Unit 2 - Notes

ECE221 7 min read

Unit 2: Power Amplifiers

Power amplifiers (also known as large-signal amplifiers) are designed to deliver a large amount of power to a load, such as a loudspeaker, motor, or transmitting antenna. Unlike small-signal amplifiers that primarily amplify voltage, power amplifiers handle high voltage and high current to achieve significant power gain.

1. Class A Large Signal Amplifiers

In a Class A amplifier, the operating point (Q-point) is situated near the center of the active region on the load line.

Conduction Angle: The transistor conducts for the entire $360^\circ$ of the input cycle.
Operating Characteristics: Because the transistor is always ON, it continuously dissipates power, leading to significant heat generation even when there is no input signal.
Advantages: Excellent linearity, minimal distortion, and simple circuit design.
Disadvantages: Very low efficiency and high power dissipation.
Direct-Coupled (Series-Fed) Class A: The load is connected directly in series with the collector. The maximum theoretical efficiency is only 25%.

2. Second Harmonic Distortion

Because power amplifiers handle large signal swings, they operate over a wide, nonlinear portion of the transistor's characteristic curves. This nonlinearity alters the shape of the output waveform, introducing distortion.

Mechanism: When a pure sinusoidal signal is applied, the nonlinear transfer characteristic (due to the exponential relationship between base-emitter voltage and collector current) generates harmonics.
Second Harmonic: The most prominent distortion in single-ended large signal amplifiers is the second harmonic (a frequency twice the fundamental frequency).
Mathematical Representation:
The output collector current $i_C$ can be expressed using a power series:
$i_C = I_Q + a v_{be} + b v_{be}^2$
If $v_{be} = V_m \cos(\omega t)$ , then:
$i_C = I_Q + a V_m \cos(\omega t) + b V_m^2 \cos^2(\omega t)$
Using the trigonometric identity $\cos^2(\theta) = \frac{1 + \cos(2\theta)}{2}$ :
$i_C = I_Q + \frac{b V_m^2}{2} + a V_m \cos(\omega t) + \frac{b V_m^2}{2} \cos(2\omega t)$
The term $\frac{b V_m^2}{2} \cos(2\omega t)$ represents the second harmonic distortion.
Percentage of Second Harmonic Distortion ( $D_2$ ):
$D_2 = \left| \frac{I_{2m}}{I_{1m}} \right| \times 100\%$
Where $I_{1m}$ is the amplitude of the fundamental and $I_{2m}$ is the amplitude of the second harmonic.

3. Transformer Coupled Audio Power Amplifier

To improve efficiency and maximize power transfer to the load (which often has a low impedance, like an $8\,\Omega$ speaker), a transformer is used to couple the amplifier to the load.

Impedance Matching: The transformer matches the low impedance of the load ( $R_L$ ) to a higher impedance reflected to the primary side ( $R_L'$ ).
$R_L' = \left(\frac{N_p}{N_s}\right)^2 R_L = n^2 R_L$
Where $N_p/N_s$ is the turns ratio ( $n$ ).
DC vs. AC Load Line:
- DC Load Line: Because the primary winding of an ideal transformer has zero DC resistance, the DC load line is a nearly vertical line.
- AC Load Line: The AC load line has a slope of $-1/R_L'$ and intersects the DC load line at the Q-point.
Advantages: Higher efficiency, DC isolation of the load, and ideal impedance matching.

4. Efficiency of Transformer-Coupled Class A Amplifiers

The primary benefit of the transformer-coupled Class A amplifier over the series-fed version is the dramatic increase in maximum theoretical efficiency.

DC Power Input ( $P_{DC}$ ):
$P_{DC} = V_{CC} I_Q$
AC Power Output ( $P_{AC}$ ):
$P_{AC} = \frac{V_{CE(peak)} I_{C(peak)}}{2}$
Maximum Efficiency:
In an ideal scenario, the output voltage can swing from $0$ to $2V_{CC}$ , and the output current can swing from $0$ to $2I_Q$ .
$P_{AC(max)} = \frac{V_{CC} I_Q}{2}$
$\eta_{max} = \frac{P_{AC(max)}}{P_{DC}} = \frac{V_{CC} I_Q / 2}{V_{CC} I_Q} = 0.5 \text{ or } 50\%$
Real-world Efficiency: Due to transformer losses and transistor saturation voltages, practical efficiencies are usually between 30% and 40%.

5. Push-Pull Amplifiers

A push-pull amplifier utilizes two active devices (transistors) to amplify the input signal.

Operation: One transistor amplifies the positive half-cycle of the input signal ("push"), while the other amplifies the negative half-cycle ("pull").
Advantages:
1. Elimination of Even Harmonics: Due to the symmetrical arrangement, even-order harmonics (like the 2nd harmonic) cancel out in the output load.
2. No DC Core Saturation: In a transformer-coupled push-pull amplifier, the DC currents flow in opposite directions in the primary winding halves, canceling magnetic flux and preventing core saturation.
3. Higher Output Power: Two transistors share the load, allowing for greater overall power output.

6. Class B Amplifiers

In a Class B amplifier, the Q-point is set exactly at the cutoff region ( $I_Q = 0$ ).

Conduction Angle: Each transistor conducts for exactly $180^\circ$ (one half-cycle) of the input signal.
Efficiency: Because there is no zero-signal DC current, standby power dissipation is zero.
$\eta_{max} = \frac{\pi}{4} \approx 78.5\%$
Cross-Over Distortion: The most significant drawback of a pure Class B push-pull amplifier. Because a silicon transistor requires approximately $0.7\text{V}$ ( $V_{BE}$ ) to turn on, there is a dead zone where neither transistor conducts when the input signal transitions through zero. This results in a flattened or "stepped" zero-crossing in the output waveform.

7. Class AB Amplifiers

Class AB was developed to eliminate the crossover distortion inherent in Class B amplifiers while maintaining higher efficiency than Class A.

Operating Point: The Q-point is set slightly above cutoff. A small biasing voltage (usually provided by diodes or a $V_{BE}$ multiplier) is applied to keep both transistors just slightly ON during the zero-crossing.
Conduction Angle: Transistors conduct for slightly more than $180^\circ$ but much less than $360^\circ$ (typically around $190^\circ$ to $200^\circ$ ).
Performance:
- Crossover distortion is effectively eliminated.
- Efficiency is slightly lower than Class B but significantly higher than Class A (typically 60% - 70%).
- It is the most common topology used in high-fidelity audio power amplifiers.

8. Reading the Datasheet of a 2N3055 Power Transistor

The 2N3055 is a classic, widely used NPN silicon power transistor housed in a TO-3 metal case, designed for general-purpose switching and amplifier applications. Understanding its datasheet is crucial for designing reliable power amplifiers.

Key Parameters to Extract from the Datasheet:

Absolute Maximum Ratings:
- $V_{CEO}$ (Collector-Emitter Voltage with Base Open): Usually 60V. Exceeding this causes avalanche breakdown.
- $I_C$ (Continuous Collector Current): Typically 15A. The maximum continuous current the device can handle.
- $P_D$ (Total Power Dissipation): Typically 115W at a case temperature of $25^\circ\text{C}$ . This value derates linearly as temperature increases.
Thermal Characteristics:
- $\theta_{JC}$ (Thermal Resistance, Junction-to-Case): Around $1.5^\circ\text{C/W}$ . This dictates how well heat flows from the semiconductor junction to the metal case. A heat sink is strictly required to operate near maximum power.
Electrical Characteristics:
- $h_{FE}$ (DC Current Gain / Beta): For power transistors, this is relatively low. For the 2N3055, $h_{FE}$ is typically 20 to 70 at $I_C = 4\text{A}$ . Because it drops significantly at high currents, high base drive currents are required.
- $V_{CE(sat)}$ (Collector-Emitter Saturation Voltage): Typically around 1.1V at $I_C = 4\text{A}$ . Important for calculating power losses in switching applications or maximum swing in amplifiers.
- $f_T$ (Transition Frequency): Typically around 2.5 MHz. This indicates the frequency at which $h_{FE}$ drops to 1. The 2N3055 is relatively slow, making it suitable for audio frequencies but poor for high-frequency RF.
Safe Operating Area (SOA):
- The SOA graph is perhaps the most critical chart for linear power amplifier design. It plots $I_C$ versus $V_{CE}$ and defines the boundary where the transistor can operate without self-destruction.
- It accounts for limits based on maximum current, maximum power dissipation (thermal limit), and secondary breakdown (a localized hotspot failure mechanism in BJTs). When designing a Class AB audio amplifier using the 2N3055, the AC load line must remain strictly inside the SOA under all operating conditions (including reactive loads like speakers).

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