# Characterization of Light-To-Frequency Converter for Visible Light Communication Systems
## 4 Results and Discussion  
In this section, LTF characterization and the proposed VLC system performance analysis are evaluated, considering the input optical signal \(P_{in}(t)\), variation of the link distance, LTF output frequency \(f_{O}\), and SNR. We assume that the VLC channel is corrupted by AWGN. First, the LTF performance was evaluated in function of the input constant optical signal, and we proceeded with the distance variation between the transmitter LED and the LTF receiver. Figure 3 depicts LTF output frequency and optical input power versus link distance. It can be seen in Figure 3a that LTF output maximum frequency was 780 kHz (LTF saturation frequency) at the 5 mW optical input power, with 5 cm minimum link distance. On the other hand, we can see in Figure 3b that when the power input is 10 \(\mu\)W, the link distance that achieves the minimum output LTF frequency 1.6 kHz is 110 cm. This result is consistent with the inverse-square law, as the LED is a Lambertian source [16]. The estimated LTF responsivity value during the experiment was \(R_{e}=30.34\) MHz\(/\left(\mu\text{W}/\text{cm}^{2}\right)\). This result enables the LTF to detect optical power levels of the order of nW. However, in this paper, the minimum optical power reference was limited to 10 \(\mu\)W, which generates a respective frequency \(f_{o}=2\) kHz. This configuration was important for us to experiment with a minimum frequency in the modulating signal OOK. Additionally, based on the data presented in Figure 4, the LTF conversion factor \(R_{e}\) will positively affect the SNR of the system. Therefore, to generate an LTF output frequency \(f_{o}\) approximate to saturation, a measured SNR equal to 18.75 dB with link distance of 5 cm was found in the experiment, as illustrated in Figure 4a; for the case of less frequency \(f_{o}=1.6\) kHz, the SNR was around \(-35.15\) dB, with maximum link distance of 110 cm, as illustrated in Figure 4b. The parameters estimated for the LTF are significantly different from those of the data sheet [15], because the experiment was performed under specific physical conditions and a white light LED was used. Figure 3: Experimental setup. Estimated \(f_{O}\) and optical power under various link distance: (**a**) LTF output frequency versus link distance; (**b**) optical input power versus link distance. The relationship \(f_{o}=f_{D}\) is the dark condition (without optical power). Figure 5 summarizes the results for the dark frequency \(f_{D}\) versus link distance. We can see that when link distance ranges from 20 cm to 40 cm, the condition \(f_{D}<35\) Hz is reached, which indicates the presence of external optical sources, that is, oscilloscope, AWG, and power supplies. With this approach, it is important to mention that in the experimental setup, we do not consider focusing optical power on the LTF sensor. The result in Figure 6 clearly shows the LTF output frequency response to light intensity variations on photodiode. At the transmitter side, the electrical OOK signal is applied to modulate the white light LED with a modulating frequency \(f_{\mathrm{OOK}}=1\) kHz and 50% of duty cycle, as shown in Figure 6a. After free space optical transmission, the OOK signal is detected by an LTF receiver and generates an electrical signal. Then, the electrical OOK signal is converted to frequency by a current-to-frequency converter, as shown in Figure 6b. Figure 4: Model description: (**a**) signal-to-noise ratio (SNR) versus LTF output frequency; (**b**) SNR versus link distance. Figure 5: Dark frequency versus link distance. LTF converter generates a frequency around the \(f_{o}=13.88\) kHz when the LED transmit optical power when duty cycle is one, and, if duty cycle is zero, the LTF output frequency is \(f_{o}=f_{D}\), with \(f_{D}\ <35\) Hz. The \(f_{D}\ll\ f_{OOK}\); therefore, for LTF frequency estimation, it was necessary that we use the period measurement technique, for maximum data-acquisition rate (this data-acquisition rate depends on the resolution of the timer) [14; 15].