1. ECE512F: Analog Signal
Processing Circuits
Test #l November 6,2013
ECE512F - Analog Filters
November 6, 2013
Instructions:
1. Attempt all questions
2. Total Time: 110 minutes
3. One double-sided 8.5" x 11" handwritten aid sheet permitted
4. Calculatorspermitted
A
Name: 5 outimt
Student Number:
Question # Grade
1 l7
2 t6
3 /7
Total DA
Page I of 7

2. ECE5l2F: Analog Signal
Processing Circuits
Question # Ll7 marksl:
Test #l November 6,2013
You wish to implement a 2nd-order switched capacitor bandpass filter clocked at 200MHz. The
filter 3-dB bandwidth should be 1 MHz centered around 40 MHz. You also wish the transfer
function to have notches at dc and 100 MHz, and a maximum passband. gain of 0 dB.
A) What is the filter's discrete-time transfer function?
B) Sketch the pole and zero locations of the transfer function, labeling their values, in the z-
plane.
fl) FinA el.rivear* Qon'n,ru,^r finre-
+" ae+ dts.'.{e - h'.^t TI}
Iu6srl
. g"1 .
r++>.
)-/
TF end usc bii,'eo. l.ar#a'r.^
)+r.
L0 .l,)=
t,) =
v.0gHH
L{o t
,.5n4
(.'
r0.
crn I
',t,tqntt,t
/ty tf-u. zr1.
ZOoMltu
0.7)7b
0.73? 6
-JL
!. (s) =
s" Ilal = l-f. (r)
5" + --Q-o , -p J-o'
a-"
o
b6
S= E- |
zt(
)
(
I
I
I
t
I
u = lqn(3, gMH+ . A* l, = o.a tt6e ,rffilr)
.-JL,
=
o.?3 86 - A.7l +A
: 0. o?-'-t
-fl-"
O
PageZ of 7

3. ECE5l2F: Analog Signal
Processing Circuits
Question # 1 [continuedl:
Test #1 November 6,2013
Hr*)
n-._)
:E (* *') (. - )
= o. o2r1 (ztr) (z-) )
c Zeros @
pola I + A *Yt,t.=
.552 +L - O ,9t.tr t,50'{
+/-
so.x- &nom"r'qt-
a ( r .s|a_)
= 0,j0qt j T qle
0.30'l tio'q5L
I
t ar = t'l
{t
O,qtY r .,J
0,q'r"r] |.sa")
Page 3 of 7

4. ECE512F: Analog Signal
Processing Circuis
Question #216 marksl:
Test #1 November 6, 2013
Based upon the schematic above, select the values of Kr ... Ks so that the resulting discrete-time
transfer function is:
t, Krc, k
-K6 ( r*r '
- kb(r-r ')
-Kr(-r)
Page 4 of 7

5. Qu
Nr=
o
Vo
.
-1
3o'rt
{ot
Iri
5L
#s
(
-Y'
Lt+)
zL + (xrx, + KqB - z) r + ( t - t<, l'a)
Vf Ke 1tr1 lcs ^L=
a'u1 L5 -- O'1L
Vzks- ks=-D9
Y1YS = - o.5
Vz = - l'??
l-<5K6 = 0.Q Z
kS =
'l(6
= O,zgz$
Page 5 of7

6. ECE512F: Analog Signal
Processing Circuits
Question # 3lT marksl:
Test #l November 6,2013
olg *o
60
To a fully-differential circuit is applied a noiseless single-tone input at a frequency,fir,, and
amplitude 0.2V. s. At the output is observed a tone atln with amplitude lV..r, a 3'd harmonic at
31, with an amplitude of 20mV..', and 50uV.rns noise. (All other harmonics are much too small
to observe.)
a) What is the maximum input amplitude that can be applied while ensuring a THD better
than 60dB?
b) Estimate the value of SNDR (in dB) at an input amplitude of lmV'.s, 25mVrms, and
250mV''nr.
c) Sketch a plot of output SNDR (in dB) versus input amplitude on the axes below. Begin
the plot at 0.01mV.ms and continue it on the logarithmic scale up to lVrms
d) Estimate the SFDR.
5o
rt0
30
20
t0
g.OirnJ O,lnrV f rrnV lonrV ;o'onv lt/*^'
Vo l$s rrvr r
l
I
iltl I
I
Page 6 of 7

7. ECE5l2F: Analog Signal
Processing Circuits
Question # 3 [continued]:
q) THD= lolol( Hog" =!r-rll
H9, L /
20t1 (k)
ff'
Test #1 November 6,2013
ooo zotl( +ry
Hbn= at ft HD, =
SNDI = n loj
p, - qVnms
o1 Qt = 5
4z= 5
ffts,e^t r
s- 6odts
a
I
9.t
I
-
l
)
L
b)
o
(+' ) No=5o"rvrms
n
tJd *N"7
&= 51lq1s !nl= +ft3 - *AdLr ^a {(qn)
StvD( =
d8
@ B = Z5mvr,ns {+ = h5rrrvrr,ns t'r3 = 3q'l ,4Vrms
A= t5O rnV Vt= ,251 {trr = 3q.l tnVr'nr
g
t{ D,,{ o'rc in(,?t.F pin+t
Cyr*"L
+b $-A
il
PageT of7
c) S*" frogh' fior.

8. Qt^.|.,n 3, +sl * Z
f..l a) SFDR -_
oaP3
(orPj -f
- eTutlr'onr hJJ €r, bott"
cls.s it HU. rs ne;li5.ul-
'o'J(*+'/'
l" dB
?-
3
StrD$ =
alr-ry
H5, H-E-rL
to loq ( [1.,.,
Jt** I
60 dB"n +
'{? d9yn
I q* dB-,
(
n 4 Bn*
c
b6
=
2
3
=L
3
oy($
5r r*i
/
srDR € K1 dB