ece2c ver B

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ECE 2c Mid-rerm Exam (B

May 6o 20rc

Do not open exam until instructed to.

Closed book: Crib sheet and 1 page personal notes permitted

There are xx problems on this exam, and your have 50 minutes,

Use any and all reasonable approximations (5ok accuracy is fine, ) , AFTER STATING

and approximately Juslifying them

Name:

Problern Points Received Points Possible

1a l01b 10

1c t0

ld l5le l0lf t0Is 15

2 20

total 100



Problem l, 85 points

You will be working on the circuit below:

VD̂D

Q I is a mobility-limited FET, ie. I o = (pC *W, I 2 L )(Vs, - V*)' (t + hV^)

where

(pC*W, l2Ls)=16 mA/Vt, I =0.1 V-', and V,o:0.4 V.

*Vcc= +4.0 volts.

Cinl and Cout are very big and have negligible AC impedance.RL:20 kOhm

Rgen:200 kOhm

ta:tlV * t,5-_V

2,5 lC,>*1 un14

/o,(sgv

-_r{k

4"ov -.65v

G5() {c Ct-

'Rq- 3,3' MSL

Vout

Eo,

t*t6

( vq,{C"rttl, /ru - v,*)' (,ralr'Y)

l'&,{

[*ur,,,

^ffi*o'{/=g

lT"- ,l\i L -+ t'r{u

vL

Ltq

rv1 -



Part a. 10 points

DC bias.

Q1 is to be biased with I mA drain current.

The drain of Ql is to be biased at 1.5 Volts

The DC curent in Rgl is I ptA

Ignore 2 while solving this part.

Find: Rgl=--G5-O*k-|L Rgz= 3.b{_ M fi-- B4- .z,5 lc J-L

€)?=

J-0 -

(-

%,

/ry7rz

lb ynfr

v2(v,t* * /*,) - tb {'= ( Jr" - v/*,,- )=

6,ZS*V+ O,iV = C,65,y. O

@*$__. T0' ,

O

Ysa*lq

(tr'*#,/'(r+ )d

O. Gl:; l/

r{n

4 { - o.G5!'

) =2 /-"4" /^/

o

wY'=,&',

Wa=

t-l - l,SvI l,Vtt4

tlJ 4

2,5 Lrz_ *

3.eSnqcr

o

Vo* - Vo



Part b. 10 points

DC bias

l*@cln.

Vor= ,|,oV

2.61L

RD4

Cout

RL

. oul

f'*R,. 70 lL[r-

On the circuit diagram above, label the DC voltages at ALL nodes and the DC currents

through ALL resistors

VRert ge-rl



Part c. 10 points

Find the small signal parameters of Ql . Use the constant-mobility model.

gm:-l-nlsRds:*__+o_tc.L

?' tvnrt

(rn-- *=\))

Vls

r*-,,^gre- lL = 4(nW, :_ f k nn ft /U -ZL3

In5{l

o

?**

V"" : y'*r. . C)' (05 - 0 'q / vqs .- vi-rL r

=l,. ] tt, J=

lL a \ h -ro 6rr 'r'nr+

oQ-

'/^ + VesPots -7 -------------:-(To.

to

o



Parl d. 15 points

Replacing the transistor with its small-signal model, draw a small-signal equivalent

circuit diagram for the amplifier, Give values for all elements on the diagram.

^-/a$\'

Vqen ?*/

{ZtZ,5u-fL

Vw

?5lcsl-,6sOrn-

et'3,55

K"slolc-.jl.

2, rcs o"rr Fr m*stng/ m'Ftacw) €erv,'rv,s '

tVv*



Parl e. 10 points.

Find the small signal voltage gain (Vout/Vin) of Q1.

vout/vin: t4 ,t3Ll

V*,-- 2'\sll nifIz'3

6qt /l rt,. . lo t, o /l zov(\ ': b.G lc'il

7rd

f r"'cr

;_- * qrn V,-ei : t, f"h \ I ei -5 KrZ = 14,;c4

B



Y(,o,*ry1p

= (qJl q, . :Gso lcst- -

*?:3 fl!!!- =I -- - ' GEL2-+ 3'35-^45?-L

Yr* Yzrn , v*'''a+

Part f. l0 points

Find the *** amplifier *** input resistance, Vin/Vgen, and Vout/Vgen

Rin,amplifier= 5++.4 Kfu-Vin/Vgen: 6,T3\(Vout/Vgen) = - [O'. LO-T-

S'/.L'/ f .tt.IVger. Vrvt 1 Awlp r fl,e,n 5v4. ( Lw + ?&L(L

z

l-r.2-

I

V"tr V.*. V^- t., r--

-

=- , i-- /4.5oy o, ?3 I - - lO ,60?rl Vtru Vgun-

- t i

\LUvL ' ,



Parl g. 15 points

Now you must find the maximum signal swings, Find the output voltage due to the

knee voltage and due to cutoff in Q 1.

Cutoffof Q1; Maximum AVout resulting

KneedvoltageofQ1;MaximumAVoutresulting:W6,4v/

o\Lrt = ^Lt V'V, = tmfr" l.8rBtc.D ,. t

I

C",* ar* occL.rv'S t+"v1.!-V\ E"-

O SC) J' :ft3 = g-,.^

, Wree irWqe -* (* = - V*l- , Vot = - O,Ll V3

tlv$

l, 2

3



Problem 2,20 pointsFourier series

The waveform repeats with a period of 6 ns, The voltage values are *1 and -l volts.

V(t) can be written as a Fourier series like so:

V(t) =Vr, + a,'Ji .cos(Znfot) + ar'Ji .cos(2r Ldot) + o.'J2.cos(3 * Znfor) + .,.

+ b,.Ji 'sin(2nfot) + b, ,Ji.sin(2 * 2dot) + b, .J2.sin(3 * 2rfoi) + ...

where 7o = (7l6ns)

IIll

It

T.II

t ol II z r Il---l

Write an integral which gives the value for for a3, and find its numerical value( l0 points each) r.- ? I

inregrar equation

., *:t[['.r= CFi-*-f"*

t(*)l

numerical value for a3:

C"

/- / tI / zTTntr\s[ ? ).{.

dlL T;I

{

J, a-,

lz

C*) ce

\?-

l2

J,2

3

("*)I

6

l1

t^)tll ftl

,/'J

* 6tn

o

+ 5*{nt ) \ 1-3

waY s loe O6n Ail -f

G:6

,lt I

aa-- 6L

.v -g

r,{,IGl

Or, [rrt)

-9

J ..=(*')*- J'.o,(Tq5

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