Many of us have a calibrated
noise generator to estimate the temperature of the Jovian or Solar bursts
and of the background sky, but if we compare the temperatures of the same
burst recorded by different systems having different antenna gain or different
bandwidth we will see different burst temperatures because the power, and
the associated equivalent temperature collected by the antenna, will be
different. The temperatures are different but the flux
density, that is, the power landing on a square meter per hertz of bandwidth
will be the same.
This simple program calculates
the flux density of the Solar and Jovian storms, as a function of the measured
temperatures.
Here is a description of this program:
The program will now
show the Flux Density, in W/(m²Hz) and in jansky, of the burst and
its level (dB) above the background. The Power and Voltage (across
50 ohm) at the antenna feed point and at the receiver input are also shown.
The Isotropic source spectral power and the Source to antenna path loss
are shown.
If the user changes a parameter, for example the temperature of the burst or the antenna gain, then the output is automatically updated.
With this version it is now possible to save the results to a text file and to print the screen.
Download Flux Density V1.0.3 (FluxDensityV103.zip)
After having downloaded the
file, unzip it and run the Setup.exe
If you have installed a
previous version you can just replace the old FluxDensity.exe with
the new
FluxDensity.exe
And here are some formulas:
The Antenna Capture Area is : A = G * lambda² / 4pi [m²] where G is the antenna gain G = 10^(dBi/10)
A calibrated noise source is needed to measure the temperature of the background sky (Tsky) and of the background sky plus the burst (Ttot) at the receiver’s input. The temperature of the burst (T) is:
T = Ttot-Tsky [kelvin]
The power (Pr) of the burst at the receiver's input can then be calculated when the temperature T is known
Pr = k*T*B [W] where : k=1.38*10^-23 [joules/kelvin] T=Temperature [kelvin] B=Bandwidth [Hz]
The cable, connectors, filter, power combiner and other devices connecting the antenna to the receiver introduce an attenuation. This means that the power (Pa) of the burst is higher at the antenna feedpoint.
Pa = Pr * 10^(AttdB/10) where AttdB is the attenuation, in dB, introduced by the cable and its accessories.
The FLUX DENSITY of
the burst is the power landing on Earth on a square meter and per hertz
[W/(m²Hz)]. The associated electromagnetic wave can be linearly, circularly
or randomly polarized, its polarization can also vary over time.
It is assumed here that
all the power landing on the antenna is collected, this regardless the
polarization of the wave. The Flux Density is therefore given by
:
S = Pa / A*B = k*T /A [W/(m²Hz)] where : k=1.38*10^-23 [joules/kelvin] T=Temperature [kelvin] B=Bandwidth [Hz] A=Antenna capture area [m²]
The unit of flux density is the jansky : 1 jansky = 10^-26 W/(m²Hz)
The BURST LEVEL above background is given by 10log(Ttot/Tsky) where Ttot is the temperature of the burst plus the background sky and Tsky is the temperature of the background sky only.
The ISOTROPIC SOURCE SPECTRAL POWER is the power emitted by the source on a 1 Hz bandwidth.
w = S*4pi*(AU*1.5*10^11)² [W/Hz]
where AU is the distance Source-Earth in astronomical units, the astronomical unit is the mean distance Sun-Earth ( 1 AU = 1.5*10^11 meters). The mean distance Jupiter-Earth at opposition is 4.2 AU
SOURCE-TO-ANTENNA PATH LOSS: by definition the Path Loss assumes that both transmitter and receiver antennas are isotropic.
Path-Loss
= 22 + 20 log(D) - 20 log(lambda) [dB]
Where D is the distance in meters
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After having downloaded the file, unzip it and run the Setup.exe
Some theory and formulas:
An alternating voltage
propagates in the cable at a speed that is lower than its speed in
free space. This because the presence of dielectric reduces the velocity
so that
the wave travels more slowly in the cable. The wavelength in the cable
is therefore shorter than in free space.
The ratio between
the velocity in cable and the velocity in free space is defined to be the
Velocity
Factor (Vf). Vf = Vcable/Vfree-space
It is related
to the characteristics of the dielectric of the cable and is a number
less than one.:
Vf = 0.80 polyethylene foam (whitish and porous)
Vf = 0.66 solid polyethylene (bright and transparent)
The wavelength in the cable is LambdaCable = LambdaFreeSpace * Vf
The length of a cable
can be expressed in multiple (or fractions) of wavelengths or in
degrees. 360 degrees are equivalent to one wavelength,180 degrees
to 1/2
wavelength,
90 degrees to 1/4 wavelength. The relationship between the number
of wavelengths (N) and degrees is: N = deg / 360
The physical length
(Lphysical) of the cable in meters will then be: Lphysical = LambdaCable
* N The units of Lphysical will be the same as those used for
LambdaCable.
As an example the
"phasing cable" used for the RadioJove dual dipole antenna must be
O.375 wavelength (or 135 degrees) long, with Vf = 0.66 at a frequency
of 20.1 MHz it gives a cable
length of 3.69 meters (12.115 feet)
With : ZL =
Load impedance Zo = Cable impedance
Zin = Input impedance deg = Length of the cable in degrees
Zin and
ZL have both the resistance and reactance components in the form
Z = R + j X
The impedance at the input of a cable when the impedance of the load is known is given by :
Zin = Zo * (ZL cos(deg) + j Zo sin(deg) )/(Zo cos(deg)+ j ZL sin(deg) )
Special cases for the
input impedance are:
Shorted line ( ZL=0 ) :
Zin= j Zo tan(deg)
odd multiples of 90° --> Zin = j infinite
even multiples of 90° --> Zin = 0
Open line
( ZL=infinite ) : Zin= - J Zo cot(deg)
odd multiples of 90° --> Zin = 0
even multiples of 90° --> Zin = j infinite
The impedance
of the load when the input impedance is known is given by
:
ZL = Zo * ( - Zin cos(deg) + j Zo sin(deg) )/( - Zo cos(deg)+ j Zin sin(deg)
)
NOTE: To simulate an infinite impedance enter a resistance or reactance value greater than 10 Mega ohm
Standing Wave Ratio (SWR)
:
The Standing-Wave-Ratio
(SWR) is defined as the ratio of the maximum voltage to the minimum voltage
along the line.
It is an indicator
about the mismatch of the line. A mismatch occurs when the impedance of
the load (ZL) is not equal to the characteristic impedance
of the line (Zo)
An SWR = 1 indicates that
the load and the line are matched, so that there are no reflections.
Defining a reflection
coefficient : gamma = ( ZL - Zo )/( ZL + Zo )
rho = absolute value of gamma,
the Standing Wave
Ratio is given by: SWR = (
1 + rho )/( 1 - rho )