Capacitance between adjacent coils?

[hobbs125]

Hi everyone.

I am trying to determine the capacitance between two adjacent coils.

Each coil is identical, made of 20 awg wire consisting of 10 layers of 20 turns each, spaced about 1 inch apart and wound on a 1 1/2 inch diameter coil former.

How would I go about finding/calculating the capacitance per unit area so I can model the coils as a transmission line?

Any help here will be greatly appreciated:)

 

[Baluncore]

A transmission line will be very poor model of those coils because being multiple layers they have a complex internal capacitance.

There would be many transmission line modes available.

If the coils were treated as lumps of inductance then the capacitance between the coils could be calculated on the assumption that each coil was a rectangular plate, separated by a parallel gap.

What are you trying to do here?

 

[hobbs125]

Thanks for the reply.

I am trying to make a 1/4 wave impedance transformer.

Just wondering how to go about doing it. And how to calculate things correctly.

 

[Baluncore]

More information will be helpful.

I am trying to make a 1/4 wave impedance transformer.

That requires you know;
The centre frequency?
Is it a single frequency or does it need some bandwidth?
The source impedance?
The load impedance?
Is it a single sided or a differential signal?

Your transformer will have a length of ¼ wavelength, (adjusted for velocity factor),
and an impedance that is close to the geometric mean of the source and load impedances.

 

[hobbs125]

I'm actually trying to design a tlt to use for low frequency range. I know. ... bad idea... the line will be very long with all kinds of problems etc.

I just want to see if it's possible. The initial problems i see with pulsing with low frequency are that the impedances in the circuit will be more frequency dependent.

The center frequency will be 50kHz unidirectional pulses. The source impedance will be about 10k ohms at that frequency. The load impedance is about 300 ohms.

So, I know I need the tlt (common mode) to have a Zo of sqrt 10,000 x 300 = 1700 ohms at the center frequency. The problem is, how do I go about designing it?
I know I will need a total length equal to 1/4wave and I know how to calculate that. But how do I calculate/estimate the Zo of the tlt?

Also, will it even be possible to get a match at 50kHz or will the frequency dependent impedances prevent it?

How do I design it to have a more broadband response?

 

[Baluncore]

My recommendation is that you avoid transmission lines at 50 kHz. The necessary line length of about one km results in high losses because a ¼WT relies on internal reflections to operate. The effect of line resistance is therefore significantly increased.

There are a many ways to make a good matching network at 50 kHz.

You should start by considering a simple network. See this calculator; http://home.sandiego.edu/~ekim/e194rfs01/jwmatcher/matcher2.html

Obviously you could use a ferrite core transformer. The weight of a ferrite core at those frequencies is often much less than you might expect for the same power at 60 Hz or audio frequencies. The impedance ratio is 33.3 so the turns ratio will need to be 5.77 which comes out at say 23:4, 52:9 or 75:13.

You could also use lumped inductance and capacitance over several stages to make a high pass filter with the required impedance transformation. The principle is similar to a series of ¼ wave transformers, but each stage or section of the filter lowers the impedance by another sub-GM step.

Only half as many inductors are needed for a single sided lumped line signal path. Is your signal one sided or balanced differential?

How wide does your bandwidth at 50 kHz need to be?
How much power are you expecting to transmit?

 

[Baluncore]

QWTs are inherently narrow band devices. If you have short pulses at 50 kHz pulse repetition rate, only the fundamental will pass the QWT.

To pass pulses you will need a wideband transformer or a ladder of high pass filters.
You need to know the spectrum or Fourier coefficients of the pulse you wish to transform.

If the shape of your pulses is important you will need to use a pulse shaping network.

You could also sharpen your pulses by using a non-linear transmission line.

 

[hobbs125]

Thank you for the replies. I wish I had your knowledge. I might have had my circuit working months ago.

I read using a magnetic core increases the effective line length. When taking that into account the length can be reduced by a factor of 45 given the permeability is 2000. So I still wonder if it's possible or just too complex.

I need the bandwidth to be about 500Hz.
Power is going to be 50 watts.

And yes I do need a good clean waveform. That is one reason why I was looking at using a tlt. I was hoping for it to perform a dual purpose, impedance transformation as well as pulse shaping.

Never heard of a non linear tlt so I'll go and do some reading. Thanks for the suggestions so far.

 

[hobbs125]

One question though:

If I use two coils wound on the same core but with a space between them wouldn't the equivalent circuit be a ladder of lc filters with different capacitances?

Just my thinking but if you compare the same turn on each coil then the distance between turns would vary (if you started winding each coil on opposite ends then worked them towards each other) which would result in a changing capacitance...

 

[Baluncore]

Two air cored coaxial coils would have that sort of effect but the coupling would be very hard to control without a magnetic core. I expect the matching would be at a very much higher frequency than 50 kHz.Let's clarify the difference between sine waves and pulses.

A 50 kHz centre frequency with a 500 Hz bandwidth will only pass a sign wave, not a rectangular pulse. That 50 kHz sinewave will take 1/500 = 2 ms to rise or fall. The Q will be about 50,000 / 500 = 100.

A square wave at 50 kHz is made from odd harmonics of the sine wave fundamental at 50 kHz. The 3rd harmonic at 150 kHz will have a 1/3 amplitude, A/5 at 250 kHz, A/7 at 350 kHz … to infinity.
Unless your transformer network passes the first dozen or so harmonics, your rectangular wave will become rounded.

That is why a broadband transformer or a multi-stage high pass filter is needed for pulses.
A QWT will only work with narrow band sine waves because it uses a delayed reflection to operate.

There are various techniques that can make slow wave delay lines. Those are not economic for low pulse rates. They are typically used for delays of a couple of microseconds maximum.

A much better way to perform the impedance transformation might be to take the output of your power amplifier from the emitter circuit of the output transistor, rather than from the collector. Is that an option?

 

[hobbs125]

Ok. What you said makes a lot of sense. Thanks.

And yes, I could take the output from the emitter side. .. what we're you suggesting?

 

[Baluncore]

The collector circuit appears as a high impedance current source so it makes a good voltage amplifier.

An emitter follower acts as a very low impedance so it makes a good current amplifier. Another advantage is that the load appears between ground and the emitter.

Your first stage should have voltage gain to provide the required output voltage. The final stage should be an emitter follower to provide the output current.

By using a power mosfet as your final stage it will generate an output current determined by the output voltage / load impedance without a need for continuous base or gate drive current.