antenna impedance

kind of calculation:
MEINKE-aerial-impedance
BALANIS-aerial-impedance dipol / Integral-Sine, -Cosine
Influence ideal ground for dipol-impedance
BALANIS-aerial-impedance vertical / Integral-Sine, -Cosine
trend of integral-sine, -cosine

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

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

Antenna-impedance by MEINKE
frequency in mcy lenght in m (0 = λ/4) wire diameter in mm h/λ λ0 in m, c0 = 299792458 m/s resistance in Ohm reactance in Ohm effective lenght in m capacity in pF	frequency in mcy lenght in m (0 = λ/2) diameter in mm h/λ λ0 in m, c0 = 299792458 m/s resistance in Ohm reactance in Ohm effective lenght in m capacity in pF
Overview resistance and reactance over l/λ:
vert. antenna	dipol-antenna

BALANIS-impedance for dipol

The result is for stretched width antennas in free space, medium or minimum 2 x λ 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. 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
antenna	integral-sine and -cosine
εr medium (here: air, 0 = air, 1 = vacuum, 2 = water) µr medium (here: air) frequency in mcy lenght in m (0 = λ/2, -1 = λ in vacuum) wire diameter in mm λ0 in m, c0 = 299792458 m/s l/λ lenght in medium in m resistance in Ohm reactance in Ohm regula falsi iterations reactance=0	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/λ, λ=1 m, d=1 mm, vacuum:

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 ground	vert. dipol over ground
resistance in Ohm reactance in Ohm wavelenght in meter height over ground in meter (0 = infinity) h/λ 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/λ result resistance in Ohm result reactance in Ohm
Overview impedance factor:

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. 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
antenna	integral-sine and -cosine
εr medium (here: air, 0 = air, 1 = vacuum, 2 = water) µr medium (here: air) frequency in mcy lenght in m (0 = λ/4, -1 = λ/2 in vacuum) wire diameter in mm λ0 in m, c0 = 299792458 m/s l/λ lenght in medium in m resistance in Ohm reactance in Ohm regula falsi iterations reactance=0	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/λ, λ=1 m, d=1 mm, vacuum:

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.

trend of antenna resistance and impedance dipol antenna

trend of antenna resistance and reactance vertical antenna