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There is a thermodynamic problem embedded in the design a broadband antenna matching network, named "entropy". The issue is well covered by:

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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

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or as an actual software based broadband automated calculation, here:

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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.

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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.

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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".)

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Here is a link to a Motorola app note from the early days of bipolar power RF transistors (like 2N3375):

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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".

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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:?

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I had to go thru the "Wayback Machine" to see a copy of the original pdf.

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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!).

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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. . .

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Jim/VEZ

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