Unit4 - Subjective Questions

Feedback in Amplifiers:
Feedback is the process of taking a portion of the output signal (voltage or current) of an amplifier and feeding it back to the input circuit. This feedback signal is then combined with the external input signal to modify the overall performance of the amplifier.

Positive (Regenerative) Feedback:

• Definition: When the feedback signal is in phase with the original input signal, it adds to the input.
• Effect: It increases the overall gain of the amplifier but reduces stability.
• Application: Primarily used in oscillator circuits to generate continuous waveforms without an external input.

Negative (Degenerative) Feedback:

• Definition: When the feedback signal is out of phase (typically by 180 degrees) with the input signal, it subtracts from the input.
• Effect: It reduces the overall gain but improves other critical performance characteristics such as gain stability, bandwidth, noise reduction, and distortion.
• Application: Widely used in almost all practical amplifier circuits.

Derivation of Closed-Loop Gain:
Let an amplifier have an open-loop gain of . A fraction of the output, denoted by the feedback factor , is fed back to the input.

1. Let the external input signal be and the output signal be .
2. The feedback signal is .
3. In negative feedback, the actual input to the basic amplifier is the difference between the source signal and the feedback signal:
   
4. The output voltage is given by the basic amplifier gain acting on :
   
5. Expanding the equation:
   
6. Rearranging terms to group :
   
7. The closed-loop gain is the ratio of output voltage to source voltage:
   

Gain Stability:
The term is called the desensitivity factor. If , the closed-loop gain approximates to . Since is determined by a passive resistor network, it is highly stable and independent of variations in transistor parameters, temperature, or the open-loop gain .

Effect of Negative Feedback on Bandwidth:
Negative feedback significantly increases the bandwidth of an amplifier. For a given amplifier, the gain-bandwidth product is generally constant. Since negative feedback reduces the overall gain by a factor of , the bandwidth must increase by the exact same factor to maintain a constant product.

Mathematical Relationships:

1. Let the original amplifier have a lower cutoff frequency and an upper cutoff frequency . The original bandwidth is .
2. With negative feedback, the upper cutoff frequency is extended (increased) by the desensitivity factor:
   
3. The lower cutoff frequency is reduced (improved):
   
4. The new bandwidth with feedback () becomes:
   
5. Since in practical amplifiers, the new bandwidth is approximately . Therefore:
   
   
   This shows that the bandwidth is increased by the factor at the cost of reduced gain.

Feedback Topologies and Impedance Effects:
There are four basic ways to connect a feedback network, depending on whether voltage or current is sampled at the output, and whether it is mixed in series or parallel (shunt) at the input. The factor modifies the impedances depending on the connection:

1. Voltage-Series Feedback: Samples output voltage and mixes in series.
   • Input Impedance (): Increases;
   • Output Impedance (): Decreases;
2. Voltage-Shunt Feedback: Samples output voltage and mixes in parallel.
   • Input Impedance (): Decreases;
   • Output Impedance (): Decreases;
3. Current-Series Feedback: Samples output current and mixes in series.
   • Input Impedance (): Increases;
   • Output Impedance (): Increases;
4. Current-Shunt Feedback: Samples output current and mixes in parallel.
   • Input Impedance (): Decreases;
   • Output Impedance (): Increases;

Rule of Thumb: Series mixing always increases input impedance, while shunt mixing decreases it. Voltage sampling always decreases output impedance, while current sampling increases it.

Effect on Noise:
Amplifiers inherently generate internal noise due to active components like transistors. If the noise is generated within the amplifier itself, applying negative feedback reduces this internally generated noise at the output. If is the noise without feedback, the noise with feedback () is given by:

Effect on Non-linear Distortion:
Large signals can push an amplifier into its non-linear operating regions, causing harmonic distortion. Negative feedback strongly opposes these non-linear changes because the feedback signal contains the distorted components, which are then subtracted from the input, heavily suppressing the distortion.
If is the distortion present without feedback, the distortion with feedback () is:

Working Principle of RC-Coupled BJT Amplifier:
An RC-coupled amplifier uses a BJT configured (usually in Common Emitter mode) with a voltage-divider biasing network. When an AC signal is applied to the input, the transistor amplifies the base current into a much larger collector current. The amplified signal is developed across the collector resistor and is coupled to the next stage or load through a capacitor.

Role of Components:

1. Coupling Capacitors ( and ):
   • They block DC components, ensuring that the DC biasing of one stage does not interfere with the previous or next stage or the signal source/load.
   • They allow the AC signal to pass through. Their reactance is low for AC signals.
2. Emitter Bypass Capacitor ():
   • It is connected in parallel with the emitter resistor .
   • It provides a low-reactance path for AC signals, bypassing . If is absent, the AC signal would drop across , creating a negative feedback effect that significantly reduces the voltage gain.

Frequency Response of RC-Coupled Amplifier:
The frequency response curve plots the voltage gain against the frequency of the input signal. It is divided into three regions:

1. Low-Frequency Region:

   • The voltage gain is low and increases with frequency.
   • Reason: At low frequencies, the capacitive reactance () of the coupling and bypass capacitors is very high. They act as open circuits, blocking parts of the signal and causing a significant voltage drop, which reduces the overall gain.

2. Mid-Frequency Region:

   • The voltage gain remains constant and at its maximum.
   • Reason: Here, the reactance of the external capacitors is small enough to act as short circuits, while the internal parasitic capacitances of the transistor are still too high to have a shunting effect. The gain depends solely on the transistor's parameters and external resistors.

3. High-Frequency Region:

   • The voltage gain falls off as frequency increases.
   • Reason: At high frequencies, the inter-electrode/parasitic capacitances of the BJT (e.g., base-collector capacitance) and wiring capacitance present a very low reactance path. They act as partial short circuits, shunting the AC signal to the ground and reducing the output gain.

Cascaded Amplifier Systems:
A cascaded system consists of multiple amplifier stages connected in series, where the output of the first stage is fed as the input to the second stage, and so on.

Necessity of Cascading:

1. Higher Gain: A single amplifier stage rarely provides the sufficient voltage or power gain required for practical applications (e.g., radio receivers). Cascading allows for high total gain.
2. Impedance Matching: Different stages can be used to match impedances. For example, a first stage might provide high input impedance, middle stages provide voltage gain, and the final stage provides low output impedance for driving a load.

Effect on Overall Voltage Gain:
The total overall voltage gain () of a cascaded amplifier is the product of the individual voltage gains of all the stages, provided loading effects are considered.

Effect of Cascading on Bandwidth:
When identical amplifier stages are cascaded to increase the overall voltage gain, the overall bandwidth of the system decreases. This phenomenon is known as bandwidth shrinkage.

• Lower Cutoff Frequency (): Increases as more stages are added. The combined low-frequency response drops faster because the multiple high-pass filters (formed by coupling capacitors) cascade their attenuation.
• Upper Cutoff Frequency (): Decreases as more stages are added. The combined high-frequency response drops due to the cascading effect of the low-pass filters (formed by parasitic capacitances).

Mathematical Formula:
For identical cascaded stages, if the bandwidth of a single stage is (assuming so ), the overall upper cutoff frequency and bandwidth is given by:

Differences between Voltage and Power Amplifiers:

Operation of Class A Power Amplifier:
In a Class A power amplifier, the transistor is biased such that the Q-point is exactly at the center of the AC load line. As a result, the transistor conducts for the entire (full cycle) of the input AC signal.
Because the transistor is always ON, it accurately amplifies the whole waveform without clipping, resulting in minimum distortion.

Disadvantages and Efficiency:
The major drawback of Class A operation is that the transistor continuously draws DC current from the supply even when there is no AC input signal, leading to high continuous power dissipation and low efficiency.

Maximum Theoretical Efficiency:
The efficiency is defined as the ratio of AC output power to DC input power:

1. Series-Fed Class A: The load is connected directly in series with the collector. The maximum theoretical efficiency is 25\%.
2. Transformer-Coupled Class A: The load is matched using a transformer, removing DC power loss in the collector resistor. The maximum theoretical efficiency increases to 50\%.

Class B Power Amplifier:
In a Class B power amplifier, the DC biasing is arranged such that the Q-point lies exactly at the cutoff region on the load line. Consequently, the transistor conducts only for one half-cycle () of the input signal. To amplify a full cycle, two complementary transistors (a push-pull arrangement) are used, where one amplifies the positive half and the other amplifies the negative half. Its maximum theoretical efficiency is or approximately 78.5\%.

Crossover Distortion:
Crossover distortion is a major drawback of standard Class B amplifiers.

• A practical BJT requires a minimum base-emitter voltage ( for silicon) to turn ON.
• Since the transistors in Class B are biased exactly at zero volts, any input signal between and fails to turn either transistor ON.
• This creates a "dead zone" where the output remains zero during the time the signal crosses the zero-axis.
• The resulting output waveform is severely distorted at the zero-crossing points, hence the name "crossover distortion".

Working of Push-Pull Class B Power Amplifier:
A push-pull Class B amplifier uses two transistors to amplify the complete cycle of an input signal, overcoming the limitation of a single Class B stage.

Circuit Arrangement:
It typically uses either a center-tapped transformer or a complementary symmetry pair (one NPN and one PNP transistor).

Operation (using Complementary Symmetry as an example):

1. Both transistors are biased near cutoff.
2. Positive Half-Cycle: When the input AC signal goes positive, it forward-biases the NPN transistor, causing it to conduct. The PNP transistor is reverse-biased and remains OFF. The NPN transistor "pushes" current into the load.
3. Negative Half-Cycle: When the input signal goes negative, the NPN transistor turns OFF. The PNP transistor becomes forward-biased and conducts. The PNP transistor "pulls" current from the load.
4. Reconstruction: The two half-cycles are combined at the output load. Because one handles the top half and the other handles the bottom half, the complete waveform is reconstructed.

This setup delivers high power output and improved efficiency (up to 78.5\%) while canceling out even-harmonic distortion.

Limitations to Overcome:

• Class A has excellent linearity but very poor efficiency (lots of heat generation).
• Class B has excellent efficiency but suffers from severe crossover distortion at the zero-crossing points.

The Class AB Solution:
A Class AB power amplifier combines the best of both designs by shifting the Q-point slightly above the cutoff region.

• Biasing: It uses a small, steady forward-bias voltage (often provided by biasing diodes) to keep the transistors just on the edge of conduction (e.g., pre-biased at ).
• Conduction Angle: As a result, each transistor conducts for slightly more than (between and ).
• Overcoming Crossover Distortion: Because the transistors are already slightly conducting before the AC signal is applied, the "dead zone" required to overcome the drop is eliminated. This completely removes the crossover distortion characteristic of Class B.
• Efficiency vs. Linearity: It maintains much higher efficiency than Class A (ranging from 50\% to 70\%) while delivering a clean, distortion-free output comparable to Class A.

Comparison of Power Amplifiers:

Voltage Regulator:
A voltage regulator is an electronic circuit that provides a stable and constant DC output voltage, regardless of changes in the input (source) voltage or variations in the load current.

Key Performance Metrics:

1. Line Regulation (Source Regulation):

   • It is the measure of the regulator's ability to maintain a constant output voltage when the input line voltage fluctuates.
   • Formula:
   • Ideally, line regulation should be zero.

2. Load Regulation:

   • It is the measure of the regulator's ability to maintain a constant output voltage when the load current changes (from no load to full load).
   • Formula:
   • Where is the no-load voltage (zero current) and is the full-load voltage (maximum current).
   • Ideally, load regulation should be 0\%, meaning the output voltage does not drop when current is drawn.

Zener Diode Shunt Voltage Regulator:
A Zener diode acts as a voltage regulator when operated in its reverse breakdown region (Zener region), where the voltage across it () remains remarkably constant despite large variations in current.

Circuit Construction:

• The unregulated input voltage () is connected through a series current-limiting resistor ().
• The Zener diode is connected in parallel (shunt) with the load (), in reverse-biased configuration.

Working Principle:

1. Varying Input Voltage: If increases, the total current increases. The Zener diode absorbs this extra current (Zener current increases), but maintains a constant voltage across itself. The excess voltage is dropped across .
2. Varying Load Current: If the load demands more current ( increases), the Zener diode decreases its own current to compensate, ensuring the total current remains relatively constant, thus keeping the output voltage stable.

Key Equations:

• Total source current:
• Output voltage:
• Current distribution:

Transistor Series Voltage Regulator:
A series voltage regulator places a control element (usually a BJT, known as the pass transistor) in series with the load. Its purpose is to act as a variable resistor to absorb any voltage fluctuations, ensuring the load sees a constant voltage.

Circuit Elements and Operation:

1. A Zener diode provides a constant reference voltage () at the base of an NPN transistor.
2. The collector is connected to the unregulated input voltage, and the emitter is connected to the output load.
3. The output voltage is given by: , where is the base-emitter voltage drop of the transistor.

Regulation Mechanism:

• If tries to decrease (due to a drop in input voltage or an increase in load current): Because is fixed, the base-emitter voltage increases (). This causes the transistor to conduct more heavily (turning ON harder), reducing its effective collector-emitter resistance. More voltage is passed to the output, bringing back up to the regulated level.
• If tries to increase: decreases, the transistor conducts less, its internal resistance increases, and it drops more voltage, bringing back down.
  Thus, the transistor dynamically adjusts its conduction to regulate the output.

Proof of Gain Stability Improvement:
Let the closed-loop gain of a negative feedback amplifier be , the open-loop gain be , and the feedback factor be .
The relationship is given by:

To find how a change in open-loop gain () affects the closed-loop gain (), we differentiate with respect to using the quotient rule:

To find the fractional change, divide this result by the original gain :

Conclusion:
The term is the fractional change in closed-loop gain, and is the fractional change in open-loop gain. The equation proves that the fractional change in closed-loop gain is reduced (divided) by the desensitivity factor . This means the feedback amplifier's gain is highly stable against internal variations.

Part 1: Initial Closed-Loop Gain
Given:

• Open-loop gain,
• Feedback fraction,

The closed-loop gain is:

Part 2: New Closed-Loop Gain after 10% Drop
If open-loop gain drops by 10\%, the new open-loop gain is:

The new closed-loop gain is:

Conclusion:
Even though the internal open-loop gain dropped by a massive 10\% (from 1000 to 900), the overall closed-loop gain only dropped from 50 to 49.72, which is a minuscule change of just . This numerically demonstrates the excellent gain stability provided by negative feedback.