Unit 2

MOS Inverter Static Characterstics

Noise Margin Definition

1) High Noise Margin = $NM_H = V_{OH} - V_{IH}$

2) Low Noise Margin = $NM_L = V_{IL} - V_{OL}$

$V_{OH}$ = Max O/P voltage when O/P level is logic '1'

$V_{OL}$ = Min O/P voltage when O/P level is logic '0'

$V_{IL}$ = Max I/P voltage which can be interpreted as logic 0

$V_{IH}$ = Min I/P voltage which can be interpreted as logic 1

$V_{out}$ = f($V_{in}$)

$V_{out}^{'}$ = f($V_{in} + \Lambda V_{noise}$)

$V_{out}^{'}$ = f($V_{in}) + \frac{d}{dv_{in}}V_{out} V_{noise}$ + Higher order terms neglected

Resistive type nMOS Inverter :

Assumption - 1) Channel length modulation effect is neglected

2) $V_{SB} = 0$ i.e No barriers => NMOS $V_T$ is always $V_{TO}$

$I_{DS} = \frac{kn}{2} (V_{in} - V_{TO})^2$

$I_{DS} = \frac{kn}{2} [2(V_{in} - V_{TO})(V_{out})-V_{out}^2]$

Calculation of critical parameter :

1) Calculation of $V_{OH}$

When $V_{in} = 0, T_N$ is off,

we know that

$V_{out} = V_{DD} - I_RR_L$

$V_{out} = V_{DD} = V_{OH}$

=> $V_{OH} = V_{DD}$

2) Calculation of $V_{OL}$

When $V_{in} = V_{DD}$

and $V_{out} = = V_{OL}$

$I_R = \frac{V_{DD} - V_{out}}{R_L}$

But $I_R = I_D$

$\frac{V_{DD} - V_{out}}{R_L} = \frac{Kn}{2}[(V_{gs} - V_{TO})V_{DS} - V_{DS}^2]$

$\frac{V_{DD} - V_{OL}}{R_L} = \frac{Kn}{2}[(V_{in} - V_{TO})V_{OL} - V_{OL}^2]$

Quadratic equation in 1/OL correct sol is

$V_{OL} = V_{DD} - V_{TO} + \frac{1}{K_nR_L} - ((V_{DD} - V_{TO} + \frac{1}{K_nR_L})^2 - \frac{2V_{OD}}{K_nR_L})^{1/2}$

1. Calculation of $V_{IL}$

When $V_{in} \gt V_T$ $I_N$ is in saturation

=> $V_{DS} \gt V_{gs} - V_{TO}$ or $V_{out} \gt V_{in} - V_{TO}$

$I_{DS} = \frac{Kn}{2}[V_{in} - V_{TO}]^2$

$I_R = \frac{V_{DD} - V_{out}}{R_L}$

=> $I_D = I_R$

$\frac{Kn}{2}[V_{in} - V_{TO}]^2 = \frac{V_{DD} - V_{out}}{R_L}$

At $V_{IC}$, $\frac{dV_{out}}{dV_{in} = 1}$

$V_{tc} = \frac{1}{K_nR_L} + V_{TO}$

1. Claculation of $V_{IH}$

While $V_{in}\gtV_{out - V_{TO}}$ $T_N$ is in linear

$V_{out} \lt V_{in} - V_{TO}$

$I_R = I_D$

$\frac{V_{DD} - V_{out}}{2} = \frac{Kn}{2}[2(V_{in} - V_{TO})V_{out} - V_{out}^2]$

D.W.R.T. $V_{in}$

=> $V_{IH} = 2V_{out} + V_{TO} - \frac{1}{K_nR_L}$ ----------------(2)

Substitute $V_{IH}$ in (1) to get,

$V_{out} (at V_{IH}) = (\frac{2V_{DD}}{3K_nR_L})^{1/2}$ -------------------(3)

(3) in (2)

$V_{IH} = V_{TO} + (\frac{2 V_{DD}}{3K_nR_L})^{1/2} - \frac{1}{K_nR_L}$