Optoelectronics, Fiber-Optic Receivers & Photon Counting
PIN Photodiode Responsivity & Shot-Noise SNR Formula
Convert Photodiode Quantum Efficiency eta and Wavelength lambda (um) into Responsivity R = (eta * lambda_um)/1.24 (A/W), Signal Photocurrent (uA), Combined Poisson Shot + TIA Thermal RMS Noise, and Electrical SNR (dB).
Combine Poisson photon shot noise and transimpedance thermal noise in quadrature!
In fiber-optic transceivers and LiDAR front ends, an InGaAs or Silicon PIN photodiode converts incident optical power P_opt into photocurrent I_p = R_resp * P_opt! Because each photon carries Planck energy h*c / lambda = 1.24 / lambda_um eV, external Quantum Efficiency eta (electrons generated per incident photon) maps directly to Responsivity R_resp (A/W) = (eta * lambda_um) / 1.24—explaining why Responsivity RISES with longer wavelength at fixed quantum efficiency! Simultaneously, discrete electron arrivals generate irreducible Poisson Shot-Noise Variance sigma_shot^2 (uA^2) = 0.00032 * I_p_uA * BW_GHz (from 2 * q * I_p * BW with q = 1.6*10^-19 C), which adds in quadrature with Transimpedance Amplifier (TIA) input-referred thermal noise I_th_uA: I_noise_rms = SQRT(0.00032 * I_p_uA * BW_GHz + I_th_uA^2), yielding Electrical SNR_dB = 10 * LOG10((I_p_uA / I_noise_rms)^2)!
Verify on a 10 GHz 1550 nm C-Band InGaAs PIN Receiver—Quantum_Efficiency eta = 0.80 (80%, B2), Wavelength lambda = 1.55 um (B3 -> Responsivity = (0.80 * 1.55) / 1.24 = 1.0000 A/W in E2), Incident_Optical_Power = 50 uW (-13.0 dBm, B4 -> Signal Photocurrent I_p = 50.00 uA in E3), Receiver_Bandwidth = 10.0 GHz (B5 -> Shot-Noise RMS = SQRT(0.00032 * 50 * 10) = 0.40 uA), and TIA_Thermal_Noise_RMS = 0.30 uA (B6): Combined RMS Noise is SQRT(0.40^2 + 0.30^2) = 0.5000 uA (E4), delivering Electrical SNR = 10 * LOG10((50 / 0.50)^2) = 40.00 dB (E5)!
| PIN Receiver Metric (eta=80%, 1.55 um, P_opt=50 uW, BW=10 GHz, I_th=0.30 uA) | Formula | Verified Output |
|---|---|---|
| Photodiode Responsivity (A/W) | (eta * lambda_um) / 1.24 | 1.0000 A/W |
| DC Signal Photocurrent (uA) | Responsivity_A_W * P_opt_uW | 50.00 uA |
| Total Shot + Thermal Noise (uA) | SQRT(0.00032 * I_p * BW_GHz + I_th^2) | 0.5000 uA (0.4000 uA Quantum Limit) |
| Electrical Receiver SNR (dB) | 10 * LOG10((I_p / I_noise_rms) ^ 2) | 40.00 dB (41.94 dB @ I_th=0) |
PIN Photodiode Shot-Plus-Thermal Electrical SNR (dB) Formula
Validate 0 < eta <= 1, lambda_um > 0, P_opt_uW > 0, BW_GHz > 0, and non-negative TIA thermal noise I_th_uA >= 0!
=LET(et_q, B2, lm_u, B3, p_uw, B4, bw_g, B5, th_n, B6, IF(OR(et_q <= 0, et_q > 1, lm_u <= 0, p_uw <= 0, bw_g <= 0, th_n < 0), "Invalid Photodiode Spec", LET(rs_p, (et_q * lm_u) / 1.24, i_ph, rs_p * p_uw, vr_n, 0.00032 * i_ph * bw_g + (th_n ^ 2), ROUND(10 * LOG10((i_ph ^ 2) / vr_n), 2))))Quantum Shot-Noise-Limited Ceiling Check (Set TIA Thermal Noise = 0 uA)
Zero out TIA_Thermal_Noise B6 = 0 uA: Total RMS Noise E4 hits the irreducible quantum shot-noise floor 0.4000 uA, capping Electrical SNR E5 at 41.94 dB!
=IF(ISTEXT(E5), E5, ROUND(SQRT(0.00032 * E3 * B5 + (B6 ^ 2)), 4))Try the example
Use the original values or change them to test your understanding.