Study Problems for Midterm 1 Solution

Prof. Parker EE 477 Spring 2006

Assume for the problems below that Vdd = 2.5 v, V_tp0 is -.6 v. and V_tn0 is .6 V.

Assume ß_n (k_n)= 219.4 W/L µ A(microamps)/V₂ and ß_p (k_p)= 51 W/L µ A/V₂

Assume Tox = 57 angstroms for thinox, and 5000 angstroms for thick oxide.

1. Compute the charge density in the depletion region of the channel of an NMOS transistor when N_A = 10¹⁶/cm³ . The value for q is given in the front cover of the text. Assume x_d = 50 angstroms.

Use Equation 3.12 in the text. N_A , x_d , and q are known.

2. Compute the worst-case gate capacitance of a unit size NMOS transistor using the dielectric constants in the front cover of the text.

Use the Equation 3.96 in Section 3.6 of the text to compute C_gd. W = 4 lambda, L = 2 lambda, lambda = .125 microns. Tox = 57 angstroms. dielectric constant for silicon dioxide is 35.1345 X 10^-14 farads/cm. an angstrom is 10^-8 cm. Therefore C_gd = .767 x 10^-15 farads or .767 femtofarads.

3. An inverter with both NMOS and PMOS transistors in saturation has Vin = 1.6 v. Compute the ratio of the transistor ß's.

The magnitude of ß_p over ß_n is about 11, using the equations on pages 206 or 208 of the text, or the equation in lecture. Remember that the text uses k instead of beta.

4. For the inverter in problem 3, what is the range of values of Vout at that point?

vout > 1 v. and vout < 2.2 v. using the approach shown in class

5. For the circuit shown in the homework 3 solution to problem 1 , which transistor(s) would be subject to the body effect?

All nmos transistors with source not grounded and all pmos transistors with source not tied to Vdd.

6. A transmission gate is in the following state: V_in = 2.5 v. V_out = 1.9 v. At time t=0, Vg rises from 0 v. to 1.5 v. instantaneously. What region of operation is the NMOS transistor in at t=0⁺ ? As t approaches infinity?

Cutoff and cutoff.

.

7. Two PMOS transistors are connected in series through shared diffusions. The gate voltage applied to both transistors is 0 v. The voltage at the input diffusion is 0 volts. Solve for the voltage at the output diffusion.

I am assuming Vtpbe = -.9 v. Without that assumption, the answer would have been Vout = .6 v.

The transistor closest to the input has source = .9 v., and Vds = .9 v. The transistor closest to the output has source = Vout = .9 v. Vds for the second transistor = 0 v.

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