Prob. / Score
1 / /10
2 / /15
3 / /15
4 / /10
5 / /15
Total

EECS140

Fall 2005

Midterm 1

Name______

SID______

1)  Fill in the following table. Do NOT use a calculator!

dB / Power ratio
3 / 2
-3 / 1/2
6 / 4
-20 / 0.01
60 / 1,000,000 or 106
-63 / 10-6/2 = 5x10-7
57 / 106/2 = 5x105
-4 / 10-10+3+3=0.1*2*2=0.4
14 / 1020-3-3=100/2/2=25

2)You make measurements on a transistor and find that with the source grounded and the drain voltage at 5V, the drain current increases from 1mA to 4mA as the gate voltage increases from 3V to 4V. When the gate voltage is 4V, the drain current increases from 4mA to 4.1mA when the drain voltage increases from 5V to 6V. What is Vt and lambda for this device? What is gm and ro when the drain voltage is 5V and the gate voltage is 4V?

Vt / 1mA=unCoxW/L(3- Vt)2
4mA=unCoxW/L(4- Vt)2
l / Use ro: 10k = 1/(l 4mA) à l=1/40
gm @ Vds=5, Vgs=4 / Id=4mA, Vdsat=2 à gm=4mS
ro @ Vds=5, Vgs=4 / (6V-5V)/(4.1mA-4mA) = 10k

Also ok for l: I= x(1+l Vds) 4mA=x(1+ l 5V) 4.1mA=x(1+ l 6V) à l = 1/35
3) Fill in the following table for a single-pole amplifier

Gm [S] / Ro [W] / CL [F] / Av / wp [rad/s] / wu [rad/s]
5m / 10k / 1p / 50 / 100M / 5G
0.5m / 20k / 5p / 10 / 10M / 100M
100m / 50 / 5p / 5 / 4G / 20G

4) You have a single-pole amplifier with a low frequency gain of 100, and a gain of 10 at 10MHz. What is the gain at 100kHz, 5MHz, and 20MHz?

Frequency / Gain
100kHz / Wp=1MHz, so A(100kHz) = A0 = 100
5MHz / A(5MHz) = 2*A(10MHz) = 20
20MHz / A(20MHz) = (1/2)*A(10MHz) = 5

5)  What is the total impedance and the impedance seen seen “looking up” and “looking down” at the output node indicated in each circuit? Write your answer in terms of gmp , gmn, ron, and rop. Assume that all nmos devices have transconductance gmn and output resistance ron, and all pmos devices have transconductance gmp and output resistance rop. Write the full expression for up and down, and then the simplified total impedance assuming that gm*ro > 1 for all combinations of gm and ro.

Full expression / Simplified expression
for Ro, assuming gm ro >1
Ro1, up / rop / Ro1= rop || ron
Ro1, down / ron
Ro2,up / 1/(gmn +1/ ron) = (1/gmn)|| ron / Ro2= 1/gmn
Ro2,down / ron
Ro3,up / rop(1+ gmpRs+Rs/rop) Rs=1/(gmp +1/ rop) / Ro3= ron || 2rop
Ro3,down / ron
Ro4,up / (1/gmp)|| rop = 1/(gmp +1/ rop) / Ro4=(1/gmp) || (1+ ron / rop) /gmp
Ro4,down / (1/gmp)(1+ ron / rop)