Below is an example of an NMOS with the given parameters:

μn = 300 sq. cm / v.sec

tox = 200 x 10

Ɛo . Ɛr = 3.9 x 8.85 x 10

W = 10μm, L = 1μm

VGS = 1V, VT = 0.5V

λ ~ 0 (device is long channel, so VA and ro are high)

C0v ~ 0

VDD = 1.8

RL = 10K

ID = Bias current or DC current = 1/2μn Cox . (VGS - VT)2 (1 + λ

Since lambda value is 0.

Calculating: Cox = Ɛo . Ɛr / tox

=> tox = 200 x 10

Hence, Cox = Ɛo . Ɛr / tox = 3.9 x 8.85 x 10

Now, μn = 300 cm

=>

= 63.75 μA

=

Now, let us calculate

Our transistor is working in the

To find VDS: VDS = VDD - (voltage drop over this transistor which is RL x ID)

Since, VDD = 1.8V

Now we are sure that the transistor is working in the saturation region.

Let's calculate the gain (G or Av) now.

CGS = 2/3 WL Cox + WCov (Here, WCOV is zero)

At last, we will calculate fT

μn = 300 sq. cm / v.sec

tox = 200 x 10

^{-10}mƐo . Ɛr = 3.9 x 8.85 x 10

^{-14}F/cmW = 10μm, L = 1μm

VGS = 1V, VT = 0.5V

λ ~ 0 (device is long channel, so VA and ro are high)

C0v ~ 0

VDD = 1.8

RL = 10K

Let us calculate:

ID = Bias current or DC current = 1/2μn Cox . (VGS - VT)2 (1 + λ

**VDS) = 1/2μn Cox . (VGS - VT)2**Since lambda value is 0.

Calculating: Cox = Ɛo . Ɛr / tox

=> tox = 200 x 10

^{-10}m = 200 x 10^{-8}cmHence, Cox = Ɛo . Ɛr / tox = 3.9 x 8.85 x 10

^{-14}/ 200 x 10^{-8}**=> Cox = 0.172 x 10**^{-6}F/cm^{2}Now, μn = 300 cm

^{2}/ V.sec=>

**ID**= 1/2 . 300 . 0.17 x 10^{-6}. (10/1) . (1 - 0.52)= 63.75 μA

=

**63.75 x 10**^{-6}ANow, let us calculate

**gm**= 2ID / (VGS - VT) = 2 x 63.75μ / (1/2) =**255****μs**Our transistor is working in the

*saturation*region. To show that, VDS > VGS - VTTo find VDS: VDS = VDD - (voltage drop over this transistor which is RL x ID)

Since, VDD = 1.8V

**VDS****= 1.2 v**which is higher than VGS - VT i.e. > (1 - 0.5)Now we are sure that the transistor is working in the saturation region.

Let's calculate the gain (G or Av) now.

**G**= gm (ro || RL) = gm. RL = 255μ x 10k ~**2.5 appx.**CGS = 2/3 WL Cox + WCov (Here, WCOV is zero)

**CGS = 10 x 10**^{-15}F = 10fFAt last, we will calculate fT

**f****T**= gm / 2πCGS =**4GHz**for this transistor.

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