Doherty RF Amplifier Back-Off Efficiency & PAPR Formula

Double 5G macro-cell PA efficiency at 6 dB PAPR back-off with Doherty load modulation!

Modern 5G NR and Wi-Fi 7 OFDM waveforms exhibit high Peak-to-Average Power Ratios (PAPR ~ 6–9 dB), forcing base-station RF power amplifiers (PAs) to operate far below peak saturation power P_peak most of the time! While an ideal sinusoidal Class-B PA achieves PI() / 4 = 78.54% drain efficiency at peak rail swing, backing off average power to P_avg = P_peak / 4 (-6.02 dB OBO, voltage swing v_r = SQRT(P_avg / P_peak) = 0.50) cuts Class-B efficiency in half to (PI() / 4) * v_r = 39.27%, dumping massive waste heat into tower heatsinks! William H. Doherty’s 1936 active load-modulation architecture splits amplification into a Carrier PA (loaded at 2 * R_opt while the Peaking PA stays off for v_r <= 0.5) and a Peaking PA that turns on above v_r > 0.5, yielding Symmetric 2-Way Doherty Efficiency = (PI() / 4) * (2 * v_r) for v_r <= 0.5 and (PI() / 4) * (v_r^2 / (1.5 * v_r - 0.5)) for 0.5 < v_r <= 1—restoring the full 78.54% peak efficiency right at -6 dB back-off!

Verify on a 5G Massive-MIMO Radio Unit—Average_Transmit_Power P_avg = 25 W (B2) and Peak_Envelope_Power P_peak = 100 W (B3 -> Linear Crest Ratio = 4.00x = 6.02 dB PAPR in E2, normalized voltage v_r = SQRT(0.25) = 0.50): Classical Class-B Efficiency plunges to 0.3927 (39.27% in E3); Symmetric Doherty Efficiency rebounds to PI() / 4 = 0.7854 (78.54% in E4); achieving a 2.0000x Efficiency Gain Multiplier (cutting DC supply draw from 63.66 W to 31.83 W in E5)!

Symmetric 2-Way Doherty Drain Efficiency Piecewise Formula

Validate 0 < P_avg <= P_peak and branch cleanly at the v_r = SQRT(P_avg / P_peak) = 0.50 (-6 dB) peaking-amplifier turn-on transition point!

=LET(p_av, B2, p_pk, B3, IF(OR(p_av <= 0, p_pk <= 0, p_av > p_pk), "Invalid RF Backoff Power", LET(v_rt, SQRT(p_av / p_pk), et_m, PI() / 4, IF(v_rt <= 0.5, ROUND(et_m * 2 * v_rt, 4), ROUND(et_m * ((v_rt ^ 2) / (1.5 * v_rt - 0.5)), 4)))))

Full-Saturation Convergence Check (Set P_avg = 100 W)

Set Average_Power B2 = 100 W (= P_peak, CW unmodulated carrier): both Class-B (E3) and Doherty (E4) converge to PI() / 4 = 0.7854 with Gain Ratio E5 = 1.0000!

=IF(ISTEXT(E4), E4, ROUND(E4 / E3, 4))

Further reading

• Arte Sheets Lesson — Quarter-Wave Impedance Transformer & VSWR Formula
• Arte Sheets Lesson — RF VSWR, Reflection Coefficient & Return Loss Formula