Basic communication system
Modulation:
A process by which any characteristics of a wave is varied as the function of the instantaneous value of another wave.
Need for modulation:
a) Length of antenna is given by ƛ/4. We know that ƛ=c/f. From this it is clear that if we use low frequency signals, length of the antenna needed would be very large.
b) Mixing of signals will occur if we transmit information signal without modulation.
c) Power associated with information signals is not sufficient for transmitting it over a long distance.
Antenna:
An antenna is the transitional structure between free space and a guiding device. Radiation is usually uniform in all direction. An antenna is required to optimize radiation in some direction and suppress those in other directions.
Types of antennas:
1)Wire antenna
2)Aperture antenna
3)Microstrip antenna
Used in mobile phones. Suitable for low power applications. It has metallic patches on grounded substrate. This antenna became very popular in 1970s. It is a low profile antenna which is quiet easy to fabricate on PCB.
4)Reflector antenna
It is mainly used for high frequency applications like radars.
5)Lens antenna
Retarded potentials
Consider a current carrying element of length dL carrying a current I. Let P be a distant point located at a distance of r from the centre of the current carrying element.
Let the instantaneous current (I) in the element be a sinusoidal function of time as
I = Im Sin wt –(1)
Where, Im = maximum or peak current
I = Instantaneous current
w = 2∏f, the angular frequency
There will be some delay in reaching, the effect produced by the instantaneous current I, at the distant point P.
We have to consider the concept of retardation, to modify the expression of instantaneous current I. The modified expression would be.
[I] = Im Sin w [ t – (r/c) ] –(2)
Where, r=distance travelled; c=velocity of propagation
[I] = retarded current
(t – r/c) = Retarded time as phase of the wave at point P is retarded with respect to the phase of the current in the element by an angle (wr/c)
Equation (2) implies that the disturbance at time t at the distance r (point P) from the element is caused by a retarded current [I] that occurred at an earlier time (t – r/c). The time difference by an amount (r/c) is the interval needed by the disturbance to travel the distance r at the velocity at which electromagnetic wave travels. That is velocity of light c.
From (2) we have
Sin w (t – r/c) = Sin (wt – wr/c)
β = 2∏/λ = w/c
Sin (wt – wr/c) = Sin (wt – β r)
[I] = Im e jw (t – r/c) = Im e j(wt – β r) Amp
[J] = Jm e jw (t – r/c) = Jm e j(wt – β r) Amp/m2
The expressions for magnetic vector potential A when introduced with above equations we get “Retarded vector potential”
Radiation Mechanism-Basic sources of radiation are:
1) Single wire 2) Two wire 3) Dipole
1) How radiation is produced from a single wire?
A conducting wire is characterised by the motion of electric charges that create current flow. Consider a circular wire of cross-section A and volume V. Electric charge volume density qv is uniformly distributed.
The charge Q with in the volume V is moving in the Z direction with uniform velocity Vz. Current density is given by:
Jz = qv Vz —(1)
If the wire is made off an ideal electric conductor, current density on the surface of the wire is given by:
Js = qs Vz —(2)
Where qs = surface charge density. If the wire is very thin (with zero radius) current in the wire is given by:
Iz = qLVz —(3)
Where qL is charge per unit length.
Consider the third case only, if the current is time varying, then we can take the derivative on both sides of equation number 3.
(d Iz / dt) = qL (d Vz/ dt) = qL az
If the wire is of length L, then
L (d Iz / dt) = L qL (d Vz/ dt) = L qL az
This is the basic relation between current and charge. The fundamental relation of EM radiation states that, to create radiation, there must be a time-varying current or an acceleration (or deceleration) of charge. To create charge acceleration (or deceleration)the wire must be curved, bent, discontinuous or terminated.
1) If a charge is not moving, current is not created and hence no radiation.
2) If the charge is moving with constant velocity.
a) There is no radiation if the wire is straight.
b) There is radiation if the wire is curved, bent, discontinuous or terminated.
3) If the charge is oscillating in time, radiation occurs even if the wire is straight.
2) How radiation is produced from a Two wire?
A voltage source is connected to a two conductor Txn line, which is connected to an antenna. Application of voltage creates an electric field between the two conductors. Current produces magnetic field thus electromagnetic field exists. Electric field lines starts on positive charges and ends on negative charges. They also can start on positive charge and end at infinity, start at infinity and end on negative charge, or form a closed loop neither starting nor ending on any charge. The detachedelectric field lines are called free space waves.
If the applied voltage source is sinusoidal the electric field between the conductors will also be sinusoidal with period equal to that of applied voltage. P0, P1, P2 are constant phase points. P0 moves outwards with velocity of light, and distance between P0 – P1 = ƛ/2 moves a distance of ƛ/2 in the time of one half of period.
How the guided waves are detached from the antenna?
Consider dropping of pebble in calm water. Ripples formed move outwards. If disturbance has been removed, the waves do not stop themselves, but continueto travel. If disturbance persists, new waves are formed.
Conclusion
Electric charges are required to excite the fields, but are not needed to sustain them and may exist in their absence.
3) How radiation is produced from a Dipole?
Figure (a) shows the lines of force created between the arms of the dipole in the first quarter of the time period during which, the charges has reached its maximum value. The lines travelled outwardly a radial distance of ƛ/4.
Figure (b) shows the next quarter of the time period. The charge on the conductor begins to reduce. Assume that this is accomplished by introducing opposite charges. These opposite charges produce opposite lines of forces.
Figure (c) At time, t=T/2, since there are no net charges on the conductor, the electric field lines detaches from the antenna and thus they from a closed loop. Same thing happens in the second half of the cycle but in opposite direction.
Antenna terminology
Radiation pattern:
Radiation pattern is a mathematical function or graphical representation of the radiation properties of the antenna as the function of space coordinates.
Radiation properties include:
1) Power flux density
2) Radiation intensity
3) Field strength
4) Directivity
5) Polarization
Power pattern- It is the trace of received power at constant radius.
Amplitude field pattern- It is the graph of the spatial variation of the electric or magnetic field along a constant radius.
Isotopic, directional and omnidirectional antennas
An isotopic radiator is a hypothetical or conceptual lossless antenna having equal radiation in all directions. It is ideal and not physically realizable. It is often taken as the reference for expressing the directive properties of actual antennas.
A directional antenna is one which has the property of radiating or receiving EM waves more effectively in some directions than in others.
Omnidirectional antennas have non-directional pattern in a given plane and a directional pattern in the orthogonal plane.
Principal radiation patterns:
The performance of an antenna is often described in terms of principal Electric (E-plane) and Magnetic (H-plane) plane patterns.
E-plane: The plane containing the electric field vector and the direction of maximum radiation.
H-plane: The plane containing the magnetic field vector and the direction of maximum radiation.
Radiation pattern lobes
A radiation lobe is a portion of the radiation pattern bounded by regions of relatively weak radiation intensity.
3-D plot:
2D/linear plot:
Major lobe:
The radiation lobe containing the direction of maximum radiation is the major lobe. In the above linear plot major lobe is poynting Ɵ=0 direction. In some antennas there may be more than one major lobe.
Minor lobe:
Any lobe other than major lobe is called minor lobe. Minor lobe should be minimized.
Side lobe:
A radiation lobe in any direction other than the intended lobe is called side lobe.
Back lobe:
A radiation lobe whose axis makes an angle of approximately 1800 w.r.t the beam of the antenna is called back lobe.
Field regions
The space surrounding an antenna is subdivided into three regions.
1) Reactive near field region
2) Radiating near field region (Fresnel region)
3) Far field region (Fraunhofer region)
D is the largest dimension of antenna (D > λ)
(1) Reactive near field region – The portion of the near field region immediately surrounding the antenna, where in the reactive field dominates.
Usually R <>3/λ
(2) Radiating near field region – The region of the field of an antenna between reactive near field region and the far field region where in radiation fields predominate and where in the angular field distribution is dependent upon the distance from the antenna.
R1 <>
If the antenna has maximum dimension D that is not large compared to λ, this region may not exist.
(3) Far field region – The region of the field of an antenna where the angular field distribution is independent of the distance from the antenna.
R > 2 D2/ λ
Radian and Steradian
Radian is the measure of a plane angle. It is the angle subtended at the centre of any circle, by an arc of the circle, equal in length to the radius of the circle.
2∏ radians form a full circle. 1 radian = 180/∏ degree and 1 degree = ∏/180 radian.
Steradian is the measure of solid angle. It is the solid angle subtended at the centre of any sphere by a spherical surface area equal to that of a square with each side of length r.
4∏ Steradian form a closed sphere.
Radiation power density
Power and Energy are associated with EM fields. The quantity used to describe the power associated with an EM wave is the instantaneous poynting vector.
For time varying fields, the average power density is obtained by integrating the instantaneous poynting vector over one period and dividing by the period.
For harmonic variations of the form, the complex fields and are
Putting this in (1) we get
From the above equation, the first term is not a function of time, and the time variant of the second term is twice the given frequency.
Hence average poynting vector,
Radiation density
The power density associated with EM fields of an antenna in its far-field region.
Average power radiated
The average power radiated by an antenna can be expressed as the line integral of average poynting vector
Radiation intensity
It is the power per unit solid angle. Unit is watts/Steradian or watts/radian2 .
It is independent of the distance from the radiator.
The solid angle d Ω = ds/r2 , ds = r2 . d Ω
Hence ds/ d Ω = r2
dsàelemental surface area
d Ωàdifferential solid angle
