# Analysis of Pre-Driver and Last-Stage Power--Ground-Induced Jitter at Different PVT Corners
## 4 PSIJ Sensitivity Study of Two-Stage Driver
### Frequency Sensitivity of PSIJ Transfer Function  
The last-stage PSIJ is determined by sweeping the frequency of the applied sinusoidal voltage waveform at \(V_{DDQ}\), while pre-driver stage supply \(V_{DD}\) is kept constant, as shown in Figure 8b. Similarly, the same experiment is performed for the pre-driver stage, as shown  
Figure 8: Frequency and amplitude-dependent PSIJ TF characterization (**a**) of pre-driver stage, (**b**) of last stage, (**c**) of driver’s IO stages. in Figure 8a. In the combined PSIJ impact, the distinct supply case of the driver's IO stages is considered for this experiment, as shown in Figure 8c. Figure 9 shows the PSIJ transfer function of the above three studied cases, as the supply noise frequencies of the separate and combined contributions of the pre-driver and last stage are swept. Table 6 summarizes the supply settings to obtain the PSIJ TF shown in Figure 9.  
The comparison, which is shown in Figure 9, between the theoretical jitter TF \(S_{IO}^{th}(f)\) of the IO buffer (e.g., black dashed line curves), which is defined in Equation (5), follows a similar waveform trend as the experimental results of the PSIJ \(S_{IO}(f)\) function. The difference between (\(S_{IO}^{th}(f)\) vs. \(S_{IO}(f)\)) at low frequency (e.g., \(f<100\) MHz) can have several explanations. Firstly, the conditions used in the simulation data to derive \(S_{IO}^{th}(f)\) is a clock signal against a random bit pattern used to derive \(S_{IO}(f)\). Moreover, the deviation between the theoretical and experimental results can be due to the accuracy of the space model level used in the simulations or the derivation of theoretical function  
The PSIJ TF of the pre-driver shows a peak value around \(200\) MHz. However, the \(S_{L}(f)\) shows a flat response until reaching \(200\) MHz. The pre-driver's jitter is the main contributor to the IO buffer's total jitter. \(S_{p}(f)\) has a bandwidth of [\(120\) MHz \(-\)\(200\) MHz], which defines the \(V_{DD}\) signal frequency range that generates the highest PSIJ. As the PSV's frequency increases and exceeds \(200\) MHz, the PSIJ number starts to decrease. At higher frequency (\(f>2\) GHz), the PSIJ of both IO driver stages decreases and is dominated by the input data pattern timing distortion. The eye diagrams shown in Figure 10 demonstrate the PSIJ sensitivity to the frequency of the last-stage supply variations, as the pre-driver-stage supply kept constant. Figure 11 shows the eye diagram sensitivity to the last-stage supply frequency, as the supply voltage variations of the pre-driver is \(123\) MHz. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**PSIJ TF**} & \multirow{2}{*}{**Supplies**} & \(V_{DD}\) & \multicolumn{2}{c}{\(V_{DDQ}\)} \\ \cline{3-5}  & & \(a_{k}\) (V) & \(f_{k}\) (MHz) & \(a_{k}\) (V) & \(f_{k}\) (MHz) \\ \hline \(S_{k}(\cdot)\) & 0 & 0 & 0.16 & \([10-11\times 10^{3}]\) \\ \hline \(S_{p}(\cdot)\) & 0.16 & \([10-11\times 10^{3}]\) & 0 & 0 \\ \hline \(S_{SO}(\cdot)\) & 0.16 & \([10-11\times 10^{3}]\) & 0.16 & \([10-11\times 10^{3}]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental settings of the frequency sensitivity of the PSIJ TF of the driver’s IO stages of the results shown in Figure 8.  
Figure 9: PSIJ experimental and theoretical TF variations due to the separate and the combined impacts of the supply voltage variations of the driver’s IO stages as \(a_{L}=a_{P}=160\) mV. It is worth noting that the driver's total PSIJ jitter \(S_{IO}\)\((f)\) depends on the phase difference between the supply voltage variations (e.g., \(\varphi_{VDQ}-\varphi_{VDQ}\)).