A minimum-size inverter is fabricated in a 0.25μm technology to has (W

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A minimum-size inverter is fabricated in a 0.25μm technology to has (W/L)p = (W/L)n = 0.25/0.25, Vtn = −Vtp = 0.5 V, μnCox = 267 μA/V2, μpCox = 93 μA/V2. The supply voltage VDD = 2.5V. In a procedure to determine VIL: Are Qn and Qp matched? Given the Q's data above and by equating the currents flowing in Qn and Qp at VIL: a) Derive equation (1) in two variables Vin and Vout. b) Differentiate equation (1) with respect to Vin and put dVout/dVin = −1 to get equation (2) in Vin and Vout. Eliminate Vout between equations in (1) and in (2) to get a value for Vin = VIL. Determine the low noise margin NML. Derive the expression for the inverter threshold VM and determine its value using the same parameters above. Comment on the symmetry of the inverter VTC (Voltage Transfer Characteristics) around VDD/2.

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A minimum-size inverter is fabricated in a

0.25 μ m

technology to has

(W / L) p = (W / L) n = 0.25 / 0.25

V_{t n} = - V_{t p} = 0.5 V, μ_{n} C_{o x} = 267 μ A / V^{2}, μ_{p} C_{o x} = 93 μ A / V^{2}

. The supply voltage

V_{D D} = 2.5 V

. In a procedure to determine

V_{LI}

Are $Q_{n}$ and $Q_{p}$ matched?
Given the $Q$ 's data above and by equating the currents flowing in $Q_{n}$ and $Q_{p}$ at $V_{L}$ : a) Derive equation (1) in two variables $V_{in}$ and $V_{out}$ . b) Differentiate equation (1) with respect to $V_{in}$ and put $d V_{out} / d V_{in} = - 1$ to get equation (2) in $V_{in}$ and $V_{out.}$
Eliminate $V_{out}$ between equations in (1) and in (2) to get a value for $V_{in} = V_{I L}$ .
Determine the low noise margin $N M L$ .
Derive the expression for the inverter threshold $V_{M}$ and determine its value using the same parameters above.
Comment on the symmetry of the inverter VTC (Voltage Transfer Characteristics) around ${V D D}_{D D} / 2$ .