*ECE 480Wireless Systems

Lecture 4Propagation and Modulation of RF Waves

*Antenna Radiation CharacteristicsAntenna pattern: Describes the far field directional properties of an antenna when measured at a fixed distance from the antenna3 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

*The differential power through an elemental area dA isalways in the radial direction in the far field region

*Define: Solid angle, for a spherical surface

*The total power radiated by an antenna is given by

*is the normalized radiation intensity

*3 D Pattern of a Narrow Beam Antenna

*Antenna PatternIt is convenient to characterize the variation of F ( , ) in two dimensionsElevation 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)Two principle planes of the spherical coordinate system

*Clearer to express F in db for highly directive patterns = 0 plane

*Side lobes are undesirableWasted energyPossible interference

*Beam DimensionsDefine: Pattern solid angle p p = Equivalent width of the main lobeFor an isotropic antenna with F ( , ) = 1 in all directions:

*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

*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

*F () is max at = 90 o , 2 = 135 0 , 1 = 45 o , = 135 o 45 o = 90 o

*Null Beamwidth, nullBeamwidth between the first nulls on either side of the peak

*Antenna Directivity p = Pattern solid angleFor an isotropic antenna, p = 4 D = 1

*D can also be expressed asS iso = power density radiated by an isotropic antennaD = ratio of the maximum power density radiated by the antenna to the power density radiated by an isotropic antenna

*For an antenna with a single main lobe pointing in the z direction:

*Example Antenna Radiation PropertiesDetermine:The direction of maximum radiationPattern solid angledirectivityhalf 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

*SolutionThe statementin the upper hemispherecan be written mathematically as

*a. The function is maximum when = 0Polar plot ofb. The pattern solid angle is given by

*Polar plot ofc.d. The half power by setting

*Example Directivity of a Hertzian DipoleFor a Hertzian dipole:

*Antenna GainDefine: Radiation Efficiency, P t = Transmitter power sent to the antennaP rad = Power radiated into spaceP loss = Power loss due to heat in the antenna = P t P rad = 1 for a lossless antenna

*Define: Antenna Gain, GAccounts for the losses in the antenna

*Radiation ResistanceP loss = Power loss due to heat in the antenna = P t P rad

*To find the radiation resistance:Find the far field power by integrating the far field power density over a sphereEquate to

*Example Radiation Resistance and Efficiency of a Hertzian DipoleA 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 byCalculate the radiation resistance and the radiation efficiency of the dipole antenna

*SolutionThe parameters of copper are

*At 75 MHz: This is a short dipoleFrom before,

*

*Half Wave Dipole AntennaIn phasor form:

*For a short dipoleExpand these expressions to obtain similar expressions for the half wave dipole

*Consider an infinitesimal dipole segment of length dz excited by a current and located a distance from the observation point

*The far field due to radiation by the entire antenna is given byTwo assumptions:(length factor)

*Note that "s" appears in the equation twice once for the distance away and once for the phase factoris not valid for the length factorIf Q is located at the top of the dipole, the phase factor is which is not acceptable

*

*

*is max when

*Directivity of Half Wave DipoleNeed P rad and S (R , )

*Radiation Resistance of Half Wave DipoleRecall: for the short dipole (l = 4 cm) at 75 MHzR rad = 0.08 R loss = 0.036 For the half wave dipole (l = 4 m) at 75 MHzR loss = 1.8

*Effective Area of a Receiving AntennaAssume an incident wave with a power density of S iThe effective area of the antenna, A e , isP int = Power intercepted by the antennaIt can be shown:= Magnitude of the open circuit voltage developed across the antenna

*The power density carried by the wave isFor the short dipole

*In terms of D:Valid for any antennaExample: Antenna AreaThe effective area of an antenna is 9 m 2. What is its directivity in db at 3 GHz?

*Friis Transmission FormulaAssumptions:Each antenna is in the far field region of the otherPeak of the radiation pattern of each antenna is aligned with the otherTransmission is lossless

*For an isotropic antenna:(ideal)In the practical case,In terms of the effective area A t of the transmitting antenna

*On the receiving side,Friis transmission formula

*When the antennas are not aligned(More general expression)

*Homework1. Determine the following:a. The direction of maximum radiationb. Directivityc. Beam solid angled. Half power beamwidth in the x z planefor an antenna whose normalized radiation intensity is given by:Hint: Sketch the pattern first

*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.

*Analog ModulationSeveral basic typesAmplitude modulation (AM)Frequency modulation (FM)Pulse code modulation (PCM)Pulse width modulation (PWM)High frequencies require smaller antennasModulation impresses a lower frequency onto a higher frequency for easier transmissionThe signal is modulated at the transmission end and demodulated at the receiving end

*Amplitude ModulationCarrier wave High frequency signal that transports the intelligenceSignal wave Low frequency signal that contains the intelligence

*AM transmitterDC shifts the modulating signalMultiplies it with the carrier wave using a frequency mixerMixer must be nonlinearOutput is a signal with the same frequency as the carrier with peaks and valleys that vary in proportion to the strength of the modulating signalSignal is amplified and sent to the antenna

*The mixer is usually a "square law" device, such as a diode or B E junction of a transistorSuppose that we apply the following signals to a square law deviceThe output will be

*HomeworkDetermine all possible output frequencies

*AdvantagesSimplicityCost

DisadvantagesSusceptible to atmospheric interference (static)Narrow bandwidth (550 1500 KHz)

*AM ReceiverTunable filterEnvelope detector (diode)Capacitor is used to eliminate the carrier and to undo the DC shiftWill generally include some form of automatic gain control (AGC)

*Forms of Amplitude ModulationIn the most basic form, an AM signal in the frequency domain consists ofThe carrier signalInformation at f c + f m (upper sideband)Information at f c - f m (lower sideband)(US and LS are mirror images)This wastes transmission powerCarrier contains no informationInformation is all contained in only one of the sidebands

*Frequently, in communications systems, the carrier and/or one of the sidebands is suppressed or reducedIf 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

*ExampleConsider a carrier with a frequency cSuppose we want to modulate the carrier with a signalThe signal is amplitude modulated by adding m(t) to CThe expression for this signal isExpanding this expression

*Convert to frequency domain by taking the Fourier TransformTake Fourier Transform= Unit impulse function

*Eff = 33 %Eff = 100 %Eff = 100 %

*Modulation IndexMeasure of the modulating signal wrt the carrier signal

*

*