Need help for given circuit how to calculate aspect ratio

Given C1 = 200fF , C2=1pF, R=100k, Rin = 50, Power > 200uW, Gain > 15bd
Calculte (W/L)1 and (W/L)2

As you didn't state your process, operating voltage, Vb and operating frequency, I used my own parameters:
90nm process, VDD=1.8V , Vb=0.9V . With C2/C1 = 5 you can't achieve a Gain > 15dB , so I had to reduce C1 to 120fF .

So a gain of about 15 dB can be achieved between 40 .. 100MHz at a power consumption < 200µW, s. the following PDF:

Thanks for reply and for the answer

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Vtn = 0.3 V, Vtp = 0.38 V, Kn = 730μA/V2, Kp = 91μA/V2,
Power < 200uW, Mid-band Gain > 15dB, R =100K,
CLoad= 100fF, C2=1pF , C1=200fF. The voltage source (Vin) has an intrinsic impedance of 50 Ω.
1. Calculate the aspect ratio of both M1 and M2., such that DC output voltage is midrail
± 10 % .
how to find Vb in such conditions?

I think it will be an iterative process, as you don't know Vb in the beginning.

Start by equalizing the currents through both transistors, and use the strong inversion equation (which will not be valid for M2, as it will show up). Use Vb=0.9V as a first approximation, so you can calculate the aspect ratio:

(Wp/Lp) / (Wn/Ln) = kn/kp * (VGSn - Vtn)² / (VGSp - Vtp)² = 10.68 ≈ 10

Then calculate the current IDn through M1 and use this result to calculate Vb = VDD - VGSp :

IDn = 1/2 * kn/n * (Wn/Ln) * (VGSn - Vtn)² = 94µA ≈ 100µA

For the substrate factor I used n=1.4 . Then: IDp = IDn

(VGSp - Vtp)² = 2n/kp * (Lp/Wp) * IDp
(VGSp - Vtp) = 0.5374V
VGSp = 0.5374 + Vtp ≈ 0.16V --> sub-threshold = weak inversion operation

Vb = VDD - VGSp = 1.64V

An analysis for M1 with minW/minL shows a necessary Vb=1.63V , I=150µA and a gain=15dB @ 40MHz.
C1 had to be reduced to less than 100fF.

Thanks very helpful
one more thing, how to calculate the total noise current at the output , if its dependence
on bias and aspect ratio of both transistors.

damonsalv said:

one more thing, how to calculate the total noise current at the output , if its dependence on bias and aspect ratio of both transistors.

Click to expand...

No experience here. I'd (also) have to study the textbooks, and that's just not my preference now ;-), sorry!

oh k thanks for helping so far