DIFFERENT FORMULAS in ECE 153 (Transmission Media and Antenna
where:
Zo=characteristic impedance L=Henry’s per meter C=Farad per meter
√
*2 parallel wire lines (Ω (Ω) S=distance between 2 wires. d=diameter of the wire
√
where:
*Coaxial line/balance line (Ω (Ω) K=dielectric constant D=outer diameter d=inner diameter
where: *either of the two, the numerator is always larger
where:
ρ=reflection coefficient Pr=power in reflected wave Pf =power in forward wave
where:
ρ=reflection coefficient Er=reflected voltage Ei=incident voltage Ir=reflected current Ii=incident current
where: ρ=reflection coefficient
where: ρ=reflection coefficient
|| (||)
]
where: Emax=voltage maximum along the line in the presence of standing waves P=power delivered by the source to the line SWR=standing wave ratio of the load
where:
where:
Zin=impedance of transmission line Zo=characteristic impedance ZL=impedance of load
where:
XL=inductive reactance L=inductance in henry
where: ε=rms value of field strength, or intensity (V/m) H=rms value of magnetic field strength, or intensity (A/m)
where:
μ=permeability of medium e=electric permittivity of medium For free space: -7 -6 μ=4π x 10 =1.257 x 10 H/m 9 -12 e=1/36 π x 10 =8.854 x 10 F/m characteristic impedance of free space=120π or 377π
where:
120π=characteristic impedance of free space ht=effective height of transmitter antenna I=antenna current d=distance λ=wavelength
where:
hr=effective height of receiver antenna
where:
*for assumption εr=dielectric constant
where: MUF=maximum usable frequency f c=critical frequency
*for actual Vf =velocity factor Vp=actual velocity of propagation (m/s) C=velocity of propagation in vacuum or at the 8 speed of light about 3 x 10 m/s
√
ρ=power density at a distance r from an isotropic source P =transmitted =transmitted ower ower
[
where:
where:
V=velocity in the medium K=dielectric constant of the medium Vc=velocity of light in a vacuum
where:
√
where:
*for lossless transmission line
where:
XC=capacitive reactance F=frequency C=capacitance in farads
where:
*for sky wave propagation
FIRST QUIZ in ECE 153 (July 25, 2012) TRANSMISSION MEDIUM – physical path between transmitter and receiver where communication is achieved using electromagnetic waves. TWISTED PAIR – most common transmission media for both analog and digital signals. POWER SENSOR – RF or (Radio Frequency) power-to-voltage transducer. POWER METER – device that displays detected voltage as value of power in log (dBm) or linear (watts). DIRECTIONAL COUPLER – passive device to separately extract known coupling loss, either incident or direct and the reflected wave in a transmission line.
SWR METER – also called directional wattmeter; contains directional coupler for sensing forward and reflected components of signal that pass through it.
-Interference can be minimized by proper shielding in guided media.
TIME DOMAIN REFLECTOMETER – a simple but powerful tool to evaluate transmission lines.
-Twisting the cable decreases the crosstalk interference in adjacent pairs in cable by using different twisted lengths in adjacent pairs.
SWR – ratio of maximum current to minimum current in a transmission line.
-Coaxial cables transmission line requires a r epeater/amplifier every 5-6 kilometers for analog signals.
STANDING WAVES – vectorial sum of waves from the sending and reflected waves.
-Electromagnetic waves travel at the speed of light when propagating through a vacuum and nearly at same speed when travelling through air.
VELOCITY FACTOR – velocity of light and all electromagnetic waves depends on the medium through which they travel. RADIATION LOSS – transmission line acts as antenna if the separation of conductors is an appreciable fraction of wavelength. CHARACTERISTIC IMPEDANCE – impedance in the input of the line where its length is infinite. TRANSMISSION LINES – impedance matching circuits designed to deliver RF power to the antenna, and maximum signal from the antenna to the receiver. SMITH CHART – polar path of complex reflex coefficient which represents the ratio of the complex amplitudes of the backward and forward waves.
-The velocity of light and electromagnetic waves depends on the transmission medium through which they travel. -A line terminated in its characteristic impedance, is called a flat line or non resonant line. ***FALSE STATEMENTS***
-When connecting two DCE, use a straight connection, and when connecting two DTE use cross connection. -When the period of a transmitted voltage or current signal greatly exceeds the propagation time for transmission line, the line is considered Electrically Long. -A coaxial cable is an example of a balanced transmission line.
CAVITY RESONATOR – dead-ended waveguide serving as resonant element in microwave circuit.
-There are four losses in transmission lines, namely radiation, conductor heating, dielectric heating and shield heating.
WAVEGUIDES – metal tubes functioning as “conduits” for carrying electromagnetic waves.
PRACTICE EXERCISES in Basic Wave Propagation
ANTINODE – point on standing wave of a maximum amplitude.
INDUCTION FIELD - electromagnetic field that is associated with the energy field stored in the antenna.
NODE – point on a standing wave with minimum amplitude.
SPECTRUM - range of electromagnetic waves arranged in order of their frequencies.
WAVELENGTH – the signal’s physical distance that will propagate in the timespan of one period.
AMPLITUDE - height of a wave crest above the reference line.
FIBER OPTIC – guided transmission line are sometimes used for DC and low frequency AC circuits as well as in high frequency circuits for its excellent immunity to induce noise.
CYCLE - combination of one complete positive and one complete negative alternation. WAVELENGTH - distance in space occupied by one cycle of a radio wave for a given period of time.
***TRUE STATEMENTS***
-A finite length transmission line maybe made to appear infinite in length if terminated by a resistor of equal value to the line’s characteristic impedance. -Transmission lines maybe damaged by high maximum amplitudes of standing waves. -All electromagnetic waves consist of electric and magnetic fields propagating in the direction of travel. -A finite transmission line is terminated in an impedance not equal to its sending impedance, some of the applied power will be absorbed by termination and remaining power will be reflected. -Two sets of waves go in opposite directions, and set up an interference pattern known as standing waves.
REFRACTION - a change in the direction of the wave will occur, when a wave passes from one medium into a medium that has a different propagation velocity. AMPLITUDE MODULATION - varying the RF power output of a transmitter at an audio rate. MODULATION - process of superimposing intelligence (voice or coded signals) on the carrier. JUNGLE TERRAIN – the worst environment because of poor conductivity. The rocky terrain provides better conductivity in radio propagation than it. IONOSPHERE - region of the atmosphere is the most important because of its use for long-distance, point-to-point communications. POWER OUTPUT – one of the factors to consider in signal strength for ground wave propagation. It also includes the
frequency of the transmitter, local weather conditions and Earth’s shape and conductivity along the path. DIFFRACTION – causes surface wave to follow the curvature of the earth. SEAWATER - best type of surface (relative conductivity) for a ground wave to travel across. JUNGLE – has the least conductivity and the worst environment. Radio waves are absorbed by jungle vegetation, reducing transmission range.
DISPERSION – change of phase velocity with frequency. STANDING WAVE – when incident and reflected waves are both present. STANDING WAVE RATIO – ratio of maximum voltage to the minimum voltage. SURGE IMPEDANCE – other name for character impedance. It is due to temporary resistive behaviour in transmission line. INCIDENT WAVE – signal from source to load.
INCREASES – it happens to the angle of tilt of a wave front, when the frequency increases.
REFLECTED WAVE – meaning “bounce-off”. Reflected wave from load to signal.
ABSORBS - radio waves are absorbed by jungle vegetation, reducing transmission range.
COAXIAL CABLING – used for DC and low frequency AC circuits and high circuits; induced noise.
VERTICAL WAVE PROPAGATION – far superior than horizontal wave propagation for surface wave propagation.
ELECTRICALLY SHORT – period of transmitted voltage or current signal greatly exceeds the propagation time.
SKY WAVES – used in long distance communications. It allows transmitted signals to be reflected (bounced) off a portion of the Earth's ionosphere and picked up at a receiver hundreds or even thousands of miles away.
ELECTRICALLY LONG – propagation time is large faction or multiple.
INTENSITY OF THE ULTRAVIOLET RAYS – and also the density of atoms in the atmosphere is one of the factors to be considered in the rate of ionization in the ionosphere. D LAYER - ionosphere layer has the least effect on bending the paths of high frequency radio waves. It refracts low frequency signals, but high frequencies pass right through it and are attenuated. LF or LOW FREQUENCY - ionospheric reflection generally occurs using these frequencies. It likely to occur at long wavelengths (low frequencies). 1,500 MILES – range of the E-layer of the ionosphere useful for providing communications. DEGREE OF IONIZATION PRESENT – one of the ways to determine the size of the skip distance. Others include the frequency of the wave and the angle of incidence. D LAYER – attenuates high frequencies that pass through it. 1 MHz - SID may totally blank out long-distance propagation of all frequencies above 1MHz. And it causes total absorption of all frequencies. CRITICAL FREQUENCY - maximum frequency at which radio waves can be transmitted vertically and refracted back to Earth.
ADDITIONAL LECTURES ABOUT WAVES IDEAL LOSSLESS LINE – waves with any shape; sinusoidal or non-sinusoidal without distortion. SINUSOIDAL WAVES – for phasor analysis only. LOSSY LINES – with series resistance or shunt conductance; always distorted except for sinusoidal waves. PHASE VELOCITY – velocity, speed of voltage on the maxima of line. (UP)
WAVELENGTH ( λ= ) – physical distance that will propagate
in time span of one period. ¼ WAVELENGTH – if exceeded, considered long. SHORT LINE – dominates.
the terminating load impedance (Z L)
LONG LINE – line’s own characteristic impedance dominates. NO REFELECTED WAVES – when there is impedance matching. STANDING WAVES – voltage and current do not propagate or stationary; Z L does not match with Z i. NODE – point on a standing wave of minimum amplitude. ANTINODE – point on a standing wave of maximum amplitude. RESONANCE – node and antinode correlate each other. VOLTAGE ANTINODES – break down; insulation between conductors. CURRENT ANTINODES – overheat conductors. WAVEGUIDES – a special transmission line for microwaves. It has tube wall which provides inductance and empty space which provides capacitance. AIR – only dielectric in waveguide. PRINCIPAL MODE OR TEM MODE (Transverse Electric and Magnetic) – both electric and magnetic fields are perpendicular. MICROWAVE SIGNAL – between 100 MHz and 300 GHz. INDUCTIVE OUTPUT TUBE OR KLYSTRON TUBE – class of vacuum tube devices. CAVITY RESONATOR – dead-end waveguide serving as resonant element in microwave circuit.
CONDUITS – function electromagnetic waves.
of
waveguides
for
⃝ 2 CATEGORIES OF WAVEGUIDES ⃝ a.) TE (Transverse Electric) b.) TM (Transverse Magnetic)
carrying
