Low-frequency power amplifiers
A class B amplifier dissipates more heat at two thirds of its maximum amplitude than at full power. And with 12 mA of quiescent current its small-signal distortion drops from 20 % to less than 1 %.
01What changes with power
In a signal amplifier, gain and noise matter. In a power amplifier, which drives a loudspeaker or a motor, efficiency comes to the front, because whatever does not reach the load is dissipated as heat in the transistors, along with large-signal distortion. The classes of operation are distinguished by the fraction of the cycle during which each transistor conducts:
| Class | Conduction | Maximum efficiency | Characteristic |
|---|---|---|---|
| A | The whole cycle | 25 % with a resistive load, 50 % with a transformer | Minimum distortion, dissipates even with no signal |
| B | Half a cycle each transistor | 78.5 % | No quiescent consumption, crossover distortion |
| AB | Somewhat more than half a cycle | Almost like B | The quiescent current eliminates the crossover |
| C | Less than half a cycle | Close to 100 % in the limit | Only with a tuned load, at radio frequency |
| D | Switching | Over 90 % in practice | Pulse-width modulation and an output filter |
The introduction to the classes with the circuits is in power amplifiers, in the technician program. Here we calculate efficiency, dissipation and distortion.
02Class B: efficiency and dissipation
In the complementary pair of followers, each transistor conducts one half-cycle. With ±\( V_{CC} \) supplies, a load \( R_L \) and a sinusoidal output of amplitude \( V_p \), the supply delivers an average current of \( V_p/(\pi R_L) \) per branch:
The dissipation in the transistors is the difference between what the supply delivers and what the load receives, and it is not maximum at full power but at an intermediate amplitude. Differentiating:
03Crossover distortion and class AB
A bipolar follower needs about 0.6 V between base and emitter to conduct. In class B, while the input is between −0.6 V and +0.6 V neither transistor conducts and the output stays at zero: this is crossover distortion, which affects small signals the most, precisely the ones the ear perceives in the most detail. Class AB separates the bases with a bias voltage, two diodes or a \( V_{BE} \) multiplier, so that a quiescent current \( I_Q \) flows through the transistors and one of them is always conducting.
Two complementary followers with the exponential model \( i_C = I_S e^{v_{BE}/V_T} \) (\( I_S = 10^{-12} \) A), ±15 V supplies and an 8 Ω loudspeaker. Above, the input (gray) and the output (blue); below, the currents of the two transistors. The output is solved exactly at each instant.
The quiescent current brings a risk: the base–emitter voltage of a bipolar transistor falls about 2 mV per degree. If the transistors heat up and the bias is fixed, the current rises, they heat up more and are destroyed: this is thermal runaway. It is avoided with emitter resistors of a few tenths of an ohm and by mounting the \( V_{BE} \) multiplier on the same heat sink, so that its voltage falls together with that of the output transistors.
04Thermal design
Heat flows from the junction to the ambient through thermal resistances in series, from junction to case, from case to heat sink and from heat sink to air. With the dissipated power \( P_D \):
Besides the thermal limit, datasheets give the safe operating area: at high voltage and moderate current, a bipolar transistor can fail through second breakdown even though the power is within the limit. Reactive loads, such as a loudspeaker, put voltage and current out of phase and take the operating point into that region.
05In the lab
Build an unbiased complementary pair, observe the crossover distortion with a small signal and measure the distortion with an analyzer. Add two diodes between the bases and repeat.
Measure the average current of the supplies and the power in the load for several amplitudes, and compare the efficiency with \( \pi V_p/(4 V_{CC}) \).
With a class AB amplifier without emitter resistors, measure the quiescent current while the heat sink is heated with a hair dryer. Repeat with 0.22 Ω resistors.
06Common mistakes
- Sizing the heat sink for the maximum output power. The maximum dissipation occurs at about two thirds of the maximum amplitude.
- Measuring distortion only at full power. Crossover distortion is worse with small signals.
- Biasing class AB with a fixed voltage. Without thermal compensation, the quiescent current runs away.
- Forgetting the safe operating area with reactive loads. A loudspeaker is not a resistor.
07Self-assessment
What efficiency does a class B amplifier have with ±20 V and 12 V peak at the output?
\( 0.785 \cdot 12/20 \approx 47 \) %.
How much does each transistor of a class B amplifier with ±24 V across 4 Ω dissipate at most?
\( 24^2/(\pi^2 \cdot 4) \approx 14.6 \) W.
Why is crossover distortion worse with small signals?
Because the ±0.6 V dead zone is a larger fraction of the signal.
A transistor dissipates 10 W with θjc = 1 °C/W and θcs = 0.5 °C/W. With air at 30 °C and a junction at 130 °C, what heat sink is needed?
\( 100/10 - 1.5 = 8.5 \) °C/W.
08Further reading
- Douglas Self. Audio Power Amplifier Design. 6th ed., Focal Press, 2013. The reference book on crossover distortion, biasing and thermal stability.
- Bob Cordell. Designing Audio Power Amplifiers. 2nd ed., Routledge, 2019. The complete design, from the input pair to the safe operating area.
- Adel S. Sedra and Kenneth C. Smith. Microelectronic Circuits. 8th ed., Oxford University Press, 2020. Class A, B and AB output stages with their efficiency and dissipation analysis.