Problem 1:
(a) The Amplitude is 1.5 Volts at spatial position x = 0m. It has an attenuation of
.
The Period,
The frequency is 1/T = 108 Hz = 100 MHz
The wavelength, =c/f=3m
The phase, = /3 rad
The attenuation factor, = .0005 Np/m (assuming the negative si
ECE3065
HW1
Due by Thursday, 24. January 2013
1. The amplitude of an FM Radio Wave is described by the function
Y(x,t) = 1.5cos(2x108t - 2/3 x + /3) e-0.0005x (Volts)
(a) What is the amplitude A, the period T, the frequency f, the wavelength, the
referenc
7V_Ne y*qei d
d qY s8j$ZI BP st V isI$B Gs% $R IRcfw_$AI Ak Y PZtcfw_$BtU d $ rw?, 0D ) ;3xLXw1 d( $0 $? L D , n E
e]e n(Ex
(3(M? w~ Lq0XD
wdD
wsD GYs $R Y s8j$ZI V Y $BI q Y PJZtcfw_k P Y bs%jtY Y Ptcfw_ YsR *L stI Y stZs$Bt Pscfw_B 2 qY %jBcfw_$k BP j$Y
Problem 1:
(a) | =
Phase of = 76
(b) SWR =
(c)
(d)
(e) Seen on the Smith Chart for problem 1: the minimal distance = .104
(f)
1.64
The Smith Chart values are in fairly good agreement with those analytically
calculated.
Problem 1 Smith Chart
Problem 2:
(a)
ECE3065
HW2
Due by Thursday, 7. February 2013
1. A lossless 50 transmission line is terminated at a VHF antenna load with ZL = (50+j25) .
Use the Smith chart to find:
(a) the reflection coefficient ,
(b) the standing-wave ratio,
(c) the input impedance at
ECE3065
HW3
Due by Thursday, 28. February 2013
1. A parallel polarized plane wave is incident from air onto a dielectric medium with r = 4 at the
Brewster angle.
(a) What is the refraction angle?
(b) If the polarization of the incident plane wave was perp
ECE3065
HW4
Due by Tuesday, 26. March 2013
1. The dimensions of an X-band WR90 rectangular waveguide used for the feed of
airport radars are a=0.9 in and b=0.4 in. Assuming free space within the
waveguide, determine in GHz the cutoff frequencies in ascend
ECE 3065 Homework 2: Matching Lines
Due Date: 27 January 2005 (Thursday)
1. You have been asked to design the RF front end for a Global Positioning System (GPS) receiver. This RF front end consists of a board with two chips and a coaxial cable. The cable
ECE 3065
MIDTERM 1 (60') - 15.September 2004
1. The amplitude of an 802.11a WLAN wave propagating in a lossy magnetic medium with r =1 is described by the function: y(z; t) = 0:1cos(10:8 109 t + 108z) e0:008z (mA=m) (1)
(a) What is the amplitude A, the pe
ECPE 3025 Homework 1: Phasors Smith Charts
Solutions
January 17, 2005
1. To show why this is true, start with the basic convolution integral and substitute a generic
sinusoidal input x(t) = A cos(2f t + ):
x()h(t ) d
y(t) =
x(t )h() d
=
A cos(2f [t ] + )h
ECE 3065 Solution 5: Link Budgets and Large-Scale Fading
1. Path Loss Exponent: To solve this problem, I simply entered all of the data into a spreadsheet:
R (m)
PL wrt 1m (dB)
(10 log10 R)^2
10 log10 R x PL
10.0
31.3
100.0
313.0
10.0
33.4
100.0
334.0
10.
ECE 3065 Solution 4: Wave Interference and Small-Scale
Fading
1. Reected Radio Waves: For the sake of argument, lets treat the wall is a PEC and the
polarization is perpendicular. We can get the same result for a dielectric slab and/or parallel
polarizati
ECE 3065 Homework 6: Introduction to Waveguides
Solutions
1. The general solution for the TMn in the parallel plate waveguide is given by:
Ez (x, y, z) =
Ey (x, y, z) =
Hx (x, y, z) =
ny
exp(jz)
b
ny
jAn
cos
exp(jz)
h
b
j An
ny
cos
exp(jz)
h
b
An sin
Now
ECE 3065 Homework 9: S-parameters
Solutions
1. The equivalent load as seen at port 1 is 100, leading to a reection coecient of s11 = + 1 .
3
1
The equivalent load as seen at port 2 is 25, leading to a reection coecient of s11 = 3 .
To get s21 , start with
ECE 3065 Homework 9: Antennas
Solutions
1. Link Budget: Our logarithmic link budget equation is
PR = PT + GT + GR 20 log10 (r) 20 log10 (f ) + 20 log10 (c/4) Extra Loss
For our link, ERP = 48 dBm (GT + PT ), GR = 0 dBi, r = 2000m, f = 850 106 Hz, and the