Audio Power Lecture 1-2 | Notability

Fundamentals of Audio Power Signals

Audio power amplification involves increasing the power level of weak audio signals within the audible frequency spectrum ($20\,\text{Hz}$ to $20\,\text{kHz}$) to a level sufficient to drive output transducers such as loudspeakers or headphones.

The electrical power delivered to a resistive load $R$ (representing speaker impedance, typically $4\,\Omega$, $8\,\Omega$, or $16\,\Omega$) is defined using root-mean-square (RMS) voltage $V_{\text{rms}}$ and RMS current $I_{\text{rms}}$:

$P_{\text{avg}} = V_{\text{rms}} \times I_{\text{rms}} = \frac{V_{\text{rms}}^2}{R} = I_{\text{rms}}^2 \times R$

For a pure sinusoidal signal with peak voltage $V_{\text{peak}}$, the relationships between RMS voltage, average power, and peak power are given by:

$V_{\text{rms}} = \frac{V_{\text{peak}}}{\sqrt{2}}$

$P_{\text{avg}} = \frac{V_{\text{peak}}^2}{2 \times R}$

$P_{\text{peak}} = \frac{V_{\text{peak}}^2}{R} = 2 \times P_{\text{avg}}$

Amplifier Classes and Operating Parameters

Audio power amplifiers are categorized according to their bias point (Q-point) and the conduction angle of the active amplifying devices over a full $360^\circ$ ($2\pi\,\text{rad}$) signal cycle.

• Class A Amplifier: The output transistor conducts continuously during the full signal cycle ($360^\circ$ conduction angle). It delivers high linearity and low distortion, but continuously draws power regardless of input signal amplitude.

  • Theoretical Maximum Efficiency: $\eta_{\text{max}} = 25\%$ for direct-coupled resistive loads, or $\eta_{\text{max}} = 50\%$ for transformer-coupled loads.

  • Thermal Dissipation: Maximum power dissipation occurs under quiescent (zero-input) conditions.

• Class B Amplifier: Consists of complementary push-pull transistors where each device conducts for half of the signal cycle ($180^\circ$ conduction angle).

  • Theoretical Maximum Efficiency: $\eta_{\text{max}} = \frac{\pi}{4} \approx 78.5\%$

  • Crossover Distortion: Non-linear distortion occurs near the zero-crossing region due to the transistor base-emitter turn-on threshold ($V_{\text{BE}} \approx 0.7\,\text{V}$).

• Class AB Amplifier: Applies a small continuous DC bias voltage to keep both output devices slightly ON at idle. The conduction angle is slightly greater than $180^\circ$.

  • Theoretical Maximum Efficiency: Typically ranges between $50\%$ and $70\%$

  • Advantage: Eliminates crossover distortion while maintaining efficiency significantly higher than Class A.

• Class D Amplifier: A switching topology where output transistors switch rapidly between fully ON and fully OFF states using Pulse Width Modulation (PWM).

  • Theoretical Maximum Efficiency: Exceeds $90\%$

  • Reconstruction: Uses a low-pass LC filter at the output to remove high-frequency switching artifacts and extract the audio signal.

Power Efficiency and Thermal Dissipation

The efficiency $\eta$ evaluates how effectively DC input power from the power supply $P_{\text{DC}}$ is converted into AC signal output power delivered to the load $P_{\text{out}}$:

$\eta = \frac{P_{\text{out}}}{P_{\text{DC}}} \times 100\%$

The remaining energy is converted into thermal energy within the active devices, defining internal power dissipation $P_{\text{diss}}$:

$P_{\text{diss}} = P_{\text{DC}} - P_{\text{out}}$

For a Class B push-pull amplifier operating with symmetric DC supply rails ($+V_{\text{CC}}$ and $-V_{\text{CC}}$) driving a peak load voltage $V_{\text{peak}}$:

$P_{\text{DC}} = \frac{2 \times V_{\text{CC}} \times V_{\text{peak}}}{\pi \times R}$

$P_{\text{out}} = \frac{V_{\text{peak}}^2}{2 \times R}$

$P_{\text{diss}} = \frac{2 \times V_{\text{CC}} \times V_{\text{peak}}}{\pi \times R} - \frac{V_{\text{peak}}^2}{2 \times R}$

Maximum transistor heat dissipation occurs when the peak output voltage reaches:

$V_{\text{peak}} = \frac{2 \times V_{\text{CC}}}{\pi}$

Key Audio Performance Metrics

• Total Harmonic Distortion (THD): Quantifies the total power of unwanted harmonic frequencies expressed as a ratio of the fundamental signal voltage: $\text{THD} = \frac{\sqrt{V_2^2 + V_3^2 + V_4^2 + \dots + V_n^2}}{V_1} \times 100\%$

• Damping Factor (DF): Indicates the amplifier's ability to exert control over loudspeaker driver motion: $\text{DF} = \frac{R_{\text{load}}}{R_{\text{out}}}$

• Signal-to-Noise Ratio (SNR): Measures the ratio of maximum unclipped signal power to background noise floor power, expressed in decibels ($\text{dB}$).