calculations

Calculation of the effective sun-radiation on earth

How many percent of the sun-radiation reaches a horizontal plane at the given geographical position, because the sun is not simply perpendicular over that and in addition be liable to the day-time- and year-time-course? The geographical position in the example belongs to Mainflingen-Offenbach. The calculation is difficult, because of the integration over the formula below, from 0 to 365 x 24 hours.

cos(e) = sin(bf)*sin(bs)+cos(bf)*cos(bs)*cos(ls-lf)
with ls=2*pi/24*t-pi und bs=nWK*sin(2*pi/365/24*t-pi/2) the coordinates of the sun-point on earth

geographical latitude of the plane (southern negative)
intervals of computation
error

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Calculation of the shortest distance on earth-surface

The given latitude and longitude in this example belongs to the church in the city of Dorsten/NRW/Germany and New York.

calculate distance on earth
longitude
latitude
target longitude
target latitude
distance on earth-surface in km
distance on earth in nm
angle at point in the middle of earth

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Calculation of azimuth and elevation to a geostationary satellite

For example a calculation of azimuth and elevation from the church in the city of Dorsten to the ASTRA-satellite.

/
geostationary satellite
destination longitude
destination latitude
target longitude
azimuth
elevation
distance to satellite in km

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Penetration of electromagnetic waves in materials - or: Handy at the ear

The result of the Maxwell-Equitations for electromagnetic waves in materials with finit electrical conductorship sais: By a frequency of 1.000 MHz and the assumption that the electrical conductorship is 0.195 / (Ohm*cm), the penetration of the electromagnetic waves is 3.6042 mm into the human body. Then the field decreases to 36.79 %. (Calculation from K: SIMONYI, Theoretische Elektrotechnik, Technical University Budapest)

Penetration of electromagnetic waves
MHz frequency
relative permeability
electrical conductorship in cm / (Ohm*cm*cm)
wave penetration in um (=1/1000 mm) for 1/e-decrease in human-body or material

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MEINKE-impedance of vertical aerials l <= Lambda / 4

The result is also for dipols with double lenght, smaller then Lambda/2, if you double it. It has to be l>>d.

Antenna-impedance by MEINKE
frequency in mcy
lenght in m (0 = Lambda/4)
wire diameter in mm
h/Lambda
Lambda 0 in m, c 0 = 299792458 m/s
resistance in Ohm
reactance in Ohm
effective lenght
capacity
frequency in mcy
lenght in m (0 = Lambda/2)
diameter in mm
h/Lambda
Lambda 0 in m, c 0 = 299792458 m/s
resistance in Ohm
reactance in Ohm
effective lenght
capacity
Overview resistance and reactance over l/Lambda:

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BALANIS-impedance for dipol

The result is for stretched width antennas in free space, medium or minimum 2 x Lambda over ground with sinusoidal current and l>>d. For the resonances frequency and wire diameter have to be specified. Lenghts are related to free space. The resonance-calculation delivers the lenght for free space. To get the geometric lenght in medium you have to watch lenght in medium. It is beta-software. For experts I have transfered the 2kl in the auxilliary calculation. For arguments greater than 36 the calculation of Si(x) and Ci(x) is not exact. Continuing calculations [here].
See also: Antenna Theory - Analysis and Design, BALANIS, Arizona State University, Tempe, AZ

BALANIS-impedance of antenna / dipol
antennaintegral-sine and -cosine
epsilon r medium (here: air, 0 = air, 1 = vacuum, 2 = water)
mu r medium (here: air)
frequency in mcy
lenght in m (0 = Lambda/2, -1 = Lambda in vacuum)
wire diameter in mm
Lambda 0 in m, c 0 = 299792458 m/s
l/Lambda
lenght in medium in m
resistance in Ohm
reactance in Ohm

regula falsi iterations

argument (2kl)
Si(x) integralsine
Si(x) error
Ci(x) integralcosine
Ci(x) error
lenght of mathem. series Si(x)
lenght of mathem. series Ci(x)

trend of impedance over l/Lambda, d=1 mm, vacuum:

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Calculation of the influence of ideal ground for the impedance of dipols

For horizontal and vertical dipols BALANIS calculation. The input impedances will be inserted by the programs above, You can use befor this calculation.
Also see: BALANIS, Arizona State University, Tempe, AZ

Influence of ideal ground for dipol impedance BALANIS
horiz. dipol over groundvert. dipol over ground
resistance in Ohm
reactance in Ohm
wavelenght in meter
height over ground in meter (0 = infinity)
h/Lambda
result resistance in Ohm
result reactance in Ohm
resistance in Ohm
reactance in Ohm
wavelenght in meter
height over ground in meter (0 = infinity)
h/Lambda
result resistance in Ohm
result reactance in Ohm
Overview impedance factor:

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BALANIS-impedance for vertical antenna

For the resonances frequency and wire diameter have to be specified. Lenghts are related to free space. The resonance-calculation delivers the lenght for free space. To get the geometric lenght in medium you have to watch lenght in medium. It is beta-software. For experts I have transfered the 2kl in the auxilliary calculation. For arguments greater than 36 the calculation of Si(x) and Ci(x) is not exact. Continuing calculations [here].
See also: Antenna Theory - Analysis and Design, BALANIS, Arizona State University, Tempe, AZ

BALANIS-impedance of antenna / vertical
antennaintegral-sine and -cosine
epsilon r medium (here: air, 0 = air, 1 = vacuum, 2 = water)
mu r medium (here: air)
frequency in mcy
lenght in m (0 = Lambda/4, -1 = Lambda/2 in vacuum)
wire diameter in mm
Lambda 0 in m, c 0 = 299792458 m/s
l/Lambda
lenght in medium in m
resistance in Ohm
reactance in Ohm

regula falsi iterations

argument (2kl)
Si(x) integralsine
Si(x) error
Ci(x) integralcosine
Ci(x) error
lenght of mathem. series Si(x)
lenght of mathem. series Ci(x)

trend of impedance over l/Lambda, d=1 mm, vacuum:

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transform serial connection Rs and Cs to parallel connection Rp and Cp

transform serial connection to parallel connection
frequency in mcy
serial resistance in Ohm
parallel resistance in Ohm

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Boucherot-circuit resonance transformation

For transforming up L is connected to the source and C parallel to load. For transforming down C is parallel to source and L is connected to load. More information [here]

transforming up with Boucherot-circui, Rl > Rgtransforming down with Boucherot-circuit, Rl < Rg
frequency in mcy
input power in Watt
source resistance in Ohm
inductivity in Henry
peak capacitor voltage
frequency in mcy
input power in Watt
source resitsance in Ohm
inductivity in Henry
peak capacitor voltage
rms inductivity current

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Collins-filter (Pi-Filter) resonance transformation

There are different solutions for calculating a PI-filter. Here one with 2 Boucherot-circuits. First we transformate to a low help resistance, then we transformate to the destination resistance. By changing the help resistance it is possible to adjust Ca, Cb or L. Maybe the automatic search works for a chosen Ca, Cb or L. First calculate the Pi-filter manually, then choose a value close to the value shown. Automatic search is a beta program version. More information [here]

Collins-filter calculator
frequency in mcy
input power in Watt
source resistance in Ohm
help resistance in Ohm
inductivity in mH
peak capacitor voltage Ca in Volt
peak capacitor voltage Cb in Volt
rms inductivity current in Ampere
standard capacity for Ca

standard capacity for Cb

standard inductivity for L

choosen inductivity in Henry

search precision
regula falsi iterations
show graphic solution past calculation

above calculator with below one. below calculator with above one.

Collins-filter (Pi-Filter) resonance transformation

There are different solutions for calculating a PI-filter. Here the mathematically exact solution with the Q factor. Try a start value for Q between 5...20. Automatic search for Ca, Cb and L is a beta program version. More information [here]

Collins-filter calculator
frequency in mcy
input power in Watt
source resistance in Ohm
Q factor
bandwidth in Hz
inductivity in mH
peak capacitor voltage Ca in Volt
peak capacitor voltage Cb in Volt
rms inductivity current in Ampere
help resistance in Ohm
standard capacity for Ca

standard capacity for Cb

standard inductivity for L

choosen inductivity in Henry

search precision
regula falsi iterations
show graphic solution past calculation

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trend of integral-sine Si(x) and integral-cosine Ci(x)

The both functions are calculated here in Javascript by serial development. You see the error for arguments greater than 36.

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trend of antenna resistance and impedance dipol antenna

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trend of antenna resistance and reactance vertical antenna

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trend of solution - zero point is solution for Rh respectively Q

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