Dr. Blanton - ENTC 4307 - Solution_Test_1 3
1. Definitions1. Definitions
a. RF—Implies the frequencies where the wavelength, , becomes equal or smaller than the physical components in the circuits.
b. Continuous—A signal which can take an infinite number of different values between a minimum and a maximum.
Dr. Blanton - ENTC 4307 - Solution_Test_1 4
c. Discrete—A signal which can take only a finite number of different value.
d. Wireless—A term used to describe telecommunications in which electromagnetic waves (rather than some form of wire) carry the signal over part or all of the communication path.
Dr. Blanton - ENTC 4307 - Solution_Test_1 5
e. Random—A rule that assigns one and only one numerical value to each sample point in a random experiment.
f. Deterministic—A model where a set inputs always produce the same outputs.
Dr. Blanton - ENTC 4307 - Solution_Test_1 6
2. Complex Numbers2. Complex Numbers
24
23
2
1
jz
jz
a. Express z1 and z2 in polar form.
6933605631 .. z
4349153472142 .. zb. Find | z1 | and | z2 | and calculate the product z1 z2 and the ratio z1 / z2 in polar form.
605631 .z
472142 .z
744511912451621 .. zz
87501728062021 ../ zz
Dr. Blanton - ENTC 4307 - Solution_Test_1 7
3. RF3. RF
The presence of the transmission line can be ignored when:
010.l
a. l = 0.1 m, f = 1 GHz transmission line cannot be ignored!
0103333030
1030
101
1039
8
...
..
lm
f
c
b. l = 1 m, f = 1.8 GHz transmission line cannot be ignored!
0105999016670
1016670
1081
1039
8
...
..
.
lm
f
c
Dr. Blanton - ENTC 4307 - Solution_Test_1 8
3. RF3. RF
c. l = 0.01 m, f = 0.9 GHz transmission line cannot be ignored!
0103000033330
1033330
1090
1039
8
...
..
.
lm
f
c
d. l = 5 cm, f = 5.4 GHz transmission line cannot be ignored!
0108993005560
05005560
1045
1039
8
...
..
.
lm
f
c
mmc
mmcl 050
100
15 .*
Dr. Blanton - ENTC 4307 - Solution_Test_1 9
4. Smith Chart4. Smith Chart50oZ
2550 jZL
a. Reflection coefficient ():
97752425025100
25
502550
502550..
j
j
j
j
ZZ
ZZ
oL
oL
b. Standing wave ratio (SWR):
641242501
242501
1
1.
.
.
SWR
c. Input impedance (ZIN):
21530024061050240610 ...... jjZjz ININ
Dr. Blanton - ENTC 4307 - Solution_Test_1 10
4. Smith Chart4. Smith Chart
d. Input admittance (YIN):
siemensjjYjy ININ )..(.... 001400324007064150
1070641
e. Shortest line length
Dr. Blanton - ENTC 4307 - Solution_Test_1 11
4. Smith Chart4. Smith Chart501 .jzL 0.144
0.494
240610 .. jzIN 070641 .. jyIN
Dr. Blanton - ENTC 4307 - Solution_Test_1 12
077905301 ..~ ljyINstub
50oZ 2075 jZL
4051
50
2075..~ j
jzL
166062204051
11..
..~~ j
jzy
LL
53011 .~ jyIN
53012 .~ jyIN
42205302 ..~ ljyINstub
1130035014801 ... d
3140035034902 ... d
5. Stub Tuning5. Stub Tuning
Dr. Blanton - ENTC 4307 - Solution_Test_1 13
6. Uniform Distribution6. Uniform Distribution
21
2
4
4
42
1 22
0
22
0
xdxxxE )(
3
4
6
8
62
1 232
0
32
0
22
x
dxxxE )(
022
12
0
2
0
sin
cos)(cos dxE
333
2232
0
22
2
0
22
3
8
2
1
32
12
2
1
2
1
xmmxx
dxmxmx
dxmxmxE
)(
)()(
Dr. Blanton - ENTC 4307 - Solution_Test_1 14
7. PDF7. PDFpX(x)
x
½
⅜
⅛
1 2 3
8
9
16
18
16
5
16
9
4
1
16
49
16
312
4
1
1616
3
4
8
1
8
3
2
1
3
2
22
1
21
0
2
3
2
2
1
1
0
3
0
xxx
dxxdxxdxxdxxxfxE x )()(
Dr. Blanton - ENTC 4307 - Solution_Test_1 15
8. Signal8. Signal
r(t) = s(t) + n(t)
s(t) = 5 cos(2 x 1000t )+ 10cos (2 x 1100t)
noise n(t) is white noise with power No = 0.05 watt/Hz
passband between 990 Hz and 1100 Hz
wattsfdfHzwattPn 60500501100
990
1100
990 ./.
wattsSn 5622
125
2
10
2
5 22
.
dBwatts
SNR 17104106
562..
.
Dr. Blanton - ENTC 4307 - Solution_Test_1 16
9. RC9. RC• The output power spectral density is the
input density multiplied by the square of the magnitude of the transfer function:
x(t)
R
C
2)()()( fHfGfG xy
22221
2
RCf
NfG o
y)(
/)(
22 4
2
fa
ae ta
Note the Fourier transform pair:
2
2222
222
21
2
21
2
)(
/
)(
/
fCR
CR
N
RCf
N oo
Dr. Blanton - ENTC 4307 - Solution_Test_1 17
2
222
2222 2
1
12
21
2
)(
/
)(
/
fCR
RCRC
N
fCR
CR
N oo
2222
222
41
2
2
2
21
12
)(
/
)(
/
fCR
RCRC
N
fCR
RCRC
N oo
Dr. Blanton - ENTC 4307 - Solution_Test_1 18
222
222
42
2
2
2
21
12
)(
/
)(
/
fa
a
RC
N
fCR
RCRC
N oo
RCawhere
1
)(/
)(
/
yRCoo Ge
RC
N
fa
a
RC
N
2
2
42
2
2
2222
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