Simple Exact Algorithm for Transistor Sizing of Low-Power High-Speed Arithmetic Circuits

Algorithm 1

Proposed transistor sizing algorithm (SEA) for optimizing

Simple Exact Algorithm (SEA)

Group all the transistors in the circuit using Transistor

Grouping Rules;

Initialize $W_i$, width of the transistors in group $i$, so that:

$W_i=k_i\times W^{*};$

$k_i=1;\hspace{1em}\mathrm{\hspace{0.17em}\hspace{0.17em}}i=\mathrm{1,2},\dots ,n$

$W^{*}=$ 0.13 $\mu$m;

Initialize S, the step size and $m$, the number of step sizes;

for ($t=1$ to$\mathrm{\hspace{0.17em}\hspace{0.17em}}m$) $\{$

 // This loop sweeps $W^{*}\mathrm{\hspace{0.17em}\hspace{0.17em}}$ to obtain $W_{\text{opt}}$.

 $W^{*}=W^{*}+s;$

 Compute the target parameter, $\mathrm{\Theta }\mathrm{\hspace{0.17em}\hspace{0.17em}}$and save it to an array;$\}$

$W_{\text{opt}}\mathrm{\hspace{0.17em}\hspace{0.17em}}$is the point where $\mathrm{\Theta }\mathrm{\hspace{0.17em}\hspace{0.17em}}$has become minimum for that;

$W_i=k_i\times W_{\text{opt}};$

do $\{$

 for ($i\mathrm{\hspace{0.17em}\hspace{0.17em}}$= 1 to $n$) $\{$

 // This loop sweeps $k_i$.

 for ($t=1$ to $m$) $\{$

  $k_i=k_i+s;$

  Compute $\mathrm{\Theta }\mathrm{\hspace{0.17em}\hspace{0.17em}}$and Save it to another array;$\}$$\}$

$k_i$ is the point where $\mathrm{\Theta }\mathrm{\hspace{0.17em}\hspace{0.17em}}$has become mimimum for that;$\}$

while (all $k_i$’s converge to an specific value);