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
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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 -
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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
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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
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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
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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*
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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
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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 ' ,
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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
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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