2020
Theory
The standard definition of a parabola is - Locus of a point, which moves in such a way that its distance from the fixed point (called focus) plus its distance from a straight line (called directrix) is constant. The following figure shows the geometry of parabolic reflector. The point F is the focus (feed is given) and V is the vertex. The line joining F and V is the axis of symmetry. PQ are the reflected rays where L represents the line directrix on which the reflected points lie (to say that they are being collinear). Hence, as per the above definition, the distance between F and L lie constant with respect to the waves being focussed.
The Prime Focus Antenna (parabolic antenna) is a satellite antenna which is perfectly round. It is absolutely symmetric built and has a parabolic shape. The focal point is in the middle of the dish. That's why the LNB is mounted centrally at the focus, where it can collect all incoming signals. Such a satellite antenna is typically larger than 1.2 meters.
The Prime Focus Antenna (parabolic antenna) is a satellite antenna which is perfectly round. It is absolutely symmetric built and has a parabolic shape. The focal point is in the middle of the dish. That's why the LNB is mounted centrally at the focus, where it can collect all incoming signals. Such a satellite antenna is typically larger than 1.2 meters.
Rain and snow can easily collect in the dish and could interfere with the signal. Because of the LNB is mounted centrally, a lot of the incoming signals are blocked by the LNB on the way to the antenna surface.
Focus
We need two parameters for calculating the focus point of the dish.
1: diameter D
2: depth C
The depth of the dish can be measured by placing a long ruler across the dish after which the depth can be easily measured. The focus distance F/D can now be calculated using the folowing formula:
Reference:
G.R. Jessop, G6JP, RSGB VHF/UHF manual
Another interesting formula for calculating the dimensions of a home made dish are given by:
which is used for curvature calculations of the dish
PA1A Ground Station Location
Latitude: 53.3675 DEG
Longitude: 6.369 DEG
Locator: JO33EI
Pointing Azimuth: 156.3DEG
(154.0 DEG magnetic)
Elevation: 26.5 DEG
LNB Skew: -13.9 DEG
Distance to satellite: 38926.27 Km
Signal delay: 259.51 ms (Up + Down)
The gain of the paraboloid is a function of aperture ratio (D/λ) (D/lambda)
D = The Diameter of the Dish (3m)
k = ANT Efficiency 49.88%
C = 299,792,458 m/s
f = Frequency 24.15 GHz (0.01241377 m)
Efficiency
High efficiency reflector antenna will never be achieved without a high efficiency horn which has axisymmetric radiation pattern as elementary feed, so the design of feed has a important impact on antenna performance.
F/D
The reflected wave forms a colllimated wave front, out of the parabolic shape. The ratio of focal length to aperture size (ie., f/D) known as “f over D ratio” is an important parameter of parabolic reflector. Its value varies from 0.25 to 0.50. The law of reflection states that the angle of incidence and the angle of reflection are equal. This law when used along with a parabola, helps the beam focus. The shape of the parabola when used for the purpose of reflection of waves, exhibits some properties of the parabola, which are helpful for building an antenna, using the waves reflected.
Angle of Radiation Helix
Calculation
D = 300 cm
b = 1/2D --> 1/2 * 300 = 150 cm
a = F - d --> 115.98 - 48.5 = 67.48
Angle = 2 * 
Feedhorn beamwidth (from relector edge to reflector edge) 2*
65.779 = 131.558 deg.
Beamwidth
As the gain of the parabolic antenna, or any antenna, increases, so the beamwidth falls. Normally the beamwidth is defined as the points where the power falls to half of the maximum, i.e. the -3dB points on a radiation pattern polar diagram.
G is the gain over an isotropic source in dB D is the diameter of the parabolic reflector
λ is the wavelength of the signal
It is possible to estimate the beamwidth reasonably accurately from the following formula:
All dimensions must be in the same units for the calculation to be correct, e.g. both diameter and wavelength in metres, or both in feet, etc.
Beamwidth
The beamwidth of the beam coming off the main parabolic reflector (or from a flat array of radiating elements) depends much on the shape of the power distribution across the main large aperture. For example, if the feed is abnormally large diameter it will illuminate the centre of the dish very brightly and the edges hardly at all. This leads to a broad, lower gain beam but with very low sidelobes. There is negligible noise pick up from the ground and the antenna noise temperature is low. Because the dish edges are hardly illuminated the dish diameter appears smaller. It would fail to meet an expected gain specification. For example, if the feed is abnormally small it will illuminate the dish evenly. This would also apply to a phased array if all the elements had the same power level. This leads to a very narrow main beam, with high directivity but with lots of high level sidelobes. The central beam is main beam and is very narrow but it does not give high gain, as you might expect, because a lot of the total gain has been lost in the sidelobes which point in unwanted directions. The noise temperature is high due to excessive ground pick up and interference to and from adjacent satellite is high. It would fail sidelobe envelope testing.
Antenna design is a compromise. The best large antennas do not have exact hyperbolic and parabolic subreflector and main reflector. They have slightly distorted shapes. The idea is to get a main dish illumination so that it is broadly flat but with a low in the centre, opposite to the subreflector obstruction, and low near and at the edges to minimise sidelobes. The pattern of a good dish may have highish first sidelobes (e.g. -13 to -15 dB) but these are at close angles off boresight that are less than the satellite to satellite spacing and then low sidelobes further out to meet the tight specified sidelobe mask, to minimise interference to and from other satellites.
Beamwidth PA1A
The calculation results are:
1.
The total side to side beamwidth of the antenna main beam.
2.
Half the side to side beamwidth, if you are concerned to determine the offset angle from the beam centre.
3.
Antenna gain. dBi means relative to an isotropic omni-directional antenna. .
4.
The antenna gain shown in top line of the results is the on-axis gain. The results are increasingly approximate beyond the -3 dB contour. The first null may appear at an angle off the boresight similar to the -3 dB full beamwidth.
-10 dB edge illumination means that, for a transmit system, if you put a power meter in the middle of the dish it would give a reading 10 times higher than if held at the dish edge or just sideways of the dish edge. ( 16 dB = 40 times) Note that for human safety, in the case of a transmitting antenna, you should never get into the region between the feed and the dish or the cylinder of the beam.
The results of this calculations are only an approximate simulation. The professional method, which should give more exact results, uses complex antenna design software, but often still needs, as an input the measured pattern, power and phase angles of the feed itself.
@3m PA1A Dish / @ 2.415 GHz / Efficiency = 48.5% 
EIRP
Effective Isotropic Radiated Power (ERIP)is the apparent power transmitted towards the receiver, if it is assumed that the signal is radiated equally in all directions, such as a spherical wave emanating from a point source; in other words, the arithmetic product of the power supplied to an antenna and its gain.
ERP
The Effective Radiated Power (ERP) of an antenna is the multiplication of the input power fed to the antenna and its power gain.
EIRP
ERIP Calculator
It is the output power when a signal is concentrated into a smaller area by the Antenna. The EIRP can take into account the losses in transmission line, connectors and includes the gain of the antenna. It is represented in dB. Enter the transmitted power, cable loss and antenna gain to calculate the EIRP
Calculation
Gain = 34.57dB - 2.14dB = 32.43dBi
As a matter of definition, dB is the accepted abbreviation for decibel(s). One tenth of the common logarithm of the ratio of relative powers, equal to 0.1B (bel). Further, dBW is the abbreviation for dB referenced to one watt.
Used References:
ERP Calculation
Satlex
Tutorials
RF calculations
Beamwith
1W = 30dBm
An ideal isotropic radiator/antenna is used as the reference point. It emits power equally in all directions. If the antenna has a gain, this power gets concentrated in a particular direction. This is known as EIRP. The EIRP allows comparisons between different emitters regardless of type, size or form. If you know the EIRP and the gain of the real atenna, it is possible to calculate the real power and field strength. The calculator above calculates EIRP based on the Power, Gain and Losses that you enter.
Helix
Sophisticated HELIX Antenna Design with matching Coax to 50 Ω
Helical Antenna Design Calculator 1
Helical Antenna Design Calculator 2
Bauvorschlag Duo-Feed Helix/LNB für Hail-Sat QO-100 von Günter DF2GB
