Unit2 - Subjective Questions

Power Amplifier: A power amplifier is a circuit designed to deliver a large amount of power to a low-resistance load (such as a loudspeaker or motor). It handles large voltage and current signals.

Differences:

• Primary Function: Voltage amplifiers increase the voltage level of a weak signal, while power amplifiers increase the power level of a signal to drive a heavy load.
• Transistor Application: Voltage amplifiers use transistors with low power dissipation; power amplifiers use power transistors with large power dissipation capabilities.
• Beta (): Voltage amplifiers typically have a high (>100), whereas power amplifiers have a lower (20 to 50).
• Coupling: Voltage amplifiers often use RC coupling, whereas power amplifiers frequently use transformer coupling for impedance matching.

In a Class A large signal amplifier, the transistor is biased such that it operates in the active region for the entire of the input AC signal cycle.

Key Characteristics:

• Operating Point (Q-point): The Q-point is located roughly at the center of the AC load line.
• Conduction Angle: The transistor conducts for the full ( radians) of the input cycle.
• Distortion: Because it operates in the linear region of its characteristic curve, the output signal is an exact replica of the input signal, resulting in very low distortion.
• Efficiency: The primary drawback is its low overall efficiency. The transistor continuously dissipates power even when no input signal is applied. The maximum theoretical efficiency is for a series-fed and for a transformer-coupled Class A amplifier.

For a series-fed Class A amplifier, the DC power supplied by the source () is:

The AC power delivered to the load () is:

where and are peak AC voltage and current.
For maximum efficiency, the Q-point is at the center of the load line. Thus, the maximum peak voltage swing is and the maximum peak current swing is .
Substituting these maximum values into the AC power equation:

The maximum efficiency () is the ratio of maximum AC power to DC power:


Therefore, the maximum theoretical efficiency is .

Second Harmonic Distortion occurs when a large signal swings the transistor into the non-linear portions of its characteristic curves.

• Cause: The dynamic transfer characteristic of a transistor is not perfectly linear. A pure sinusoidal input signal produces an output current that contains the fundamental frequency and additional harmonics (multiples of the fundamental frequency).
• Mathematical Representation: The output collector current can be expressed as:
  
  where represents the second harmonic component.
• Significance: The second harmonic is usually the most prominent distortion component in single-ended Class A amplifiers. It causes the output waveform to be asymmetrical (e.g., flattened peaks). It reduces the audio quality in audio amplifiers. Push-pull configurations are often used specifically to cancel out even harmonics, including the second harmonic.

A Transformer Coupled Audio Power Amplifier uses a step-down transformer to couple the output of the amplifier to the load (like a speaker).

Construction:

• The primary winding of an output transformer is connected between the transistor's collector and the DC supply .
• The secondary winding is connected to a low impedance load, .

Working:

• The transformer provides impedance matching. A speaker usually has a very low impedance ( to ), while the transistor requires a higher load impedance for maximum power transfer.
• The effective impedance seen by the primary is , where is the turns ratio.
• The DC resistance of the primary winding is very low, reducing DC power loss compared to a series-fed resistor, thereby improving the efficiency to a theoretical maximum of .

In a transformer-coupled Class A amplifier, the primary DC resistance is assumed to be zero. Therefore, .

The DC power input is:

The AC power output is:

Under maximum signal conditions, the peak voltage swing can reach , and the peak current swing can reach .
Substituting these values:

The maximum efficiency () is:


Thus, the theoretical maximum efficiency is .

In a Class B amplifier, the transistor is biased exactly at the cut-off point.

Operating Principle:

• Conduction Angle: The transistor conducts for only one-half of the input signal cycle ( or radians).
• Biasing: Zero DC bias is applied to the base-emitter junction (in ideal cases), meaning the Q-point is on the X-axis of the load line ().
• Efficiency: Because the transistor is completely off during the other half-cycle, no DC quiescent current flows, significantly reducing wasted power and increasing efficiency. The theoretical maximum efficiency is .
• Distortion: A single Class B transistor produces severe distortion since only half the waveform is reproduced. To reproduce the full waveform, two transistors are used in a push-pull arrangement.

A Push-Pull Amplifier uses two active devices (transistors) that operate on alternating halves of the input signal cycle to deliver power to the load.

Basic Principle:

• An input signal is split into two out-of-phase signals (using a center-tapped transformer or a phase inverter).
• One transistor is driven by the positive-going signal, and the other is driven by the negative-going signal.
• During the positive half-cycle of the original input, transistor 1 conducts (pushes current to the load) while transistor 2 is off.
• During the negative half-cycle, transistor 2 conducts (pulls current from the load) while transistor 1 is off.
• An output transformer (or complementary symmetry setup) recombines these two halves into a complete sine wave across the load.
• Advantage: This configuration cancels out even-order harmonics, reducing distortion, and allows high efficiency (typically operated in Class B or AB).

In a Class B push-pull amplifier, each transistor conducts for half a cycle.
DC Power Input:
The average DC current drawn from the supply is .

AC Power Output:
The AC power delivered to the load is:

Efficiency ():

Maximum Efficiency:
Efficiency is maximum when the voltage swing is maximum, i.e., .


The theoretical maximum efficiency of a Class B push-pull amplifier is .

Cross-over Distortion is a specific type of distortion that occurs in Class B push-pull amplifiers.

• Why it occurs: In a Class B amplifier, transistors are biased at cutoff (zero base-emitter voltage). However, a practical silicon transistor requires a minimum forward voltage (cut-in voltage, ) across the base-emitter junction to start conducting.
• Effect: When the input AC signal crosses zero (moving from positive to negative or vice-versa), there is a small interval where the input voltage is between and . During this brief period, neither transistor is turned on.
• Result: The output waveform stays at zero for a short time at each zero-crossing point, creating a "dead band." This makes the output waveform look distorted near the zero-crossing, hence the name "cross-over distortion."

A Class AB amplifier eliminates cross-over distortion by applying a small, non-zero forward bias to the transistors.

• Biasing Mechanism: Diodes or a resistor divider network are used to bias the base-emitter junctions slightly above zero volts (e.g., just around the cut-in voltage, for silicon).
• Operating Cycle: Because of this small bias, the transistors are already slightly "on" even when no input signal is present. They conduct for slightly more than of the input cycle.
• Elimination of Distortion: When the input signal crosses zero, one transistor begins to turn off while the other is already beginning to turn on. The smooth transition ensures there is no "dead band" where both transistors are off, effectively eliminating cross-over distortion while retaining an efficiency close to that of a Class B amplifier.

Comparison of Power Amplifiers:

1. Class A:

   • Conduction Angle: ()
   • Q-point Position: Center of the active region (middle of load line)
   • Maximum Efficiency: (RC coupled), (Transformer coupled)

2. Class B:

   • Conduction Angle: ()
   • Q-point Position: Exactly on the cut-off point (X-axis)
   • Maximum Efficiency:

3. Class AB:

   • Conduction Angle: Between and
   • Q-point Position: Slightly above the cut-off point
   • Maximum Efficiency: Between and

4. Class C:

   • Conduction Angle: Less than
   • Q-point Position: Below the cut-off point (deep into cut-off)
   • Maximum Efficiency: Extremely high, approaching (used mainly in RF tuned amplifiers).

A Complementary Symmetry Push-Pull Amplifier uses two transistors of opposite types (one NPN and one PNP) with matched characteristics.

Working:

• Both transistors are connected in an emitter-follower configuration, sharing the same input signal at their bases.
• During the positive half-cycle of the input signal, the NPN transistor is forward-biased and conducts, supplying current to the load. The PNP transistor is reverse-biased and stays off.
• During the negative half-cycle, the PNP transistor is forward-biased and conducts, drawing current from the load, while the NPN transistor turns off.
• The combined action produces a full AC wave across the load.

Advantages:

1. No Transformers Needed: It eliminates the need for bulky and expensive input (center-tapped) and output transformers.
2. Frequency Response: The absence of transformers greatly improves the low and high-frequency response of the amplifier.
3. Cost and Size: Lighter, smaller, and cheaper to construct.

When reading the datasheet for a 2N3055 (a widely used NPN power transistor), the following key absolute maximum ratings and electrical characteristics are critical:

• (Collector-Emitter Voltage): Maximum voltage it can withstand without breaking down (typically 60V for 2N3055).
• (Continuous Collector Current): Maximum continuous current it can handle (typically 15A).
• (Total Power Dissipation): Maximum power it can dissipate safely at a specific case temperature (typically 115W at C case temperature).
• (DC Current Gain): Beta value, which is usually low for power transistors (typically 20-70 at ).
• (Junction Temperature): The maximum safe operating temperature for the semiconductor junction (typically C).
• Thermal Resistance (): Important for designing the heat sink.

Significance of Heat Sinks and Thermal Resistance:

• Power Dissipation: Power transistors in amplifiers dissipate large amounts of power in the form of heat at the collector junction. If this heat is not removed, the junction temperature () will exceed its safe limit, destroying the transistor.
• Thermal Resistance (): It is a measure of a material's resistance to heat flow, expressed in C/W. The total thermal resistance from junction to ambient is (Junction-to-case, Case-to-sink, Sink-to-ambient).
• Heat Sinks: A heat sink is a metallic structure with a large surface area attached to the transistor. It lowers the , allowing heat to flow efficiently from the transistor case to the surrounding air.
• Result: By keeping the total thermal resistance low, a heat sink ensures the junction temperature remains safely below its maximum rating, even at high power dissipation levels.

In a standard push-pull amplifier using identical transistor types (e.g., both NPN), the two transistors must be driven by signals that are out of phase with each other.

Role of Phase Inverter:

• A phase inverter (or phase splitter) circuit takes a single input signal and provides two output signals of equal amplitude but opposite phase ( phase shift).
• This replaces the bulky input center-tapped transformer, reducing weight and cost while improving frequency response.
• Common Configuration: A split-load phase inverter is often used. It consists of a single transistor with load resistors in both the collector and emitter circuits. The signal taken from the collector is out of phase with the input, while the signal taken from the emitter is in phase with the input. Thus, the two outputs are out of phase with each other and can drive the push-pull pair.

The 5-point method is a graphical technique used to determine the harmonic distortion components from the dynamic transfer characteristics (or load line) of an amplifier.

Procedure:

1. Identify the quiescent collector current .
2. Apply an input signal and identify 5 points on the output current waveform corresponding to specific input phase angles:
   • (at )
   • (at )
   • (at )
   • (at )
   • (at )
3. Using mathematical Fourier analysis, formulas are derived for the DC component (), fundamental component (), second harmonic (), third harmonic (), and fourth harmonic () in terms of these measured currents.
4. The fractional harmonic distortion for the -th harmonic is calculated as .
5. The Total Harmonic Distortion (THD) is then found using the root mean square of individual distortions:
   
   This method allows engineers to evaluate the linearity of the amplifier practically.

In a Class B push-pull amplifier, the power dissipated by the transistors () is the difference between DC input power and AC output power.

To find the maximum power dissipation, we differentiate with respect to and set it to zero:

This gives the voltage swing for maximum dissipation: .
Substituting this back into the equation gives the total maximum power dissipated by both transistors:

Since there are two transistors sharing this heat, the maximum power dissipated by each transistor is half of this value:

Or roughly .

Based on its robust specifications (), the 2N3055 is an NPN epitaxial-base power transistor heavily used in general-purpose switching and amplifier applications.

Common Applications:

1. Audio Power Amplifiers: Used in the output stages of high-fidelity audio amplifiers (often paired with its complementary PNP counterpart, the MJ2955, in Class AB configurations).
2. Linear Power Supplies: Acts as a series pass element in regulated DC power supplies due to its high power dissipation capacity.
3. Motor Control: Used to drive DC motors in industrial applications.
4. Inverters and Switching Regulators: Handles high currents needed for switching applications.
5. Relay Drivers: Used where high current capability is required to drive heavy mechanical relays.

Conversion Efficiency () of a power amplifier is defined as the ratio of the AC signal power delivered to the load to the total DC power drawn from the power supply.

Why it is low for RC-coupled Class A:

1. Continuous Quiescent Current: In Class A, the transistor is biased in the center of the active region, drawing a high constant DC current () from the supply even when no AC signal is present. This results in continuous DC power loss.
2. Collector Resistor Dissipation: In an RC-coupled configuration, a significant portion of the DC power is dissipated as heat in the collector load resistor () and emitter resistor (), which contributes nothing to the AC output.
   Due to these inherent losses, the theoretical maximum efficiency is only , and practically, it is often between and .