I cannot solve these problems..need some help

[ur_sagar_54]

Problem 1

Given the layout below, find its corresponding circuit. Simplify the circuit if possible and give the sizes of all transistors. Assume L=2λ, where λ=1µm.

"how can we fine the size of a transistor"



Problem 2

Assume that the edge variation due to etching of the top plate of a capacitor is 0.05 μm and that capacitor top plates are to be laid out as squares. It is desired to match two equal capacitors to an accuracy of 0.1%. Assume that there is no variation in oxide thickness. How large would the capacitors have to be to achieve this matching accuracy?

Hint: Consider the worst mismatch between the two capacitors.


Problem 3

Show that a circular geometry minimizes the perimeter-to-area ratio for a given area requirement when compared to a square and a rectangle.

Hint: Consider the area for the circle, the square, and the rectangle to be the same.


Problem 4

The following figure shows various ways to implement the layout of a resistor divider. Choose the layout that best achieves the 2:1 ratio. Explain why the other choices are not optimal.



Problem 5

Calculate the values for CGB, CGS, and CGD for an n-channel device of length 1µm and width 5µm. Assume VD = 2V, VG = 2.4V, VS = 0.5V, VB = 0V, and Cox=24.7x10-4 F/m2.

Hint: First determine if device is in triode or saturation. Note that VSB ≠ 0, therefore you need to compute the correct VTH taking into account the body effect.

 

[lladnar23]

#3 is pretty easy: for a circle, A=pi*r^2 and P=2pi*r, so P/A=2pi*r/(pi*r^2)=2/r.
For a sqaure, A=s^2 and P=4s, so P/A=4/s.

 

[lsimeon]

hey lladnar23,

you have a point on your answer but i think it is incomplete..the task is to show that a circular geometry minimizes the perimeter-to-area ratio for a given area requirement when compared to a square and a rectangle, so, where is your conclusion? and how can you relate the two parameters that you gave (r and s).

 

[Paramjyothi]

For the Q#3, say if we consider Area =16um2 and perform the calculations for retrieving the values of Radius (r) for circle = 2.25um, Side (s) for square = 4um, & Length (l) = 8um, Breadth (b) = 2um for rectangle we get Perimeter/Area (P/A) as follows:

Circle: P/A=0.884
Square: P/A=1
Rectangle: P/A=1.25

Thus proved that Circular geometry has min perimeter/area ratio.

Added after 22 minutes:

Hello Sagar,

In your query you say layout below n figure below but you haven't attached any figures. So attach the figures for problem solving.