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

1. Fundamentals of Electrical Laws

1.1 Ohm’s Law

Ohm's Law states that the current () flowing through a conductor between two points is directly proportional to the voltage () across the two points, provided the physical conditions (like temperature) remain constant.

• Formula:
  • = Voltage in Volts (V)
  • = Current in Amperes (A)
  • = Resistance in Ohms ()
• Limitations: Not applicable to non-linear devices (diodes, transistors), non-metallic conductors, or varying temperatures.

1.2 Kirchhoff’s Laws

These laws govern the conservation of charge and energy in electrical circuits.

A. Kirchhoff’s Current Law (KCL)

• 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 a node is zero.
• Principle: Conservation of Charge.
• Formula:

B. Kirchhoff’s Voltage Law (KVL)

• Statement: In any closed loop (mesh), the algebraic sum of all voltage drops (across resistors) and EMFs (voltage sources) is equal to zero.
• Principle: Conservation of Energy.
• Formula: or

1.3 Circuit Division Rules

Voltage Division Rule (Series Circuits)

Used to find the voltage across a specific resistor in a series circuit.

• The voltage drops across resistors are proportional to their resistance values.
• Formula:

Current Division Rule (Parallel Circuits)

Used to find the current flowing through a specific branch in a parallel circuit.

• Current divides inversely proportional to resistance.
• Formula (for two resistors ):
  • Current through :
  • Current through :

2. Basics of Semiconductors

Semiconductors are materials (typically Silicon or Germanium) whose conductivity lies between conductors and insulators.

2.1 Intrinsic Semiconductors

• Definition: Semiconductors in their purest form without any impurities.
• Carrier Concentration: The number of free electrons () equals the number of holes (). .
• Conductivity: Low at room temperature; increases with temperature.

2.2 Extrinsic Semiconductors

Formed by adding impurities (doping) to intrinsic semiconductors to increase conductivity.

3. PN Junction Diode

3.1 Construction and Formation

Formed by metallurgically joining a P-type semiconductor and an N-type semiconductor.

• Depletion Region: Near the junction, electrons from the N-side diffuse to the P-side and recombine with holes. This creates a region devoid of free carriers containing only immobile ions.
• Barrier Potential: An electric field is created across the depletion region ( for Silicon, for Germanium).

3.2 Biasing and Working

1. Forward Bias:
   • P-terminal connected to Positive (+), N-terminal to Negative (-).
   • Depletion width decreases.
   • Current flows easily once barrier potential is overcome.
2. Reverse Bias:
   • P-terminal connected to Negative (-), N-terminal to Positive (+).
   • Depletion width increases.
   • Ideally no current flows (practically, a tiny leakage current exists).

3.3 V-I Characteristics

The Voltage-Current characteristic curve describes the diode's behavior.

• Forward Region: Current rises exponentially after the Knee Voltage (Cut-in voltage).
• Reverse Region: Minimal current (Reverse Saturation Current) until Breakdown Voltage is reached, where current spikes dangerously.

3.4 Applications

A. Rectifiers

A rectifier converts Alternating Current (AC) into pulsating Direct Current (DC).

• Half-Wave Rectifier: Uses 1 diode. Conducts only during the positive half-cycle of input AC. Efficiency .
• Full-Wave Bridge Rectifier: Uses 4 diodes in a bridge topology. Conducts during both positive and negative half-cycles. Efficiency .

B. Diode as a Switch

• ON State: When Forward Biased, resistance is very low (), acting as a closed switch.
• OFF State: When Reverse Biased, resistance is very high (), acting as an open switch.

4. Bipolar Junction Transistor (BJT)

A BJT is a three-terminal, current-controlled device used for amplification and switching.

4.1 Construction

• Terminals:
  • Emitter (E): Heavily doped, emits carriers.
  • Base (B): Lightly doped, very thin, passes carriers from E to C.
  • Collector (C): Moderately doped, large physical size, collects carriers.
• Junctions: Emitter-Base Junction () and Collector-Base Junction ().

4.2 Types

1. NPN: P-type base sandwiched between two N-regions. (Current flows C to E).
2. PNP: N-type base sandwiched between two P-regions. (Current flows E to C).

4.3 Modes of Operation

4.4 Working of NPN Transistor (CE Configuration)

In the Common Emitter (CE) configuration, the Emitter is common to both input and output.

• Biasing: Base-Emitter is Forward Biased (), Collector-Base is Reverse Biased ().
• Process:
  1. Electrons from the N-type Emitter cross into the P-type Base.
  2. Since the Base is thin and lightly doped, only a few electrons () recombine with holes (constituting Base Current ).
  3. The remaining electrons () are attracted by the high positive potential of the Collector, crossing (constituting Collector Current ).
• Current Equation:

4.5 CE Configuration Characteristics

Input Characteristics

• Plot of Input Current () vs Input Voltage () at constant Output Voltage ().
• Resembles the forward characteristics of a diode. Current increases after .

Output Characteristics

• Plot of Output Current () vs Output Voltage () at constant Input Current ().
• Three Regions:
  1. Cut-off: Both junctions reverse biased; .
  2. Saturation: Both junctions forward biased; increases rapidly with .
  3. Active: forward, reverse; is constant regardless of (amplification region).