## 4 Simulation Results  
Table 10 shows the maximum attained bandwidth versus the magnitude of the signal gain at the 3 dB frequency point. It is clear that the smaller the feedback resistance is, the wider the maximum  
Figure 8: The pre-equalization circuit.  
bandwidth is achieved. The gain decreases down till 200 \(\Omega\), and then the performance of the system starts to deteriorate.  
To understand why the performance of the system starts to deteriorate, the time response of the second stage of our circuit is studied. It is observed that below 200 \(\Omega\), the operational amplifier starts acting as an attenuator and not as an amplifier. The time response of the second stage of our circuit alone yields the gains depicted in Table 11. So, even when the 180\({}^{\circ}\) phase reversal occurs in the frequency response of the entire circuit which occurs at 430 MHz, in the case when \(R_{f}\) = 150 \(\Omega\), the 3 dB bandwidth is noticeably less due to the gain magnitude.  
The \(T_{r}\) and \(T_{f}\) are 20 ns and 130 ns, respectively, and the total response time is about 150 ns, while the fall time, on the other hand, is longer because of the phosphor's slow response. Data rates of 20 Mb/s, 200 Mb/s, and 2 Gb/s, are convolved with the responses of the both the unequalized and equalized LEDs, as depicted in Figure 9a-c, respectively. At 20 Mb/s, the data can still be recovered without the need for equalization, as can be seen from Figure 9a. The data after equalization is almost identical to the transmitted data. The limitations of the LED modulation bandwidth become apparent at higher speeds. At 200 Mb/s, the need for equalization is apparent. However, the response after equalization shows that the data can still be recovered with a low BER. On the other hand, at 2 Gb/s, the data almost seems unrecognizable without equalization, and even with equalization, the BER would still be very high. The bit error calculations caused by the LED limited bandwidth shown in Figure 9 (taking 50 samples/bit duration) shows that at 20 Mbit/s both the unequalized and equalized LEDs have zero error. On the other hand, only the equalized LED has zero error at 200 Mbit/s, while at 2 Gbit/s, the error occurs in both cases but is significantly less with the equalized LED.  
The BER is calculated with different numbers of random bits up to 200,000 in order to verify the consistency of the obtained results and the efficiency of the proposed circuit. At 20 Mbit/s, the BER was negligible using both the un-equalized and equalized systems. At a higher data rate of 200 Mbit/s, the equalized system was able to eliminate the un-equalized LED BER of 0.36. On the other hand, at 2 Gbit/s, the proposed equalized system reduced the 0.49 BER to 0.27 (i.e., 44.2% improvement). However, at high speeds (i.e., 2 Gbit/s), the BER for both cases is still very high and cannot be  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(R_{f}\) (\(\Omega\)) & **Maximum Attained Bandwidth (MHz)** & **Gain at 3 dB Frequency (dB)** \\ \hline
500 & 345 & \(-\)42.3 \\
450 & 355 & \(-\)43.1 \\
400 & 366 & \(-\)44.3 \\
350 & 377 & \(-\)45.4 \\
300 & 390 & \(-\)46.7 \\
250 & 403 & \(-\)48.2 \\
200 & 416 & \(-\)50.1 \\
150 & 345 & \(-\)52.5 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Effect of varying the feedback resistance \(R_{f}\)  
\begin{table}
\begin{tabular}{c c} \hline \hline \(R_{f}\) (\(\Omega\)) & **Gain (dB)** \\ \hline
500 & 8.20 \\
450 & 7.31 \\
400 & 6.28 \\
350 & 5.15 \\
300 & 3.86 \\
250 & 2.28 \\
200 & 0.34 \\
150 & \(-\)2.05 \\ \hline \hline \end{tabular}
\end{table}
Table 11: The gain of the second stage of the proposed circuit at different \(R_{f}\) values.  
employed in a practical communication system. Future work will include addressing solutions for high data rate transmission.