# Finding the CMOS transistor width ratio

## Homework Statement

Calculate the ration of $w_p/w_n$ if n and p transistors in CMOS inverter necessary for the least delay time $t_p$ if the circuit is used in a chain of circuits.
a) What is $w_p$ in that circuit if you're given : b) Calculate the maximum short circuit current if $V_{DD} = 3.3V$.

## Homework Equations

3. The Attempt at a Solution [/B]
The minimum delay time for a CMOS circuit in this scenario is given if $B$ which is $B=\frac{\frac{w_p}{L_p}}{\frac{w_n}{L_n}}$ equals $B=\sqrt{\frac{Rd_p}{Rd_n}}$ where $R_d$ is dynamic resistance of a transistor calculated from a formula $R_d=\frac{3}{4}\frac{V_{dd}}{I_{dsat}}*(1-5/6λV_{dd})$. So all i need to do is calculate both resistances devide them and get what $B$ equals so i can calculate $w_p$.
For a N-Mos transistor $I_{dsat}=1/2*\frac{μ_nC_{ox}w_n}{L_n}*(V_{dd} - V_t)^2$ (Just for easier calculation i'm ignoring the short canal and effects of $E_{cn}$. Putting all into equation and divind the parts which are the same i get:
$\frac{Rd_p}{Rd_n} = 270/70\frac{w_n}{w_p}$ and if i use that $w_p = B*w_n$ since the lengths are the same i get $\frac{Rd_p}{Rd_n} = 270/70\frac{1}{B}$ and finally taking a square root and extracting $B$ i get that $B=1.56$. This makes $w_p = 624nm$. I have no way of checking if this is correct as no solution is given. Could you check and possibly correct the mistakes i made?

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