The 4 times rule for matching transformer impedance

Hi all, I have always heard and used the 4 times rule for the impedance of a transformer winding. Example; To match 50 ohms to 400 ohms, the primary inductance should be 200 ohms at the lowest frequency of interest. 4 x 50 = 200 ohms XL. Tonight I'm searching for a reference for the 4 times. I found this;

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The math is more than I can handle, but his conclusion is;

"In this article we have analyzed the impedance transformation properties of broadband RF transformers taking into account the finite inductive reactance of their primary and secondary windings. We have shown that the ?four times the impedance? design guideline for the inductive reactance of the transformer windings yields an impedance transformation that departs from its ?ideal? behavior by no more than 3%, and introduces a phase shift of no more than 14 degrees."

Now some may quibble with the 3% and 14 degrees as being picked out of the air (me) but something needs to be picked and those numbers seems reasonable.

Also, they reference Broadband RF transformers,

Can I assume that scales to audio transformers?

Mikek

Reply to
amdx
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The model applies to the low end of the frequency range. The high end is controlled by other phenomena. In a broadband transformer, the high end is effected by the length of the transmission line of the windings compared to the wavelength and associated phase shift.

For audio transformers, the formula is an usable approximation for the low end, although the leakage inductances of the windings will affect the results, adding attenuation and phase shift earlier when going toward the low end of the frequency range.

--

Tauno Voipio
Reply to
Tauno Voipio

Yes, as I understand it, low end frequency response is the first to degrade as the inductance of the winding is decreased.

I understand there is an effect increasing response of the high end by the interwinding capacitance.

My end thought/goal is to match a very high Q crystal radio tank circuit at resonance. The R at resonance could be over 1 Megaohm. So, I'm trying to find out, do I need a primary impedance of 4 times

1 megaohm? Then I would add a secondary winding with taps to reflect back the 2000 ohm headphone. The best transformers in the crystal radio world seem to be an autoformer with 359 Henries and a UTC 0-15 listed as a 15k to 1Meg transformer. I find no inductance data on the UTC transformer. I want to know Is UTC matching 1 Megaohm at 100Hz using the 4 times rule? That would mean they have an inductance over 2000 Henries. I don't Know about that! The UTC 0-15 transformer is on Catalog Page 16 here,
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I tried ringing it with 470pf and 1290pf, I get a peak but with a Q less than 1 and L of 2550 Henries and 2000 Henries, at 145 and 100 Hz. So I don't know if that is real. The DC resistance is "posted" as 5000 ohms. So Q will be low. I'm not going to measure it because I'm afraid of magnetizing my core. Back to the bench, I'll ring the 15k winding and try extrapolating from that data.

Thanks, Mikek

Reply to
amdx

You are going to _buy_ your audio transformers, right? So let the tranny designer worry about the inductance! Impedance transforms as the square of the turns ratio, in your example, a ratio of 2.8 to 1.

Reply to
Wond

I rang the 15K winding and that data is poor. with 1290pf resonance is 700 Hz, Q=0.83 Calculates to 40 Henries. with 470pf resonance is 800Hz, Q-0.81 Calculates to 84 Henries. Nothing seems right. The self capacitance may be messing with me. Thoughts, Thanks, Mikek

Reply to
amdx

It's just Magic Numbers. Why not -3dB and 45 degrees? Why not -1dB? Why not -20dB?

For wideband amps where you might be wanting to chain a few together, -1 or -2dB is a good compromise because you'll end up with -3dB sooner or later, thus not ending up with an unexpectedly high LF limit. If you need extra pulse flatness, you can crank down the phase margin arbitrarily -- but don't cry if you run out of cores to do it!

Tim

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Seven Transistor Labs 
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Reply to
Tim Williams

!!??

Rewind the damned tank. It's just another transformer!

Better still, if you need impedance transformation in the end, construct the tank as two coupled resonators, each with different taps suiting their external connections. Coupling can be a bridging C, L or proximity (k and stray C).

Tim

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Electrical Engineering Consultation 
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Reply to
Tim Williams

So... you agree the 4 times number is arbitrary, but it does produce a transformer that is pretty darn good as a rule of thumb to wind transformers. This is the first time I ever saw a treatment of the rule.

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Mikek

Reply to
amdx

Why don't you try to find what the Bible says about it, retard.

Reply to
bloggs.fredbloggs.fred

If you are going to capitalize "bible" then you should capitalize "the" as well, retard.

As in The Bible.

But we know that you are full of nothing but babble and pablum. Your post here proves that. Most of your other posts do as well.

Hell, most times you don't even make it past utter retard into pablum level stupidity. But that is the Bloggstard for you.

Reply to
DecadentLinuxUserNumeroUno

No need to be angry. If you don't want to play with me, go home.

The tank is designed to tune the AM band 550KHz to 1700kHz with a variable cap. The design also is built with minimum losses. The working numbers are around 240uh with a 15pf to 365pf variable capacitor. Did you have a different design in mind?

Yep, but you still need to match the headphones to one of the resonating high Q inductors, or the diode, witch also is match best matched to the inductor.

Reply to
amdx

Do you know anything about the 4 times rule? Mikek

Reply to
amdx

Audio transformers generally spec a frequency range based on the

3dB-down points, assuming the primary and secondary are both connected to their specified resistive source/loads. -3 dB is 30% down.
--
John Larkin         Highland Technology, Inc 
picosecond timing   laser drivers and controllers 
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Reply to
John Larkin

There is a simple way: Take the signal out from a tap in the tank coil, instead of from the top. If you want to keep the tank Q, you should also avoid coupling the antenna directly to the tank top end.

Your tank circuit impedance level (or loaded Q) will vary in a wide range along with the tuning, anyway.

--

-TV
Reply to
Tauno Voipio

Hmm... if the graph in the paper holds true, at 3db down the phase angle is 32*. Not that I would hear that.

Thanks, Mikek

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Reply to
amdx

yes, however would you not have a lower voltage on a tap meaning a lower drive to the headphones.

Absolutely, change the station and everything needs to be readjusted. Even the diode is characteristics are chosen depending on signal level.

Thanks, Mikek

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Reply to
amdx

< snip >

I would suggest that you tap the coil on the tank circuit, far enough down to match whatever audio transformer you can get (or possibly just your earphones).

You have a tradeoff between a high impedance tapping point that'll have higher voltage to swamp out the diode drop but will be more difficult to match to, or a lower impedance tapping point that'll match better but will show more loss in the diode.

--
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Reply to
Tim Wescott

As per usual, you have no idea what you're talking about. Take your bubblegum education and go somewhere the idiots give your kind any credence.

Reply to
bloggs.fredbloggs.fred

** The low frequency performance of an audio transformer is dominated by core saturation, so the lower -3dB point is level dependant. Honest makers spec this frequency when tested at half the rated power level.

The primary inductance of a tranny with laminated steel or permalloy core is high and non-linear, long as there is no air gap, so only rarely sets the -3dB point.

.... Phil

Reply to
Phil Allison

BloogsTard makes another pathetic, useless, empty post.

Reply to
DecadentLinuxUserNumeroUno

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