# Characterization of Light-To-Frequency Converter for Visible Light Communication Systems
## 3 Characterization of the LTF for a VLC System  
In this section, we present the characterization of the LTF converter and the analysis of the proposed VLC.  
In particular, an EMC 3030 HV white light LED, Tektronix TDS 3034C oscilloscope, THORLABS PM100D instrument and an LTF TCS3200 were used for the experimental setup, as shown in Figure 2. In the TCS3200, the light-to-frequency converter reads an array of 8 \(\times\) 8 photodiodes with 16 photodiodes with blue filters, 16 with red filters, 16 with green filters, and the remaining 16 photodiodes are clear with no filters. For this experimental setup, the TCS3200 device was configured for its maximum output frequency and only the blue channel was used for the VLC system as the blue component of a white LED lighting has the highest bandwidth [18; 19; 20]. Given the nature of the proposed experiment, it is necessary to bear in mind that the central wavelength of the blue filter in the LTF is \(\lambda_{c}=\) 470 nm and the total area of the photodiodes is \(A_{r}=\) 0.1936 cm\({}^{2}\)[14].  
Figure 2: Experimental setup for the characterization of the LTF converter.  
The schematic diagram of the experimental characterization for the LTF converter is shown in Figure 2. It consists of an optical transmitter based on a white light LED and a LTF converter acting as VLC receiver. For convenience, the LTF converter is represented as a two connected subsystems block: a photodiode and a CTF converter.  
In order to analyze the performance of the LTF converter, it is necessary to derive a mathematical expression for the signal-to-noise ratio at the VLC receiver output. In this way, using Equation (1) to represent the output current of the photodiode \(i_{t}(t)\) within the LTF block, the output signal of the CTF subsystem, \(f_{0}\), can be estimated using the following expression:  
\[f_{0}=R_{CTF}R(\lambda)E(\lambda)+R_{CTF}n(t) \tag{7}\]  
where \(R_{CTF}\) is the CTF responsivity. Now, it is important to remark that the expression for \(f_{0}\), given by Equation (7), does not alter the LTF model as an analogy could be made between the terms of Equations (6) and (7), that is, \(R_{CTF}R(\lambda)\) with \(R_{e}(\lambda)\) and \(R_{CTF}n(t)\) with \(f_{D}\). The aforementioned statement can be demonstrated by considering an analysis of the units for each variable. The term \(R_{CTF}\) denotes a conversion factor between the input current in amperes (A) and output frequency in Hertz (Hz) of the CTF subsystem; therefore, the units of \(R_{CTF}\) are Hz/A. Next, \(R(\lambda)\) is the conversion factor between the optical irradiance and the photocurrent output then its units are \(\frac{\mathrm{A}}{\mathrm{\mu W/cm^{2}}}\). Thus, the term \(R_{CTF}R(\lambda)\) will be given in the units of \(\mathrm{Hz}/\left(\mathrm{\mu W/cm^{2}}\right)\), which is equivalent to the units of \(R_{e}(\lambda)\) in Equation (6). Conducting a similar analysis for the term \(R_{CTF}n(t)\), it can be shown that it has the same units as that of the dark frequency \(f_{D}\). It is also important to note that the noise variance is scaled by the factor \(R_{CTF}\), such that \(\sigma_{f_{0}}^{2}=R_{CTF}^{2}\sigma^{2}\), of the stochastic process \(R_{CTF}n(t)=f_{D}\).  
Once we have obtained an expression for the dark frequency \(f_{D}\), the SNR value in Equation (5) can be estimated as a function of the incident irradiance and the frequency of the LTF, that is,  
\[SNR=\frac{\left(R_{CTF}R(\lambda)E(\lambda)\right)^{2}}{\sigma_{f_{0}}^{2}}= \frac{\left(f_{0}-f_{D}\right)^{2}}{\sigma_{f_{0}}^{2}} \tag{8}\]  
where  
\[E(\lambda)\ =\frac{Ar}{P_{in}(t)} \tag{9}\]