5. Power Amplifiers

Small-signal amps swing millivolts. Power amps swing volts at many amperes, driving speakers, motors, antennas, transmitters. The challenge is efficiency: dissipating 100 W as heat in a tiny package is not viable, and battery-operated devices live or die by efficiency.

5.1 Classification by conduction angle

Power amps are categorized by how long during each AC cycle the active device conducts:

5.2 Class A

Transistor conducts for the entire AC cycle. Signal swings around a fixed bias point, with the transistor always passing some current.

• Pros. No crossover distortion, completely smooth transfer function, simplest topology.
• Cons. The transistor always dissipates power. With no signal, the device is biased at half the maximum collector current, dissipating $V_{CE} \cdot I_C$ = some fraction of the supply power continuously. Maximum theoretical efficiency for a direct-coupled class-A stage is 25%. Transformer-coupling raises this to 50% but still wastes serious heat.

Used in audiophile valve amplifiers (where its smoothness is valued and the inefficiency is romanticized as "warm sound"), low-power op-amp output stages, and high-purity instrumentation.

5.3 Class B push-pull

Two transistors handle the two halves of the cycle: one conducts only when the signal is positive, the other only when negative. Each transistor sees 180° of conduction per cycle.

        V_CC
         │
         ├── NPN transistor Q1 (handles positive half)
         │
         ├── output to speaker
         │
         ├── PNP transistor Q2 (handles negative half)
         │
        V_EE

• Pros. With no signal, no current flows. Perfect zero-signal idle. Maximum theoretical efficiency 78.5%.
• Cons. Crossover distortion. Right at zero crossing, neither transistor conducts (because each needs 0.7 V of $V_{BE}$ to start), so the output sticks at zero briefly while the input passes through the dead band. Audible as a harsh edge in audio, especially at low signal levels where the dead zone is a large fraction of the signal swing.

5.4 Class AB: the audio standard

Slight forward bias on both transistors so each conducts a few degrees past 180°. This eliminates the crossover dead band at a tiny efficiency cost. Modern audio power amps are virtually all class AB complementary symmetry: an NPN handles the positive half, a PNP the negative, with bias voltage between their bases set so both barely conduct at zero signal.

The bias voltage is usually generated by a "$V_{BE}$ multiplier" (a small transistor with a resistor divider on its collector-base path) thermally coupled to the output transistors so the bias tracks temperature. Without this thermal tracking, you cannot maintain a clean class-AB zero crossing across the temperature range.

5.5 Thermal stability and runaway

Power transistors run hot, and their $V_{BE}$ falls about 2 mV per °C. At fixed bias that means more current flows when the transistor heats up, which means more heat, which means more current, a positive-feedback loop ending in destruction. To prevent thermal runaway:

• Emitter ballast resistors (small, around 0.1 to 0.47 Ω) provide local current-feedback that opposes runaway. As the device heats and tries to draw more current, the voltage across the ballast resistor rises, reducing the effective $V_{BE}$ and pulling the current back.
• Bias-tracking diodes or $V_{BE}$ multipliers mounted on the same heatsink as the output transistors. The diode's $V_F$ (or the multiplier's $V_{BE}$) falls with temperature, lowering the bias voltage as the transistor heats up.
• Heatsinks with good thermal coupling, sometimes with active fans. The thermal resistance from junction to ambient must be low enough that the steady-state junction temperature stays below the device's safe-operating-area limit.

A blown power amp very often has at least one cooked output transistor and a blistered ballast resistor: the runaway happened, the transistor ran away, and the failure typically takes the ballast with it.

5.6 Class C

Conducts only at signal peaks. The output is severely distorted, but if the load is a resonant LC tank, the tank rings sinusoidally, producing a clean RF output regardless of the harsh transistor waveform. The tank "fills in" the missing parts of the cycle from its stored energy.

Very efficient (up to 90%) because the transistor is either off (no power dissipation) or saturated (low $V_{CE}$ times high $I_C$, but only briefly). Used in:

• AM and FM transmitters of every kind, including broadcast.
• RFID-tag readers (the ones at warehouse doors).
• Microwave ovens, where the magnetron is a giant class-C oscillator running at 2.45 GHz.
• ISM-band radio modules in IoT.

5.7 Class D: the modern champion

The transistor is fully on or fully off, switched by pulse-width modulation (PWM) at a frequency well above the signal band (typically 200 kHz to 2 MHz for audio). The output filter (an LC low-pass) integrates the PWM into a clean reconstructed waveform.

   audio in ──[comparator vs triangle wave]── PWM ──[half-bridge MOSFETs]── LC filter ── speaker

Theoretically 100% efficient because off transistors dissipate no power, and on transistors dissipate very little ($V_{DS,on} \cdot I_D$, with $V_{DS,on}$ in millivolts).

• Pros. Wildly efficient (90% real-world), small heatsinks, runs cool.
• Cons. Needs a careful LC output filter to remove the switching frequency, can radiate EMI, and needs negative feedback to suppress switching artifacts.

Used in:

• Modern Bluetooth speakers (battery efficiency is everything).
• Class-D guitar amplifiers (light enough to carry up the stairs).
• High-end home theater amplifiers.
• Solar inverters (turning DC from the panels into clean 60 Hz AC).
• Variable-speed motor drives in EVs and industrial automation.
• Wireless charging inverters (the same PWM trick applied to a coil).

Hardware-security tie-in. The current draw of a class-AB amplifier is essentially proportional to the absolute value of the audio signal. If the amp is processing voice that contains a passcode being spoken, the supply rail current modulates with the audio envelope. An attacker measuring the supply rail (with a current probe, or with a coupling cap and a hidden microphone-like detector elsewhere on the same power network) can recover the audio envelope. This is one mechanism behind the "supply-rail acoustic side channel" attacks that have been demonstrated against laptops processing speech.

5.8 Distortion measures

For audio: Total Harmonic Distortion (THD) is the fraction of output power at harmonics not present in the input.

$\text{THD} = \frac{\sqrt{V_2^2 + V_3^2 + V_4^2 + \cdots}}{V_1}$

where $V_n$ is the RMS amplitude of the $n$-th harmonic. High-end audio targets THD below 0.01%. Guitar amplifiers may have THD of 1 to 10%; the "warmth" of tube amps and overdrive pedals is harmonic distortion deliberately added for tonal effect. Intermodulation distortion (IMD) measures the unwanted sum-and-difference frequencies generated when two tones are present simultaneously, which is often a more audible defect than THD.

The distortion-reducing power of feedback (section 3.3) is exactly what makes high-end audio possible: the underlying transistors may have 1 to 5% open-loop distortion, and the feedback divides that down to milli-percent levels.