# Why does the turns ratio for transformer work at any frequency?

#### sparkfishes

Joined Oct 19, 2009
16
I have tried to understand this for several months - I have read up on it but can not get the two subjects to separate - as it were

If voltage in an inductor is related to the rate of change of the magnetic field -i.e. the frequency of the pulsed/AC supply
Then why does the voltage of transformers not rely or be affected by frequency
Why does the turns ratio for transformers hold true for any frequency?

Obviously I would not be asking this question if I did not need a simple answer - no long formulae please

#### Papabravo

Joined Feb 24, 2006
12,945
Because Ohm's law is true.

At sufficiently high frequencies inductors stop looking like inductors and start looking like a bunch of capacitors in parallel.

#### t_n_k

Joined Mar 6, 2009
5,447
If voltage in an inductor is related to the rate of change of the magnetic field -i.e. the frequency of the pulsed/AC supply
Then why does the voltage of transformers not rely or be affected by frequency
Hi sparkfishes,

You seem misguided in your understanding of transformers. Of course its true that the law of induction means that the voltage across an inductor increases with frequency when the inductor is driven by a source other than an ideal (or solid) voltage source. But most transformers are operated as fixed voltage fed devices - anything else is a special case.

If you took a 120V 60Hz (primary) transformer and supplied it with a 120V 1Hz source you would probably damage /destroy it if you left it on long enough. Why? The current would be excessive and the primary winding would probably overheat. If you kept V/f constant, then the range of operation would be quite wide - especially if going down in frequency. This is what happens with variable speed induction motor drives - in which the motor is a kind of power transformer with a mechanically rotating shorted secondary.

All transformers are designed to support a primary side supply voltage / frequency combination within a specified range. The transformer magnetizing inductance is a key design parameter. Since you don't want any equations I won't trouble you with the details.

Also you couldn't expect a mains frequency power transformer (50 or 60Hz) to successfully operate in the 10's of kHz region. The losses would become prohibitive and it would be useless for such an application.

As to the turns ratio and the constancy of primary-to-secondary voltage ratios ....

Yes, over the allowable operating frequency range for the transformer, the ratio will be essentially constant if the (usually small) changes in losses are ignored. For instance it's usually no problem to operate a transformer at either 50Hz or 60Hz provided an appropriate derating factor is applied when necessary. You might eventually need some equations to clarify these matters.

#### t06afre

Joined May 11, 2009
5,934
If you Google the term 'transformer saturation' will you find a lot of information.

#### hobbyist

Joined Aug 10, 2008
887
Very WELL explained. T. N. K.

Thats why wall apliances always have the voltage rating as well as the 50 - 60 HZ rating.

#### Ratch

Joined Mar 20, 2007
1,070
sparkfishes,

Why does the turns ratio for transformers hold true for any frequency?
Because once the transformer is manufactured, its turns ratio cannot be changed without disassembling the transformer and rewinding it. That is why driving it with a different frequency is not going to change its turns ratio.

Ratch

#### sparkfishes

Joined Oct 19, 2009
16
I obviously did not phrase my question clearly ... but thanks to all of you that responded.
My question does not involve the manufacture of transformers or the slight difference between 60 Hz and 50 Hz. OR supplying varying frequency or voltage of the supply

Transformers are two inductors and the primary induces the current/voltage in the secondary within the rules of the turns ratio.

However, inductance ( and therefore the voltage) is dependent on the rate of change - viz. the frequency of the applied emf

If I induce a emf from the collapsing magnetic field in coil at 100 Hz it will be a higher voltage at 1kHz.
A 3v supply will easily produce 600 V at 1Khz ( I am assuming this value. I could do the maths but have not - I can easily produces 1000 V from 12v using a coil and rotating magnets and feeding a transistor to pulse the coil)

So, if I - theoretically - supply a transformer with 3v at 1Hz to the primary
I get 600 V in the collapsing field alone. If the secondary has a turns ratio of 1:10 ( step up 10 x) then why is the output not 6000V instead of 30V?

#### t_n_k

Joined Mar 6, 2009
5,447
Transformers are two inductors and the primary induces the current/voltage in the secondary within the rules of the turns ratio.
A transformer is a device which has two or more mutually coupled windings which share a common magnetic circuit.

However, inductance ( and therefore the voltage) is dependent on the rate of change - viz. the frequency of the applied emf
Inductance is a fixed value for a particular inductor construction and in principle is not frequency dependent.

If I induce a emf from the collapsing magnetic field in coil at 100 Hz it will be a higher voltage at 1kHz.
That's probably true but that's not how you operate a transformer. You seem to be confusing the notions of steady state operation and transient operation.

I can easily produces 1000 V from 12v using a coil and rotating magnets and feeding a transistor to pulse the coil
I thought you were discussing transformers - not coils with rotating magnets and pulsing transistors

So, if I - theoretically - supply a transformer with 3v at 1Hz to the primary
I get 600 V in the collapsing field alone. If the secondary has a turns ratio of 1:10 ( step up 10 x) then why is the output not 6000V instead of 30V?
Perhaps you could supply a well reasoned analysis using a practical circuit model which leads to the values you have indicated here. Forum members can then understand what are the real issues in your questions and comment more effectively. One can't really discuss the game unless the rules of the game are clear. Again I repeat the point that your focus seems to be on transient behaviour rather than on steady state AC behaviour in a transformer.

#### rjenkins

Joined Nov 6, 2005
1,013
The simple thing is to think in terms of 'Turns per Volt' (or volts per turn).

If the primary of a 240V transformer has eg. 1200 Turns, that's five turns per volt.
To get 12V out, you would use a secondary with 60 turns.

Or - and this the key fact - you could tap the primary at 60 turns from one end and get 12V at the tap using the single winding as an autotransformer.

The actual turns per volt will vary with the design frequency and power, but whatever the design the voltage on a winding will be equally distributed over the total turns.

You can tap some fraction of that winding to get a specific voltage, or equally add another winding with the correct number of turns to get a required voltage.

In real world applications, with mains power transformers, the secondary often has more turns than required for the output voltage. This is to allow for voltage drop 'on load' due to the winding resistance. The change between off-load voltage and the voltage at the transformers rated full load is the Regulation figure which you will often see in catalog listings of transformers.

#### sparkfishes

Joined Oct 19, 2009
16
Thanks again for your replies and my apologies for not being able to get my question across clearly
1) a transformer is two inductors coupled through / by a single core
2) AC is applied to the Primary and AC is not only changing polarity it is also varying in voltage as per the sine wave - so I don't under stand the references to stead state or solid voltage
3 The same effect ( transforming the voltage / current) can be achieved by using a pulsed DC supply
4) In both cases the ratio of turns is equal to the volts/current ratio
by convention this is irrespective of the frequency

The magnetic field induced in the core rises and falls as the power to the inductor changes - either polarity, or on -off
The collapsing field induces a voltage in the secondary coil -

Now, take the case of a single coil with a similar iron core and the field is induced from an external source - a magnet going past it
This is the same as the field being caused by an AC current - the field rises and collapses and produces EMF
Also inducing a magnetic field by pulsing the coil will give a voltage from the collapsing field that is frequency dependent - the faster it is pulsed the higher the voltage

So in these cases the voltage IS frequency dependent the faster the magnetic field ( or power to the coil) is switched on and off the higher the voltage obtained

So why is the output voltage of a transformer not affected by in coming frequency ?

#### davebee

Joined Oct 22, 2008
540
By comparing a single-winding coil to a transformer, I think maybe you're only looking at half the story.

A transformer works like this -

changing voltage -> changing current -> changing flux -> changing current -> changing voltage

The changing flux generates a back EMF that opposes the primary current flow, so in
the steady state, only a small primary current may flow even though the resistance of the wires may be very low.

At a higher frequency, less flux is needed to generate this back emf, so less is generated.

In the secondary, the lower flux at the higher frequency is just enough to produce the secondary voltage.

So you're right in that a higher frequency of flux change would generate a higher voltage, but I think that the missing part is that the primary voltage generates less flux due to the higher frequency.

#### t_n_k

Joined Mar 6, 2009
5,447
The magnetic field induced in the core rises and falls as the power to the inductor changes - either polarity, or on -off
The collapsing field induces a voltage in the secondary coil -

Now, take the case of a single coil with a similar iron core and the field is induced from an external source - a magnet going past it
This is the same as the field being caused by an AC current - the field rises and collapses and produces EMF
Also inducing a magnetic field by pulsing the coil will give a voltage from the collapsing field that is frequency dependent - the faster it is pulsed the higher the voltage
Suppose we are discussing the ubiquitous conventional AC transformer.

Consider firstly how the magnetic field is produced in a transformer core.

Normally it is created in response to the applied AC voltage - conventionally the AC voltage connected to the primary side. The law of induction tells us that the magnetic flux produced in the core depends on the general relationship e=Nd$$\phi$$dt.
So the primary voltage + primary turns combination 'dictates' the flux value established in the core.

Let's put in some numbers. Suppose our transformer has a primary winding of 240 turns and 240V rms at 50 Hz is applied. Suppose the secondary has 24 turns.

The voltage flux relationship for a sinusoidal source is the well known equation

Erms=4.44fN$$\phi max$$

where f is the frequency, N is the number of turns and $$\phi max$$ is the peak flux [in Weber] in the core.

So if Erms=240, f=50Hz and N=240 turns

$$\phi max$$=240/(4.44x50x240)=4.505 milli Weber

The same flux links the the secondary

So E_sec=4.44x50x24x4.505x10^-3=24Volts as expected.

Let's double the frequency to 100Hz and leave everything else the same.

At 100Hz we find the the peak flux has changed to

$$\phi max$$=240/(4.44x100x240)=2.2523 milli Weber

This is the important point to note - the peak flux in the core has halved as the frequency was doubled. That is, the magnetic flux established in the core satisfies the condition to sustain the applied primary AC voltage at that particular frequency.

Again we show the secondary voltage in this case at 100Hz

E_sec=4.44x100x24x2.2523x10^-3=24Volts - again as expected.

#### t_n_k

Joined Mar 6, 2009
5,447
The law of induction tells us that the magnetic flux produced in the core depends on the general relationship e=Nd$$\phi$$dt.
Latex got the better of me

That should be

e=Nd$$\phi$$/dt

#### t_n_k

Joined Mar 6, 2009
5,447
2) AC is applied to the Primary and AC is not only changing polarity it is also varying in voltage as per the sine wave - so I don't under stand the references to stead state or solid voltage
"Steady state" is a term routinely used in AC circuit analysis. It may "grate" that the term is somewhat incongruous, but through conventional use we are stuck with it. It is a useful concept to the extent that there are often transient conditions in AC systems due to disturbances or changes which have a finite period of effect while the underlying settled, longer term dynamic state is another case - perhaps the latter might be better termed as "quasi steady state". But I doubt that will help anyway.

BTW thanks for your interesting questions - it's always good to have a robust discussion and try to get the heart of the physical realities that are often (at first) hard to perceive in the mathematics which is used to model that reality.

#### t_n_k

Joined Mar 6, 2009
5,447
Hi sparkfishes,

A final observation - from me anyway.

I take your point that if you drive an inductor with a constant AC current at increasing frequency then the voltage will increase proportionately (or proportionally? -whichever you prefer) with respect to the AC frequency.

You could indeed drive a transformer primary winding with a constant AC current source of varying frequency and transform to a secondary winding voltage which also transforms by the same factor with respect to frequency.

Of course the driving source must itself be capable of increasing it's voltage magnitude output by the same proportion, as it's driving frequency increases.

The reality is that the majority of transformers are voltage driven - not current driven. You buy a transformer with a specified rated primary voltage and rated Volt-Ampere capacity. You normally connect it to the mains supply - probably with the intention of obtaining a lower value and / or isolated voltage supply. As long as you drive the primary at a fixed ('solid') AC voltage, a reasonable (practical) change in frequency will have no effect either on the primary (since it's been fixed by the supply) or secondary voltage value.

That's it from me on this thread. Hopefully other members can address any ongoing questions for you.