ECEI02 (Fall 2012), Homework 2 Solution

Problem 1. The amplifier below has a gain of 15 at ID = 0.25 rnA. Find (W/Lh and (W/Lh if An = 0.05/V, Ap = 0.15/V, J-LpCox = 40 J-LA/V2, and J-LnCox = 100 /-lA/V2 (Ignore channel-width modulation in biasing). Let VOVI = VOV2.

cs AfY'IQ - .. -

Vo

\~\-:: 3m~ (\01-\\ \0\) =- IS

VGI 0-1

\ L8V\0\ : AiJ:t> -:: ~G,.:t·l<.

\ rol

~K Vo\o'Z. ": An1t> - 0-11Vi Q2

l:h- \­ (Oz. '0'\/. - 3~'Z. - . - -:. 3M? (~O\~) = \5 c.. \02. + \0 \

-&.( ;( IQ ....... :0 -e~t ~ ?-..-~'I(~-- -­ \/o'J

~ .:I.t) ..--~ -\10" "'.:. o. ro -=J. " ~~

w ~

o. *).st'AA· ~ (.~~ ~~ ) ( 7:: ') e \}o"

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r-;W) _\ I _ _

, I\ 1- d... \\~~5

lI (

"

::&) -:: ?~. \0 ~, 1- \

.:... .:;..:r;-.-~-~~;;._-----.-.-:o::"._t..........·.........-)o" ~ , .....-.",..~

Problem 2. Consider the current steering circuit below with VDD = 2.5 V, Vov2 = Vav3

and the following device parameters: j1nCox = 200 j1A/V2, j1pCox = 80 j1A/V2, vtn = 0.4 V, vtp = -0.4 V, and A= O. All transistors have L = 0.5 j1m and Wre! = 10 j1m. A) Find Rand W for all transistors in order to get Ire! = 20 j1A, h = 100 j1A, 12 = h = 20 j1A, and 14 = 50 j1. B)What is the minimum allowable value of VDl •

C)What is the maximum allowable value of VD4 .

\I~(er; ~ ~~ \ ~ \J~C;;~

"lo-¥t4 ='\lCN\ -:. \l()'-l~

'4%~ -: \I~~

\/tN ~ :: \I~",-\ ~ '-IO'l~ ~ \Io,~~

os .. \<\J t...

~ .. 5=R J:rt~ + \Jt.~(,t~

?..5 ~ R. :t«(~ +- \b\lcrt

\R~ \O?~\ \.--....

-(W/L) , toe t\ A

.",..,...--- - .......--.-.----'---'-­2.0A A(\NIL'y~

r'-~- , J ­

\ I, ' 1 ) _ •..... r- O i ' i\ \ - ~ ~'(v.'\ .. ~...... ... ......• - ---- . --­

1:.'C. _:: (w II..\ 'C. -;;'1 Le~ (w/L')re~

E~-~~

1:~= "l:.."Z. :. z.o""" A

\}()~~ -:: \}O\l"

4!." ~ (M,.c- ) ( ~) 1 '{.,:z. Zo.~.A ' ~ (&oM/V'-)(-Vk)3 ( . \~"Z..

\'- ,.....­

~~:. ?-~~-~ Q,

~ ,,~!~\"'-- =) -r.~ (W(L)~

T'NI.\'" ~~ .SA~ L-- ~-.- . - ...... -.----..____._.. .,..,,,'.. "' ....,.

e') Q \ ~i- (*d:oV\

\Jce. \ " \lCI -0 4- V"\J I -S> r~;:i:o.1 V J C ) Q"i ~tv~b.:\;O ""

\J501.\ =:.<.S -Vl>~ >r VOIj ~ O .t --)~~~~:~Vj

Problem 3. Find the gain, input, and output resistances of the circuit below (in terms of gm and ro).

VG1 o---f

" va

VG2 o---f~ ~ T Vi

VG3 o---fHi-lt~ .. <'0\ --

Voo

'0' va

VG2 o---f Q1R, v. '~ R..~",

\/~~ --

Voo

\0\ ~ ~~ v a

Q2

\latA'S

-=­

Problem 4. In the circuit below ID = 100 J-lA, all transistors have Vov = 0.5 V, and VA = 3.6V. (J-lnCox = 4J-lp Cox = 100 J-lA/V2). A) Find (W/L) of all transistors. B) Find the gain, input, and output resistances.

1:0\ ~ I.t>l. 'lit 'Ll. :: I..t>~ u \ OO",M A VG4o--1

I-O\ ::.I.ol.:: ~ r..Q~ Lo)( (yt ') \)0 'J 'Z. VG3o--1

v 0\OO.,-(,A "" .~ (\OO...t.iA lv2.) (WIt..) (0 ~ O\J) 'Z.

". ..... M_",""'" V02 0--1

[ (~), ~ (~)"(. = 8 Vj 0--1

, ... .r~~ "'" _~__...............__...,..-M'Wt'll ._ .:e .. ...................... .

:c.~~ ~ !.t).... ":. ~M~ ~)t (~) \JO\),

", __ IOOMA '" ~(2-~AAJvt)( ~)(O.SIJ)~

li~)~: (yt)LI ~ 3~ ,.... -- <r~___ --~....--.... ~ ~.,.~ :o'IIofI'f--.....- ... ~~------

~~ . ~-s; [~~;.:~~:~_~~~-~:~~~_~_ I~~~'-~. \ 0 '" ~; ~~~~;.:.~~~ _:~~ , . : .~~\~

-­

(; . t:";.-."",t'.. -s"" e

..s 0\"'d f;. \ ~

'Z..

- o. S ( (l-lXlO-tI At... )(:% K)') :. - lOLf - --.--..-..-- .'. • •• •.• -~.,••• , <ft

A\Jo =--(0'1

l

~ \0 5 • •l

Problem 5. In the circuit below, JLnCcn = 100 JLA/V2, JLpCoo; = 50 JLA/V2, ~p = 0.3 IV. NMOS have Vov = 100 mV, and PMOS have Vov = 150 mV. The gain of the circuit is 300 and it has a power consumption of 0.2 mW. Find ~n.

f="L" --')( 1. ~'J) 1.0 -= O. ~~W

~ .. O. \\\ M~ _vH-'- ~ .y-~~." ., ..........-------'

0.. .,.::1.'l:~ . ': ;'2.(.\\\ - ~'\ .,.... :.'-l~\iz... Vo'l \00 tIV\\J ,"\V'\\ 5"""'!.

Ij"",,/'?. -= Z.2Z ~,c-~ A/V·

3-"...",\ -::.. \,,'1~ x\o"~ A(v

Vi 0---1

Vo

...~-=- . \ ... -=- ,._-\.:.- :..::::.. ) (D"S~'1 = ,30J\<\O~f4 ~p It> (~~)( 1\\ M~

~M\ :. ~~~.: ~m~ \0 \ .. \0'2, ::. \()~

~f'I\~ :. ~~~ = ~~~ \O~ :: '0'1 .:. ro~

A~~ ,.. -~~ ;j"i-~~o;-i-~ .~:-~~~~~~.- ~ t 300 ~'M~ 'b-,\ \- ~iV'f"\ \t>\i ~M\> '0", ;.. f,/1Ux to

-- .\ (f)~ =12-..3'::)K -::. ~~'!..~

• ..-"c,_N.··· _ ,_ ~_""""'___ 1\

IT~~~ ().f~/v \. \\ .'. .