Bipolar Junction Transistor (BJT) – Comprehensive Bullet-Point Notes

Introduction

• A Bipolar Junction Transistor (BJT) is a three-terminal semiconductor device that amplifies signals in terms of voltage, current, or power.
• Common applications: oscillators, digital switching, computers, satellites, mobile phones, modern communication systems.
• Term “bipolar” denotes that both electrons and holes (two opposite polarities of charge carriers) participate in current conduction.

Construction of a BJT

• Two basic types:
  • pnp: n-type layer sandwiched between two p-type layers.
  • npn: p-type layer sandwiched between two n-type layers.
• Layers / terminals:
  • Emitter (E): moderate size, heavily doped → injects large number of majority carriers.
  • Base (B): very thin & lightly doped → passes most injected carriers to collector.
  • Collector (C): largest area, moderately doped → collects carriers & dissipates heat.
• Ratios (typical design rules):
  • Total width : base width ≈ $150:1$
  • Doping (emitter or collector) : base doping ≥ $10:1$
• Two internal p-n junctions:
  • Emitter–Base junction (J_E)
  • Collector–Base junction (J_C)

Basic Operation (Transistor Action)

• Normal/Active mode biasing:
  • Emitter–Base junction forward-biased (FB).
  • Collector–Base junction reverse-biased (RB).
• Using a pnp for explanation (reverse polarities for npn):
  • Forward bias $V_{EE}$ drives majority holes from emitter → base.
  • Base is thin/lightly doped, so only ~2 % recombine (forms base current $I_B$).
  • Remaining ~98 % holes diffuse across base → reach reverse-biased collector region, swept into collector, producing collector current $I_C$.
• Kirchhoff current law at one node: $I<em>E = I</em>C + I_B$.
• $I_C$ has two parts:
  • Majority component (from emitter flow).
  • Minority component (reverse saturation) $I_{CO}$ (with emitter open).
  • $I<em>C = I</em>{C\,Majority} + I_{CO\,Minority}$.
• Key design point: thin, lightly doped base between heavily doped emitter & moderately doped collector → enables transistor action.
• Two back-to-back diodes cannot substitute a transistor because:
  1. Doping profiles are not satisfied.
  2. Diffusion mechanism that transfers nearly entire emitter current to collector is absent.

Circuit Symbols

• Arrow on emitter indicates conventional current when the emitter junction is forward biased.
  • Arrow outward (from emitter) → npn.
  • Arrow inward → pnp.

Modes of Operation (Bias Combinations)

Common-Base (CB)

• Base is common to input (E–B) & output (C–B).
• Low input resistance (≈ $20\,\Omega$), very high output resistance (50 kΩ–1 MΩ).
• Current gain $\alpha$ (< 1) but very good voltage gain.
• Used as input stage & at high frequencies.
• Early Effect / Base-Width Modulation: Increasing $V_{CB}$ (reverse bias) widens depletion in base, reducing effective base width ⇒
  1. Fewer recombinations → $I_B$ ↓
  2. Greater minority-carrier gradient → $I_E$ ↑
  3. Extreme case: Punch-through (base width → 0) → breakdown.
• Assumption for analysis once ON: $V_{BE} \approx 0.7\,\text{V}$ (Si).

CB Characteristics

• Input (IE–VBE) resembles diode FB curve; shifts with $V_{CB}$.
• Output (IC–VCB): three regions
  • Cut-off (below $I<em>E=0$): only $I</em>{CBO}$ flows.
  • Active (flat portions): $I<em>C \approx \alpha I</em>E$, independent of $V_{CB}$.
  • Saturation (left of $V<em>{CB}=0$): both junctions FB, $I</em>C$ rises sharply.
• Definitions:
  • $\alpha<em>{dc}= \dfrac{I</em>C}{I_E}$ (0.9 – 0.998).
  • $\alpha<em>{ac}= \dfrac{\Delta I</em>C}{\Delta I<em>E}\big|</em>{V<em>{CB}}$ (≈ $\alpha</em>{dc}$).
  • Total collector current: $I<em>C = \alpha I</em>E + I_{CBO}$.

Common-Emitter (CE)

• Emitter common; input (B–E), output (C–E).
• Medium input resistance (~1 kΩ); high output resistance (50–500 kΩ).
• Provides high current gain $\beta$ (50 – 400) and medium voltage gain → huge power gain.
• Widely used in amplifiers & cascaded stages.

CE Characteristics

• Input (IB–VBE): diode-like; higher $V<em>{CE}$ reduces $I</em>B$ at constant $V_{BE}$ (Early effect).
• Output (IC–VCE) regions:
  1. Cut-off: $I<em>B \approx 0$ yet $I</em>C = I<em>{CEO}$ (larger than $I</em>{CBO}$). $I<em>{CEO}=\dfrac{I</em>{CBO}}{1-\alpha}=(\beta+1)I_{CBO}$.
  2. Active: C–B RB, E–B FB. $I<em>C = \beta I</em>B + I<em>{CEO}$ (normally $\beta I</em>B$ dominates).
  3. Saturation: $V<em>{CE}\le V</em>{CE(sat)}$ (~0.2 V Si); both junctions FB; $I<em>C$ no longer proportional to $I</em>B$.
• Current gains:
  • $\beta<em>{dc}= \dfrac{I</em>C}{I_B}$ (50 – 400 typical).
  • $\beta<em>{ac}= \dfrac{\Delta I</em>C}{\Delta I<em>B}\big|</em>{V_{CE}}$.
• Relations between $\alpha$ & $\beta$:
  • $\alpha = \dfrac{\beta}{\beta+1}$
  • $\beta = \dfrac{\alpha}{1-\alpha}$
• Collector current expressions:
  • $I<em>C = \beta I</em>B + I_{CEO}$
  • or $I<em>C = \beta I</em>B + (\beta+1)I_{CBO}$.

Common-Collector (CC) (Emitter-Follower)

• Collector common to both circuits.
• Input resistance very high (100 kΩ – 500 kΩ), output resistance low (~100 Ω).
• Current gain ≈ $\beta+1$; voltage gain < 1 (≈ unity).
• Ideal for impedance matching—drives low-impedance load from high-impedance source.
• Output & input characteristics similar to CE; analysis uses CE curves.

Key Parameters & Formulae (Summary)

• Current relation: $I<em>E = I</em>C + I_B$.
• CB: $I<em>C = \alpha I</em>E + I_{CBO}$.
• CE: $I<em>C = \beta I</em>B + I_{CEO}$.
• Leakage currents:
  • $I_{CBO}$: collector current with emitter open.
  • $I<em>{CEO}$: collector current with base open $\Rightarrow I</em>{CEO} = \dfrac{I<em>{CBO}}{1-\alpha} = (\beta+1)I</em>{CBO}$.
• Typical silicon diode drop assumed: $V_{BE(on)} = 0.7\,\text{V}$.

Amplification Concept (CB Example)

• Given $R<em>i = 20\,\Omega,\; V</em>i = 200\,\text{mV}$ → $I<em>i = V</em>i/R_i = 10\,\text{mA}$.
• With $\alpha \approx 1$ ⇒ $I<em>L \approx I</em>i$.
• Using $R<em>L = 5\,\text{k}\Omega$ → $V</em>L = I<em>L R</em>L = 50\,\text{V}$.
• Voltage gain $A<em>v = V</em>L/V_i = 250$ (output signal 250× input amplitude).

Comparison of Configurations

• Doping asymmetry (heavy E, light B, moderate C) cannot be replicated with discrete diodes.
• In a transistor, injected majority carriers diffuse through base and are swept by collector field; diodes lack this through-transport mechanism.

Solved-Example Highlights

• Example results illustrate use of $\alpha$, $\beta$, leakage currents, and relationships:
  • $\beta = 49$ when $\alpha=0.98$, etc.
  • Calculation of $I<em>C, I</em>E, I_B$ from given parameters.
• Key takeaway: small base currents (µA) control larger emitter/collector currents (mA).

Multiple-Choice / Concept Reinforcement (Key Ideas)

• BJT is current-controlled current device.
• Contains two p-n junctions ⇨ two depletion layers.
• Base: lightly doped; Collector: largest & moderately doped; Emitter: heavily doped.
• Arrow on symbol gives conventional current direction when E–B is FB.
• Amplifier operation ⇒ active region.
• Cut-off: both junctions RB; Saturation: both FB.
• Leakage currents rise steeply with temperature; $I<em>{CEO} \gg I</em>{CBO}$.
• CE input resistance ≈ 1 kΩ; lowest $R_{out}$ in CC configuration.

Fill-in / Short Concept Statements

• Base is lightly doped.
• Terminals: emitter, base, collector.
• For amplification: E–B forward, C–B reverse.
• Arrowed line in symbol = emitter.
• \alpha < 1, typically 0.9–0.998.
• CE: emitter common.
• CC used for impedance matching.

Review & Practice Notes

• Understand biasing combinations and regions (cut-off, active, saturation, inverse active).
• Master characteristic plots (CB & CE): label axes and regions.
• Prove relations $\alpha\text{–}\beta$, derive leakage-current formulas.
• Temperature dependence: leakage currents roughly double every 10 °C in Si.
• Practice conversions between $\alpha$, $\beta$, and current components in both configurations.

Ethical / Practical Implications

• High transistor densities (IC era) demand thermal management; leakage currents affect standby power and reliability.
• Proper biasing prevents thermal runaway and ensures faithful amplification.

Real-World Connections

• BJTs still favored in RF power stages and discrete-component designs despite MOS dominance in digital ICs.
• Concepts (saturation, cut-off) directly map to logic-level switching in TTL families.

Quick Formula Sheet

• $I<em>E = I</em>C + I_B$
• $I<em>C = \alpha I</em>E + I_{CBO}$ (CB)
• $I<em>C = \beta I</em>B + I_{CEO}$ (CE)
• $I<em>{CEO} = (\beta+1) I</em>{CBO}$
• $\beta = \dfrac{\alpha}{1-\alpha}, \; \alpha = \dfrac{\beta}{\beta+1}$
• $V_{BE(on)} \approx 0.7\,\text{V (Si)},\; 0.3\,\text{V (Ge)}$
• Early Voltage concept (slope of output curves) models finite output resistance in active region.