Power amplifiers and linear voltage regulators

Why it matters

Instruments must drive real loads, such as actuators, valve positioners, loudspeakers and long cables, and every analog circuit in them needs clean, stable supply rails. Power amplifiers are judged by how much of the supply power reaches the load and how much becomes heat; linear regulators turn a rippling, drifting rectifier output into the quiet DC that precision analog circuits need, at the cost of dissipating the difference.

Key ideas

Classes of operation (by the fraction of the cycle each output device conducts):

• Class A: conducts for the full 360°. Biased at mid-supply, very linear, but draws full current even with no signal. Maximum efficiency 25 % with a resistive (series-fed) load, 50 % with a transformer- or inductor-coupled load.
• Class B: each device conducts for 180°. A complementary push-pull pair (npn pushes, pnp pulls) shares the cycle; with no signal there is no quiescent current, so efficiency is high: up to π/4 = 78.5 %.
• Class AB: each device conducts for slightly more than 180°. Two diodes (or a V_BE multiplier) between the bases pre-bias both transistors at the edge of conduction, eliminating the crossover distortion that Class B shows near zero crossings, where neither transistor conducts until the input exceeds about ±0.6 V. Efficiency is close to Class B; this is the usual audio output stage.
• Class C: conducts for less than 180°. Very efficient, but only usable with a tuned (LC) load at radio frequencies.
• Class D: the output devices switch fully on or off with pulse-width modulation, and an LC filter recovers the signal. Efficiency above 90 %.

Class B power balance. With ±V_CC supplies, load R_L and output peak V_p, the load receives V_p²/(2R_L) while the supplies deliver 2V_CC·V_p/(πR_L), so efficiency rises linearly with V_p. Transistor dissipation is not largest at full output: it peaks at V_p = 2V_CC/π, where total device dissipation is 2V_CC²/(π²R_L), about 40 % of the maximum output power (20 % per transistor). Heat sinks are sized from this figure.

Thermal runaway. In a BJT stage, rising temperature lowers V_BE and raises current, which raises temperature further. Class AB stages use small emitter resistors and thermally coupled bias diodes to prevent it.

Linear (series) regulator. Four blocks: a stable reference (Zener or bandgap), a sampling divider R₁–R₂ on the output, an error amplifier comparing the two, and a series pass transistor that drops the excess voltage. Negative feedback holds the sampled output equal to the reference, so V_o = V_ref(1 + R₁/R₂). Protection includes current limiting (a sense resistor that turns on a transistor at about 0.6–0.7 V) and thermal shutdown.

Dropout and efficiency. The pass device needs a minimum input-output difference, the dropout voltage: about 2 V for a classic 78xx regulator, as low as 0.1–0.3 V for a low-dropout (LDO) regulator. Efficiency is roughly V_o/V_in and the pass device dissipates (V_in − V_o)·I_L, so linear regulators are best for small headroom or low current, while switching regulators handle large step-downs efficiently but add switching noise.

Three-terminal regulators. Fixed types (78xx positive, 79xx negative) and adjustable types (LM317) hold a fixed reference voltage (1.25 V for the LM317, from its datasheet) between OUT and ADJ.

Formulas

η = P_out / P_dc — efficiency (P in W).

η_max = 25 % (Class A, resistive load), 50 % (Class A, transformer-coupled), π/4 = 78.5 % (Class B).

P_out = V_p² / (2·R_L) — sinusoidal output power (W); V_p peak output (V).

P_dc = 2·V_CC·V_p / (π·R_L) — Class B push-pull, supplies ±V_CC.

η = (π/4)·(V_p / V_CC) — Class B efficiency at any amplitude.

P_out(max) = V_CC² / (2·R_L), P_D,total(max) = 2·V_CC² / (π²·R_L) at V_p = 2V_CC/π.

V_o = V_ref·(1 + R₁/R₂) — series regulator; R₁ top, R₂ bottom of the sampling divider.

V_o = 1.25 V·(1 + R₂/R₁) + I_ADJ·R₂ — LM317-type adjustable regulator (I_ADJ ≈ 50 µA, often neglected).

P_pass = (V_in − V_o)·I_L, η ≈ V_o / V_in — linear regulator.

I_limit ≈ V_BE / R_sc ≈ 0.7 V / R_sc — current-limit threshold.

Worked examples

Example 1 (standard: Class B). A complementary push-pull Class B stage runs from ±20 V into 8 Ω and delivers a 16 V peak sine. Find P_out, P_dc, efficiency and the dissipation per transistor. What is the worst-case total device dissipation?

1. P_out = V_p²/(2R_L) = 256/16 = 16 W.
2. P_dc = 2V_CC·V_p/(πR_L) = 2 × 20 × 16/(π × 8) = 25.5 W.
3. η = 16/25.5 = 62.8 % (check: (π/4)(16/20) = 62.8 %).
4. Device dissipation = 25.5 − 16 = 9.5 W total, 4.7 W per transistor.
5. Worst case: P_D,total(max) = 2V_CC²/(π²R_L) = 800/(9.87 × 8) = 10.1 W (5.1 W each), at V_p = 12.7 V.

Answer: P_out = 16 W, P_dc ≈ 25.5 W, η ≈ 62.8 %, 4.7 W per transistor; worst case 10.1 W total.

Example 2 (GATE level: series regulator). An op-amp series regulator uses a 5.1 V Zener reference and a sampling divider R₁ = R₂ = 10 kΩ. The input is 15 V and the load draws 0.5 A. A 1.2 Ω current-sense resistor sets the limit. Find V_o, pass-transistor dissipation, efficiency and the current limit. Also find the output of an LM317 with R₁ = 240 Ω and R₂ = 720 Ω.

1. V_o = V_ref(1 + R₁/R₂) = 5.1 × 2 = 10.2 V.
2. P_pass = (V_in − V_o)·I_L = (15 − 10.2) × 0.5 = 2.4 W.
3. η ≈ V_o/V_in = 10.2/15 = 68 %.
4. I_limit ≈ 0.7/R_sc = 0.7/1.2 = 0.58 A.
5. LM317: V_o = 1.25(1 + 720/240) = 1.25 × 4 = 5.0 V (I_ADJ neglected).

Answer: V_o = 10.2 V, P_pass = 2.4 W, η ≈ 68 %, I_limit ≈ 0.58 A; LM317 output 5.0 V.

Common mistakes

• Using 78.5 % as the efficiency at any output level; it applies only at full swing (V_p = V_CC).
• Assuming transistor dissipation is greatest at maximum output; it peaks at V_p = 2V_CC/π.
• Mixing peak and rms values in P = V²/R.
• Calling the input-output difference the dropout voltage; dropout is the minimum difference the regulator needs.
• Writing V_o = V_ref·R₁/R₂ instead of V_ref(1 + R₁/R₂).
• Forgetting crossover distortion when a Class B stage has no bias network.

For GATE IN

Expect efficiency, output power and dissipation numericals for Class A and Class B stages, the conduction angle of each class, crossover distortion, and series-regulator questions: output voltage from a reference and divider, pass-device dissipation, current limiting and LM317 settings. Practise the Class B power equations until you can find the dissipation peak without notes.

Quick check

1. A Class B stage has V_CC = 12 V and V_p = 6 V. Efficiency?
2. Maximum efficiency of a series-fed Class A amplifier?
3. A 5 V regulator runs from 9 V at 0.3 A. Pass-device dissipation?
4. Conduction angle of a Class AB output transistor?

Answers: 1. About 39.3 %. 2. 25 %. 3. 1.2 W. 4. Slightly more than 180° (less than 360°).