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"L Impedance Match" to 50 Ohm Coax

 

Merry Christmas to ALL from Los Angeles, California !!!!

1). Need a Formula for designing an "L Impedance Matching Circuit" for matching 50 Ohms to an Antenna with a known Antenna Input Impedance ? ?( Z ). ?Any Web Sites for referral or Formulas ? ? So far have not found any.

2). Question: ?In winding a Toroid there are many ways to get a Turns Ratio of 3:1, such as - 6 Turns to 2 Turns, 9 Turns to 3 Turns, etc. ? Is there a "GENERAL RULE" for determining the number of Turns that is best ?? ? [ I believe EACH winding on the Toroid needs to operate below it's Self Resonant Freq inorder to act as an Inductor. ? ?Maybe for a "Broad Band" Toroid, a Higher Number of Turns ( increases R ) is better because it lowers the Q = Xl / R of the Inductor ??

Any Comments and Help would be APPRECIATED !!!! ? ? ?THANK YOU

Garey Wittich
 

Why not use SIMNEC 2.5, this versatile tool from AE6TY does the job, including the transmission line and much more. Lots of support and tutorials available.
?
?
If you want to do the calculations on your own, her are the formulas:
?
regards, Fred
 

I suggest you try The free program
TLW which can match using several different methods like L, T, and Pi.
?
 

For a broadband transformer the “rule of thumb” is that the reactance of the low impedance winding should be 4x the impedance ?at the lowest frequency of operation. So for a 50 to 450 ohm transformer operating down to 4 MHz. you need a reactance of 200 ohms at this frequency. ?So you calculate the inductance required and the number of turns. ?If 5 turns are required then you need 15 for the other winding.?
 

There is a thermodynamic problem embedded in the design a broadband antenna matching network, named "entropy". The issue is well covered by:
?
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Microwave_and_RF_Design_III_-_Networks_(Steer)/07%3A_Chapter_7/7.2%3A_Fano-Bode_Limits
?
or as an actual software based broadband automated calculation, here:
?
?
However, below 30 mhz, the ever present background noise is many times the universal thermal/Black-body noise, especially if you are living in an urbanized area.
?
Without playing with the math, if you need to change impedance of an electronic circuit (exempting transformers), you will get to the idea of "Q", which is roughly the ratio of reactance to resistance at a single frequency. "Q" also is the inverse of bandwidth in a network. . . That exchange occurs when you passively transfer between impedances, which also forces an exchange of bandwidth.
?
There is an transformer configuration network called a Brune network that creates a "negative inductance". (With apologies to every reader who has done a manual root extraction and wound up with the "beast".)
?
?
?
Here is a link to a Motorola app note from the early days of bipolar power RF transistors (like 2N3375):
?
?
I recall that someone implemented an internet site that automated the various equations in the AN721 app note but the page has morphed into a "404 error".
?
?
As for your transformer, the "Wayback machine" has a copy of the 2001 article:
"Fabricating Impedance Transformers for Receiving Antennas" which was on the web at:?
?
?
I had to go thru the "Wayback Machine" to see a copy of the original pdf.
?
Usually below 30 mhz, the background and man-made electrical noise is 20 db (or more!) above thermal noise and precise receiver impedance matching is a waste of time. A loss of capital and effort that could have been used tuning for signals. Above 50 mhz, the noise figure becomes more important as does the height of your antenna and time of year (E-skip!).
?
Anyway, for those that got to the bottom of the reply, the math used above is why you were taught "synthetic division" of polynomials back in junior high school. . .
?
Jim/VEZ
?
 



"Fabricating Impedance Transformers for Receiving Antennas"? is available at IRCA Reprints, #A-155, index at? https://dxer.ca/images/stories/2019/irca-reprint-index.pdf?

https://dxing.info/? also still has a copy, I believe.

best wishes,

Nick


?

On Thu, 26 Dec 2024 10:11:46 -0800, "James Redding WA9VEZ via groups.io" <wa9vez@...> wrote:
?
There is a thermodynamic problem embedded in the design a broadband antenna matching network, named "entropy". The issue is well covered by:
?
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Microwave_and_RF_Design_III_-_Networks_(Steer)/07%3A_Chapter_7/7.2%3A_Fano-Bode_Limits
?
or as an actual software based broadband automated calculation, here:
?
?
However, below 30 mhz, the ever present background noise is many times the universal thermal/Black-body noise, especially if you are living in an urbanized area.
?
Without playing with the math, if you need to change impedance of an electronic circuit (exempting transformers), you will get to the idea of "Q", which is roughly the ratio of reactance to resistance at a single frequency. "Q" also is the inverse of bandwidth in a network. . . That exchange occurs when you passively transfer between impedances, which also forces an exchange of bandwidth.
?
There is an transformer configuration network called a Brune network that creates a "negative inductance". (With apologies to every reader who has done a manual root extraction and wound up with the "beast".)
?
?
?
Here is a link to a Motorola app note from the early days of bipolar power RF transistors (like 2N3375):
?
?
I recall that someone implemented an internet site that automated the various equations in the AN721 app note but the page has morphed into a "404 error".
?
?
As for your transformer, the "Wayback machine" has a copy of the 2001 article:
"Fabricating Impedance Transformers for Receiving Antennas" which was on the web at:?
?
?
I had to go thru the "Wayback Machine" to see a copy of the original pdf.
?
Usually below 30 mhz, the background and man-made electrical noise is 20 db (or more!) above thermal noise and precise receiver impedance matching is a waste of time. A loss of capital and effort that could have been used tuning for signals. Above 50 mhz, the noise figure becomes more important as does the height of your antenna and time of year (E-skip!).
?
Anyway, for those that got to the bottom of the reply, the math used above is why you were taught "synthetic division" of polynomials back in junior high school. . .
?
Jim/VEZ
?
 

There is an updated version of John Bryants transformer paper:
?
?
regards, Fred
 

Just a quick gauge on thermal noise vs. antenna noise:

Define (ONLY for the purpose of simplicity) "antenna noise" as the increase in receiver noise experienced by connecting your combination antenna and feedline to your receiver regardless of frequency.? Again, this definition is ONLY for the sake of simplicity and keeping math out of the argument.

If your "antenna noise" is greater than a 50 ± j 0 load at room temperature attached instead of the feedline, don't bother with matching or worry about mismatches or preamps.? You are antenna noise limited and no preamp or other means of matching can or will improve that.? In reality, even a good preamp can and will degrade the noise performance and possibly also dynamic range.

A bit more:? A matched load produces 3 dB of thermal noise.? With a good receiver and a well designed and quiet front end, that 3 dB is just detectable.? However, as stated in the original email, at HF frequencies and many times even 50-MHz, the real antenna noise exceeds this 3 dB of thermal noise.?

Dave - W?LEV


On Sat, Dec 28, 2024 at 10:05?PM Nick Hall-Patch via <nhp=[email protected]> wrote:


"Fabricating Impedance Transformers for Receiving Antennas"? is available at IRCA Reprints, #A-155, index at? ?

? also still has a copy, I believe.

best wishes,

Nick


?

On Thu, 26 Dec 2024 10:11:46 -0800, "James Redding WA9VEZ via " <wa9vez=[email protected]> wrote:
?
There is a thermodynamic problem embedded in the design a broadband antenna matching network, named "entropy". The issue is well covered by:
?
?
or as an actual software based broadband automated calculation, here:
?
?
However, below 30 mhz, the ever present background noise is many times the universal thermal/Black-body noise, especially if you are living in an urbanized area.
?
Without playing with the math, if you need to change impedance of an electronic circuit (exempting transformers), you will get to the idea of "Q", which is roughly the ratio of reactance to resistance at a single frequency. "Q" also is the inverse of bandwidth in a network. . . That exchange occurs when you passively transfer between impedances, which also forces an exchange of bandwidth.
?
There is an transformer configuration network called a Brune network that creates a "negative inductance". (With apologies to every reader who has done a manual root extraction and wound up with the "beast".)
?
?
?
Here is a link to a Motorola app note from the early days of bipolar power RF transistors (like 2N3375):
?
?
I recall that someone implemented an internet site that automated the various equations in the AN721 app note but the page has morphed into a "404 error".
?
?
As for your transformer, the "Wayback machine" has a copy of the 2001 article:
"Fabricating Impedance Transformers for Receiving Antennas" which was on the web at:?
?
?
I had to go thru the "Wayback Machine" to see a copy of the original pdf.
?
Usually below 30 mhz, the background and man-made electrical noise is 20 db (or more!) above thermal noise and precise receiver impedance matching is a waste of time. A loss of capital and effort that could have been used tuning for signals. Above 50 mhz, the noise figure becomes more important as does the height of your antenna and time of year (E-skip!).
?
Anyway, for those that got to the bottom of the reply, the math used above is why you were taught "synthetic division" of polynomials back in junior high school. . .
?
Jim/VEZ
?



--
Dave - W?LEV
 

Agreed, and you need 3dB more noise with an actual antenna connected at any specific frequency, in order to ensure that your antenna is constrained by your local noise floor, so a 6dB rise in noise relative to a 50 ohm load should be aimed for.
?
Regards,
?
Martin
?
On Sun, Dec 29, 2024 at 04:11 PM, W0LEV wrote:

However, as stated in the original email, at HF frequencies and many times even 50-MHz, the real antenna noise exceeds this 3 dB of thermal noise.?

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