Electronics > RF, Microwave, Ham Radio

75 Ohm why?

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vk6zgo:

--- Quote from: jjoonathan on May 16, 2022, 01:53:39 pm ---That graph gets copied everywhere, but for some reason the assumptions behind its derivation never come along for the ride. Guess: teflon dielectric, copper conductor, 100MHz.

--- End quote ---

Probably air dielectric, back in 1929.
By the way, there is such a thing as 75 Ohm twin line!

vk6zgo:

--- Quote from: A.Z. on May 16, 2022, 07:16:19 pm ---
--- Quote from: gbynum on May 16, 2022, 06:53:03 pm ---
--- Quote from: jjoonathan on May 16, 2022, 01:53:39 pm ---Guess: teflon dielectric, copper conductor, 100MHz.

--- End quote ---
I doubt Teflon was around in 1929 :)

--- End quote ---

but nylon was...

--- End quote ---
Nylon sucks as a dielectric.
Air dielectric coax cables used various spacers, including Perspex, & porcelain.
The former was used up to the 1950s in some coax I have seen.

vk6zgo:
Medium wave broadcasting used a plethora of impedances, from 600 \$\Omega\$, to 200 \$\Omega\$, depending on the open wire line used.
One place I worked at, used  a "6 wire" cable, consisting of two paralleled conductors mounted on a standoff insulator, with four conductors at earth potential, mounted on a square steel frame surrounding them.---sort of "ersatz" coax! ;D

E Kafeman:

--- Quote from: radiolistener on May 16, 2022, 10:18:55 pm ---
--- Quote from: E Kafeman ---An ideal a 1/2 wave center-feed dipole antenna in free space have an impedance around 83 Ohm.

--- End quote ---
No, ideal half-wave dipole with center feed and wire thickness 0.001 wavelength placed in a free space has Z = 73.1 + j*42.5 Ω.

--- End quote ---

There is no NO except No, You is very misunderstanding, it is all too basic knowledge if you know anything about antenna math. If you want to accuse someone having wrong, do you need to have own knowledge and in this case at least know anything about wave math.

I'll try to explain at a low level:

Circle chart with 2π circumference and it related math is where it often start when learning wave theory at school,  how waves behaves and related math expressions such as: 32+4i2=52. i is a way to tell it is an imaginary value.
Even more basic can it be written (3X,4Y).
3 and 4 express a position in a 2D coordinate system. It is an rectangular expression for the actual value which have a length of 5. It is same relations for an dipole antenna impedance. Assume 72+j42 as complex impedance. Impedance value is then 83.3 Ohm (722x422=83.32).

73.1 + j42.5 Ω is a expression in rectangular form, in a coordinate system.  It describes in this case an impedance with a vector value of 84 Ohm.
Ideal impedance value with added exemptions for air dielectric for this dipole is around 83 Ohm expressed as an vector length.
Using your rectangular numbers "73.1 + j42.5 Ω", then is "84.6 Ω ∠30.2o" same value expressed as impedance with an specified angle. Many calculators have inbuilt translators between these math forms so it is not complicated to calculate.

These angles are expressed in degrees but can also be expressed in radians which often is to prefer when doing antenna calculations or any wave related calculations. A circle with circumference 2π radians is perhaps remembered?
Typical half-wave dipole antenna impedance with air as dielectric is an absolute vector length with a value around 83 Ohm and with an angle of "π/6", which can be expressed in this form "83Ω ∠ π/6".
Radian is of very basic and usable angle-value when calculating impedance in any form related to antennas.

Another kind of impedance is characteristic impedance in free space which is approximated to 120π Ohm. No need to specify angle for that value as it already is stated in its expression but it can be written including angle.

radiolistener:

--- Quote from: E Kafeman on May 18, 2022, 07:15:38 pm ---You is very misunderstanding, it is all too basic knowledge if you know anything about antenna math. If you want to accuse someone having wrong, do you need to have own knowledge and in this case at least know anything about wave math.
--- End quote ---

What do you mean when you're talking about "misunderstanding"?

I calculated radiation resistance value according to the math taken from old-school antenna modelling books, here is the formula which I used for a center-feed half-wavelength dipole:

Za = Ra + j*Xa

where

Ra = (Zenv / (2*pi)) * ((EulerGamma + log(2 * k * l) - Ci(2 * k * l) + cos(2 * k * l) / 2 * (EulerGamma + log(k * l) + Ci(4 * k * l) - 2 * Ci(2 * k * l)) + sin(2 * k * l) / 2 * (Si(4 * k * l) - 2 * Si(2 * k * l))));

Xa = (Zenv / (2 * pi)) * (Si(2 * k * l) + sin(2 * k * l) / 2 * (EulerGamma + log(k * l) + Ci(4 * k * l) - 2 * Ci(2 * k * l) - 2 * log(l / r)) + cos(2 * k * l) / 2 * (2 * Si(2 * k * l) - Si(4 * k * l)));

Zenv = sqrt( (μ0*μ) / (ε0*ε) );

k = 2 * pi / lambda

Za - antenna impedance
Ra - active part (due to antenna radiation)
Xa - reactive part (due to reflection from environment)
Zenv - environment impedance (around antenna)
k - wave number
l - dipole arm length
r - dipole arm conductor radius
lambda - wave length
μ0 - vacuum permeability constant
ε0 - vacuum permittivity constant
μ - environment relative permeability
ε - environment relative permittivity
EulerGamma - Euler-Mascheroni constant
Si(x) - sine integral function
Ci(x) - cosine integral function

For vacuum μ=1 and ε=1, so Zenv = 376.73 Ω.
For air μ=1 and ε=1.0006, so Zenv = 376.62 Ω.
As you can see air environment impedance is almost the same as for vacuum (free space).

For a half-wave dipole I got result as Za = 73.1 + j*42.5 Ω.
If you don't believe, you can check my calculations.

To calculate Ci(x) and Si(x) you can use Casio online calculator: https://keisan.casio.com/exec/system/1180573427

For example, if you open the book "ANTENNA THEORY ANALYSIS AND DESIGN, Constantine A. Balanis, Wiley 2005", you can find exactly the same radiation impedance value for a center-feed half-wave dipole, see chapter 4.6 HALF-WAVELENGTH DIPOLE, page 184. See picture in attachment. You can find the same value using different approach, include induced EMF method.

Exactly the same value 73 + j*43 Ω for a half-wave dipole is mentioned in different sources, so I think my calculations are correct. Isn't it?

Of course that math doesn't include thermal loss in the antenna radiator conductor, but since it is small enough we can ignore thermal losses due to radiator heating in that discussion.


--- Quote from: E Kafeman on May 18, 2022, 07:15:38 pm ---73.1 + j42.5 Ω is a expression in rectangular form, in a coordinate system.  It describes in this case an impedance with a vector value of 84 Ohm.

--- End quote ---

Za = 73.1 + j*42.5 Ω is antenna radiation resistance of the half-wave dipole.
Active part Ra=73.1 Ω here describes resistance due to energy loss for antenna radiation.
Reactive part Xa=42.5 Ω here describes resistance due to energy reflection from environment.

This is what I'm talking about when I said about 73.1 + j*42.5 Ω. You're needs to match coax feeder impedance with that 73.1 + j*42.5 Ω value. Not with 84 Ω.

I'm not sure what is the reason to mention about impedance modulus 84 Ω in context of antenna matching with coax feeder. Can you explain please?


--- Quote from: E Kafeman on May 18, 2022, 07:15:38 pm ---Circle chart with 2π circumference and it related math is where it often start when learning wave theory at school,  how waves behaves and related math expressions such as: 32+4i2=52. i is a way to tell it is an imaginary value.
Even more basic can it be written (3X,4Y).
3 and 4 express a position in a 2D coordinate system. It is an rectangular expression for the actual value which have a length of 5. It is same relations for an dipole antenna impedance. Assume 72+j42 as complex impedance. Impedance value is then 83.3 Ohm (722x422=83.32).
--- End quote ---

We all know about complex numbers and Polar/Cartesian coordinate system. But if you use scalar length 83 of a complex impedance vector 73+j43, you will lose important things (related to wave flow direction) which is very mandatory for impedance matching. Because 73 Ω and 43 Ω here have different meaning. 73 Ω here is resistance due to energy loss for antenna radiation. While 43 Ω is reactance due to reflected wave, note - this is not energy loss. This reflected wave flows back from antenna to the source. With proper impedance matching you can catch reflected wave energy and push it back into antenna again.

Impedance matching is not just about resistance transformation. It also needs to conjugate reactive part of impedance in order to keep reflected wave inside antenna+matching circuit system.

This is why vector antenna analyzer is much more useful for impedance measurement than scalar one.

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