Analog Electronics (EX-305) - Unit 5 Short Notes

UNIT 5: AMPLIFIERS

1. Small Signal Amplifiers

• Definition: Amplifiers designed to amplify low-level signals (mV range) with minimal distortion. Operate in the linear region of the device (active region for BJT, saturation for JFET/MOSFET).

• Design Considerations (BJT vs FET):

  • BJT (Current-controlled): Requires proper biasing (voltage divider, emitter bias) to set stable Q-point. Small signal parameters: h-parameters (hybrid) or g-parameters.

  • FET (Voltage-controlled): Naturally high input impedance. Self-bias is common. Key parameters: transconductance (gₘ) and output resistance (rₒ).

• Key Performance Metrics: Voltage gain (Aᵥ), current gain (Aᵢ), power gain (Aₚ), input impedance (Zᵢ), output impedance (Zₒ).

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Exam Focus: Past papers rarely ask direct design of small-signal amplifiers but expect understanding of Q-point stabilization (from Unit 3) as a prerequisite for any amplifier design.

2. Power Amplifiers

• Definition: Designed to deliver high power to a load (speaker, motor). Efficiency (η) is critical—ratio of AC power delivered to DC power supplied.

• Classification by Conduction Angle (Q-point location):

• Class B Push-Pull Operation:

  • Each transistor conducts for half the cycle (positive/negative halves).

  • Crossover Distortion: Occurs around zero-crossing when both transistors are off. Reduced by Class AB biasing (slight forward bias).

  • Numerical Problem Pattern: Given Vcc, Rᴸ, and Vₚₚ (peak-to-peak output), calculate:

    1. Maximum AC Power: \( P_{ac(max)} = \frac{(V_{pp}/2)^2}{2R_L} \)

    2. DC Input Power: \( P_{dc} = \frac{2V_{CC}}{\pi} I_{C(max)} \) (for ideal)

    3. Efficiency: \( \eta = \frac{P_{ac}}{P_{dc}} \times 100\% \)

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Common Pitfall: Forgetting that Vₚₚ is peak-to-peak. Always divide by 2 to get peak voltage (Vₘ) before using \( P = V_m^2/(2R_L) \). Class B efficiency derivation assumes ideal transformer coupling.

3. Feedback Amplifiers

• Feedback: Portion of output signal fed back to input.

  • Positive Feedback: Increases gain, used in oscillators (unstable).

  • Negative Feedback: Degenerative—reduces gain but improves performance. Exam Focus:

• Four Basic Topologies (based on feedback signal type & mixing method):

  1. Voltage-Series (Series-Shunt): Sample voltage, feed back in series. Voltage amplifier (high Zᵢ, low Zₒ). Example: Inverting Op-Amp.

  2. Voltage-Shunt (Shunt-Shunt): Sample voltage, feed back in shunt. Transresistance amplifier (low Zᵢ, low Zₒ).

  3. Current-Series (Series-Series): Sample current, feed back in series. Transconductance amplifier (high Zᵢ, high Zₒ). Example: CE amplifier with emitter resistor.

  4. Current-Shunt (Shunt-Series): Sample current, feed back in shunt. Current amplifier (low Zᵢ, high Zₒ).

• Effects of Negative Feedback (NFB):

  • Gain Reduction: \( A_{vf} = \frac{A_v}{1 + A_v \beta} \) (where β = feedback factor)

  • Bandwidth Increase: Gain-Bandwidth Product (GBP) is constant.

$$ \boxed{A_{v0} \cdot f_0 = A_{vf} \cdot f_{bf}} $$

    Where \( A_{v0} \) = open-loop gain, \( f_0 \) = open-loop BW; \( A_{vf} \) = closed-loop gain, \( f_{bf} \) = closed-loop BW.

*   **Reduced Distortion & Nonlinearity**

*   **Improved Input/Output Impedance:** Depends on topology (series feedback ↑Zᵢ, shunt feedback ↓Zᵢ; voltage feedback ↓Zₒ, current feedback ↑Zₒ).

*   **Increased Stability & Reduced Sensitivity** to component variations.

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Derivation Must-Know: From \( A_{vf} = A_v/(1+A_v\beta) \), for large \( A_v\beta \), \( A_{vf} \approx 1/\beta \). Bandwidth extension: \( f_{bf} \approx f_0 (1 + A_v\beta) \). Hence \( A_{vf} f_{bf} \approx A_v f_0 \).

4. Differential Amplifiers (Diff-Amp)

• Basic Circuit: Two identical transistors (BJT or FET) with common emitter/source resistor (Rₑ or current source) and collector/drain loads. Two inputs (V₁, V₂), one output (usually taken differentially, Vₒ = V_{c1} - V_{c2}).

• Modes of Operation:

  • Differential Mode (DM): \( V_1 = -V_2 \). Output \( V_{od} = A_d (V_1 - V_2) \). Ideal: Common-mode rejection.

  • Common Mode (CM): \( V_1 = V_2 \). Output \( V_{oc} = A_c (V_1) \). Ideal: \( A_c = 0 \).

• CMRR (Common-Mode Rejection Ratio):

  • Definition: Ratio of differential gain to common-mode gain.

$$ \boxed{CMRR = \frac{A_d}{A_c}} $$

*   **Significance:** Measures ability to reject noise/interference common to both inputs (e.g., power supply ripple). **Higher CMRR is better.**

*   **In dB:** \( \boxed{CMRR_{dB} = 20 \log_{10}\left(\frac{A_d}{A_c}\right)} \)

*   **Numerical Example (from Jun 2024):**

    Given: \( A_d = 1V / 10mV = 100 \), \( A_c = 5mV / 10mV = 0.5 \)

    \( CMRR = 100 / 0.5 = 200 \)

    \( CMRR_{dB} = 20 \log_{10}(200) \approx 46 \, \text{dB} \)

• Applications: Input stage of Op-Amps, Instrumentation Amplifiers (3-Op-Amp INA), Noise cancellation in balanced lines.

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Key Point: A perfect differential amplifier has infinite CMRR. In practice, CMRR is limited by mismatch in transistor parameters and Rₑ not being infinite (use current mirror or active load to improve).

5. Differential Amplifier & Op-Amp Input Stage

• The differential pair is the core input stage of every operational amplifier (Op-Amp).

• The high CMRR of the diff-pair directly translates to the high CMRR of the Op-Amp.

• Single-Ended Output: Often only one collector/drain output is used (referenced to ground), converting differential output to single-ended. CMRR is slightly reduced but still high.

6. Summary of Past Paper Hotspots for Unit 5

1. Power Amplifiers (Class A/B): Efficiency derivation, push-pull operation, crossover distortion.

2. Feedback: Types (4), effects—especially gain-bandwidth trade-off derivation.

3. Differential Amplifier: DM vs CM operation, CMRR definition & numerical calculation in dB.

4. Link to Op-Amps: Diff-amp as Op-Amp input stage (conceptual link).

5. Numericals: Class B power calculations, CMRR (dB), feedback bandwidth.

Final Exam Strategy: For 7-mark questions, always include circuit diagram (even if rough), waveform sketches (for power amps), key formulas boxed, and a comparison table where applicable (e.g., power amp classes, feedback topologies).