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Practice MCQ

Unit 1 - Notes

ECE249

Unit 1: Fundamentals of Electrical Laws, Semiconductor Devices and its Applications

Part A: DC Circuit Analysis Fundamentals

1. Ohm’s Law

Ohm’s Law is the most fundamental relationship in circuit theory.

Statement: At a constant temperature, the current ( $I$ ) flowing through a conductor is directly proportional to the potential difference ( $V$ ) across its ends.
Formula:

Where:
- $V$ = Voltage (Volts)
- $I$ = Current (Amperes)
- $R$ = Resistance (Ohms, $\Omega$ )
Limitations:
- Does not apply to non-linear devices (e.g., diodes, transistors).
- Does not apply if physical conditions (temperature, pressure) change.
- Does not apply to non-metallic conductors (e.g., electrolytes).

2. Kirchhoff’s Laws

Kirchhoff’s laws deal with the conservation of charge and energy in electrical circuits.

A. Kirchhoff’s Current Law (KCL)

Principle: Conservation of Charge.
Statement: The algebraic sum of currents entering a node (junction) is equal to the sum of currents leaving the node. Alternatively, the algebraic sum of currents at any node is zero.
Formula:
$\sum I_{entering} = \sum I_{leaving}$
or
$\sum I = 0$

B. Kirchhoff’s Voltage Law (KVL)

Principle: Conservation of Energy.
Statement: In any closed loop (mesh), the algebraic sum of all voltage drops and voltage rises (EMFs) is equal to zero.
Formula:
$\sum V_{rise} = \sum V_{drop}$
or
$\sum V = 0$
Sign Convention (Standard):
- Moving from $-$ to $+$ is a Voltage Rise ( $+$ ).
- Moving from $+$ to $-$ is a Voltage Drop ( $-$ ).

3. Circuit Division Rules

A. Voltage Division Rule (VDR)

Applicable only to Series Circuits. In a series circuit, current is constant, but voltage divides proportionally to resistance.

For two resistors $R_1$ and $R_2$ in series with a source voltage $V_s$ :

Voltage across $R_1$ :
$V_1 = V_s \times \frac{R_1}{R_1 + R_2}$
Voltage across $R_2$ :
$V_2 = V_s \times \frac{R_2}{R_1 + R_2}$

B. Current Division Rule (CDR)

Applicable only to Parallel Circuits. In a parallel circuit, voltage is constant, but current divides inversely proportional to resistance.

For two resistors $R_1$ and $R_2$ in parallel with a total entering current $I_s$ :

Current through $R_1$ :
$I_1 = I_s \times \frac{R_2}{R_1 + R_2}$
Current through $R_2$ :
$I_2 = I_s \times \frac{R_1}{R_1 + R_2}$

Part B: Basics of Semiconductors

Semiconductors are materials with conductivity between conductors (copper) and insulators (glass). The most common materials are Silicon (Si) and Germanium (Ge).

1. Band Theory of Solids

Valence Band: The energy band containing valence electrons.
Conduction Band: The energy band containing free electrons responsible for conduction.
Forbidden Energy Gap ( $E_g$ ): The energy difference between the valence and conduction bands.
- Insulators: Large gap ( $> 5$ eV).
- Conductors: Overlapping bands (No gap).
- Semiconductors: Small gap ( $Si \approx 1.1$ eV, $Ge \approx 0.72$ eV).

2. Intrinsic Semiconductors

Definition: Extremely pure semiconductor material with no impurities.
Mechanism: At 0K, it acts as an insulator. At room temperature, thermal energy breaks covalent bonds, creating electron-hole pairs.
Carrier Concentration: Number of electrons ( $n$ ) = Number of holes ( $p$ ).
$n = p = n_i$ (Intrinsic concentration).

3. Extrinsic Semiconductors

Formed by Doping (adding a specific impurity to an intrinsic semiconductor to increase conductivity).

A. N-Type Semiconductor

Dopant: Pentavalent impurity (5 valence electrons) like Phosphorus (P), Arsenic (As), Antimony (Sb).
Mechanism: 4 valence electrons form bonds with Si; the 5th electron becomes a free electron.
Carriers:
- Majority Carriers: Electrons.
- Minority Carriers: Holes (thermally generated).
Charge: Electrically neutral overall.

B. P-Type Semiconductor

Dopant: Trivalent impurity (3 valence electrons) like Boron (B), Gallium (Ga), Indium (In).
Mechanism: 3 valence electrons form bonds; a vacancy (hole) is created in the 4th bond.
Carriers:
- Majority Carriers: Holes.
- Minority Carriers: Electrons (thermally generated).
Charge: Electrically neutral overall.

Part C: PN Junction Diode

1. Formation and Working

When a P-type block is joined with an N-type block:

Diffusion: Holes from P-side diffuse to N-side; Electrons from N-side diffuse to P-side.
Depletion Region: A region creates near the junction containing immobile ions (negative ions in P-side, positive ions in N-side) and no free charge carriers.
Barrier Potential ( $V_b$ ): An electric field forms opposing further diffusion.
- Silicon: $\approx 0.7$ V
- Germanium: $\approx 0.3$ V

2. Biasing Modes

A. Forward Bias

Connection: P-terminal to Battery Positive; N-terminal to Battery Negative.
Effect: External field opposes the barrier potential. The depletion width decreases.
Result: Current flows easily once voltage exceeds the knee voltage ($0.7$V for Si).

B. Reverse Bias

Connection: P-terminal to Battery Negative; N-terminal to Battery Positive.
Effect: External field aids the barrier potential. The depletion width increases.
Result: Ideally no current flows. Practically, a tiny Reverse Saturation Current ( $I_0$ ) flows due to minority carriers.

3. V-I Characteristics

The graph of Current ( $I$ ) vs Voltage ( $V$ ) across the diode.

Forward Region (1st Quadrant): Current is small until cut-in voltage ($0.7$V), then increases exponentially.
Reverse Region (3rd Quadrant): Very small constant leakage current ( $nA$ or $\mu A$ ).
Breakdown: If reverse voltage is too high, the junction breaks down (Avalanche or Zener breakdown), leading to a massive current surge.

4. Applications of Diode

A. Diode as a Switch

ON Switch: When Forward Biased, it acts as a short circuit (ideal) or small resistor (practical).
OFF Switch: When Reverse Biased, it acts as an open circuit.

B. Diode as a Rectifier

Rectification is the process of converting AC (Alternating Current) to DC (Direct Current).

Half-Wave Rectifier:
- Component: Single diode.
- Working: Conducts only during the positive half-cycle of input AC.
- Efficiency: Max 40.6%.
- Ripple Factor: 1.21 (High ripple).
Full-Wave Rectifier (Center-Tapped):
- Components: Two diodes, Center-tapped transformer.
- Working: D1 conducts in positive half; D2 conducts in negative half. Current flows through load in the same direction for both halves.
- Efficiency: Max 81.2%.
Bridge Rectifier:
- Components: Four diodes in a bridge topology.
- Working: D1 & D3 conduct in positive half; D2 & D4 conduct in negative half. No center-tapped transformer required.
- Efficiency: Max 81.2%.
- Ripple Factor: 0.48 (Smoother DC).

Part D: Bipolar Junction Transistor (BJT)

A BJT is a three-terminal, current-controlled semiconductor device consisting of two PN junctions back-to-back.

1. Construction and Terminals

Terminals:
- Emitter (E): Heavily doped, moderate size. Emits charge carriers.
- Base (B): Lightly doped, very thin. Controls the flow of carriers.
- Collector (C): Moderately doped, largest size (to dissipate heat). Collects carriers.
Types:
- NPN: P-type base sandwiched between N-type Emitter and Collector (Most common due to higher electron mobility).
- PNP: N-type base sandwiched between P-type Emitter and Collector.

2. Fundamental Current Equation

Applying KCL to the transistor:

I_E = I_B + I_C

Since the base is very thin and lightly doped,

I_B

is very small (

\approx 2\%

of total), so

I_E \approx I_C

3. Modes of Operation

Biasing of the Emitter-Base Junction ( $J_{EB}$ ) and Collector-Base Junction ( $J_{CB}$ ) determines the mode.

Mode	$J_{EB}$ Bias	$J_{CB}$ Bias	Application
Active	Forward	Reverse	Amplifier
Saturation	Forward	Forward	Switch (Closed/ON)
Cut-off	Reverse	Reverse	Switch (Open/OFF)

4. Common Emitter (CE) Configuration

In this configuration, the Emitter is common to both input and output circuits.

Input: Applied between Base and Emitter.
Output: Taken between Collector and Emitter.

Working (NPN in Active Mode)

Forward Bias ( $V_{BE}$ ): Electrons from the Emitter are pushed into the Base.
Base Region: Since the base is thin and lightly doped, only a few electrons recombine with holes (constituting small Base current $I_B$ ).
Reverse Bias ( $V_{CB}$ ): The strong positive potential at the Collector attracts the remaining majority of electrons from the Base across the junction.
Result: Large Collector current $I_C$ flows controlled by small $I_B$ .

Characteristics

A. Input Characteristics ( $I_B$ vs $V_{BE}$ keeping $V_{CE}$ constant)

Resembles a forward-biased diode.
Current remains zero until barrier potential is overcome, then rises exponentially.

B. Output Characteristics ( $I_C$ vs $V_{CE}$ keeping $I_B$ constant)

Cut-off Region: $I_B = 0$ , $I_C \approx 0$ . Transistor is OFF.
Active Region: $I_C$ is nearly constant for a fixed $I_B$ . $I_C$ is proportional to $I_B$ . Used for amplification.
Saturation Region: Both junctions forward biased. $V_{CE}$ is very small ($0.2$V). $I_C$ increases rapidly with $V_{CE}$ .

Current Gain ( $\beta$ )

In CE configuration, the current gain is the ratio of output current to input current:

\beta = \frac{I_C}{I_B}

(Typical values of

\beta

range from 20 to 500).