# Free Space Optic Receiver with Strongly Overlapped Photodetectors' Field of View
## 2 Free Space Optic (FSO) Receiver Design
### Selecting a Suitable Photodetector  
Many types of photodetectors exist. In terms of dynamic parameters, photodiodes or avalanche photodiodes are best suited for the proposed receiver. The latter include internal amplification. Generally, ordinary photodiodes and avalanche photodiodes use a simple PN junction and are quick enough only for visible light wavelengths. For the near infrared spectrum and high cut-off frequencies, PIN photodiodes and NPIP avalanche photodiodes have been developed. Another consideration involves the internal amplification and conditions for using avalanche photodiodes. Internal amplification cannot improve the signal to noise ratio \(SNR_{in}\) in the optical part, as in Equation (1). The input useful signal and input noise are both amplified in the same manner. Internal amplification is afflicted with its own noise, which increases with the magnitude of amplification. Internal amplification is therefore kept low and set only to a necessary magnitude that ensures that the photodetector noise current \(i_{nPD}\) is triple the follow-up amplifier noise current \(i_{nA}\). Mathematically written:  
\[i_{nPD}\leq 3i_{nA}\quad[\mathrm{A}]. \tag{19}\]  
Equation (19) requires commentary. First, the photodetector noise current \(i_{nPD}\) depends not only on the photodetector amplification magnitude but also on the photodetector background light level. Second, the internal amplification photodetector is unnecessary if the ordinary photodetector noise current \(i_{nPD}\) exceeds the noise current \(i_{nA}\) of the follow-up amplifier. It is obvious that the photodetector environmental conditions, particularly background light level, are important. The discussed FSO receiver's high background light levels means that Equation (19) is fulfilled even with ordinary PIN photodiodes. The decision above is not yet complete. It is also necessary to choose between PIN photodiodes with small active area and high cut-off frequency or PIN photodiodes with large active area and low cut-off frequency. Because the sensitivity of any photodetector is proportional to its active area and because a high communication radius depends not only on power LEDs but also on high sensitivity photodetectors, the latter PIN photodiodes are the best option. The typical representatives are BPW34 (Vishay, Malvern, PA, USA, 2011) or BP104F (Vishay, Malvern, PA, USA, 2011) devices. They were not selected randomly. BPW34 or BP104F are inexpensive and readily available. Compared with each other, neither have any large differences in peak sensitivity wavelength, rise and fall times, etc. An exception is the spectral bandwidth range. According to their datasheets, BPW34 is a wide spectral bandwidth photodiode covering wavelengths from 430 to 1100 nm, whereas BP104F is a narrow spectral bandwidth photodiode covering wavelengths from 800 to 1100 nm. The spectral bandwidth range plays an important role during photodiode noise current \(i_{nPD}\) optimization. It is expressed as follows:  
\[i_{nPD}=\sqrt{\overline{j^{2}(f)}B}\quad[\mathrm{A}], \tag{20}\]  
where \(B=f_{h}-f_{l}\) is the useful signal bandwidth, and the photodiode noise power current spectral density is given by the well-known Schottky equation:\[\overline{J^{2}(f)}=2 qI_{0}\quad\left[\text{A}^{2}\text{Hz}^{-1}\right], \tag{21}\]  
where \(q\) is the electron charge and \(I_{0}\) is the dark current of the photodiode. From Equation (21), only quantity \(I_{0}\) remains which may be tuned by the user. The dark current \(I_{0}\) has three components: \(I_{dg}\) (darkness generation current induced by phonons), \(I_{db}\) (darkness background current induced by far infrared /FIR/ photons), and finally \(I_{pb}\) (photocurrent background induced by near infrared /NIR/ and visible light photons). Written mathematically [1]:  
\[I_{0}=I_{dg}+I_{db}+I_{pb}\quad\left[\text{A}\right]. \tag{22}\]  
The magnitudes of currents vary according to the application, and usually only one of these currents becomes dominant.