The pull up to pull down ratio for an n mos inverter driven by another n mos inverter can be evaluated from:

(A) Vinv = Vt − \(\rm\frac{V_{t d}}{\sqrt{Zpu/Zpd}}\)

(B) Vinv = \(\rm\frac{−V_{t d}}{\sqrt{Zpu/Zpd}}\)

(C) \(\rm\frac{W_{pd}}{L_{pd}}\)(Vinv − Vt)2 = \(\rm\frac{W_{p u}}{L_{p u}}\)(−Vtd)2

(D) \(\rm\frac{W_{p d}}{L_{p d}}\)(Vinv − Vt) = \(\rm\frac{W_{p u}}{L_{pu}}\)(−Vtd)2

Choose the correct answer from the options given below:

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  1. (A), (B) only
  2. (B), (C) only
  3. (C), (D) only
  4. (A), (C) only

Answer (Detailed Solution Below)

Option 4 : (A), (C) only
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Detailed Solution

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Concept:

An n mos inverter driven by another n mos inverter circuit is given as:

F1 Madhuri Engineering 23.02.2023 D5

An nmos inverter has a pull up transistor (Q2) that is n-type MOSFET in depletion mode and has a pull down transistor(Q1) that is n-type MOSFET  in enhancement mode.

F1 Madhuri Engineering 23.02.2023 D6

both MOSFET will be in saturation when Vin = 0.5 Vdd.

Saturation current equation is given as:

I\(\frac{k\ W{(V_{GS}-V_t)}^2}{2L}\)

In depletion mode,n type provides depletion current Vgs ≤ 0. for max depletion current Vgs=0 is taken.

In depletion mode ,now current equation is written as :

ID = \(\frac{k\ {(-V_t)}^2}{2}\) × \(\frac{W_{pu}}{L_{pu}}\)

in enhancement mode, current equation is wriiten as:

 Vgs= Vinv

ID =\(\frac{k\ {(V_{inv}-V_t)}^2}{2}\) × \(\frac{W_{pd}}{L_{pd}}\)

current will be same in depletion mode and enhancement mode so written as:

  \(\frac{k\ {(-V_t)}^2}{2}\)× \(\frac{W_{pu}}{L_{pu}}\) = \(\frac{k\ {(V_{inv}-V_t)}^2}{2}\) × \(\frac{W_{pd}}{L_{pd}}\)

\(\frac{{(-V_t)}^2}{2}\) × \(\frac{W_{pu}}{L_{pu}}\) =  \(\frac{ {(V_{inv}-V_t)}^2}{2}\) × \(\frac{W_{pd}}{L_{pd}}\)

we know \(Z\propto\)  \(\frac {L}{W}\) ( since \(I_D\propto\) \(\frac {W}{L}\) )

so rewritten as:​

\(\frac{{(-V_t)}^2}{2}\) × ​\(\frac{L_{pd}}{W_{pd}}\) = \(\frac{{(V_{inv}-V_t)}^2}{2}\) × \(\frac{L_{pu}}{W_{pu}}\)

\((-V_t)^2\) × Zpd  =  \((V_{inv}-V_t)^2\) × Zpu   

this equation can be written as:

Vinv = Vt −  \(\rm\frac{V_{t d}}{\sqrt{Zpu/Zpd}}\) ​

so A and C are correct.

correct option is 4.​​​

 
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