The 4 times rule for matching transformer impedance

[amdx]

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;


http://www.scribd.com/doc/116333646/The-Four-Times-the-Impedance-Rule-for-Broadband-RF-Transformer-Windings-Where-Does-it-Originate#scribd

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

[Tauno Voipio]

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

[amdx]

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

> 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.
>

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

> 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.
>

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,
http://www.junkbox.com/electronics/utc_transformer_catalog_1963.pdf
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

[Wond]

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.

[amdx]

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

[Tim Williams]

"amdx" <noj...@knology.net> wrote in message
news:m9f6p8$6gu$1...@dont-email.me...

> 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.

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

--
Seven Transistor Labs
Electrical Engineering Consultation
Website: http://seventransistorlabs.com

[Tim Williams]

"amdx" <noj...@knology.net> wrote in message

news:m9gobk$77s$1...@dont-email.me...

> 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.

!!??

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).

[amdx]

On 1/18/2015 11:24 AM, Tim Williams wrote:
> "amdx" <noj...@knology.net> wrote in message
> news:m9f6p8$6gu$1...@dont-email.me...
>> 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.
>
> 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
>

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.
http://www.scribd.com/doc/116333646/The-Four-Times-the-Impedance-Rule-for-Broadband-RF-Transformer-Windings-Where-Does-it-Originate#scribd



Mikek

[bloggs.fred...@gmail.com]

On Saturday, January 17, 2015 at 9:46:34 PM UTC-5, amdx wrote:
<snip dumb question>

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

[DecadentLinuxUserNumeroUno]

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.

[amdx]

On 1/18/2015 11:27 AM, Tim Williams wrote:
> "amdx" <noj...@knology.net> wrote in message
> news:m9gobk$77s$1...@dont-email.me...
>> 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.
>
> !!??
>
> Rewind the damned tank. It's just another transformer!

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?

> 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).
>

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.

> Tim
>

[amdx]

Do you know anything about the 4 times rule?
Mikek

[John Larkin]

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

jlarkin att highlandtechnology dott com
http://www.highlandtechnology.com

[Tauno Voipio]

On 18.1.15 20:03, amdx wrote:
> On 1/18/2015 11:27 AM, Tim Williams wrote:
>> "amdx" <noj...@knology.net> wrote in message
>> news:m9gobk$77s$1...@dont-email.me...
>>> 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.
>>
>> !!??
>>
>> Rewind the damned tank. It's just another transformer!
>
> 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?

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

[amdx]

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

---
This email has been checked for viruses by Avast antivirus software.
http://www.avast.com

[amdx]

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

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

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

[Tim Wescott]

< 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.

--
www.wescottdesign.com

[bloggs.fred...@gmail.com]

On Sunday, January 18, 2015 at 12:50:14 PM UTC-5, DecadentLinuxUserNumeroUno wrote:
<snip drivel>

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.

[Phil Allison]

John Larkin wrote:

>
> 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.

** 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

[DecadentLinuxUserNumeroUno]

On Sun, 18 Jan 2015 14:39:50 -0800, bloggs.fredbloggs.fred wrote:

> As per usual,

BloogsTard makes another pathetic, useless, empty post.

[Tauno Voipio]

On 18.1.15 23:05, amdx wrote:
>
>>> 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?
>>
>> 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.
>>
>
> yes, however would you not have a lower voltage on a tap meaning
> a lower drive to the headphones.

Yes - the same applies when you scale the impedance down on the
audio side. There is no free lunch ...

--

-TV

[bloggs.fred...@gmail.com]

No originality at all- such a boring nobody of a non-entity- sad.