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Self Resonant Frequency in a Solenoid

  1. Apr 20, 2009 #1
    Hey guys,

    As a hobby I've decided to pick up EE and I've been reading quite a bit and I'm interested in building some basic circuits and determining the SRF in some coils that Ive wound.

    I have found that you can calculate SRF using this formula:
    .........29.85 x (H/D)
    F = -------------------
    ...............N x D

    I dunno if this will post right, it should be (H/D) to the power of (1/5)

    F= self resonant frequency in Mhz of an 'isolated' coil
    H= coil height in meters
    D= coil diameter in meters
    N= total number of turns

    I'm confused about this formula though, what is "coil height"?

    Its obviously not the diameter since that is covered with another variable - If it is the "Length of the coil", is that the unwound length of the wire? or the physical length of the actual coil itself?


    This formula will give you 1 value as a function of the properties of your coil. So obviously there is only 1 SRF for a given coil.

    So why arnt the harmonics of that SRF also in resonance? I ask this because these harmonic frequencies are sort of in the same phase as the SRF. Obviously I've missed something though.

    Can anyone point me in the right direction?

    Thanks in advance!
  2. jcsd
  3. Apr 20, 2009 #2


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    That is an interesting formula.

    The "height of a coil" apparently has the coil resting on one end and refers to the height of the coil as a wound coil if you do that.

    The resonance of the coil depends on its stray capacitance which is mainly due to the capacitive coupling between adjacent turns of the coil. It is also the capacitance to all other coil turns but the adjacent coil effect is the most important.
    So, your formula would probably only apply for one size wire with a particular insulation.

    It would be very useful to include the spacing of the turns as this has a huge effect on the capacitance. Even if the turns are close-wound, there will be insulation on the wire which provides spacing. Increasing the spacing increases the resonant frequency but also reduces the inductance for a given length of former.

    re your other query: The coil will have only one parallel resonant frequency and this will not react to harmonics of that frequency. If your signal generator has harmonics from lower frequencies, the coil will react to those if they land on the coil's resonant frequency.
    Harmonics of the resonant frequency are sometimes in phase with the fundamental but often out of phase with it, so they dont provoke resonance
  4. Apr 20, 2009 #3
    Thanks very much for your reply

    lol sounds like there's a better way to determine the SRF of a coil...

    Yea, sounds like there's another formula that I should be using...

    Ahh, thats helpful thanks :)

    I guess I should just say what I'm doing - that might make it easier... I'm trying to build a tank circuit to resonate at its SRF - I'd like to know how many turns to make the coil so the SRF is my desired frequency. Lets say 35KHz

    Id then like to take that frequency and feed it to the grid on a triode for amplification but lets just focus on how to generate that frequency... I suppose, to start with, I need to know the proper formula for calculating that?

    Thanks again for your help :)
  5. Apr 21, 2009 #4


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    You would not depend on the self resonant frequency to tune a tuned circuit.
    You would have a parallel capacitor that had some variable component to it.

    The self resonant frequency is just an upper limit on the frequency the coil can be used at.
    You never use a coil near its self resonant frequency.

    For example, if you had a coil with 0.455 mH inductance, it would resonate with a capacitor of about 0.045473 uF at 35 KHz. At such a low frequency, you have to have big coils and capacitors.
    So, you might get a 470uH inductor at an electronics store (unless you really wanted to make one). Then you would get a 0.039 uF capacitor and a 0.0056 uF and put them and the coil in parallel. Test with a signal generator and adjust the capacitance until you get resonance by adding or subtracting capacitance. If the signal generator's low impedance, add a 100K resistor in series with it so that the low impedance doesn't damp the resonance.

    It is actually easier to test for resonance if you put the coil and capacitor in series and look for a big resonance peak at the junction of the two. You may need to put a small resistor (50 ohms?) across the output of the signal generator.

    If you wanted to make a coil yourself, you could try using potcores. I wound 30 turns on one and got an inductance of 1500 uH which is a lot more than I calculated above.
    This would resonate with 0.013785 uF at 35 kHz. 30 turns is a very easy coil to wind.

    Resonance formula:
    .........................................L = 25330 / (F^2 * C)

    .................................where L is in uH, C is in pF, F is in MHz
  6. Apr 21, 2009 #5


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    The closest thing I can think of to using a coil at or near its self resonate frequency would be a helical resonator which actually is a tuned circuit. But you are correct, to actually have a coil with connections to each end it is unlikely a good design would ever depend on self resonance.
  7. Apr 21, 2009 #6


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    Hi Phantasm, are you sure that the exponent in the numerator of that equation is (1/5) and not (1/2)? I just did a quick and nasty calculation to test whether that equation looked correct (calculating L and C and folding constants and making a liberal amount assumptions where necessary) and I got something very similar to your equation but with a (1/2) exponent where you had the (1/5). Do you have a reference for that equation?

  8. Apr 21, 2009 #7
    No, I'm not sure at all lol

    Like I said I'm just interested in learning about this stuff and I found that formula.. Then I thought "No, I ought to talk to some people who know what theyre talking about" and I found these forums

    The forumla came from here:


    I should have made it clear that I doubted that it was of any use...
  9. Apr 21, 2009 #8
    Sorry I didnt mean to conjoin the two concepts - I realize you wouldnt want a design to operate at self resonance.

    That said, self resonance is still interesting to me. So thats why I asked about how to determine it.
    Last edited: Apr 21, 2009
  10. Apr 21, 2009 #9

    Thank you so much! Thats very helpful :)

    It doesnt appear then that the core material for the solenoid has any effect on the SRF - can this be true? I would have thought that higher permeability in a substance would put more load on the circuit and offset the resonance frequency... no?

    Also, what is that constant in the formula that you presented?
    Last edited: Apr 21, 2009
  11. Apr 21, 2009 #10


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    Using a ferrite core for this reduces the number of turns required for a given inductance, but once you have that inductance it will resonate with the same capacitor at a given frequency as any other coil of the same inductance.

    Ferrites have a property of changing their permeability with frequency, so there is usually an element of cut and try when prototyping with them.

    They give good resonance effects and greatly reduce the bulk of the coil. Mine is one inch in diameter and 0.63 inches high.

    Resonance formula:
    .........................................L = 25330 / (F^2 * C)

    .................................where L is in uH, C is in pF, F is in MHz

    The only constant in this equation is the 25530.
    F is the resonant frequency
    C is the capacitance
    L is the inductance

    It is an adaptation of the standard formula for resonance but with units suitable for RF applications.
  12. Apr 21, 2009 #11
    Ofcourse - the core material will influence L. My mistake

    yes, the constant 25530, i was just curious where that comes from.. I suppose it isnt really important..

    It makes sense to build some coils and measure the output but knowing the math behind the coil helps me to aim pretty close with my builds

    Thanks again

    I'm going to re-read what you suggested about the voltmeter and signal generator - I have an older signal generator that doesnt tell me exactly what signal its outputting but i should be able to use a high impedance volt meter to register a slight rise in voltage at the SRF did i get that right?
  13. Apr 21, 2009 #12


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    The 25530 is derived from the formula for a resonant circuit:

    F= 1 / (2 * pi * Square root of (L * C))

    When you square both sides you get 4 pi squared on the bottom
    Take the reciprocal of that and you get 0.025330.
    Changing the units to convenient ones gives 25330.

    You should get very obvious resonance peaks.
    Ideally, you should be using a CRO and a frequency counter to check the effects.

    I mentioned before, but should emphasize that the signal generator can influence the resonant effect you see. If it is 50 ohm output impedance and you put it right across the tuned circuit, you won't see any resonance at all, probably. So, it needs to feed via a 100 K resistor to the tuned circuit.

    Why are you making a transmitter for 35 KHz?
  14. Apr 21, 2009 #13
    Ah I see, thanks :)

    Yes my function generator has a 50 ohm output impedance so I'll need to do as you suggest.

    35khz was an arbitrary number really - I'm not really as interested in the output frequency as I am with just how coils function near their SRF
  15. Apr 22, 2009 #14


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    Just rereading your posts, there are a couple of extra items.

    A coil near its self resonance is very sensitive to stray capacitance. You can change it just by putting your hand near it.

    Also, triodes are probably not the best choice for a following amplifier. They have an effect called Miller Effect where the plate-grid capacitance is multiplied by the gain of the triode to appear as input capacitance. So, the coil may have this capacitance across it without you being aware of it.
    I would use a FET as a source follower. Time to get familiar with semiconductors.

    To measure inductance, you could put a capacitor of known value in series with the coil (maybe 0.001 uF) and measure the frequency of the big resonance peak. This is quite spectacular and you get a voltage peak much greater than the voltage you are feeding in.
    You then calculate the inductance from the formula we discussed.
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