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impedance

Discussion in 'Misc Electronics' started by exxos, Oct 17, 2003.

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  1. exxos

    exxos Guest

    Hi all,

    I have somewhere a chart which lists transformer current and voltage in with
    the impeadance of the winding. For example "Z" will draw 1amp at 100V at
    50Hz, but how is Z worked out ?

    I would like to design a high frequency transformer which will draw say 1amp
    at about 700khz, I need to work out what the inductance would be for the
    coil.

    Anyone help ?

    Thanks,
    Chris
     
  2. Mark Little

    Mark Little Guest

    I think you need to be a bit more specific on what you want. A transformer
    is, as the name implies, something that transforms. To say that you need a
    transformer that draws 1A at 700kHz is actually meaningless. There are two
    components of a transformer's primary (input) current:

    (1) Current needed to overcome the losses in the transformer. This will be
    there irrespective of whether there is any secondaty (output) current; and
    (2) Current needed to drive the output of the transformer. This depends on
    the load connected to the secondary winding.

    Perhaps you are thinking of an inductor, the values for which you can
    determine using the information provided. The impedance is calculated by
    dividing the voltage across the inductor 100V by the current that is flowing
    in the inductor (1A) giving an impedance of 100 ohms at 700kHz. From there,
    you can work out the inducatnce by using the formula for inductive reactance
    (impedance) Z = 2 * PI * Freq * L. Of course this is a theoretical
    calculation and any practical inductor would have to account for magnetic
    and resistive losses.

    Hope this helps,
    Mark
     
  3. exxos

    exxos Guest



    Hi Mark,

    I just quoted the primary rating here, didnt think of the secondary at this
    point. Though say the primary will pull a max of 1amp at 100 volts at
    700khz, the secondary will be setup up by about 10 times to give 10kv 0.1a.
    the value for the primary would be around 40mH, though when secondary is
    added it will be a lot higher which gets to complex for me to work out. As
    long as the whole thing ( assume a secondary short ) does not pull more than
    1amp from the primary then this will probably be what im looking for.

    Thanks,
    Chris
     
  4. Mark Little

    Mark Little Guest

    Chris,
    In a theoretical transformer, the primary current when the secondary is open
    circuit is zero, but in reality, current must flow to generate the magnetic
    field that cuts the secondary winding. The "magnetising current" is governed
    by the "natural" impedance of the primary winding. In theory, the inductance
    can be made very high, reducing the magnetising current. The inductance of
    the primary depends on the permeability of the core and the precision with
    which the coil is wound. What sort of inductance you can achieve will depend
    on the construction method of the transformer. you can't simply keep adding
    turns, since the resistance of the wire will limit the current that can be
    provided and increases the heat in the transformer. It also reduce the
    coupling efficiency with the secondary winding.

    If we assume that the open circuit current of the transformer will be 5% of
    the full load, then the primary current, with open circuit secondary, will
    be 50mA. This means that the inductance of the primary (with no secondary
    load) should be in the order of 2000 ohms at 700kHz which equates to an
    inductance of 0.45mH. Depending on the type of construction, the transformer
    may require more or less more standing drive to achieve the 1A secondary
    current at the desired voltage.

    You will also need to take into account that the high voltage secondary
    winding will be close the low voltage primary winding, so insulation
    breakdown amy be an issue.

    regards,
    Mark
     
  5. Without the voltage, the impedance cannot be determined.
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  6. Note that 700Hz is radio frequency transformer design so normal
    line or even switching transformer design is inadequate due to
    conductor, skin effect , core, and insulation characteristics and
    losses. If loss is not too important and a quick experimental
    start with easily available components is needed at that power
    range look at a switching power supply transformer in a (e.g). pc.
    Otherwise, low frequency radio transmitter design..
     
  7. exxos

    exxos Guest

    Mark,

    The transformer will not have a core, I know the voltage stress will be a
    issue though for the moment I need to work out the inductance values.
    Something alone the lines of 1T primary and 100T secondary. I have a setup
    wich has 12T pri and a large coil with indcutance of about 100mH, this setup
    draws about 4amps at 50V input tot he primary, though the actual inductance
    what the driver circuit sees is somewhat a mystery :-\

    chris
     
  8. Mark Little

    Mark Little Guest

    Chris,
    The inductance of the secondary is essentially unimportant in determining
    the primary current when there is no secondary load (assuming that there is
    only minor losses in the secondary coil.

    The formula for an air core inductor with a single layer has the simplified
    formula (from ARRL handbook) where the length is >= 0.4diameter

    L = (d^2 * n^2)/(18d + 40l)
    Where L is inductance in microhenries, d is the coil diameter in inches, n
    is the number of turns and l is the length of the coil in inches.

    I would suggest that a 12T air coil would be in the order of microhenries.
    This appears to be supported by your measurements, since a 50V drive giving
    4A is an impedance of 15 ohms at 700kHz. This equates to an inductance of
    about 3.4 microhenries which is probably in the right ballpark.

    regards,
    Mark
     
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