# A New, Fast Pseudo-Random Pattern Generator for Advanced Logic Built-In Self-Test Structures
## 5 Pseudo-Random Pattern Generator DT-LFSR-TPG for LBIST Circuits with the STUMPS Architecture
The frequency was calculated with consideration of delay time contributed by the tree of XOR gates in the phase shifter as well as the propagation time of the 2-to-1 multiplexer and setup time of the D-type flip-flop that are incorporated into the first cell of each scan path. In addition, the asterisk \"\" was used to indicate the maximum operational frequencies of  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No. **} & \multirow{2}{*}{\(\mathbf{t}\)} & \multirow{2}{*}{\(\mathbf{n}\)} & \multicolumn{6}{c}{**Number of Scan Paths**} \\ \cline{3-8}  & & & & **128** & **256** & **512** & **1024** & **2048** & **4096** \\ \hline
1 & 22 & 25 & 6, 18, 4 & 12, 36, 8 & 24, 72, 16 & 47, 141, 10 & 94, 282, 20 &  
LFSR + PS units, when the frequency is not limited by the operation of the phase shifter but by the time of signal propagation down the feedback loop of an LFSR register. Both the parameters discussed above were mutually compared for test pattern generators of the DT-LFSR-TPG type and the LFSR + PS type and comparison results are summarized in Table 10 with the same layout as Table 9 but slightly different content. The topmost number in each cell of the table says how much (in percentage) the hardware overhead contributed by the DT-LFSR-TPG unit exceeds the corresponding overhead attributable to the TPG unit of the LFSR + PS type. In turn, the bottommost number in the table cell informs how much (in percentage) the maximum operating frequency for the DT-LFSR Test Pattern Generator (DT-LFSR-TPG) exceeds the frequency offered by a corresponding LFSR + PS solution. The comparison was carried out for those DT-LFSR-TPG units that offer the cheapest cost for the specific number of scan paths fed from the TPG unit (pursuant to information from Table 7). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number of**} & \multicolumn{8}{c}{**Type I LFSRs**} & \multicolumn{8}{c}{**Type II LFSRs**} \\ \cline{2-13}  & \(h_{1}\)**(x)** & \(h_{2}\)**(x)** & \(h_{3}\)**(x)** & \(h_{4}\)**(x)** & \(h_{5}\)**(x)** & \(h_{6}\)**(x)** & \(h_{1}\)**(x)** & \(h_{2}\)**(x)** & \(h_{3}\)**(x)** & \(h_{4}\)**(x)** & \(h_{5}\)**(x)** & \(h_{6}\)**(x)** \\ \hline \multirow{3}{*}{128} & 120\% & 91\% & 68\% & 51\% & 39\% & 17\% & 119\% & 92\% & 72\% & 54\% & 41\% & 17\% \\  & 73\% & 62\% & 62\% & 62\% & 62\% & 62\% & 75\% & 49\% & 40\% & 20\% & 50\% & 25\% \\ \hline \multirow{3}{*}{256} & 154\% & 141\% & 115\% & 110\% & 90\% & 76\% & 157\% & 141\% & 120\% & 107\% & 92\% & 76\% \\  & 76\% & 93\% & 62\% & 71\% & 69\% & 93\% & 70\% & 86\% & 51\% & 55\% & 55\% & 43\% \\ \hline \multirow{3}{*}{512} & 203\% & 171\% & 159\% & 152\% & 139\% & 117\% & 202\% & 172\% & 162\% & 152\% & 140\% & 119\% \\  & 129\% & 91\% & 95\% & 110\% & 99\% & 76\% & 122\% & 80\% & 83\% & 104\% & 93\% & 70\% \\ \hline \multirow{3}{*}{1024} & 208\% & 207\% & 196\% & 184\% & 178\% & 164\% & 223\% & 207\% & 196\% & 185\% & 178\% & 165\% \\  & 134\% & 134\% & 134\% & 95\% & 110\% & 102\% & 128\% & 130\% & 129\% & 90\% & 105\% & 98\% \\ \hline \multirow{3}{*}{2048} & 204\% & 210\% & 208\% & 206\% & 199\% & 194\% & 208\% & 211\% & 209\% & 206\% & 199\% & 195\% \\  & 180\% & 137\% & 139\% & 144\% & 126\% & 170\% & 167\% & 131\% & 129\% & 142\% & 121\% & 154\% \\ \hline \multirow{3}{*}{4096} & 216\% & 206\% & 219\% & 217\% & 214\% & 210\% & 219\% & 207\% & 220\% & 218\% & 215\% & 211\% \\  & 191\% & 183\% & 165\% & 139\% & 140\% & 138\% & 190\% & 170\% & 150\% & 126\% & 136\% & 128\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of implementation costs and maximum operating frequencies between test pattern generators of the LFSR + PS and DT-LFSR-TPG types.