proper Q-point placement on the AC load line maximizes the undistorted output.

Given:

Step 1: Calculate :

Step 2: Calculate :

Step 3: Calculate :

Step 4: Calculate :

Results:

Thermal Runaway:
Thermal runaway is a cumulative, self-destructive process in which increasing temperature leads to increasing collector current, which further raises the temperature, eventually destroying the transistor.

Mechanism (Cycle):

1. Collector current flows and produces power dissipation .
2. This power heats the collector junction, raising temperature.
3. Rising temperature increases (doubles every ), which increases .
4. Increased increases power dissipation, further raising temperature.
5. This positive feedback loop continues until the device overheats and fails.

Condition for Thermal Stability:

where is the thermal resistance. The rate of heat generation must be less than the rate of heat dissipation.

Prevention Methods:

• Heat sinks: Improve heat dissipation from the transistor.
• Emitter resistor (): Provides negative feedback; as rises, voltage drop across reduces , limiting .
• Voltage-divider (self) bias: Keeps Q-point stable against temperature.
• Operating at lower and : Reduces power dissipation.
• Temperature-compensating elements: Diodes or thermistors in the bias network.

Proper bias design keeping the stability factor low is the key defense against thermal runaway.

A BJT datasheet provides essential electrical, thermal, and mechanical specifications for reliable circuit design.

1. Maximum Ratings (Absolute Maximum):

• : Max collector-emitter voltage (base open). Exceeding causes breakdown.
• : Max collector-base voltage (emitter open).
• : Max emitter-base voltage (collector open).
• (max): Maximum continuous collector current.
• (max): Maximum power dissipation (must include derating with temperature).

2. Electrical Characteristics:

• / : DC current gain (often given as a range, e.g., 100–300).
• : Collector-emitter saturation voltage (~0.2 V).
• : Base-emitter turn-on voltage (~0.7 V).
• / : Leakage currents.
• : Transition/gain-bandwidth frequency — indicates high-frequency capability.
• : Output capacitance.

3. Thermal Characteristics:

• , : Thermal resistance junction-to-ambient/case (for heat sink selection).
• (max): Maximum junction temperature.

Importance in Design:

• Ensures the transistor is operated within safe limits (avoiding breakdown and burnout).
• Helps select proper biasing and load values.
• Guides heat sink requirements.
• ensures the device is suitable for the operating frequency.
• The range guides bias design so the circuit is independent of variation.

Collector-to-Base Bias (Feedback Bias):
In this circuit, the base resistor is connected between the collector and base (instead of ), providing negative feedback.

Circuit Analysis:
Applying KVL to the base loop:

Since and :

Solving for :

Deriving Stability Factor:
Differentiating with respect to :

Substituting into the general stability formula:

Analysis of Stability:

• Since the denominator is greater than 1, .
• This is better than fixed bias ().
• Feedback action: If increases, the drop across increases, reducing collector voltage, which reduces , opposing the rise in .

Conclusion: The collector-to-base bias offers moderate stability through negative feedback — better than fixed bias but generally not as good as voltage-divider bias. The larger the ratio , the better the stability.

Common Collector (CC) Configuration:
In the CC configuration, the collector is common to both input and output. Input is applied between base and collector, output taken between emitter and collector (across the emitter resistor).

Why 'Emitter Follower':

• The output (emitter) voltage follows the input (base) voltage.
• Since V is nearly constant:
  
• Any change in base voltage produces an almost equal change in emitter voltage.
• The voltage gain is approximately 1 (slightly less), and there is no phase inversion ( phase shift). Hence the emitter 'follows' the base.

Characteristics:

• Voltage gain: (less than unity)
• Current gain: High,
• Input impedance: Very high ()
• Output impedance: Very low
• Power gain: Moderate (due to high current gain)
• Phase shift:

Applications:

• Impedance matching: Connects a high-impedance source to a low-impedance load without loading effects.
• Buffer amplifier: Isolates two circuit stages.
• Current amplification: Provides high current gain.
• Voltage regulators and driver stages.

Summary: The emitter follower is primarily used as a buffer because of its high input impedance and low output impedance, providing effective impedance transformation.