Power amplifiers

Electronics and Communication Engineering (B.E./B.Tech) · Circuits and devices · free study notes for exams, placements and interviews

In short

A power (large-signal) amplifier is the final stage of an amplifier chain: it is designed not for voltage gain but to deliver watts of undistorted power into a low-impedance load such as a loudspeaker, motor, antenna or actuator. Because the signal swings over a large part of the load line, small-signal linear models are inadequate — the design is judged by output power, conversion efficiency, harmonic distortion and heat dissipation. Classes A, B, AB, C and D differ in how long the output device conducts, trading linearity against efficiency. The topic is a standard scoring area in Analog Electronic Circuits papers and in GATE EC (efficiency and distortion numericals), and the knowledge is used daily at Bharat Electronics, ISRO/DRDO (RF solid-state power amplifiers), Ahuja and Bosch (public-address systems), Texas Instruments India, Analog Devices and Qualcomm/MediaTek India (class-D audio and mobile RF PAs), and in inverter, UPS and EV traction electronics.

Explained

What makes an amplifier a "power" amplifier

Purpose: supply current and power to a load, not just voltage gain. The voltage amplifier before it sets gain; the power stage sets efficiency and distortion.
Large-signal operation: the operating point travels nearly the whole AC load line, so the transistor's non-linear transfer characteristic generates harmonics; distortion must be computed, not ignored.
Figures of merit: output power Po, DC input power Pi, conversion (collector) efficiency η = Po/Pi, total harmonic distortion THD, power dissipation Pd, and the device's figure of merit = Pd(required)/Po(max).
Impedance matching: a loudspeaker (4/8 Ω) or antenna (50 Ω) is matched to the device by a transformer, by direct emitter/source follower operation, or by an RF matching network, so maximum power transfer is approached.
Classification by conduction angle: Class A = 360°, AB = between 180° and 360°, B = 180°, C = less than 180°, D = switching (device is either fully ON or fully OFF).

Class A: series-fed and transformer-coupled

Definition: the device conducts for the entire input cycle; Q-point is near the centre of the load line. Best linearity, worst efficiency.
Series-fed (direct-coupled): load sits in the collector/drain circuit. Max theoretical η = 25%; the transistor dissipates maximum power at zero signal (VCEQ·ICQ), so the heat sink must be sized for the no-signal condition.
Why 25%: Pi = Vcc·ICQ = Vcc²/2RL (with Q at mid-point), while Po(max) = Vcc²/8RL.
Transformer-coupled: the DC resistance of the primary is almost zero, so VCEQ ≈ Vcc and VCE can swing from ~0 to 2Vcc. The reflected load is RL′ = (N1/N2)²RL. Max theoretical η = 50%; devices must withstand 2Vcc.
Advantages: no crossover distortion, lowest THD, simple single-device circuit, DC isolation and impedance matching from the transformer.
Limitations: poor efficiency, large standing current, heavy and costly audio transformer with limited bandwidth, transistor dissipation = 2 × Po(max). Used today only in low-power stages and valve/boutique audio.

Class B and class AB push-pull

Class B: Q-point at cut-off (zero bias); each device conducts for one half-cycle. Two devices in push-pull reconstruct the full wave. Max theoretical η = 78.5% (π/4); zero standing current, so no-signal dissipation ≈ 0.
Push-pull arrangements: (a) *transformer-coupled* with centre-tapped input (phase splitter) and output transformers; (b) complementary symmetry using a matched npn–pnp (or n/p-channel MOS) pair as emitter/source followers — no transformer, used in all modern audio ICs.
Single-supply vs dual-supply: a dual ±Vcc output stage drives the load directly from the mid-point; a single-supply stage needs a large coupling capacitor (which sets the low-frequency cut-off) or a bridge (BTL) connection.
Crossover (notch) distortion: near zero signal neither BJT conducts until |Vin| exceeds ~0.7 V, giving a dead zone of about 1.4 V — severe at low signal levels and the main defect of pure class B.
Class AB: a small forward bias (diode bias, VBE multiplier, or a bias resistor chain) keeps both devices slightly conducting at zero signal, removing the notch. Efficiency falls between 50% and 78.5% (typically 55–70% at rated power). All practical audio amplifiers are class AB.
Thermal stability: the bias diodes / VBE multiplier transistor are mounted on the same heat sink so that VBE tracks temperature; small emitter resistors (0.1–0.5 Ω) add local degeneration and prevent thermal runaway and current hogging between paralleled devices.
Variants: quasi-complementary (two npn outputs with a pnp driver, used when matched pnp power devices were scarce), Darlington and Sziklai (CFP) pairs for high current gain, bootstrapped driver for full positive swing.
Device stress: each transistor sees up to 2Vcc across it; peak current Vcc/RL. Maximum dissipation occurs not at full output but at Vp = 0.636 Vcc.

Class C, class D and the higher-efficiency classes

Class C: conduction angle well below 180° (typically 90–150°); collector current is a train of narrow pulses. A parallel LC tank at the output selects the fundamental and restores a sinusoid; the flywheel action is essential.
Efficiency is high (practically 70–85%, theoretically approaching 100% as the angle → 0) but distortion is unacceptable for audio. Used for RF power stages in transmitters, frequency multipliers (the tank is tuned to a harmonic) and class-C modulators.
Class D (switching amplifier): the input is converted to a PWM (or sigma-delta) pulse train at 250 kHz–1 MHz; MOSFETs switch fully ON/OFF and an output LC low-pass filter recovers the audio. Device dissipation is only conduction (I²Ron) + switching loss, so η = 90–95%.
Class D advantages: tiny heat sink, high power density, battery friendly — hence used in mobile phones, TVs, soundbars, car audio and PA amplifiers. Limitations: EMI/RFI from fast edges, dead-time and filter-induced distortion, needs careful layout; filterless (BD) modulation is common in small ICs.
Class E and F: resonant switching RF amplifiers (>90%) used in mobile base stations and RF heating.
Class G and H: class-AB output stage fed from switched (G) or signal-tracking (H) rails, improving efficiency at low levels without class-D's EMI.
Class S / other: rarely examined; know the main five plus D.

Distortion, harmonics and push-pull cancellation

Harmonic distortion: output current i = ICQ + A1 cos ωt + A2 cos 2ωt + …; Dn = |An/A1|, and THD = √(D2² + D3² + …), expressed as a percentage.
Second-harmonic distortion by the three-point method: D2 = |½(Imax + Imin) − ICQ| / (Imax − Imin) — a standard numerical in university papers. A five-point method also gives D3 and D4.
Even-harmonic cancellation: in a push-pull stage the two halves produce equal and opposite even harmonics, which cancel in the output transformer/load; only odd harmonics remain. Push-pull therefore gives low distortion *and* cancels DC flux in the transformer core (no core saturation) and rejects power-supply hum.
Clipping (overload) distortion: driving beyond the supply flattens peaks and generates high odd harmonics; the amplifier must be rated with headroom.
Other practical distortions: crossover distortion (class B), thermal/memory distortion, transformer non-linearity, and dead-time distortion in class D.
Negative feedback reduces distortion by roughly the factor (1 + Aβ), which is why real audio amplifiers wrap global feedback around the output stage.

Power devices, heat sinks and thermal design

Heat flow model: junction → case → sink → ambient, in series thermal resistances θjc, θcs (case-to-sink, reduced by thermal grease/mica washer) and θsa (sink-to-air), in °C/W.
Junction temperature: Tj = Ta + Pd(θjc + θcs + θsa); Tj(max) is typically 150 °C for silicon small-power devices and 175–200 °C for large power BJTs/MOSFETs. Indian ambient design is commonly taken as 45–55 °C inside an enclosure, not 25 °C.
Power derating: the datasheet rating (e.g. "30 W at TC = 25 °C") falls linearly with case temperature; derating factor = 1/θjc (W/°C).
Safe operating area (SOA): bounded by Imax, Vceo(max), the Pd(max) hyperbola and the second-breakdown limit (localised current crowding in BJTs). MOSFETs have no second breakdown and have a positive temperature coefficient of Rds(on), so they parallel safely.
Protection: output current limiting, VI limiter, fuses, DC-offset/speaker protection relay, and a Zobel network plus series inductor for capacitive-load stability.
Package and mounting: TO-3, TO-220, TO-247, TO-264; anodised extruded aluminium sinks, forced air or fan for >100 W.

Practical circuits, ICs and Indian standards

Typical audio IC amplifiers: LM386 (0.3–1 W, battery projects), LM380, TDA2030/TDA2050 (14–32 W class AB), TDA7294, LM3886; class-D families such as TPA31xx (TI) and TAS-series are now the default in consumer products. Lab experiments usually use a complementary-symmetry class-AB stage or TDA2030.
Discrete architecture of a real audio amplifier: differential input pair → VAS (voltage amplifier stage with Miller compensation) → VBE-multiplier bias → Darlington complementary output pair with emitter resistors → global feedback network.
Indian standards and practice: safety of audio/video electronic apparatus is covered by IS 616 (adopted from IEC 60065; the IEC family is being superseded internationally by IEC 62368-1, so check the current BIS listing). Mains-powered audio equipment falls under the BIS Compulsory Registration Scheme (CRS) under the Electronics and IT Goods (Requirements for Compulsory Registration) Order. Power ratings on Indian PA amplifiers are quoted in RMS watts; "PMPO" figures seen in the market are marketing numbers, not engineering ratings.
Noise regulation for PA use: under the Noise Pollution (Regulation and Control) Rules, 2000 (as amended), the noise level at the boundary of the public place where a loudspeaker or public-address system is used may not exceed 10 dB(A) above the ambient standard for that area or 75 dB(A), whichever is lower (for a privately owned system the limit at the boundary of the private place is 5 dB(A) above ambient), and use is barred between 10 pm and 6 am (limited festival exemptions are notified by state governments). This constrains how PA amplifiers are specified and installed.
RF side: solid-state power amplifiers (SSPAs) using LDMOS and GaN HEMT devices for radar, satcom and telecom; linearity specified as P1dB, IP3, ACPR and PAE, with Doherty and digital pre-distortion used in base stations.

Key points

Power amplifier - final large-signal stage delivering watts to a low-impedance load; judged by power, efficiency, distortion and heat.
Conversion efficiency - η = Po(ac)/Pi(dc); ideal maxima: class A series-fed 25%, transformer-coupled class A 50%, class B 78.5%, class C and class D approach 100% in theory (practically 70–85% and 90–95%).
Class A - 360° conduction, best linearity, highest standing current; maximum device dissipation occurs at zero signal.
Class B - 180° conduction, near-zero standing current, needs push-pull; suffers crossover distortion.
Class AB - small forward bias removes the notch; the class used in every practical audio amplifier.
Class C - under 180° conduction with a tuned tank load; RF transmitters and frequency multipliers only.
Class D - PWM switching with LC filter; highest efficiency, smallest heat sink, EMI the main penalty.
Reflected load - RL′ = (N1/N2)²RL; the transformer matches an 8 Ω speaker to the hundreds of ohms the device needs.
Peak device stress - in transformer class A and in push-pull, VCE(max) ≈ 2Vcc.
Worst-case dissipation in class B - total 2Vcc²/π²RL ≈ 0.4 Po(max), i.e. 0.2 Po(max) per transistor, at Vp = 0.636 Vcc — not at full output.
Push-pull cancellation - even harmonics and DC core flux cancel; only odd harmonics survive.
Second-harmonic distortion - D2 = |½(Imax+Imin) − ICQ| / (Imax − Imin); THD = √(ΣDn²).
Crossover distortion - ~1.4 V dead zone in silicon class B; worst at low signal level.
Thermal runaway - rising Tj raises ICQ in BJTs; cured by emitter resistors and heat-sink-mounted bias compensation.
Thermal equation - Tj = Ta + Pd(θjc + θcs + θsa); design for Indian ambients of 45–55 °C.
Second breakdown / SOA - BJT failure mode from current crowding; MOSFETs are free of it and parallel easily.
Distortion vs feedback - global negative feedback cuts distortion by about (1 + Aβ).
Rating honesty - specify RMS watts at a stated THD and load; PMPO is meaningless.

Formulas and examples

Po(ac) = V²rms/RL = V²p/(2RL) = I²p·RL/2 — Po in W, Vp peak output voltage (V), Ip peak load current (A), RL load resistance (Ω)
Class A series-fed: Pi = Vcc·ICQ; Po(max) = V²cc/(8RL); η(max) = 25%
Transformer-coupled class A: RL′ = (N1/N2)²·RL; Pi = Vcc·ICQ = V²cc/RL′; Po(max) = V²cc/(2RL′); η(max) = 50%
Class B/AB push-pull: Idc = 2Ip/π; Pi = 2Vcc·Ip/π; η = (π/4)(Vp/Vcc) × 100%; η(max) = 78.5%
Class B dissipation: Pd(total) = Pi − Po; Pd(total,max) = 2V²cc/(π²RL) at Vp = 2Vcc/π; per transistor = half of this
Distortion: D2 = |½(Imax + Imin) − ICQ| / (Imax − Imin); THD = √(D2² + D3² + D4² + …); P(total) = (1 + THD²)·P1
Thermal: Tj = Ta + Pd(θjc + θcs + θsa) — temperatures in °C, θ in °C/W; Pd(allowed at TC) = (Tj,max − TC)/θjc
Derating (against case temperature): Pd(TC) = Pd(25 °C) − (TC − 25) × derating factor, derating factor = 1/θjc in W/°C

Example 1 — Series-fed class A. Vcc = 20 V, directly coupled load RL = 20 Ω, Q-point at VCEQ = 10 V, ICQ = 0.5 A.

Pi = 20 × 0.5 = 10 W.
Po(max) = V²cc/(8RL) = 400/160 = 2.5 W (peak swing 10 V: 10²/(2×20) = 2.5 W ✓).
η(max) = 2.5/10 = 25%. At zero signal the transistor dissipates VCEQ·ICQ = 5 W — the heat-sink design case.

Example 2 — Transformer-coupled class A. Vcc = 12 V, turns ratio N1:N2 = 3:1, speaker RL = 8 Ω.

RL′ = 3² × 8 = 72 Ω; ICQ = Vcc/RL′ = 12/72 = 166.7 mA.
Pi = 12 × 0.1667 = 2.0 W; Po(max) = V²cc/(2RL′) = 144/144 = 1.0 W; η = 50%.
Check on the secondary: primary peak 12 V → secondary peak 4 V → Po = 4²/(2×8) = 1.0 W ✓. VCE(max) = 2Vcc = 24 V, so the transistor must be rated above that.

Example 3 — Class B push-pull, full numerical. Vcc = 24 V, RL = 8 Ω, input drives a peak output of 20 V.

Po = 20²/(2×8) = 25 W; Ip = 20/8 = 2.5 A.
Idc = 2 × 2.5/π = 1.592 A; Pi = 24 × 1.592 = 38.2 W; η = 25/38.2 = 65.4%.
Total transistor dissipation = 38.2 − 25 = 13.2 W, i.e. 6.6 W each.
At full drive (Vp = Vcc): Po(max) = 24²/16 = 36 W, η = 78.5%.
Worst-case heat: Pd(total,max) = 2 × 576/(π² × 8) = 1152/78.96 = 14.6 W, i.e. 7.3 W per transistor, at Vp = 0.636 × 24 = 15.3 V — more than at 25 W output.

Example 4 — Heat sink for the stage above. Device Pd = 7.3 W, θjc = 1.5 °C/W, θcs = 0.5 °C/W (mica + grease), Tj(max) = 150 °C, enclosure ambient Ta = 45 °C.

Allowed total θ = (150 − 45)/7.3 = 14.38 °C/W.
θsa ≤ 14.38 − (1.5 + 0.5) = 12.4 °C/W → a small extruded sink suffices; at Ta = 55 °C the requirement tightens to (95/7.3) − 2 = 11.0 °C/W.
*Derating check:* a device rated 30 W at TC = 25 °C with Tj,max = 150 °C has θjc = 125/30 = 4.17 °C/W; at TC = 75 °C its rating is 30 − 0.24 × 50 = 18 W.

Example 5 — Supply selection and distortion. Design a class-AB stage for 10 W into 8 Ω, then evaluate its distortion.

Vp = √(2 Po RL) = √160 = 12.65 V; allow ~2.4 V saturation/drop headroom → dual supply ±15 V.
Ip = 12.65/8 = 1.58 A; Idc = 2 × 1.58/π = 1.006 A; Pi = 15 × 1.006 = 15.1 W; η = 10/15.1 = 66%; total heat 5.1 W.
Worst-case per device = V²cc/(π²RL) = 225/78.96 = 2.85 W → choose devices rated ≥ 3 W on a sink.
Measured collector current: Imax = 180 mA, Imin = 20 mA, ICQ = 95 mA → D2 = |100 − 95|/160 = 3.125%. With D3 = 1.5% and D4 = 0.8%, THD = √(3.125² + 1.5² + 0.8²) = 3.56%; power rises only by (1 + 0.0356²) ≈ 0.13% over the fundamental.

Feature	Class A	Class AB	Class B	Class C	Class D
Conduction angle	360°	180°–360°	180°	< 180°	Switching (ON/OFF)
Q-point	Centre of load line	Just above cut-off	At cut-off	Below cut-off	None (PWM)
Max theoretical η	25% (50% with transformer)	50–78.5%	78.5%	~100% (70–85% real)	~100% (90–95% real)
Distortion	Lowest	Low	Crossover distortion	Very high (tank filters it)	Switching/dead-time
No-signal dissipation	Maximum	Small	~Zero	Zero	~Zero
Device dissipation per Po(max)	2 × Po	~0.2–0.3 × Po	0.2 × Po each	Low	Very low
Typical use	Low-power, valve audio	All audio amplifiers	Textbook/driver stages	RF transmitters, multipliers	Mobile, TV, car audio, PA

Where it is used

Consumer and professional audio: TVs, soundbars, Bluetooth speakers, car audio, and Indian PA amplifiers from Ahuja Radios, Bosch India and Philips — class AB in legacy designs, class D in nearly all new products.
Telecom and defence RF: LDMOS and GaN power amplifiers for 4G/5G base stations (Jio/Airtel vendor ecosystem, Ericsson, Nokia India) and SSPAs/TWTAs for radar and satcom at Bharat Electronics, DRDO (LRDE) and ISRO.
Semiconductor and IC design roles: analog/mixed-signal design and applications engineers at Texas Instruments India, Analog Devices, NXP, Infineon, Qualcomm and MediaTek working on class-D audio, haptic and RF front-end PA modules.
Industrial and power electronics: servo and motor drive output stages, ultrasonic and induction-heating generators, piezo and solenoid drivers, inverter/UPS output stages (the class-D switching idea at mains frequency).
Instrumentation and test: signal-generator output amplifiers, shaker/vibration-table drive amplifiers, biomedical stimulators.
Lab and academic work: AICTE-model Analog Electronics labs measure class-A and class-B efficiency, plot crossover distortion and verify push-pull harmonic cancellation on a distortion analyser or FFT.

Interview questions

Q: Why is the maximum efficiency of a series-fed class A amplifier only 25%? A: The device carries a large constant DC current (Pi = Vcc·ICQ) regardless of signal, while the useful AC output is limited to V²cc/8RL, giving a ratio of one quarter.
Q: How does a transformer double class A efficiency to 50%? A: The primary has almost no DC drop, so VCEQ ≈ Vcc and VCE can swing to 2Vcc; the same DC input then yields twice the AC output power.
Q: What is crossover distortion and how is it removed? A: A dead zone of about 1.4 V near zero signal where neither silicon transistor conducts; it is removed by forward-biasing both devices slightly (diode or VBE-multiplier bias), i.e. class AB operation.
Q: In a class B amplifier, at what output does the transistor get hottest? A: Not at maximum output — at Vp = 2Vcc/π ≈ 0.636 Vcc, where total dissipation reaches 2V²cc/π²RL, about 0.4 of maximum output power.
Q: Why do even harmonics cancel in a push-pull stage? A: The two halves conduct on opposite half-cycles, so their even-harmonic components are equal and oppositely phased at the load and cancel, leaving odd harmonics.
Q: Can a class C amplifier be used for audio? A: No — its conduction angle is far below 180° and distortion is enormous; it works only with a tuned tank load that reconstructs a single frequency, so it suits RF, not broadband audio.
Q: Why is class D so efficient, and what is its drawback? A: The switch is either fully on (low VDS) or fully off (no current), so ideal loss is zero; the drawbacks are EMI from fast edges, dead-time distortion and the cost/size of the output LC filter.
Q: Why are small emitter resistors used in the output pair? A: They provide local negative feedback that stabilises the quiescent current against temperature and equalises current sharing among paralleled devices, preventing thermal runaway.
Q: Why is the bias diode or VBE-multiplier transistor mounted on the heat sink? A: So its VBE falls with temperature at the same rate as the output devices', keeping the quiescent current constant instead of letting it rise.
Q: What voltage rating must the transistors in a push-pull stage have? A: At least 2Vcc, because when one device saturates the other sees nearly the full supply-to-supply swing; add margin for inductive load spikes.
Q: What is second breakdown and why do power MOSFETs avoid it? A: It is localised thermal current crowding in a BJT that destroys the junction below the rated power hyperbola; MOSFET Rds(on) has a positive temperature coefficient, so hot spots carry less current and the device self-balances.
Q: How would you specify an amplifier honestly for a tender? A: Continuous RMS output power into a stated load impedance at a stated THD (e.g. 50 W RMS into 8 Ω at 0.5% THD, 20 Hz–20 kHz), with supply, efficiency and ambient temperature stated — never PMPO.

Common mistakes

Quoting 50% for every class A amplifier — 50% applies only to the transformer-coupled case; direct-coupled series-fed class A is 25%.
Sizing the heat sink for maximum output power in class B instead of the true worst case at Vp = 0.636 Vcc (and sizing class A at full signal instead of at zero signal).
Forgetting the reflected load RL′ = (N1/N2)²RL and computing power with the 8 Ω speaker value directly.
Using Idc = Ip instead of 2Ip/π for push-pull DC input current, or mixing peak, RMS and peak-to-peak voltages in Po = V²p/2RL.
Calling class AB "class B" in a lab report, or claiming 78.5% efficiency for a measured class-AB amplifier.
Assuming small-signal hybrid-π analysis and constant gain over the whole swing, so distortion is never estimated.
Designing for Ta = 25 °C when the enclosure in an Indian installation runs at 45–55 °C, and omitting θcs for the insulating washer.