# What is the Q factor formula of a transformer

Started by November 4, 2021
```Could some electronics guru here shed some light on this ? What is the
formula for a transformer, consisting of two magnetically coupled inductors ?
For a standalone inductor it is Q = wL/R. What are L, and R in the case of
a transformer. Specifically, how does one take into account the mutual inductance,  and what is the value of R ? All hints, suggestions will be greatly appreciated. Thanks in advance.
```
```On 4.11.21 6.10, amal banerjee wrote:
> Could some electronics guru here shed some light on this ? What is the
> formula for a transformer, consisting of two magnetically coupled inductors ?
> For a standalone inductor it is Q = wL/R. What are L, and R in the case of
> a transformer. Specifically, how does one take into account the mutual inductance,  and what is the value of R ? All hints, suggestions will be greatly appreciated. Thanks in advance.
>

There is no single formula.

and calculate the result.

--

-TV

```
```On Wednesday, November 3, 2021 at 9:10:06 PM UTC-7, daku...@gmail.com wrote:
> Could some electronics guru here shed some light on this ? What is the
> formula for a transformer, consisting of two magnetically coupled inductors ?
> For a standalone inductor it is Q = wL/R. What are L, and R in the case of
> a transformer. Specifically, how does one take into account the mutual inductance, and what is the value of R ? All hints, suggestions will be greatly appreciated. Thanks in advance.

There's more than one L (it could be the primary winding inductance if the secondary
circuit is open, or the leakage of the primary winding inductance if the secondary circuit is short,
or could be a combination of primary and secondary and output load).   And, there's more than one
R (could be the electrical resistivity of conducting magnetic core elements), as well as effects like
magnetic hysteresis that aren't linear and cannot be identified with linear impedances like
inductance or resistance.

Q generally means energy stored divided by per-cycle energy loss, thus a transformer doing
something more complicated than sinewave-at-a-single-frequency lacks the 'cycle' definition.
Resonant  transformers include Tesla coils, though those don't exactly follow the
one-magnetic-circuit-coupled-to-two-electric-circuits transformer definition.
```
```whit3rd <whit3rd@gmail.com> wrote in

> On Wednesday, November 3, 2021 at 9:10:06 PM UTC-7,
> daku...@gmail.com wrote:
>> Could some electronics guru here shed some light on this ? What
>> is the formula for a transformer, consisting of two magnetically
>> coupled inductors ? For a standalone inductor it is Q = wL/R.
>> What are L, and R in the case of a transformer. Specifically, how
>> does one take into account the mutual inductance, and what is the
>> value of R ? All hints, suggestions will be greatly appreciated.
>
> There's more than one L (it could be the primary winding
> inductance if the secondary circuit is open, or the leakage of the
> primary winding inductance if the secondary circuit is short, or
> could be a combination of primary and secondary and output load).
>  And, there's more than one R (could be the electrical resistivity
> of conducting magnetic core elements), as well as effects like
> magnetic hysteresis that aren't linear and cannot be identified
> with linear impedances like inductance or resistance.
>
> Q generally means energy stored divided by per-cycle energy loss,
> thus a transformer doing something more complicated than
> sinewave-at-a-single-frequency lacks the 'cycle' definition.
> Resonant  transformers include Tesla coils, though those don't
> one-magnetic-circuit-coupled-to-two-electric-circuits transformer
> definition.
>

Don't forget other parasitics like interwinding capacitance.

We just used power in power out efficiency and plot at different
frequencies.

We had a pot core that meant that if used, the circuit would be
running at about 56 kHz, because the transformers we put that core on
got happier right there.  So that is what we would tune our stimulus
oscillator to.  But those are little tiny transformers.  Maybe
interwinding capacitance is not a big factor on larger, higher power
units.  I do not know.
```