# Review of CMOS Integrated Circuit Technologies for High-Speed Photo-Detection
## 5 Bandwidth Extension Techniques
### Inductive Peaking
They also emphasized the  
Figure 31: TIA with shunt peaking presented in [80]. Figure 30: Circuit diagrams of (**a**) shunt and series peaking, (**b**) shunt and double-series peaking, (**c**) and T-coil peaking network. important of optimizing the phase response, and they attempted to suppress the group delay variation for better phase response. Therefore, the group delay variation was suppressed to less than 8 ps, thus achieving better eye opening compared to their previous work in [98]. T-coil peaking technique was introduced in TIA design by Ehwa Womans University in 2010 [97]. As shown in Figure 34, CG topology was chosen and two T-coil networks were employed to extend the bandwidth. The first T-coil network (T-coil1) separates \(C_{PD}\) from the junction capacitances of the transistors, and the second T-coil network (T-coil2) provides shunt-peaking with \(R_{L}\) and separates the junction capacitance and the output load capacitance. BWER of 2.3 and 3-dB bandwidth of 12.6 GHz were achieved, whereas the phase response was not fully optimized. In addition to the inductive peaking techniques shown in Figures 29 and 30, an inductive feedback technique wherein an inductor is placed in series with a feedback resistor of a TIA has been proposed in the literature [44; 100; 105]. A straightforward intuition of the bandwidth extension using inductive feedback is summarized in Figure 35, where \(R_{F}\) and \(L\) denote the feedback res  
\[H(s)=\frac{\mathrm{g_{m}R}}{1+\mathrm{sRC}} \tag{14}\]0 CG TIA with T-coil peaking presented in [82]. \[H(s)=\frac{\mathrm{g_{m}R}}{1+\mathrm{sRC}} \tag{14}\]1 TIA examples with series peaking between cascaded gain stages presented in (a) [61] and (b) [71]. respectively. Assuming a simple CS amplifier whose gain and 3-dB bandwidth are -\(g_{m}R_{out}\) and \(f_{p}\) respectively, a resistive feedback improves the bandwidth by a factor of \(R_{out}\)/\(R_{L}\), where \(R_{L}\) is the resistance of the parallel combination of \(R_{out}\) and \(R_{F}\), whereas the gain is reduced by the same factor, as shown in Figure 35a. On the other hand, insulting a series inductor to \(R_{F}\), as shown in Figure 35b, results in peaking as well as the bandwidth extension. At a low frequency, since the impedance of the inductor is almost zero so that it can be neglected, the transfer function with the inductor becomes the same as that without inductor. However, the impedance of the inductor increases as the frequency increases; hence, it becomes larger than that of \(R_{F}\) at a certain frequency, which can be considered as a zero frequency. This indicates that the feedback strength decreases, and consequently, the transfer function begins to follow that without the resistive feedback. In other words, when the inductance dominates the overall feedback impedance, the feedback network becomes negligible; i.e., the transfer function exhibits a peaking as shown in Figure 35b, which follows the low-gain curve at a low frequency and the high-gain curve at a high frequency. Luxtera Inc. adopted the inductive feedback technique in the CS-stage-based TIA in 2006 [44]. They also reported that the inductor reduces the input-referred noise caused by the feedback resistor. In [100; 105], the inductive feedback was employed in the inverter-based TIA by the authors' group, in order to compensate the frequency dependent loss owing to the PD bonding parasitic impedance by utilizing the peaking illustrated in \[H(s)=\frac{\mathrm{g_{m}R}}{1+\mathrm{sRC}} \tag{14}\]2 With inductive peaking, the 3-dB bandwidth of the TIA extends from 11.4 GHz to 25.2 GHz, which corresponds to a BWER of 2.2 dB. There is an interesting inductive peaking technique proposed by TSMC Inc. in 2014, which is called a shared inductor [85]. When an inductor is shared between adjacent amplifier stages, the number of inductors used in the photodetecting circuit halves; moreover, the size of each inductor can be further reduced.