## 4 Evaluation of the Logarithmic Transimpedance Circuit  
Analitical Evaluation of the Logarithmic Transimpedance Circuit and Its Comparison to Linear Circuit  
Before proceeding to the experimental evaluation, the next section performs an analytical evaluation of the logarithmic transimpedance circuit in order to demonstrate the concept benefits. To provide a convincing analysis, the behavior of the logarithmic solution is compared to the behavior of the classical linear solution. Thus, this section simulates the logarithmic transimpedance circuit response in varying lighting conditions, ranging from 0 lux to approx. 15.000 lux. The simulation parameters are resumed in Table 2. The 15.000 lux limit has been considered based on the impact that an IR-reject optical filter and an adaptive receiver FOV can have on decreasing the illuminance of the direct sun exposure (which may reach up to 100.000 lux) at the VLC sensor level [36; 37]. In order to be even more convincing, the response of the logarithmic transimpedance circuit is compared to the response of a linear transimpedance circuit. Furthermore to provide an adequate and a fair comparison, two linear transimpedance circuits have been simulated: a linear transimpedance circuit designed in order to be highly resilient to noise (i.e., \(\approx\) 15.000 lux) and a linear transimpedance circuit designed for high sensitivity. In the first case, the simulation results (Figure 2) showed that although the resilience to noise is quite high, the sensitivity of the circuit is significantly affected, meaning that such a sensor will not be able to detect low light intensity variations, which in turn significantly affect communication distance. Now if it is to compare the sensitivity of the circuit with a VLC emitter irradiance distribution with respect to the distance, one can see that the communication distance becomes limited to just few meters. In the second case, where sensitivity was the priority, the simulation results have showed that although the higher sensitivity enables the detection of low power signals and thus, longer communication ranges, the circuit is easily saturated and consequently it is incompatible to VLC applications that imply direct sun exposure (Figure 3.). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value/Feature** \\ \hline Photodiode Type & BPX 61 \\ Photodiode Capacity & 72 pF \\ Photodiode Photocurrent & 70 nA/lux \\ Photodiode Surface & 7.02 mm\({}^{2}\) \\ Light Illuminance & 0–15.000 lux \\ Photodiode Switching Time & 20 ns \\ Operational Amplifier Supply Voltage & 5 V \\ Bias Voltage Non-inverting Input & 4.9 V \\ \multicolumn{2}{c}{Logarithmic} \\ Transimpedance solutions: & High sensitive linear circuit (R\({}_{\text{load}}\) = 100 k\(\Omega\)) \\ \multicolumn{2}{c}{Noise resilient linear circuit (R\({}_{\text{load}}\) = 4.5 k\(\Omega\))} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of the simulation parameters. Figure 3: Evaluation of the logarithmic transimpedance circuit and its comparison to the noise resilient linear circuit and to high sensibility linear circuit in low lighting conditions. The simulation results show that in low lighting conditions, the noise resilient linear circuit does not respond to light intensity variations due to its low sensitivity, whereas the logarithmic transimpedance circuit automatically increases its amplification. Figure 2: Evaluation of the logarithmic transimpedance circuit and its comparison to the noise resilient linear circuit and to high sensibility linear circuit. The simulation results show that a high sensitive linear transimpedance circuit is rapidly saturating whereas the logarithmic and the noise resilient linear prevent the photodiode saturation. On the other hand, in strong lighting conditions (up to 15.000 lux) the logarithmic transimpedance circuit is far from being saturated, preventing the communication blockage (Figure 2).