## 2 Architecture Description
### 4-to-1 TCA, Post-Amplifier, Balun, and Output Buffer  
Four copies of the regulated cascode (RGC) topology are selected as current buffers because of their low input impedance and wide bandwidth characteristics, as compared to other topologies such as the inverter, common-source, and common-gate topologies [17]. The RGC structure reduces the input impedance significantly by using the \(M_{2}\) and \(R_{2}\) stage as a local feedback to boost the transconductance of \(M_{1}\). The small-signal impedance of the RGC structure (\(Z_{in}\)) is given by (1):  
\[Z_{in}\cong\frac{1}{g_{m1}(1+g_{m2}R_{2})}, \tag{1}\]  
where \(g_{m1}\) and \(g_{m2}\) are the transconductances of \(M_{1}\) and \(M_{2}\), respectively. The signals from the current buffers combine through two stages, as shown in Figure 6. In the first stage, two inputs are summed through the output load resistor \(R_{1}\) of the RGC TIA. In the second stage, common-source amplifiers are used at the outputs of the two first-combining stages, and their currents are summed through a single resistive load \(R_{3}\). There is a common-source amplifier between the first and second combining stages that functions as a buffer and a bias shifter. To analyze the effect of the noise introduced by partitioned photosensitive cells and the TCA, the simplified circuit is illustrated in Figure 8 with noise factors [15]. The equivalent total input referred noise of the TCA is approximately given by (2):  
\[\overline{i_{n,in}}^{2}\cong\overline{\overline{v_{n,OUT}}^{2}}=4\Bigg{\{} \bigg{(}\overline{i_{n,PD}}^{2}+\overline{i_{n,CB}}^{2}\bigg{)}+\overline{ \overline{i_{n,R1}}^{2}}\Bigg{\}}.R_{1}+\frac{\left(2\overline{i_{n,C2}}^{2}+ \overline{i_{n,R3}}^{2}\right)\cdot R_{3}}{Z_{T,TCA}} \tag{2}\]  
Figure 7: Simulated input voltage and sink current to OCP (over-current protection) circuit according to the input current. where \(\overline{\overline{i_{n,PD}}^{2}}\) is the noise from a single photosensitive cell, \(\overline{\overline{i_{n,CB}}^{2}}\) is the generated noise in the current buffer stage, \(\overline{\overline{i_{n,C2}}^{2}}\) is the generated noise in the second combining stage, and \(\overline{\overline{i_{n,R1}}^{2}}\) and \(\overline{\overline{i_{n,R3}}^{2}}\) are the thermal noise from \(R_{1}\) and \(R_{3}\), respectively. In this analysis, we assume that:  
\[\overline{\overline{i_{n,PD}}^{2}}=\overline{\overline{i_{n,PD}}^{2}}= \overline{\overline{i_{n,PD}}^{2}}=\overline{\overline{i_{n,PD}}^{2}}=\overline {\overline{i_{n,PD}}^{2}}\] \[\overline{\overline{i_{n,CB}}^{2}}=\overline{\overline{i_{n,CB}}^ {2}}=\overline{\overline{i_{n,CB2}}^{2}}=\overline{\overline{i_{n,CB}}^{2}}= \overline{\overline{i_{n,CB4}}^{2}}\] \[\overline{\overline{i_{n,C1}}^{2}}=\overline{\overline{v_{n,C1,1} }^{2}}=\overline{\overline{v_{n,C1,2}}^{2}}=\overline{\overline{v_{n,C1,2}}^ {2}}\] \[\overline{\overline{i_{n,C2}}^{2}}=\overline{i_{n,C2,1}}^{2}= \overline{i_{n,C2,2}}^{2}.\]  
In (2), the receiver noise with a large-area photodetector, even though it is partitioned, is increased in the developed TCA. The noise generated in the first combining stage with the current buffer is also the dominant factor of the equivalent total noise. The post-amplifier is realized using a two-stage common-source amplifier. The first stage has an active inductor load, consisting of a transistor \(M_{4}\) and a resistor \(R_{4}\), to increase the overall bandwidth [18]. The second stage controls the pulse polarity and the DC bias. The balun converts the single-ended TCA output signal to differential signals. The balun and output buffer are illustrated in Figure 6. The balun is a differential amplifier with differential inputs biased at the same DC level. In this study, the same DC voltage as compared with the output voltage of the TCA is applied through additional DC bias port \(VB\). The output buffer is also a differential amplifier, and it is designed to match the output impedances to 50 \(\Omega\) on both the positive and negative outputs.