Unit 2 - Notes

ECE182 10 min read

Unit 2: Bipolar Junction Transistors

1. Structure of BJT

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

1.1 Layers and Terminals

The BJT consists of two back-to-back PN junctions, forming three distinct regions:

Emitter (E): Heavily doped to inject a large number of charge carriers into the base. It is moderate in size.
Base (B): Very thin and lightly doped to allow most injected carriers to pass through to the collector with minimal recombination.
Collector (C): Moderately doped and physically the largest region to dissipate the heat generated during operation. It collects the majority of the carriers injected by the emitter.

1.2 Types of BJTs

NPN Transistor: Consists of a P-type base sandwiched between two N-type layers (Emitter and Collector). The majority charge carriers are electrons.
PNP Transistor: Consists of an N-type base sandwiched between two P-type layers. The majority charge carriers are holes.

2. Current Components in a BJT

In a standard Active mode operation (Emitter-Base junction forward-biased, Collector-Base junction reverse-biased):

Emitter Current ( $I_E$ ): The total current flowing out of (or into) the emitter. It is the sum of the base and collector currents.
Base Current ( $I_B$ ): A very small current (typically in $\mu A$ ) caused by the recombination of a small percentage (1-5%) of carriers in the base region.
Collector Current ( $I_C$ ): The majority of the emitter current that crosses the base and reaches the collector (typically in $mA$ ).

2.1 Fundamental Current Equation

I_E = I_B + I_C

2.2 Amplification Factors

Common-Base Current Gain ( $\alpha$ ): The ratio of collector current to emitter current.
$\alpha = \frac{I_C}{I_E}$
(Typical values: 0.95 to 0.998)
Common-Emitter Current Gain ( $\beta$ or $h_{FE}$ ): The ratio of collector current to base current.
$\beta = \frac{I_C}{I_B}$
(Typical values: 50 to 400)
Relationship between $\alpha$ and $\beta$ :
$\beta = \frac{\alpha}{1 - \alpha} \quad \text{and} \quad \alpha = \frac{\beta}{\beta + 1}$

3. Transistor Configurations

Depending on which terminal is common to both the input and output circuits, BJTs can be connected in three configurations.

3.1 Common Base (CB) Configuration

Common Terminal: Base is grounded/common to both input and output.
Input: Emitter
Output: Collector
Characteristics: Low input impedance, high output impedance, current gain $\approx 1$ ( $\alpha$ ), high voltage gain. Good for high-frequency applications.

3.2 Common Emitter (CE) Configuration

Common Terminal: Emitter is grounded.
Input: Base
Output: Collector
Characteristics: Moderate input and output impedance, high current gain ( $\beta$ ), high voltage gain, and high power gain. Produces a $180^\circ$ phase shift between input and output. Most widely used configuration.

3.3 Common Collector (CC) Configuration (Emitter Follower)

Common Terminal: Collector is grounded (often tied to $V_{CC}$ for AC).
Input: Base
Output: Emitter
Characteristics: Very high input impedance, very low output impedance, voltage gain $\approx 1$ , high current gain. No phase shift. Primarily used for impedance matching.

4. Characteristics (Input and Output)

Transistor characteristics are graphical representations of the relationship between voltages and currents. We focus primarily on the CE Configuration as it is the most prevalent.

4.1 Common Emitter Input Characteristics

A plot of Base Current ( $I_B$ ) versus Base-Emitter Voltage ( $V_{BE}$ ) at a constant Collector-Emitter Voltage ( $V_{CE}$ ).

Behavior: Resembles the forward-bias characteristic of a standard PN junction diode.
Cut-in Voltage: The current $I_B$ remains close to zero until $V_{BE}$ exceeds $\approx 0.7V$ for Silicon ( $\approx 0.3V$ for Germanium).
Effect of $V_{CE}$ : As $V_{CE}$ increases, the effective base width decreases (Early Effect), slightly reducing $I_B$ for a given $V_{BE}$ .

4.2 Common Emitter Output Characteristics

A plot of Collector Current ( $I_C$ ) versus Collector-Emitter Voltage ( $V_{CE}$ ) for various constant values of Base Current ( $I_B$ ). The graph is divided into three distinct regions:

Active Region:
- EB junction is forward-biased, CB junction is reverse-biased.
- $I_C$ increases almost linearly with $I_B$ ( $I_C = \beta I_B$ ).
- Curves are nearly horizontal. Used for linear amplification.
Saturation Region:
- Both EB and CB junctions are forward-biased.
- Occurs at very low $V_{CE}$ (typically $< 0.2V$ ).
- $I_C$ is maximum and largely independent of $I_B$ . The transistor acts as a closed switch.
Cut-off Region:
- Both EB and CB junctions are reverse-biased.
- $I_B = 0$ , $I_C$ is nearly zero (only a tiny leakage current, $I_{CEO}$ , flows).
- The transistor acts as an open switch.

5. Transistor as an Amplifier

To act as an amplifier, the BJT must be biased in the Active Region.

Mechanism: A small AC signal is applied to the forward-biased input (Base-Emitter). This causes minor fluctuations in the base current ( $I_B$ ).
Because $I_C = \beta I_B$ , these small fluctuations in $I_B$ result in large fluctuations in the collector current ( $I_C$ ).
When this large alternating $I_C$ flows through an external load resistor ( $R_C$ ), it produces a large voltage swing across $R_C$ , effectively amplifying the input signal.
Phase Shift: In a CE amplifier, an increase in input voltage increases $I_C$ , which increases the voltage drop across $R_C$ . Since $V_{CE} = V_{CC} - I_C R_C$ , the output voltage $V_{CE}$ drops. Therefore, the output is $180^\circ$ out of phase with the input.

6. Transistor as a Switch

In digital robotics and logic circuits, the BJT is operated between two extreme regions: Cut-off and Saturation.

6.1 OFF State (Cut-off Region)

Condition: Input voltage is $0V$ or less than the threshold (e.g., $< 0.7V$ ).
$I_B = 0 \implies I_C \approx 0$ .
No current flows through the load resistor ( $R_C$ ).
Output voltage $V_{CE} = V_{CC}$ .
The transistor behaves as an Open Switch.

6.2 ON State (Saturation Region)

Condition: Input voltage is high enough to drive maximum base current.
$I_B$ is large enough that $I_C$ reaches its maximum limit imposed by the external circuit ( $I_{C(sat)} \approx V_{CC} / R_C$ ).
Output voltage $V_{CE} \approx 0V$ (specifically $V_{CE(sat)}$ , around $0.2V$ ).
The transistor behaves as a Closed Switch.

7. Transistor Biasing

Biasing is the process of applying proper DC voltages to a transistor to establish a desired operating point (Q-point) in the active region, ensuring it can faithfully amplify an AC signal without distortion.

7.1 Need for Biasing

To keep the Emitter-Base junction forward-biased and the Collector-Base junction reverse-biased.
To stabilize the Q-point against temperature variations and variations in transistor parameters (like $\beta$ ).

7.2 Thermal Runaway

When temperature increases, minority carrier leakage current ( $I_{CBO}$ ) increases. Since $I_C = \beta I_B + (\beta+1)I_{CBO}$ , $I_C$ increases. An increase in $I_C$ increases power dissipation at the collector junction ( $P_D = V_{CE} I_C$ ), raising the temperature further. If unchecked, this self-feeding cycle destroys the transistor. Proper biasing prevents thermal runaway.

7.3 Stability Factor ( $S$ )

A measure of how much the collector current changes with respect to changes in reverse saturation current ( $I_{CBO}$ ). Lower $S$ indicates better thermal stability.

S = \frac{dI_C}{dI_{CBO}}

8. DC Load Line and Operating Point

8.1 DC Load Line

Applying Kirchhoff’s Voltage Law (KVL) to the output loop of a CE configuration:

V_{CC} - I_C R_C - V_{CE} = 0 \implies I_C = -\frac{1}{R_C}V_{CE} + \frac{V_{CC}}{R_C}

This is the equation of a straight line (

y = mx + c

) plotted on the output characteristics.

Y-intercept (Saturation Point): When $V_{CE} = 0$ , maximum $I_C = V_{CC} / R_C$ .
X-intercept (Cut-off Point): When $I_C = 0$ , maximum $V_{CE} = V_{CC}$ .
Connecting these two points gives the DC Load Line.

8.2 Operating Point (Q-Point)

The Q-Point (Quiescent point) is a specific point on the load line representing the DC $V_{CE}$ and $I_C$ when no AC signal is applied.

For a linear amplifier, the Q-point is ideally placed exactly in the center of the load line. This allows for maximum unclipped swing of the AC output signal in both positive and negative directions.

9. Biasing Circuits

9.1 Fixed Bias (Base Bias) Circuit

Structure: Uses a single DC supply ( $V_{CC}$ ). A resistor $R_B$ is connected between $V_{CC}$ and the Base. A resistor $R_C$ is connected between $V_{CC}$ and the Collector. Emitter is grounded.
Analysis:
- Input Loop (KVL): $V_{CC} - I_B R_B - V_{BE} = 0 \implies I_B = \frac{V_{CC} - V_{BE}}{R_B}$
- Since $V_{CC}$ , $V_{BE}$ , and $R_B$ are constants, $I_B$ is fixed (hence "Fixed Bias").
- Collector Current: $I_C = \beta I_B$
- Output Loop (KVL): $V_{CE} = V_{CC} - I_C R_C$
Advantages: Simple circuit, requires few components.
Disadvantages: Very poor thermal stability. Since $I_B$ is fixed, any change in $\beta$ (due to temperature or replacing the transistor) results in a proportional shift in $I_C$ , drastically shifting the Q-point. $S \approx 1 + \beta$ (which is very high).

9.2 Emitter Feedback Bias

Structure: Similar to the fixed bias circuit, but an Emitter Resistor ( $R_E$ ) is added between the emitter terminal and ground.
Analysis:
- Input Loop (KVL): $V_{CC} - I_B R_B - V_{BE} - I_E R_E = 0$
- Since $I_E \approx I_C$ , we can write: $V_{CC} = I_B R_B + V_{BE} + I_C R_E$
Stabilization Mechanism (Negative Feedback):
- If temperature rises, $I_C$ attempts to increase.
- This increases the voltage drop across the emitter resistor ( $V_E = I_E R_E$ ).
- Since the base voltage ( $V_B$ ) is relatively fixed by the input network, the base-emitter voltage $V_{BE} = V_B - V_E$ decreases.
- A lower $V_{BE}$ reduces the base current $I_B$ .
- The reduction in $I_B$ brings the collector current ( $I_C = \beta I_B$ ) back down, stabilizing the Q-point.
Advantages: Significantly better thermal stability compared to Fixed Bias.
Disadvantages: $R_E$ introduces negative feedback for AC signals as well, reducing the overall AC voltage gain. (This is often mitigated by placing a bypass capacitor, $C_E$ , in parallel with $R_E$ ).

10. Data Sheet of Transistor

A transistor datasheet provides the essential electrical and physical parameters required by engineers to design robotic circuits safely and efficiently. Key parameters include:

10.1 Maximum Ratings (Absolute Limits)

Exceeding these values can permanently damage the BJT.

$V_{CEO}$ (Collector-Emitter Voltage, base open): Maximum voltage permissible between collector and emitter.
$I_C$ (Continuous Collector Current): Maximum steady current the collector can handle (e.g., 200mA for a 2N3904, up to several Amps for power transistors).
$P_D$ (Total Power Dissipation): Maximum power ( $V_{CE} \times I_C$ ) the device can dissipate without exceeding thermal limits.

10.2 Thermal Characteristics

$T_J$ (Junction Temperature): Maximum operating temperature of the semiconductor die.
Thermal Resistance ( $\theta_{JA}$ or $\theta_{JC}$ ): Indicates how well the package dissipates heat to the ambient air or a heatsink (measured in $^\circ C/W$ ).

10.3 Electrical Characteristics

$h_{FE}$ (DC Current Gain / $\beta$ ): The ratio of $I_C$ to $I_B$ . Usually specified as a range (e.g., 100-300) at a specific $I_C$ .
$V_{CE(sat)}$ (Collector-Emitter Saturation Voltage): The voltage drop across the transistor when it is fully ON (acting as a switch). Crucial for calculating power loss in robotic motor driver circuits.
$f_T$ (Transition Frequency): The frequency at which the current gain drops to 1. Indicates the maximum switching speed for high-frequency applications.

10.4 Physical Packaging

Information regarding the physical footprint, dimensions, and pinout (e.g., TO-92 for small signals, TO-220 for power transistors) to aid in PCB design.

Unit 1

Unit 3