# Free Space Optic Receiver with Strongly Overlapped Photodetectors' Field of View
## 2 Free Space Optic (FSO) Receiver Design
### Selecting a Suitable Follow-Up Amplifier
Based on Table 2 and our calculations, we concluded the following: the OPA602 BP (Texas Instruments, Dallas, TX, USA, 2002) device does not fulfil the capacitance matching conditions (\(C_{a}=1\) pF, \(C_{p}=16\) pF, \(C_{a}\)\(<<C_{p}\)); input voltage noise \(e_{n}\) is the highest, with the small input capacitance \(C_{a}\) being eliminated by the enormous \(C_{p}\) capacitance. This was confirmed by the highest \(e_{n}{}^{2}\omega_{x}{}^{2}C_{in}{}^{2}\) element. Therefore, the OPA602 BP device is not suitable for the FSO receiver design. The OP27G (Analog Devices, Norwood, MA, USA, 2015) and the OPA627 BP (Texas Instruments, Dallas, TX, USA, 2015) devices have much lower \(e_{n}{}^{2}\omega_{x}{}^{2}C_{in}{}^{2}\) values. OP27G appears to be the best for the application. For a stable feedback loop, the resistance \(R_{fb}\) must be lower than the required minimum resistance \(R_{in}\), \(R_{fb}<R_{in}\), which destroys the good noise parameters of an operational amplifier. Neither OPA602 BP nor OP27G meet with the PDA's requirements. The opposite relation \(R_{fb}>R_{in}\) is only provided by the OPA627 BP \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multirow{2}{*}{**Type**} & \(C_{a}\) & \(C_{in}\) & \(\overline{e_{n}}\) & \(f_{x}\) & \(f_{x}\) & \(\overline{e_{n}}\omega_{x}^{2}C_{in}^{2}\) & \(R_{in}\) & \(I_{a}\) & \(f_{T}\) & \(f_{p}\) & \(R_{fb}\) & \(C_{fb}\) \\  & [pF] & [pF] & [nV-Hz\({}^{-}\)1] & [MHz] & \(\overline{e_{n}}\omega_{x}^{2}C_{in}^{2}\) & [k\(\Omega\)] & [μA] & [MHz] & [kHz] & [k\(\Omega\)] & [pF] \\ \hline OP27G & 8 & 27 & 3 & 1.5 & \(0.583\times 10^{-24}\) & 28.4 & 1.82 & 8 & 281.3 & 20.96 & 5.06 \\ OPA602 BP & 1 & 20 & 13 & 1.5 & \(6.005\times 10^{-24}\) & 2.76 & 18.7 & 6.5 & 346.2 & 22.99 & 4.62 \\ OPA627 BP & 8 & 27 & 5.2 & 1.5 & \(1.751\times 10^{-24}\) & 9.46 & 5.47 & 16 & 140.6 & 41.92 & 2.53 \\ \hline \end{tabular}
\end{table} 
Table 2: Suitable operational amplifiers and their passive network components values. device, in which the \({e_{n}}^{2}{\omega_{x}}^{2}{C_{in}}^{2}\) value is three times higher and a high resistance \(R_{\phi}\) keeps thermal noise low, leading to high stage transimpedance. Therefore, the OPA627 BP is the only device suitable for the low noise PDA requirements. The capacitance \(C_{fb}\) keeps the amplifier feedback stable, bending the noise gain \(NG\) at the zero frequency \(f_{z}\) (Figure 7). It is also responsible for the shape of the PDA closed loop amplitude frequency characteristic around the high cut-off frequency point \(f_{h}\). No overshoot should exist in the frequency characteristic for a well-compensated PDA. If this is the case, the frequency characteristic is closer to the first order declining asymptote from the left, and high frequency noises are kept to their minimum. All other cases are undesirable. Even a small overshoot brings the frequency characteristic closer toward the first order declining asymptote from the right, and the PDA output is loaded with excessively high frequency noise. The capacitance \(C_{fb}\) is therefore usually set with a variable capacitor according to the frequency or time domain measurements. Time domain measurements are much easier to perform. The required instruments are an oscilloscope and an optical fast leading and trailing edge pulse generator. The PDA output voltage waveform should be as close as possible to the optical pulse generator waveform and free of overshoots. Once the feedback capacitance \(C_{fb}\) has been set, neither photodiode reverse bias nor any other items can be changed. We compared the amplifier input current \(I_{a}\) and the dark current \(I_{0}\), as in the condition in Equation (19). With the maximal allowed amplifier current \(I_{a}\) = 5.47 \(\mu\)A, the condition in Equation (19) is fulfilled under incandescent lamp illumination. Under daylight, the currents are rather the same, which is still acceptable.