RF Theory

RF Power Amplifier Theory

The PA is the hungriest, hottest, and most expensive component in any transmitter. Understanding how it works — efficiency, linearity, back-off, and the tricks engineers use to squeeze every last percent of efficiency — is essential for any RF hardware engineer.

Foundation
Why PA Design Is Different from LNA Design
When you design a Low Noise Amplifier (LNA), your main goal is minimising noise figure. A few milliwatts of power are involved. The transistor runs in its linear region and you barely notice the heat.
A Power Amplifier is the exact opposite. You are pushing the transistor to its absolute limits — maximum output power, maximum efficiency, maximum voltage swing. The transistor is deliberately driven into or near saturation. The device gets hot. Impedances are not matched for minimum noise — they're matched for maximum power transfer. And every extra percent of efficiency matters because it directly saves battery life or reduces cooling costs.
LNA (Low Noise Amplifier) 📍 Goal: Minimum noise figure ⚡ Power: 1–10 mW typical 🌡 Heat: Barely warms up 📐 Match: For min noise (Γopt) 🔑 Key spec: NF = 0.5–2 dB 🏃 Operation: Deep linear region PA (Power Amplifier) 📍 Goal: Maximum efficiency ⚡ Power: 0.5–100+ W 🌡 Heat: Needs heatsink! 📐 Match: For max power (Ropt) 🔑 Key spec: PAE = 40–70% 🏃 Operation: Near or in saturation VS
Real-world example: Your smartphone's 5G PA delivers +23 dBm (200 mW) RF output. At 35% PAE it consumes 571 mW from the battery — 371 mW becomes heat. Over a 1-hour call that's 1.3 kJ of wasted heat from just the PA. Improving PAE from 35% to 45% saves 17% battery drain — worth millions of dollars in development effort.
Must-Know Numbers
Key PA Specifications Explained

P1dB — The Compression Point

As you increase the input power to a PA, the output grows linearly — until it doesn't. The transistor starts to run out of headroom. The output compresses and the gain starts to drop. P1dB (1 dB compression point) is the output power at which the gain has dropped by exactly 1 dB from its small-signal value.
Pin (dBm) Pout (dBm) −30 −20 −10 0 +10 +20 −10 0 +10 +20 Ideal (linear gain) Gain = 20 dB Actual PA Psat ← 1 dB P1dB ≈ +24 dBm Pin@P1dB≈+4dBm OIP3 ≈ P1dB + 9−10 dB (rule of thumb) ← gain compressing here PA Output Power vs Input Power — showing compression and saturation
Why P1dB matters: In a communications system, you must keep the PA operating below P1dB — typically 3–6 dB below — to avoid distorting the signal. This is called "back-off". Operating right at P1dB means the constellation is starting to smear outward, EVM degrades, and the signal fails spectral mask requirements.

OIP3 — Third-Order Intercept Point

When two signals at frequencies f1 and f2 enter a nonlinear amplifier, they mix together and create intermodulation distortion (IMD) products at new frequencies. The most troublesome are the third-order products at 2f1−f2 and 2f2−f1 — these fall very close to the original signals and cannot be filtered out.
f |P| f₁ f₂ 2f₁−f₂ IM₃ 2f₂−f₁ IM₃ f₂−f₁ IM₂ f₁+f₂ IM₂ ← channel bandwidth → IM₃ products fall INSIDE the channel → cannot be filtered out! IM₂ far away IM₂ far away → can filter → can filter
OIP3 — Output Third-Order Intercept Point
OIP3 (dBm) = Pout_fund (dBm) + ΔIM3/2
where ΔIM3 = difference between fundamental tone and IM3 product (dB)

Rule of thumb: OIP3 ≈ P1dB_out + 9 to 10 dB

IM3 power grows 3× faster than fundamental:
For every 1 dB increase in Pin → fundamental rises 1 dB, IM3 rises 3 dB
They would theoretically meet at OIP3 (but PA saturates first)

Example: PA with P1dB = +24 dBm → OIP3 ≈ +33 to +34 dBm

PAE — Power Added Efficiency

PAE tells you what fraction of the DC power you put in actually comes out as RF — accounting for the fact that some RF power was already coming in at the input.
PA Transistor Pin (RF in) e.g. +3 dBm = 2 mW PDC (supply) e.g. 571 mW Pout (RF out) e.g. +23 dBm = 200 mW Pheat (wasted) e.g. 373 mW → heat! PAE = Pout − Pin PDC = (200−2)/571 = 34.7%
PAE and Drain Efficiency
PAE = (Pout − Pin) / PDC × 100%  ← Power Added Efficiency
DE = Pout / PDC × 100%          ← Drain Efficiency (ignores Pin)

When gain is high (≥ 10 dB), Pin << Pout so PAE ≈ DE
When gain is low (e.g. 6 dB), PAE < DE by a noticeable margin

Gain (dB) = Pout_dBm − Pin_dBm
Power gain (linear) = Pout_mW / Pin_mW
The Efficiency Story
PA Classes — The Efficiency vs Linearity Tradeoff
PA "class" refers to how much of each cycle the transistor conducts current. A transistor that conducts for the full 360° cycle (always on) is Class A. One that conducts for only half the cycle is Class B. Reducing conduction angle improves efficiency — but at the cost of linearity. This is the fundamental tradeoff in PA design.
Transistor Current vs Time — how long does it conduct each cycle? Class A 360° conduction η_max = 50% Very linear Most PA stages, LNA drivers ← 360° → Class AB >180° conduction η = 50–78% Good linearity Most common RF PA Class B 180° conduction η_max = 78.5% Push-pull needed Audio amplifiers, RF push-pull Class C <180° conduction η > 78.5% Non-linear! FM, CW transmitters only bias above cutoff slight conduction both halves bias exactly at cutoff bias below cutoff
Class A
50%max η
Always on. Most linear PA class. Low efficiency — transistor conducts even with no signal. Used where linearity is critical: driver stages, test equipment PAs.
Class AB
50–78%max η
Best compromise. Industry standard for RF PAs. Slightly non-linear but good enough with linearisation. Used in phones, WiFi, base stations.
Class B
78.5%max η
Half-wave conduction. Needs push-pull pair for both halves. Even harmonics cancel in push-pull. Used in audio and some RF balanced topologies.
Class C
>78.5%max η
Highly non-linear — only used for constant-envelope signals (FM, CW radar, FSK). Cannot amplify AM or QAM signals. Very high efficiency with tuned tank circuit.
Class D
~95%max η
Switching amplifier — transistor is fully ON or fully OFF. Used in audio amplifiers (Class D audio is everywhere). Hard to implement at RF frequencies above ~100 MHz.
Class E
100%theoretical η
Switched-mode PA where the transistor switches with zero voltage AND zero current simultaneously — zero overlap means zero dissipation. Practical efficiency 80–90% at RF. Used in IoT transmitters, RFID, drone comms.
Class F
~90%max η
Uses harmonic resonators to shape the drain voltage into a square wave and current into a half-sine. Near-zero overlap between V and I. Used in base station PAs, satellite transponders. GaN excels here.
Why most phones use Class AB and not Class E/F: Class E/F work brilliantly for constant-envelope signals. But modern phones transmit OFDM with high PAPR — the amplitude changes wildly every microsecond. Switching PAs can't track these amplitude variations and produce terrible spectral regrowth. Class AB (with digital pre-distortion) remains the standard for all variable-envelope modulations.

The Switching Classes Explained Simply

Class D — Switch Mode Voltage (purple) Current (green) No overlap → P = V × I = 0 → no heat! Class E — Zero Voltage Switching V=0 when switch closes V=0 at switch-on → zero switch loss → 100% theoretical efficiency
Optimal Impedance
Load Pull — Finding the Sweet Spot
Here's a surprising fact: the impedance that gives maximum power output is NOT the conjugate match you'd use for small-signal amplifiers. For a PA, the transistor is driven hard into its nonlinear region, so the classic conjugate match theory breaks down.
Load pull is the measurement technique used to find the actual optimal impedance. You systematically present different load impedances to the PA output while measuring Pout and PAE, then draw contour maps of constant power and constant efficiency on a Smith chart. The result is a set of "load pull contours" that look like overlapping ellipses.
50Ω Max PAE point Max Pout point conjugate match (50Ω) NOT optimal for PA! PAE = 60% PAE = 55% PAE = 45% Pout = P_sat − 0 dB Pout = P_sat − 1 dB Pout = P_sat − 3 dB How Load Pull Works 1. Build PA on test board 2. Connect tuner to PA output 3. Sweep tuner to 1000+ impedances 4. Measure Pout and PAE at each 5. Plot contours on Smith chart 6. Design output matching network to hit the optimal impedance Key Insight Max PAE and max Pout occur at DIFFERENT impedances! PA designers must choose: match for Pout, PAE, or a compromise between both Load Pull contours on Smith chart — green = PAE, blue = Pout
Linearity vs Efficiency
Back-Off and Spectral Regrowth
Back-off means deliberately running the PA below its maximum power level. You do this to keep the signal linear enough that it doesn't violate spectral emission masks. But backing off reduces efficiency dramatically — and this is the core challenge of modern PA design.
PAE vs Output Back-off OBO (dB) PAE (%) 0 20 40 60 80 0 −3 −6 −10 −14 OFDM op. point ≈34% PAE Psat = 65% Spectral Regrowth / ACPR f ← channel bandwidth → spectral regrowth! spectral regrowth! Clean PA (backed off) Compressed PA (no back-off)
ACPR — Adjacent Channel Power Ratio
ACPR = 10·log₁₀(P_adjacent / P_main_channel) dBc

Target (LTE): ACPR < −45 dBc at 5 MHz offset
Target (5G NR 100 MHz): ACPR < −45 dBc
Target (WiFi 802.11ac): spectral mask compliance at −50 dBr

Why it degrades: Memoryless nonlinearity produces IMD. OFDM with high PAPR drives the PA into compression on the peaks, creating intermodulation products that splash into adjacent channels.

Digital Pre-Distortion (DPD): Deliberately applies the inverse of the PA's nonlinearity at baseband before transmission. Can recover 10–12 dB of ACPR improvement, allowing the PA to run 3–4 dB closer to saturation → significant efficiency improvement.
The Most Important PA Architecture
The Doherty PA — Solving the Back-off Efficiency Problem
Invented by W.H. Doherty in 1936, the Doherty PA is the dominant architecture in 4G/5G base stations worldwide. It solves the fundamental problem: Class AB efficiency collapses at back-off, but you need to operate at 6–10 dB back-off to handle OFDM PAPR.
The idea: Use TWO amplifiers — a Main (carrier) PA and a Peaking PA. The Main PA handles low-power operation efficiently. The Peaking PA only turns on when the signal gets large. Together they maintain high efficiency across a wider range of output power.
Doherty PA Architecture Input Splitter MAIN PA Class AB (always on) PEAK PA Class C (turns on at −6dB) λ/4 TL + Output RF Out RF In +90° shift Efficiency vs Output Power Pout PAE 0 30% 60% 80% Psat−6dB Psat Class AB Doherty 1st peak 2nd peak OFDM region Doherty has two efficiency peaks vs Class AB one
How Doherty works: The Main PA is a standard Class AB amplifier, sized to handle average power. At low signal levels, only the Main PA is active — it runs efficiently at near-saturation. As the signal approaches peak power, the Peaking PA (Class C, normally off) switches on and adds its power to the output. This creates two peaks in the efficiency curve — one at back-off power (Psat − 6 dB) and one at full power. The average operating point falls right between them, giving much better average efficiency.
Numbers: A Class AB PA at 6 dB back-off has PAE of about 20–25%. A Doherty PA at the same back-off has PAE of 45–55%. For a 5G base station transmitting at 120W average power, the difference is: Class AB wastes 360–480W as heat. Doherty wastes 105–155W. Multiplied across 100,000 base stations — Doherty saves hundreds of megawatts of electricity globally, every day.
Handset PA Technology
Envelope Tracking — The Smart Power Supply
Doherty is great for base stations, but it's large and works best at a fixed frequency. For handsets where the PA must cover 600 MHz to 3.8 GHz across 30+ bands, a different technique dominates: Envelope Tracking (ET).
Standard PA — Fixed Supply VDD fixed ← wasted as heat (big gap between supply and signal) → Fixed supply: efficient only at peak, wastes power at back-off Envelope Tracking — Modulated Supply VDD tracking ← tiny gap → minimal wasted power → ET: supply follows signal → PA always near saturation → always efficient
The ET modulator (essentially a fast DC-DC converter running at RF signal bandwidth) continuously adjusts the PA supply voltage to track the signal envelope. The PA always operates near its compression point — regardless of whether the signal is at a peak or a trough. This maintains near-constant efficiency across the full PAPR range. Modern Qualcomm chips (using Qualcomm/RF Micro/Skyworks ET) achieve 40–50% PAE for a handset PA covering the full LTE/5G band range.
TechniqueBack-off Efficiency GainCost/ComplexityBest Application
Fixed bias Class ABLow — drops to 15% at 10dB back-offSimple, low costLow-power devices, drivers
Doherty PA+15–25% PAE at 6dB back-offModerate — extra PA + combinerBase stations, fixed frequency PAs
Envelope Tracking (ET)+10–20% PAE vs fixed supplyHigh — needs fast DC-DC converterHandsets, wideband PAs
Digital Pre-Distortion (DPD)Enables 3–4 dB less back-offRequires DSP + feedback loopBase stations combined with Doherty
ET + DPD combinedBest of both — 50–60% PAE at back-offVery complex, expensive5G massive MIMO base stations
Semiconductor Technologies
GaN vs GaAs vs LDMOS — Choosing the Right Device
The transistor technology determines the PA's fundamental capabilities — maximum frequency, breakdown voltage, efficiency, and cost. Here's how the main RF PA technologies compare:
Technology Comparison — Normalised to Best in Class Power density Efficiency (PAE) Max frequency Breakdown voltage Cost effectiveness Maturity GaN ★★★★★ 10 W/mm ★★★★ 50–70% ★★★★ up to 100 GHz ★★★★★ 100–200V ★★ expensive ★★★ maturing GaN on SiC/Si
TechnologyPower DensityMax PAEMax FreqBreakdown VKey Use
GaN on SiC8–12 W/mm60–75%100+ GHz100–200 V5G base stations, radar, satellite
GaN on Si4–6 W/mm50–65%40 GHz60–80 V5G massive MIMO, cost-sensitive
GaAs pHEMT0.5–1.5 W/mm55–70%100+ GHz15–20 VHandset PAs, satellite LNAs
LDMOS Si1–3 W/mm60–70%6 GHz65–100 V4G base stations, broadcast
Si CMOS0.05–0.2 W/mm20–40%60 GHz (mmWave)1–3 VWiFi chipsets, IoT, low power
Calculate It
Interactive PA Efficiency Calculator
Adjust the sliders to see how P1dB, back-off, gain, and supply voltage affect PAE, heat dissipation, and battery current draw.
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