# transformer ???

Discussion in 'General Electronics Chat' started by Mathematics!, Jan 5, 2010.

1. ### Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
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I am wondering about a few transformer questions

1) say you have a transformer for example one that is 120vac to 12.6vac 60hz 300mA (i.e stepdown transformer)
What happens if you where to use the same voltages with it i.e 120vac for primary and 12.6vac for secondary but you used a different frequency other then 60hz say 2000hz ,...or whatever .... How would this effect the transformer would it lessen the output voltage/current or would it damage the transformer ....etc??? Curious what would happen...
(and how to mathematically figure out what is going to be the voltage/current ...etc with this new frequency we can assume it the transformer is ideal or air cored if you want)

2) say you have a transformer that doesn't give you the coil ratio or the input voltage or output voltage.... It just gives you input is 1kohm+-10%
Is their anyway of finding out the coil ratio , input/output voltage/current , and what frequency range you could use this transformer at?

My thoughts for question one would be based on the inductive reactance calculations of the primary or secondary coil wL as current flows at a faster frequency this would induce a stronger magnetic field and that strong magnetic field would resist current change more....etc ( have stronger reactance)
But I am not positive I got the full picture ...etc?

My thoughts for question two is somehow use the approximation that
Pin = Pout (the ideal transformer ) and the fact that P=VI , V=IZ
so P = I^2*Z or V^2/Z where Z is the 1kohm reactance ,...etc
But ofcourse you only have the 2 reactances and 2 unknown voltages or currents so you would have to at least known the input voltage or current and then you could solve for the missing one.... not really sure if this is the math that accurately would describe it but it seems plausible...?

Thanks for any help

Last edited: Jan 5, 2010
2. ### Paulo540 Member

Nov 23, 2009
188
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While I don't feel qualified to comment on the others, I can say that the turns ratio is the square root of the impedance ratio so 1000/8 = 125 of which the sq root is about 11.2 There are 11.2 times as many turns on the primary as the secondary.

3. ### Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
4
Ok then my math was correct for question 2
And once you have the coil ratio and either the input or output voltage/current you would beable to use the simple math formulas to calculate the other ,....etc

But still wondering for this question one more thing if you have the coil ratio is their anyway to get how many winds they have on the primary and secondary , this could be done in an infinity amount of ways but would all these ways be equivalent in electricial terms...
For instance if the coil ratio was 1/2 then you could make 60 winds on the primary side and 120 on the secondary side or you could make 100 on prim and 200 on secondary ... But would these transformers have the same charactristics in every way or would their be something to distnuish them by?

As for the first question about the frequency I am curious to know if I got the right ideal for this as well ????

Last edited: Jan 6, 2010

Apr 5, 2008
18,867
3,702
Hello,

Take a look at the attached PDF.
It explains the use and types of transformers.

Greetings,
Bertus

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5. ### Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
4
Ok , I read thru the transformer pdf you gave me and that fully answered
the first question... which is what I thought orignally and what Paulo540 confirmed for me.... But now I definitly have the math to answer question one. (what I thought exactly)

In the pdf though it talks about 3 main different types of transformers
It gives a formula for the lowest frequency allowed for an audio transformer ...ie. 10X sqrt(2P/f) on page 6 half way down...

But this still doesn't answer my question on non-audio transformers
And it still doesn't give me a frequency range both lowest and highest frequencies that can be used on main transformers and others.

I am looking for a mathematical way of computing these frequencies based on some properties of the transformer coil ratio , voltage ,...etc
I know inductive reactance is wL and I can figure out the reactance/resistance of the primary coil by Rp = Rs * (Np/Ns)^2
so wL = Rp = Rs * (Np/Ns)^2
=>
wL = 2pi*f*L = Rp = Rs * (Np/Ns)^2

so
f = (1/2pi * L )*Rs * (Np/Ns)^2

so if you know the coil ratio , the secondary reactance/resistance, and the L then you can find the freqency of the primary coil I guess...?
Problem how do you find L ...... I have v = L di/dt but that doesn't help vary much either.........

Seems their is more to the issue for the range of frequencies ...
Fundamentally the resistance of the coil is 2pi*f*L so this is the only thing doing resistance on the primary side so it seems as you up the frequency you up the resistance and that means at a fix voltage you would be reducing the current.... if you lower the frequency then you lower the resistance so more current can flow.....
With more current flowing it would induce a greater magnetic field more magnetic flux so greater voltage in secondary .....

But I am unsure if their is a reason why using different frequencies could damage it and how to mathematically calculate this?

Another question in making a transformer does it matter how many winds the primary and secondary have if they have the correct coil ratio?
What I mean is their is infinitely many ways to make the same coil ratio ... for instance a 1/2 coil ratio can be made with 60 prim / 120sec
or 100 prim / 200sec

I can only see v = N d$\phi$/dt so if you had less turns i.e less N then you would have less voltage ,...implies less power ,...etc
But if you had lowered the turns but upped the changing magnatic flux then you could probably get the equivalent so different turns that give the same coil ratio would be identical provided you made it up with changing flux.... Yes/No? But maybe I am overlooking something...

Thanks for any help

Last edited: Jan 7, 2010
6. ### Paulo540 Member

Nov 23, 2009
188
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Think of just one side of the transformer, they design it so that there is a certain amount of inductance based on desired performance, then create the other side for mutual.

That's my dumb way of looking at it though. Im just throwing that idea out there.

I think it also has something to do with eddy currrents in the core and saturation points.

Maybe someone else can fill in the blanks

7. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
For the low frequency case ...

The primary has to support a voltage without excessive magnetization current flowing. As the frequency reduces the magnetising current increases for a constant voltage input. So one would notionally need to keep the V/f or voltage-to-frequency ratio constant to keep the magnetization current constant. There is also another issue with core saturation possible if the input voltage is not reduced proportionately with frequency. If the core saturates the magnetizing current can rise sharply.

On the high frequency side the core (eddy current and hysteresis) losses, the winding copper losses, the interwinding capacitances and winding leakage inductive reactances all tend to reduce the peformance with increasing frequency. You really need to look at the transformer equivalent circuit at a given frequency or limited band of frequencies to get a clear indication of the overall electrical performance. Mains frequency transformers are designed for mains frequency operation and as such you can't expect a very wide operating frequency band from them.

8. ### Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
4
lets assume the transformer is air core and an ideal transformer then is their any mathematical way to find out the frequency range and optimal frequency toi use this transformer with....based on the coil ratio , voltage ,...etc?
(since their is no core just air the only components of the transformer are the coil of wire this should make it easier to study as well as it being ideal so no power loss between primary/secondary)

Also is their anyway to mathematically figure out how much power a transformer can have (.ie when makeing a transformer what controls the amount of power that the primary coil has )

For example I have transformer's that are 120vac 60hz to 12.6vac 60hz at 300mA

and ones with the same ratings except rated at on the secondary 10amps

Obviously if we assume ideal conditions Pin = Pout for approximations

The first transfomer has max power 3.78Watts
The second transfomer has max power 126Watts

Their must be something that makes more current flow with the same coil ratio? Maybe it is the amount of turns in each to give the same coil ratio...duno? ( assumeing air core because I know the materail the coil is rapped around will control voltage/current as well but other then this is their anyway to control power/current )
I would think if you lessen the resistance/reactance of the primary this would make it so more current could flow with the fixed 120vac 60hz supply...and more current means more power .....

But to reduce the resistance in primary you would have to lower wL and w is fix (assuming fix frequency of opertion) so you would have to reduce the L in some way I don't know how this is controlled... ( other then v = L*di/dt which means L is equal to the voltage divide by the rate of change in current)

If I am overlooking anything please let me know.

Last edited: Jan 7, 2010
9. ### Paulo540 Member

Nov 23, 2009
188
0
The larger transformer isn't really 'making' more current flow. the wire diameter is larger so that it is able to carry higher current without melting.

As t n k noted (or at least I think is what he is suggesting), try to look at one side of the transformer and its frequency response characteristics.

Mar 8, 2009
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11. ### Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
4
Ok , I see their is alot for bench testing for this and I already know the math and physics of induction , ampere's law ,..etc

All I want to know is assume I am using 22gage wire and no core (i.e air core)

Then how many turns would I need on the primary and secondary to make

120vac 60hz --> 24vac 60hz 200mA or 10A

Meaning I am looking to create from just a coil of wires a 120vac to 24 vac main transformer that is rated for either 200mA or 10A which ever is easier to create.

Using the formulas v1/v2 = N1/N2 => 120/v2 = N1/N2 =>
if v2= 24 => 120/24 => the coil ratio is 120/24 so if I coil the wire on the primary side 24 turns and secondary side 120 turns I should have 24 vac on secondary wire approximately

But what controls how much current will flow thru the primary or thru the secondary ....some mathematical approximation still needed ?
I.e how can I figure out how much power this man made transformer will provided ... note I don't want to stick this into a wall outlet if the current is going to be more the 15amps because the circuit breaker will go and it could be potiental hazardous. ( even though I got a remote control to swtich the circuit on and off just for saftey reasons)

I know V1/V2 = I2/I1 but I don't have either I1 or I2 which amounts to knowing the approximate power...?
So I guess the question is what controls the approximate power if the coils control the amount of voltage stepped down/up ....
( assuming the core is air core and ideal then the only thing that can be changed is with the wire gage or how far apart the wire's are seperated)

Seems like this transformer is like just creating a short because 24 turns is almost like not turning the wire at all plus how big should I make the coils diameter wise.........

Thanks

12. ### Paulo540 Member

Nov 23, 2009
188
0
You don't want to run 10A through 22 gauge wire. There are guidelines for this all over the net, but keep in mind that if you stack wire, you are effectively reducing its thermal transfer abilities even further.

Also, your math on the ratio is backwards, if you have 24 Pri turns and 120 sec, you would be creating a step up transformer, increasing the voltage 5x (600V!)

A perfect inductor will block AC completely. the core is what 'translates' the current to the other side. Don't confuse the operation of a power transformer and a RF one (RF has a waveform but it rides above the zero point.)

I strongly suggest that you don't build a transformer and plug it into the wall. If you want to play around with this type of thing, use a normal 120/12v transformer and work on the safe side of that. At least you won't get murdered if something goes wrong. And the load you place on said transformer will dictate the current draw.

Last edited: Jan 8, 2010
13. ### Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
4
ok , say I am working on the 12vac side like you said for protection purposes to stepup the voltage would this work...

Taking 22gage wire and with primary coil 10 turns and secondary coil 20 turns

then mathematically v1/v2 = 10/20 = 1/2
v2 = 2*v1 => v2 = 2 * 12 = 24 vac

wondering if I do this if I am going to get approximately 24vac?
Because I could use 100 turns and 200turns same coil ratio

So if it doesn't , matter about turns then I could use 1 turn to 2 turns seems odd to use so little turns. Or if I had a coil ratio I could always use the fraction in simplest form to save wire.... seems like turns would play more of a roll then just the ratio but I don't know I only know what the math say's?

Also how close should the to coils be placed together does it matter if they overlapp....? And should the turns be made as tight as possible without over lapping or can they be streached out

Thanks I am going to test this theory tommarow

14. ### lmartinez Active Member

Mar 8, 2009
224
6
As I previously indicated, it is all in the math......