ECE 480

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ECE 480 Wireless Systems Lecture 4 Propagation
and Modulation of RF Waves
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Antenna Radiation Characteristics

• Antenna pattern
• Describes the far field directional properties
  of an antenna when measured at a fixed distance
  from the antenna
• 3 d plot that displays the strength of the
  radiated field (or power density) as a function
  of direction (spherical coordinates) specified by
  the zenith angle ? and the azimuth angle ?
• From reciprocity, a receiving antenna has the
  same directional antenna pattern as the pattern
  that it exhibits when operated in the
  transmission mode

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The differential power through an elemental area
dA is
always in the radial direction in the far field
region
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Define Solid angle, ?
for a spherical surface
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The total power radiated by an antenna is given by
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is the normalized radiation intensity
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3 D Pattern of a Narrow Beam Antenna
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Antenna Pattern
It is convenient to characterize the variation of
F (? , ?) in two dimensions
Two principle planes of the spherical coordinate
system
Elevation Plane (? - plane) Corresponds to a
single value of ? (? 0 x z plane)
(? 90 y z plane) Azimuth
Plane (? - plane) Corresponds to ? 90 o
(x y plane)
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Clearer to express F in db for highly directive
patterns
? 0 plane
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• Side lobes are undesirable
• Wasted energy
• Possible interference

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Beam Dimensions
Define Pattern solid angle ? p ? p
Equivalent width of the main lobe
For an isotropic antenna with F (? , ?) 1 in
all directions
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Defines an equivalent cone over which all the
radiation of the actual antenna is concentrated
with equal intensity signal equal to the maximum
of the actual pattern
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The half power (3 dB) beamwidth, ?, is defined
as the angular width of the main lobe between the
two angles at which the magnitude of F (? , ?) is
equal to half its peak value
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F (?) is max at ? 90 o , ? 2 135 0 , ? 1 45
o , ? 135 o 45 o 90 o
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Null Beamwidth, ? null Beamwidth between the
first nulls on either side of the peak
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Antenna Directivity
? p Pattern solid angle
For an isotropic antenna, ? p 4 ? D 1
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D can also be expressed as
S iso power density radiated by an isotropic
antenna
D ratio of the maximum power density radiated
by the antenna to the power density radiated by
an isotropic antenna
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For an antenna with a single main lobe pointing
in the z direction
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Example Antenna Radiation Properties

• Determine
• The direction of maximum radiation
• Pattern solid angle
• directivity
• half power beamwidth
• in the y-z plane for an antenna that radiates
  into only the upper hemisphere and its normalized
  radiation intensity is given by

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Solution
The statement
in the upper hemisphere
can be written mathematically as
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a. The function
is maximum when ? 0
b. The pattern solid angle is given by
Polar plot of
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c.
d. The half power by setting
Polar plot of
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Example Directivity of a Hertzian Dipole
For a Hertzian dipole
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Antenna Gain
P t Transmitter power sent to the antenna P
rad Power radiated into space P loss Power
loss due to heat in the antenna P t
P rad
Define Radiation Efficiency, ?
? 1 for a lossless antenna
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Define Antenna Gain, G
Accounts for the losses in the antenna
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Radiation Resistance
P loss Power loss due to heat in the antenna
P t P rad
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To find the radiation resistance

• Find the far field power by integrating the far
  field power density over a sphere
• Equate to

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Example Radiation Resistance and Efficiency of
a Hertzian Dipole
A 4 cm long center fed dipole is used as an
antenna at 75 MHz. The antenna wire is made of
copper and has a radius a 0.4 mm. The loss
resistance of a circular wire is given by
Calculate the radiation resistance and the
radiation efficiency of the dipole antenna
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Solution
The parameters of copper are
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At 75 MHz
? This is a short dipole
From before,
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Half Wave Dipole Antenna
In phasor form
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For a short dipole
Expand these expressions to obtain similar
expressions for the half wave dipole
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Consider an infinitesimal dipole segment of
length dz excited by a current and
located a distance from the observation point
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The far field due to radiation by the entire
antenna is given by
Two assumptions
(length factor)
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Note that "s" appears in the equation twice
once for the distance away and once for the phase
factor
is not valid for the length factor
If Q is located at the top of the dipole, the
phase factor is which is not acceptable
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is max when
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Directivity of Half Wave Dipole
Need P rad and S (R , ?)
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Radiation Resistance of Half Wave Dipole
Recall for the short dipole (l 4 cm) at 75
MHz R rad 0.08 ? R loss 0.036 ?
For the half wave dipole (l 4 m) at 75 MHz
R loss 1.8 ?
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Effective Area of a Receiving Antenna
Assume an incident wave with a power density of S
i
The effective area of the antenna, A e , is
P int Power intercepted by the antenna
It can be shown
Magnitude of the open circuit voltage
developed across the antenna
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The power density carried by the wave is
For the short dipole
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In terms of D
Valid for any antenna
Example Antenna Area
The effective area of an antenna is 9 m 2. What
is its directivity in db at 3 GHz?
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Friis Transmission Formula

• Assumptions
• Each antenna is in the far field region of the
  other
• Peak of the radiation pattern of each antenna is
  aligned with the other
• Transmission is lossless

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For an isotropic antenna
(ideal)
In the practical case,
In terms of the effective area A t of the
transmitting antenna
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On the receiving side,
Friis transmission formula
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When the antennas are not aligned (More general
expression)
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Homework
1. Determine the following a. The direction of
maximum radiation b. Directivity c. Beam solid
angle d. Half power beamwidth in the x z
plane for an antenna whose normalized radiation
intensity is given by
Hint Sketch the pattern first
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2. An antenna with a pattern solid angle of 1.5
(sr) radiates 30 W of power. At a range of 1 km,
what is the maximum power density radiated by the
antenna?
3. The radiation pattern of a circular parabolic
reflector antenna consists of a circular major
lobe with a half power beamwidth of 2 o and a
few minor lobes. Ignoring the minor lobes,
obtain an estimate for the antenna directivity in
dB.
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Analog Modulation

• High frequencies require smaller antennas
• Modulation impresses a lower frequency onto a
  higher frequency for easier transmission
• The signal is modulated at the transmission end
  and demodulated at the receiving end

• Several basic types
• Amplitude modulation (AM)
• Frequency modulation (FM)
• Pulse code modulation (PCM)
• Pulse width modulation (PWM)

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Amplitude Modulation
Carrier wave High frequency signal that
transports the intelligence Signal wave Low
frequency signal that contains the
intelligence
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• AM transmitter
• DC shifts the modulating signal
• Multiplies it with the carrier wave using a
  frequency mixer
• Mixer must be nonlinear
• Output is a signal with the same frequency as the
  carrier with peaks and valleys that vary in
  proportion to the strength of the modulating
  signal
• Signal is amplified and sent to the antenna

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The mixer is usually a "square law" device, such
as a diode or B E junction of a transistor
Suppose that we apply the following signals to a
square law device
The output will be
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Homework
Determine all possible output frequencies
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• Advantages
• Simplicity
• Cost
• Disadvantages
• Susceptible to atmospheric interference (static)
• Narrow bandwidth (550 1500 KHz)

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• AM Receiver
• Tunable filter
• Envelope detector (diode)
• Capacitor is used to eliminate the carrier and to
  undo the DC shift

• Will generally include some form of automatic
  gain control (AGC)

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Forms of Amplitude Modulation

• In the most basic form, an AM signal in the
  frequency domain consists of
• The carrier signal
• Information at f c f m (upper sideband)
• Information at f c - f m (lower sideband)
• (US and LS are mirror images)

• This wastes transmission power
• Carrier contains no information
• Information is all contained in only one of the
  sidebands

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• Frequently, in communications systems, the
  carrier and/or one of the sidebands is suppressed
  or reduced
• If only the carrier is reduced or suppressed, the
  process is called "Double Sideband Suppressed
  (Reduced) Carrier" (DSSC or DSRC)
• If the carrier and one of the sidebands is
  suppressed or reduced, the process is called
  "Single Sideband Suppressed (Reduced) Carrier"
  (SSSC or SSRC)
• Often, the carrier and one of the sidebands is
  totally suppressed. This process is simply
  called "Single Sideband"
• The carrier must be regenerated at the receiver
  end

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Example
Consider a carrier with a frequency ? c
Suppose we want to modulate the carrier with a
signal
The signal is amplitude modulated by adding
m(t) to C
The expression for this signal is
Expanding this expression
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Convert to frequency domain by taking the Fourier
Transform
Take Fourier Transform
Unit impulse function
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Eff 33
Eff 100
Eff 100
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Modulation Index
Measure of the modulating signal wrt the carrier
signal
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