A little thin on details.
Hi,
I'm sure you have a specific condition in mind, but you haven't included enough details for a good answer but, here are some suggestions.
A real transformer can be thought of as an ideal transformer with a parasitic inductor in parallel with the primary (or optionally the secondary because it's an ideal transformer).
Think about this a second. If I have an ideal transformer with a 1:2 turns ratio, whatever voltage is on the primary appears 2X on the secondary. conversely whatever voltage is on the secondary is reflected 1/2X to the primary. It's ideal (magic) so these conditions are magically enforced. Besides magically transforming voltage, an ideal transformer also magically transforms energy (and power).
So.... Say we have an ideal 1:2 transformer with 1VDC on the primary (an ideal transformer transforms frequencies down to DC), and a 1 Ohm load on the secondary, we'll see 2VDC on the secondary. 2V/1Ohm=2A. The load power is 2V*2A=4W. The ideal transformer (for all it's magic) can't create or destroy energy (or power), so there is 4 W going into the primary. If we were to replace the ideal transformer and real secondary with a load that drew an identical current (and power), we would replace it with 1/4 Ohm. 1V^2/(1/4Ohm)=4W.
Your specification is for a transformer that steps 10 volts to 200 volts. No problem except that the current going into the primary will be 400 times the current coming out of the secondary.
And then there's that parasitic inductance in parallel with the primary. The real primary you create will have a real inductance in parallel with the ideal transformer turns ratio. The inductance of the primary will be determined by the formulas in your physics book for a coil with the geometry you wind the coil in. Inductance is increased by the number of turns, and by the radius of the coil.
The lowest frequency the transformer needs to amplify dictates the impedance of the primary coil. The real inductance of the primary coil impedes the primary voltage at the lowest frequency to be seen at the primary, so that the current through the real inductance of the primary follows ohms law. If at the lowest frequency of interest, the inductance of the primary is 1 ohm, and the applied signal is 1 volt, there will be 1 amp of current flowing in the real primary with no load on the secondary. Add the secondary current * 1:N^2 to get the total real current in the primary.
You specified an air core, so just put 20 strands of wire with the primary strand in a loop. increase the loop radius or number of turns such that the no load current in the primary is acceptable. Then put all the secondary strands in series to get the desired output voltage. You may need to twist the bundle together to get close to ideal coupling between primary and secondary. There is no mention of how many volts may appear between the primary and secondary. Twisting the primary and secondary together may be a no-no.
So, given no real info about what you really want, I'd say take a piece of #12 insulated house wire and put 1000 turns around a plastic barrel for the primary. Put 20,000 turns for the secondary. at 25MHz this might work, but the parasitic capacitance from turn to turn of the primary (and secondary) might make it not work. When you get done with that, try an active circuit with some transistors or even a tube. This will be much easier especially since your source probably can't deliver the required current stepped up by 20X.
M
Hi,
I'm sure you have a specific condition in mind, but you haven't included enough details for a good answer but, here are some suggestions.
A real transformer can be thought of as an ideal transformer with a parasitic inductor in parallel with the primary (or optionally the secondary because it's an ideal transformer).
Think about this a second. If I have an ideal transformer with a 1:2 turns ratio, whatever voltage is on the primary appears 2X on the secondary. conversely whatever voltage is on the secondary is reflected 1/2X to the primary. It's ideal (magic) so these conditions are magically enforced. Besides magically transforming voltage, an ideal transformer also magically transforms energy (and power).
So.... Say we have an ideal 1:2 transformer with 1VDC on the primary (an ideal transformer transforms frequencies down to DC), and a 1 Ohm load on the secondary, we'll see 2VDC on the secondary. 2V/1Ohm=2A. The load power is 2V*2A=4W. The ideal transformer (for all it's magic) can't create or destroy energy (or power), so there is 4 W going into the primary. If we were to replace the ideal transformer and real secondary with a load that drew an identical current (and power), we would replace it with 1/4 Ohm. 1V^2/(1/4Ohm)=4W.
Your specification is for a transformer that steps 10 volts to 200 volts. No problem except that the current going into the primary will be 400 times the current coming out of the secondary.
And then there's that parasitic inductance in parallel with the primary. The real primary you create will have a real inductance in parallel with the ideal transformer turns ratio. The inductance of the primary will be determined by the formulas in your physics book for a coil with the geometry you wind the coil in. Inductance is increased by the number of turns, and by the radius of the coil.
The lowest frequency the transformer needs to amplify dictates the impedance of the primary coil. The real inductance of the primary coil impedes the primary voltage at the lowest frequency to be seen at the primary, so that the current through the real inductance of the primary follows ohms law. If at the lowest frequency of interest, the inductance of the primary is 1 ohm, and the applied signal is 1 volt, there will be 1 amp of current flowing in the real primary with no load on the secondary. Add the secondary current * 1:N^2 to get the total real current in the primary.
You specified an air core, so just put 20 strands of wire with the primary strand in a loop. increase the loop radius or number of turns such that the no load current in the primary is acceptable. Then put all the secondary strands in series to get the desired output voltage. You may need to twist the bundle together to get close to ideal coupling between primary and secondary. There is no mention of how many volts may appear between the primary and secondary. Twisting the primary and secondary together may be a no-no.
So, given no real info about what you really want, I'd say take a piece of #12 insulated house wire and put 1000 turns around a plastic barrel for the primary. Put 20,000 turns for the secondary. at 25MHz this might work, but the parasitic capacitance from turn to turn of the primary (and secondary) might make it not work. When you get done with that, try an active circuit with some transistors or even a tube. This will be much easier especially since your source probably can't deliver the required current stepped up by 20X.
M
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