How does duty cycle relate to average and peak power?

P_avg = P_peak * D. In dB: P_avg(dBm) = P_peak(dBm) + 10*log10(D). For a 1 kW (60 dBm) radar transmitter with 1% (0.01) duty cycle: P_avg = 60 + 10*log10(0.01) = 60 - 20 = 40 dBm = 10W. This relationship is fundamental for: thermal design (heatsinks must dissipate P_avg, not P_peak), power supply sizing (average current draw determines supply requirements), and safety compliance (exposure limits are based on time-averaged power). The PA itself must handle P_peak instantaneously, but thermal management is based on P_avg.

How does duty cycle affect PA selection?

PAs are rated for both peak and average power, and the duty cycle determines which limit applies. A PA rated for 100W peak / 20W average can handle: 100W at 20% duty cycle (P_avg = 20W, at the average limit). 100W at 10% duty cycle (P_avg = 10W, well within average limit). But NOT 100W at 50% duty cycle (P_avg = 50W, exceeds average rating). Exceeding the average power rating causes thermal failure even though the peak power is within spec. Pulsed PAs designed for radar often have very low duty cycle ratings (1-5%) because they are optimized for peak power and have minimal thermal mass. CW-rated PAs can operate at 100% duty cycle.

How is duty cycle regulated?

Regulatory bodies limit RF emissions based on time-averaged power. FCC Part 15: unlicensed devices specify peak and average power limits separately. A device transmitting 1W peak at 1% duty cycle has 10 mW average, which may comply even if the peak exceeds the CW limit. FCC Part 18 (ISM): limits are typically average power. MIL-STD-464: EMI limits are specified for different pulse characteristics. For RF exposure (SAR), FCC OET-65 uses time-averaged power density, so lower duty cycle reduces the exclusion zone around an antenna. Duty cycle must be accurately known and documented for compliance testing.

Fundamental Concepts

Duty Cycle

/doo-tee sy-kul/ (D)

Duty Cycle is the ratio of pulse-on time (τ) to total period (T): D = τ/T = τ×PRF. It determines average power: P_avg = P_peak×D. A 1 kW radar at 1% duty cycle dissipates only 10W average. Critical for PA thermal design, power supply sizing, and regulatory compliance (FCC limits are time-averaged). CW = 100% duty cycle.

Category: Fundamental Concepts

Formula: D = τ/T

Power: P_avg = P_pk×D

Understanding Duty Cycle

Duty cycle connects the peak performance of a pulsed system to its real-world thermal and regulatory constraints. A transmitter may produce kilowatts of peak power, but its duty cycle determines whether the heatsink can handle the heat, whether the power supply is adequate, and whether the system complies with emission limits. Understanding duty cycle is essential for specifying PAs, designing thermal management, and passing regulatory testing.

Duty Cycle Calculations

Duty cycle:
D = t_on/T ×100%
T = t_on+t_off = 1/f_rep

Average power:
P_avg = P_peak×D

Radar duty cycle:
D = τ×PRF
τ = pulse width, PRF = pulse repetition freq

Thermal impact:
T_rise ∝ P_avg = P_peak×D

Duty Cycle by Application

Application	Duty Cycle	Peak Power	Avg Power	Thermal Design
Pulsed radar	0.1-1%	1 kW-1 MW	1-1000W	Low avg, air-cooled
FMCW radar	50-100%	0.1-10W	0.05-10W	Continuous, small sink
5G TDD	50-80%	20-200W	10-160W	High avg, forced air
Wi-Fi (bursty)	1-30%	0.1-1W	0.01-0.3W	Low avg, passive
UWB impulse	<0.01%	1-10W	<1 mW	Negligible

Key Equations

Decibel conversion:
Power: dB = 10log(P₂/P₁)
Voltage: dB = 20log(V₂/V₁)

dBm to watts:
P(W) = 10^{(dBm−30)/10}
0 dBm = 1 mW, +30 dBm = 1 W

Wavelength:
λ = c/f = 300/f(MHz) meters

Comparison

Application	D typical	P_peak	P_avg	Notes
Pulsed radar	0.1–1%	1–100 kW	1–100 W	Low duty
FMCW radar	50–100%	0.1–10 W	0.1–10 W	CW-like
5G TDD	30–70%	1–10 W	0.3–7 W	DL:UL ratio
WiFi (CSMA)	5–30%	0.1–1 W	5–100 mW	Listen before talk
Pulsed PA test	1–10%	10–1000 W	0.1–100 W	Characterization

Common Questions

Frequently Asked Questions

Power relationship?

P_avg = P_peak * D. In dB: P_avg = P_peak + 10*log10(D). 1 kW at 1%: P_avg = 10W. Thermal design uses P_avg. PA must handle P_peak instantaneously. Power supply sized for P_avg.

PA selection?

PAs rated for peak AND average. 100W peak / 20W avg: max 20% duty cycle at full power. Exceeding avg rating causes thermal failure. Pulsed PAs: low duty (1-5%). CW PAs: 100% duty. Always check both specs.

Regulation?

FCC limits time-averaged power. 1W peak at 1% = 10 mW avg (may comply). SAR exposure based on time-averaged power density. Lower duty = smaller exclusion zone. Duty cycle must be documented for compliance testing.

Related Terms

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