# impedance

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

1. ### exxosGuest

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 LittleGuest

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. ### exxosGuest

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 LittleGuest

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. ### Watson A.Name - Watt SunGuest

Without the voltage, the impedance cannot be determined.
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6. ### H. DziardzielGuest

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
range look at a switching power supply transformer in a (e.g). pc.
Otherwise, low frequency radio transmitter design..

7. ### exxosGuest

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 LittleGuest

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