Discussions of analog fiber links usually focus on the laser or modulator, but the photodiode sets the output power, part of the noise floor and often the linearity limit. A few equations get you most of the way.

1. Responsivity
R = eta * q * lambda / (h c). The ideal value (eta = 1) is 1.25 A/W at 1550 nm and 1.06 A/W at 1310 nm. Practical PIN photodiodes for RF links are typically 0.7 to 0.9 A/W at 1550 nm. Photocurrent I_dc = R * P_opt, so 10 mW of received optical power gives about 8 mA.

2. RF output power
With intensity modulation index m, the RF photocurrent amplitude is m * I_dc. Into a load R_L the RF power is
P_RF = 0.5 * (m I_dc)^2 * R_L
Example: I_dc = 10 mA, m = 0.3, R_L = 50 ohm: P_RF = -6.5 dBm.
Many photodiode modules include a 50 ohm shunt resistor for a broadband match. Half the RF current then flows into the shunt, and the delivered power drops by 6 dB, to about -12.5 dBm in the example. That is the price of a flat broadband match. Reactive or narrowband matching can recover part of it.

Note the scaling: RF output is proportional to I_dc^2, so 1 dB of extra optical loss costs 2 dB of RF gain. This is why optical connector cleanliness shows up so strongly in RF link gain.

3. Noise at the output
For the same example, in the matched case (both signal and noise currents split by the shunt), in dBm/Hz:
- Thermal: kT = -174 dBm/Hz.
- Shot noise: 2 q I_dc R_L / 4, about -164 dBm/Hz at 10 mA.
- Laser RIN at -155 dB/Hz: RIN * I_dc^2 * R_L / 4, about -154 dBm/Hz.
So here RIN dominates, shot noise is 10 dB below it, and thermal noise is 20 dB below. The total is about -153.6 dBm/Hz, giving an SNR of about 81 dB in 1 MHz for the -12.5 dBm signal.
Two consequences: increasing optical power improves the SNR against shot and thermal noise, but not against RIN, since RIN noise and signal power both scale as I_dc^2. A lower-RIN laser or a balanced detector is the fix when RIN dominates.

4. Bandwidth
Two limits combine. RC limit: f_RC = 1/(2 pi R C); a 0.2 pF junction with 50 ohm gives 15.9 GHz, or 31.8 GHz with the 25 ohm seen when the 50 ohm shunt is in parallel with a 50 ohm load. Transit-time limit: roughly f_tr = 0.45 v_sat / d for a depletion width d. A smaller junction raises f_RC but reduces the area and therefore the power handling; a thinner absorber raises f_tr but increases capacitance. The overall 3 dB bandwidth is approximately 1/sqrt(1/f_RC^2 + 1/f_tr^2).

5. Saturation and linearity
At high photocurrent, the carriers in the depletion region screen the applied field (space-charge effect), the transit time stretches, and the response compresses and generates harmonics and intermodulation. Heating adds a further limit.
Practical guidance:
- Read the photodiode datasheet for RF 1 dB compression current and OIP3 at your frequency and bias, not just the maximum DC photocurrent. The RF limit is usually lower.
- Higher reverse bias helps linearity, up to the device and thermal limits.
- Standard PIN devices are typically comfortable at a few mA at microwave frequencies. Uni-traveling-carrier (UTC) and modified UTC designs carry tens of mA with much better linearity, which is why they are used in high-gain links.
- Measure two-tone intermodulation at the photodiode output with the laser at the operating point. If the IMD changes when you attenuate the optical input by a known amount, the photodiode is contributing.

6. Link design rule of thumb
For a high-dynamic-range link, run the photodiode at the highest photocurrent that keeps its own IMD below the modulator or laser IMD, choose a laser with RIN well below the shot-noise level at that current, and keep the optical path clean and low-reflection. The photodiode is often the last place people look and the cheapest place to win back several dB.