GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 39 of 65

Marks: +1, -0

A CMOS Schmitt-trigger inverter has a low output level of

0 {V}

and a high output level of

5 {V}

. It has input thresholds of

1.6 {V}

and

2.4 {V}

. The input capacitance and output resistance of the Schmitt-trigger are negligible. The frequency of the oscillator shown is ___________ Hz. (Round off to 2 decimal places.)

Your Answer:

Validate

Solution:

During

{T}_{\;\text "on "\;}

V_{c}=V(∞)-[V(∞)-V(0)] e^{\;{-t}/{τ}}

V_{C}=5-[5-1.6] e^{\;{-t}/{R C}}

V_{c}=5-3.4 e^{\;{-t}/{R C}}

{t}= {T}_{ {On}}, {V}_{ {C}}=2.4 {V}

∴ 2.4=5-3.4 {e}^{\;{-T_{o n}}/{R C}}

{T}_{ {on}}=126 × 10^{-6} {sec}

=126 µ {sec}

During

T_{\;\text "off "\;}

{V}_{ {C}}=0-[0-2.4] {e}^{\;{- {t}}/{τ}}

V_{c}=2.4 e^{\;{-t}/{R C}}

{t}= {T}_{ {off}}, {V}_{ {c}}=1.6 {V}

1.6=2.4 e^{\;{-T_{\;\text "off "\;}}/{R C}}

T_{o f f}=190.56 µ {sec}

{T}= {T} 1+ {T} 2=126+190.56

=316.56 µ {sec}

f=\;{1}/{T}=3158 {Hz}

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