# Review of CMOS Integrated Circuit Technologies for High-Speed Photo-Detection
## 5 Bandwidth Extension Techniques
### Inductive Peaking  
In this subsection, the basic principles of inductive peaking techniques are briefed and examples of CMOS photodetection circuits that adopt the peaking techniques are described. Inductive peaking technique has a long history and its integration into CMOS technology is well evaluated in the literature [101; 102; 103]. Nevertheless, an integrated inductor occupies a huge silicon area and thus increases the cost of the IC significantly. Therefore, the use of inductors in a photo-detecting IC should be considered carefully and the inductors should be optimized precisely. Fortunately, there are a lot of novel inductive peaking techniques, which have been developed to overcome the bandwidth limit of the legacy electrical link or ultra-wideband amplifier. Some of them have been adopted in high-speed photodetection circuits during the last two decades. Basically, there are two types of inductive peaking--shunt peaking and series peaking--and their examples with a simple CS stage are shown in Figure 29. Without inductive peaking, the transfer function of the CS stage is:  
\[H(s)=\frac{\mathrm{g_{m}R}}{1+\mathrm{sRC}} \tag{14}\]  
which is a simple one-pole system. On the other hand, for the shunt-inductive peaking, which is shown in Figure 29b, the inductor introduces a zero and an additional pole in the transfer function so that the transfer function becomes:  
\[H(s)=\frac{\mathrm{g_{m}(R+sL)}}{1+\mathrm{sRC}+\mathrm{s^{2}LC}} \tag{15}\]  
Figure 28: Integrating receiver based on double sampling. By placing the zero properly in accordance with the positions of the poles, the zero can compensate the dominant pole, and therefore, it improves the circuit bandwidth [102]. From a qualitative point of view, the inductor blocks the high-frequency current flowing through the resistor so that most of the bias current is solely used for charging/discharging the load capacitor, whereas the bias current is divided into the resistor and the load capacitor in the normal CS stage. Therefore, the rise/fall time reduces, which indicates that the circuit bandwidth is enhanced. The quantitative details of the bandwidth enhancement of the shunt peaking are presented in [102], and it is demonstrated that the maximum bandwidth enhancement ratio (BWER) of the shunt peaking is 1.84 with 1.5 dB peaking in magnitude response. The BWER is defined as the ratio of the 3-dB bandwidth with an inductive peaking to that without peaking. On the other hand, it is slightly more difficult to understand the principle of the series-inductive peaking in the s-domain model as compared to the shunt peaking because the inductor and the separation of the load capacitor introduce two additional poles but do not introduce any zero. Since there are three poles without a zero, the bandwidth extension is dominated by the damping factor of the transfer function, which is difficult to observe intuitively. On the other hand, a qualitative approach provides a much simple explanation. Since the high-frequency current is blocked by the series inductor, \(C1\) and \(C2\) are charged sequentially. Extremely, \(C2\) is charged after \(C1\) is fully charged. In other words, the rise/fall time of the signal is reduced as a function of the ratio of \(C1\) to \(C2\), at the expense of increased delay [103]. The BWER of the series peaking can be higher than 2.5 with a specific ratio of \(C1\) over \(C2\)[102]. In Figure 30, some advanced inductive peaking techniques are illustrated. Figure 30a shows a shunt-and-series peaking, which combines the shunt peaking and the series peaking in Figure 29. In 2004, a UCLA group proposed to employ this technique for a post-amplifier preceded by an optical TIA and achieved a BWER of 3.5 in [104]. For reference, they used different terminology in their paper; they named this technique the triple-resonance architecture. The inductive peaking technique shown in Figure 30b is widely referred to as the shunt and double series peaking.