Unit1 - Subjective Questions

Statement: 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, dimensions, etc.) remain constant.

Mathematical Expression:

• = Voltage (Volts)
• = Current (Amperes)
• = Resistance (Ohms )

Limitations:

1. Non-Linear Devices: It is not applicable to non-linear devices like diodes, transistors, and thyristors where the characteristic is not a straight line.
2. Temperature Dependence: It does not hold if the temperature changes significantly, as resistance changes with temperature.
3. Non-Metallic Conductors: It is not applicable to electrolytes and gas-discharge tubes.

1. Kirchhoff’s Current Law (KCL):

• Principle: Conservation of Charge.
• Statement: The algebraic sum of currents entering a node (junction) is equal to the algebraic sum of currents leaving the node. Alternatively, the algebraic sum of currents at any node is zero.
• Expression: or

2. Kirchhoff’s Voltage Law (KVL):

• Principle: Conservation of Energy.
• Statement: In any closed loop or mesh of an electrical circuit, the algebraic sum of all electromotive forces (EMFs) and voltage drops across resistors is zero.
• Expression: or

1. Voltage Division Rule:
Applicable to series circuits. Consider two resistors and in series across a voltage source .

• Total Resistance:
• Total Current:
• Voltage across ():
• Voltage across ():

2. Current Division Rule:
Applicable to parallel circuits. Consider two resistors and in parallel, with total entering current .

• Voltage across parallel branches is equal:
• Current through ():
• Current through ():

N-type Semiconductor:

• Formation: Formed by adding Pentavalent impurities (atoms with 5 valence electrons) like Phosphorus (P), Arsenic (As), or Antimony (Sb) to a pure intrinsic semiconductor (Si or Ge).
• Mechanism: Four valence electrons of the impurity form covalent bonds with neighboring Si atoms. The fifth electron is free to move.
• Carriers: Electrons are Majority carriers; Holes are Minority carriers.

P-type Semiconductor:

• Formation: Formed by adding Trivalent impurities (atoms with 3 valence electrons) like Boron (B), Gallium (Ga), or Indium (In) to a pure intrinsic semiconductor.
• Mechanism: Three valence electrons form bonds with neighboring Si atoms, leaving a vacancy known as a Hole.
• Carriers: Holes are Majority carriers; Electrons are Minority carriers.

Construction:
A PN junction is formed when a P-type semiconductor is joined metallurgically with an N-type semiconductor. A depletion region forms at the junction due to the diffusion of carriers, creating a potential barrier ( for Si, for Ge).

Working Principle:

1. Forward Bias:

   • Connection: P-terminal to Positive supply, N-terminal to Negative supply.
   • Operation: Holes from P-side and electrons from N-side are repelled towards the junction. They overcome the potential barrier. The depletion width decreases. Current flows easily.

2. Reverse Bias:

   • Connection: P-terminal to Negative supply, N-terminal to Positive supply.
   • Operation: Holes are attracted to the negative terminal and electrons to the positive terminal, moving away from the junction. The depletion width increases. Ideally, no current flows, but a small leakage current flows due to minority carriers.

The V-I characteristic curve is a plot of voltage across the diode () versus current through the diode ().

1. Forward Bias Region (1st Quadrant):

   • Initially, current is very small as long as the applied voltage is less than the Knee Voltage or Cut-in Voltage ().
   • When ( for Si), current increases exponentially. The diode behaves like a closed switch (low resistance).

2. Reverse Bias Region (3rd Quadrant):

   • Current is very small (micro-amperes) and constant, called Reverse Saturation Current (). This is due to minority carriers.
   • Breakdown: If reverse voltage exceeds the Breakdown Voltage (), the covalent bonds break, leading to a sharp increase in reverse current. This can damage the diode if not limited.

A PN junction diode can act as an electronic switch due to its behavior in forward and reverse bias.

1. ON State (Closed Switch):

   • When the diode is Forward Biased, the internal resistance drops to a very low value (ideally zero).
   • Current flows freely through the circuit.
   • It acts like a Short Circuit.

2. OFF State (Open Switch):

   • When the diode is Reverse Biased, the internal resistance becomes extremely high (ideally infinite).
   • Practically zero current flows.
   • It acts like an Open Circuit.

Application: Used in digital logic gates (AND, OR gates) and in switching power supplies.

1. Static (DC) Resistance ():

• It is the resistance offered by the diode to the flow of Direct Current (DC).
• It is calculated as the ratio of DC voltage to DC current at a specific operating point on the V-I curve.

2. Dynamic (AC) Resistance ():

• It is the resistance offered by the diode to the flow of Alternating Current (AC).
• It is defined as the reciprocal of the slope of the V-I characteristic curve at the operating point.
• It represents the change in voltage with respect to the change in current.

Circuit: Consists of a step-down transformer, a single diode in series with a load resistor .

Working:

• Positive Half Cycle: The diode is forward biased and conducts current through .
• Negative Half Cycle: The diode is reverse biased and acts as an open switch. No current flows.
• Output: Pulsating DC (only positive halves).

Efficiency ():
Defined as the ratio of DC output power to AC input power.

Construction: Uses a center-tapped transformer and two diodes ( and ) connected to a common load .

Operation:

1. Positive Half Cycle: Upper terminal of the secondary winding is positive. is Forward Biased (Conducts), is Reverse Biased (OFF). Current flows through and Load.
2. Negative Half Cycle: Lower terminal becomes positive relative to the center tap. is Forward Biased (Conducts), is Reverse Biased (OFF). Current flows through and Load.

Result: Current flows through the load in the same direction during both half cycles.

Peak Inverse Voltage (PIV):
When one diode conducts, the other is reverse biased. The total voltage across the non-conducting diode is the sum of voltages across both halves of the transformer secondary.

Working:

• Uses 4 diodes () in a bridge topology.
• Positive Half Cycle: and conduct. and are OFF. Path: Source Source.
• Negative Half Cycle: and conduct. and are OFF. Path: Source Source.
• Output is full-wave pulsating DC.

Advantages:

1. PIV Rating: The PIV across each diode is (half that of center-tapped), allowing the use of lower-rated diodes.
2. Transformer: No center-tapped transformer is required, making it smaller and cheaper.
3. Efficiency: Higher Transformer Utilization Factor (TUF).

Construction:
A BJT is a three-terminal semiconductor device consisting of two PN junctions. It has three doped regions:

1. Emitter (E): Highly doped, moderate size. Supplies charge carriers.
2. Base (B): Lightly doped, very thin. Controls the flow of carriers from Emitter to Collector.
3. Collector (C): Moderately doped, largest size (to dissipate heat). Collects charge carriers.

Types:

1. NPN Transistor: A thin P-layer is sandwiched between two N-layers. (Most common due to higher mobility of electrons).
2. PNP Transistor: A thin N-layer is sandwiched between two P-layers.

Biasing: The Emitter-Base junction is Forward Biased, and the Collector-Base junction is Reverse Biased (Active Mode).

Mechanism:

1. Injection: Electrons (majority carriers) from the N-type Emitter are repelled by the negative supply towards the Base.
2. Recombination: The Base is P-type, thin, and lightly doped. Only a few electrons (approx 2-5%) recombine with holes in the base, constituting the Base Current ().
3. Collection: The remaining electrons (95-98%) cross the Base and are attracted by the high positive potential of the Collector, constituting the Collector Current ().

Current Equation:
By KCL:
Since is very small, .

The mode depends on the biasing of the Emitter-Base (EB) and Collector-Base (CB) junctions.

1. Cut-off Mode:

   • EB Junction: Reverse Biased.
   • CB Junction: Reverse Biased.
   • Application: Transistor acts as an OFF switch (Open circuit).

2. Active Region:

   • EB Junction: Forward Biased.
   • CB Junction: Reverse Biased.
   • Application: Used for Amplification.

3. Saturation Mode:

   • EB Junction: Forward Biased.
   • CB Junction: Forward Biased.
   • Application: Transistor acts as an ON switch (Closed circuit).

1. Input Characteristics:

• Plot of Input Current () vs Input Voltage () keeping Output Voltage () constant.
• Resembles the forward characteristics of a PN junction diode.
• Current increases significantly after the cut-in voltage ().

2. Output Characteristics:

• Plot of Output Current () vs Output Voltage () for various fixed values of Input Current ().
• Cut-off Region: Both junctions reverse biased. .
• Active Region: is nearly constant for a given and is proportional to . Used for amplification.
• Saturation Region: is very low, increases rapidly. Both junctions forward biased.

Definitions:

• (Common Base Gain): Ratio of collector current to emitter current. (Value < 1).
• (Common Emitter Gain): Ratio of collector current to base current. (Value >> 1).

Relationship Derivation:
We know:
Divide by :
Substitute definitions:

Ripple Factor ():

• It acts as a measure of the purity of the DC output.
• It is defined as the ratio of the RMS value of the AC component (ripple) in the output to the DC component.
• Lower ripple factor indicates better DC quality (closer to pure DC).

Need for Filter:

• The output of a rectifier is "Pulsating DC," meaning it contains both DC and AC components (ripples).
• Most electronic circuits require a steady, constant DC voltage (like a battery).
• Filter circuits (Capacitors, Inductors) are used to remove the AC ripples and smooth out the waveform.

Energy Band Theory: Describes the behavior of electrons in solids in terms of energy ranges called bands (Valence Band - VB, Conduction Band - CB) separated by a Forbidden Energy Gap ().

1. Conductors:

   • VB and CB overlap.
   • eV.
   • Electrons move freely; high conductivity.

2. Semiconductors:

   • Small Forbidden Gap.
   • eV (e.g., Si = 1.1eV, Ge = 0.72eV).
   • Behave as insulators at 0K, conductors at higher temps.

3. Insulators:

   • Large Forbidden Gap.
   • eV (e.g., Diamond eV).
   • Electrons cannot jump from VB to CB; no conductivity.