RF transformer turns ratio question

[Chris Wilson]

I have never really understood turns ratio choice for RF transformers. To keep it relevant to what I am doing, let's assume I want to wind an isolation transformer to match the 50 Ohm output impedance of my 136 kHz (yes KILOHERTZ, this is LF ) amp to my antenna and loading coil which also offers 50 Ohms.  How do I decide how many turns on say a toroidal core, or an E core? 4T on the primary, 4T on the secondary? 20T on each?? I am not understanding how to optimize the number of turns. I assume once I know how to work out the "best" number of turns this will work for other transformers matching disparate impedances??

Finally, I have wound an RF auto transformer using 8T primary and 20T secondary. To give a very crude Litz wire effect I used 4 off pieces of 0.7mm OD enameled wire laid and wound neatly side by side on an E core for the 8T primary as it sees more current, and 2 off pieces of similar wire side by side for the 20T primary. I interleaved them for better "transformer action" (insert correct term.... ).

Instead of laying the wires side by side, would it have made any difference (for better or worse?) to twist them?

Thanks.

[Fank1]

Hi Chris:
In order to achieve "transformer action" the inductive reactance of the winding should be 4 or 5 times the impedance of the driving circuit.
For 50 ohms I always want the winding reactance to be about 250 ohms. At 137 kHz this works out to about 300 uH. How many turns depends upon your core.
The impedance ratio is to the square of the turns ratio, That is 1:1 ratio will give 50 ohms our for 50 ohms in. A 1:2 ratio will give you 200 ohms out.

As for interleaving you will get considerable capacitive coupling between the windings also, probably not a good thing.
Jerry

[BigBoss]

The impedances should principally be equal to source and load impedances.So, if your transformer is used to match-let say-50 Ohm to 200 Ohm, turn ration will be 2 and impedance transformation ratio will be square of this turn ratio so it'll be 4.

For 50 Ohm, the inductance value should equal to 50 Ohm @ operating frequency,similarly 200 Ohm inductive reactance should be provided @ operating frequency.

This is because of "Maximum Power Transfer Theorem"

However the facts are not so easy as spoken.Coupling inter-capacitances,core and copper losses,eddy losses etc. shift the calculated value to another value and this cannot unfortunately be easily predicted and simulated.
But that may be a starting point for your way, then you try and cut. 

[T3sl4co1l]

Hi Chris:
In order to achieve "transformer action" the inductive reactance of the winding should be 4 or 5 times the impedance of the driving circuit.
For 50 ohms I always want the winding reactance to be about 250 ohms. At 137 kHz this works out to about 300 uH. How many turns depends upon your core.

Additionally, you need enough turns to avoid saturation.  This is not very relevant to small signal or high frequency applications, but it is necessary in your case.

Saturation occurs when the flux density goes too high.  What's flux density?  It is:
B = Vrms / (4.44 * Ae * N * F)
Ae is the core effective cross sectional area (it's in the datasheet), N is the number of turns, F is the frequency, and Vrms is the sine wave voltage applied to that winding.

Just rearrange for N to get turns.

Most ferrites saturate in the 0.3 to 0.45T range (depends on exact material type).  Typically, you want B under 0.2T, which also keeps the material from getting too hot (losses depend on B, too).

At 137kHz, a "power" ferrite like #77 is fine.  You will probably find that designing for 0.2T will also satisfy the impedance requirement.

Tim