Unit 2 - Notes

ECE221

Unit 2: Power Amplifiers

1. Introduction to Power Amplifiers (Large Signal Amplifiers)

Unlike small-signal voltage amplifiers which are designed to amplify a small input voltage with minimal distortion, Power Amplifiers are designed to deliver substantial power to a load (such as a loudspeaker or motor). They handle large voltage and current swings.

Key Characteristics

Input: Large signal amplitude (often effectively the entire load line).
Output: High current and voltage swing capabilities.
Main Concern: Power efficiency ( $\eta$ ), thermal stability, and distortion handling.
Impedance Matching: Crucial for maximum power transfer to the load.

2. Class A Large Signal Amplifiers

In a Class A amplifier, the transistor is biased such that it conducts current for the entire cycle of the input signal ( $360^\circ$ conduction angle). The operating point (Q-point) is located roughly in the center of the DC load line.

2.1 Series-Fed Class A Amplifier

This is the simplest form, consisting of a transistor with a resistive load ( $R_C$ ) connected directly in series with the collector.

Operation: The transistor is always ON. Even with no input signal, a steady DC current ( $I_{CQ}$ ) flows, resulting in continuous power dissipation.
Input Power ( $P_{DC}$ ): The power drawn from the DC supply.
$P_{DC} = V_{CC} \cdot I_{CQ}$
Output Power ( $P_{ac}$ ): The AC power delivered to the load.
$P_{ac} = \frac{V_{rms}^2}{R_C} = I_{rms}^2 \cdot R_C$
$P_{ac(max)} = \frac{V_{CE(p-p)} \cdot I_{C(p-p)}}{8}$
Efficiency ( $\eta$ ):
- Maximum Theoretical Efficiency: For a resistive load Class A amplifier, the maximum efficiency is 25%. This means 75% of the power is wasted as heat.

2.2 Transformer Coupled Audio Power Amplifier

To improve efficiency and perform impedance matching, the collector resistor is replaced by the primary winding of a transformer.

Impedance Matching: The transformer transforms the load impedance ( $R_L$ , e.g., an 8 $\Omega$ speaker) to a reflected impedance ( $R'_L$ ) at the primary side.
$R'_L = \left(\frac{N_1}{N_2}\right)^2 R_L$
DC Load Line: Since the DC resistance of the transformer primary is very low (ideally $0\Omega$ ), the DC load line is a vertical line rising from $V_{CC}$ .
AC Load Line: Has a slope of $-1/R'_L$ .
Voltage Swing: Because of the inductive "kickback" (Lenz's Law), the collector voltage can swing above $V_{CC}$ , theoretically reaching up to $2V_{CC}$ .
Efficiency: Because there is no DC voltage drop across a collector resistor, less DC power is wasted.
- Maximum Theoretical Efficiency: 50%.

Summary of Class A

Pros: High linearity, low distortion (high fidelity).
Cons: Very low efficiency, high power dissipation (requires large heat sinks), high continuous current drain.

3. Second Harmonic Distortion

When large signals drive a transistor into non-linear regions of its input characteristics ( $I_B$ vs $V_{BE}$ ) or output characteristics, the output waveform is no longer a perfect replica of the input sine wave. This introduces Harmonic Distortion.

3.1 Concept

If the input is a fundamental frequency $f_1$ , non-linearity creates multiples of this frequency ( $2f_1, 3f_1$ , etc.). Second Harmonic Distortion ( $D_2$ ) refers to the component at frequency $2f_1$ . It creates an asymmetry between the positive and negative half-cycles of the output.

3.2 Three-Point Method Calculation

We can calculate the second harmonic distortion by analyzing the collector current at three points on the AC load line:

$I_{max}$ : Current at positive peak of input.
$I_{min}$ : Current at negative peak of input.
$I_{Q}$ : Quiescent current (no signal).

The amplitude of the fundamental frequency ( $I_1$ ) and the second harmonic ( $I_2$ ) can be approximated as:

$I_1 \approx \frac{I_{max} - I_{min}}{2}$
$I_2 \approx \frac{I_{max} + I_{min} - 2I_{Q}}{4}$

Percentage Second Harmonic Distortion ( $D_2$ ):

D_2 = \left| \frac{I_2}{I_1} \right| \times 100\%

D_2 = \frac{\frac{1}{2}(I_{max} + I_{min}) - I_Q}{I_{max} - I_{min}} \times 100\%

If $D_2$ is high, the output wave looks vertically shifted or squashed on one side.

4. Push-Pull Amplifiers

A Push-Pull configuration uses two transistors working in tandem.

One transistor amplifies the positive half-cycle.
The other amplifies the negative half-cycle.

Key Advantage: Harmonic Cancellation

If the two transistors are matched, the even harmonics (2nd, 4th, etc.) generated by non-linearity are in phase in the output transformer primary or load connection, effectively canceling each other out. This results in lower total distortion compared to a single-ended Class A amplifier.

5. Class B Amplifiers

In Class B operation, the transistor is biased exactly at cutoff ( $V_{BE} = 0V$ ).

Conduction Angle: $180^\circ$ (Half cycle).
Quiescent Current ( $I_Q$ ): Zero (ideally).

5.1 Complementary Symmetry Class B (Push-Pull)

Uses one NPN and one PNP transistor.

Positive Half Cycle: NPN conducts, PNP is off.
Negative Half Cycle: PNP conducts, NPN is off.
Load: Connected at the emitter junction (Emitter Follower configuration).

5.2 Efficiency

Since there is no current flow when there is no signal, power is saved.

P_{DC} = \frac{2 V_{CC} I_{peak}}{\pi}

P_{ac} = \frac{I_{peak}^2 R_L}{2}

\eta = \frac{\pi}{4} \times 100\% \approx \mathbf{78.5\%}

5.3 Crossover Distortion

This is the major disadvantage of Class B amplifiers.

Transistors (BJT) require $\approx 0.7V$ ( $V_{BE}$ ) to turn on.
For input signals between $-0.7V$ and $+0.7V$ , neither transistor conducts.
This creates a "dead zone" or flat spot at the zero-crossing point of the output waveform.

6. Class AB Amplifiers

Class AB is a compromise designed to eliminate the crossover distortion of Class B while maintaining efficiency close to Class B.

6.1 Operation

Bias Point: The transistors are biased slightly above cutoff. A small "trickle" current flows even with no signal.
Conduction Angle: Between $180^\circ$ and $360^\circ$ (typically around $190^\circ - 200^\circ$ ).

6.2 Eliminating Crossover Distortion

Diode Biasing: Two diodes are placed between the bases of the NPN and PNP transistors.
The voltage drop across the diodes ( $2 \times 0.7V = 1.4V$ ) compensates for the base-emitter turn-on voltages of the two transistors.
This ensures that as soon as the signal moves from positive to negative, the PNP turns on immediately as the NPN turns off, removing the dead zone.

6.3 Characteristics

Efficiency: Between 50% and 78.5% (usually closer to Class B).
Fidelity: Good (better than Class B, slightly worse than Class A).
Application: Most common topology for audio power amplifiers.

7. Reading Datasheet: 2N3055 Power Transistor

The 2N3055 is a classic NPN silicon power transistor used widely in power supply regulators and audio amplifiers.

7.1 Physical Description

Case: TO-3 Metal Can. (Looks like a metal hat with a rim).
Why metal? The collector is connected to the metal case to minimize thermal resistance, allowing for efficient heat sinking.

7.2 Absolute Maximum Ratings (The Limits)

$V_{CEO}$ (Collector-Emitter Voltage): 60V. The maximum voltage the transistor can withstand between collector and emitter when the base is open. Exceeding this causes breakdown.
$I_C$ (Continuous Collector Current): 15A. It can handle very high currents.
$I_B$ (Base Current): 7A.
$P_D$ (Total Power Dissipation): 115W (at case temperature ).
- Note: You cannot actually run it at 115W without a massive infinite heatsink. You must use the Derating Curve.

7.3 Electrical Characteristics (Performance)

$h_{FE}$ (DC Current Gain):
- At $I_C = 4A$ , $h_{FE} = 20 - 70$ .
- At $I_C = 10A$ , $h_{FE}$ drops to roughly 5.
- Note: Power transistors have lower Beta ( $h_{FE}$ ) than small signal transistors, and Beta drops significantly at high currents.
$V_{CE(sat)}$ (Saturation Voltage): $\approx 1.1V$ at $I_C = 4A$ . This determines the minimum voltage drop across the transistor when fully ON.
$f_T$ (Transition Frequency): $\approx 2.5 MHz$ . Low frequency response. Good for audio, bad for radio frequencies (RF).

7.4 Thermal Characteristics

$R_{\theta JC}$ (Thermal Resistance Junction-to-Case): 1.52 $^\circ C/W$ .
Calculation: Used to determine Heat Sink size.
$T_J = P_D(R_{\theta JC} + R_{\theta CS} + R_{\theta SA}) + T_{Ambient}$
Where $T_J$ must be kept below $200^\circ C$ .

7.5 Safe Operating Area (SOA)

The datasheet includes an SOA graph (Log-Log plot of $I_C$ vs $V_{CE}$ ).

The transistor must operate within the bounded area defined by:
1. Max Current limit ( $15A$ ).
2. Max Voltage limit ( $60V$ ).
3. Max Power dissipation curve ( $115W$ ).
4. Second Breakdown limit (a rapid thermal failure mode specific to BJTs).

Comparison Summary

Feature	Class A	Class B	Class AB
Operating Cycle	$360^\circ$	$180^\circ$	$180^\circ$ to $360^\circ$
Biasing	Center of Load Line	At Cutoff	Slightly above Cutoff
Efficiency (Max)	25% (Series), 50% (Transformer)	78.5%	50% - 78.5%
Distortion	Lowest (No crossover)	High (Crossover distortion)	Low (No crossover)
Power Dissipation	High (constant)	Low (zero at idle)	Low
Component Count	Low (Single Transistor)	Higher (Push-Pull Pair)	Higher (Push-Pull + Diodes)