How is average power related to peak power?

For a continuous wave (CW) signal, average power equals peak envelope power (PEP). For a pulsed signal: P_avg = P_peak times duty_cycle, where duty_cycle = pulse_width / pulse_repetition_interval. Example: a radar transmitting 10 kW peak with 1 microsecond pulses at 1000 Hz PRF has duty cycle = 0.001 and average power = 10 W. For digitally modulated signals (OFDM, QAM), the relationship involves the peak-to-average power ratio (PAPR): P_peak = P_avg times PAPR. LTE OFDM has PAPR of 8 to 12 dB, meaning peak power is 6 to 16 times average power. This is why PA design for modulated signals is so challenging: the PA must handle the peaks while operating most of the time at much lower average power.

How is average power measured?

Thermal sensors (bolometers, thermocouples, thermistors) are the gold standard for average power measurement because they inherently average the absorbed RF energy by measuring temperature rise. They are true RMS sensors regardless of waveform shape, modulation type, or crest factor. Bandwidth: DC to 110 GHz. Accuracy: plus or minus 0.5 to 2 percent. Response time: 0.1 to 10 seconds. For faster measurements, diode detectors with square-law correction are used. At low power (below minus 20 dBm), a diode operates in the square-law region where output voltage is proportional to input power, providing true average power for any waveform. Above minus 20 dBm, the diode enters the linear region and requires correction factors that depend on the signal's statistical distribution (crest factor, CCDF).

Why does average power matter for thermal design?

The junction temperature of a PA transistor is determined by average power dissipation, not peak power. P_dissipated = P_DC minus P_RF_out (average). For a PA with 50 percent drain efficiency at 40 dBm average output (10 W): P_DC = 20 W, P_diss = 10 W. This 10 W heats the die continuously. The thermal design (heat sink, thermal interface, package) must maintain junction temperature below the rated maximum (typically 150 to 200 degrees C for GaN). Peak power during signal peaks causes transient junction temperature spikes, but the thermal time constant of the die (microseconds to milliseconds) means these are usually small relative to the average heating. Exception: pulsed radar with very low duty cycle may have significant peak-to-average thermal cycling that causes fatigue.

Power Measurement

Average Power

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P_avg = (1/T)∫P(t)dt. Pulsed: P_avg = P_peak × duty cycle. OFDM: PAPR = 8-12 dB, P_peak = 6-16× P_avg. Measured by thermal sensors (bolometer, thermocouple: true RMS, DC-110 GHz) or diode detectors (square-law region <−20 dBm). Determines PA thermal loading: P_diss = P_DC − P_RF. Critical for link budgets, regulatory limits, heat sink design.

Pulsed: P_pk×DC

OFDM PAPR: 8-12 dB

Sensor: Thermal/diode

Understanding Average Power

Average power is the most operationally meaningful power measurement in RF systems. It determines how much heat the PA must dissipate, how much interference the transmitter creates for neighboring channels, whether the link budget closes, and whether the system complies with regulatory power limits. Peak power matters for linearity and breakdown, but average power governs thermal design and energy consumption.

The distinction between average and peak power becomes critical with modern wideband signals. A 5G OFDM signal with 10 dB PAPR has peak power 10 times its average: a 10 W average transmitter must handle 100 W peaks without clipping. The PA must be sized for peak power but cooled for average power, creating the fundamental design tension in modern transmitter architecture.

Average Power Equations

General definition:
P_avg = (1/T) ∫₀^T P(t) dt

Pulsed signal:
P_avg = P_peak × τ/PRI
= P_peak × DC (duty cycle)
DC = τ × PRF

Modulated signal:
P_peak = P_avg × PAPR (linear)
PAPR(dB) = 10log(P_peak/P_avg)

PA dissipation:
P_diss = P_DC − P_RF,avg
= P_RF,avg(1/η − 1)

Signal Type vs Power Relationship

Signal	PAPR	P_pk/P_avg	Duty Cycle	Thermal Impact
CW	0 dB	1:1	100%	Continuous
Pulsed radar	0 dB (pulse)	1000:1 typ	0.1%	Low average
GSM (GMSK)	0 dB	1:1	12.5% TDMA	Burst
LTE OFDM	8-10 dB	6-10:1	~100%	High average
5G NR 256QAM	10-12 dB	10-16:1	~100%	Highest

Common Questions

Frequently Asked Questions

Peak vs average?

CW: equal. Pulsed: P_avg = P_peak × DC. Radar 10 kW peak, 1μs, 1kHz PRF: DC=0.001, P_avg=10W. OFDM: PAPR 8-12 dB, P_peak=6-16×P_avg. PA sized for peak, cooled for average. 10W avg OFDM = 100W peak capability needed.

Measurement?

Thermal sensors: bolometer, thermocouple, thermistor. True RMS, any waveform, DC-110 GHz, ±0.5-2% accuracy, 0.1-10s response. Diode detectors: fast, but need square-law correction above −20 dBm. CCDF characterization needed for high-PAPR signals.

Thermal design?

T_junction from average dissipation: P_diss = P_avg(1/η − 1). 50% efficiency, 10W out: 10W dissipated. Heat sink + TIM must keep T_j < 150-200°C (GaN). Peak thermal spikes: small due to die thermal time constant (μs-ms). Low DC pulsed: fatigue from thermal cycling.

Related Terms

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Power Design

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