# Gauss based ferrite core loss

A reader of Amidon's method of rating ferrite inductors and transformers wrote to support Amidon's approach and cited a video by W0QE.

W0QE's video #80: High Power Balun with #31 Ferrite Material gives some measurements and simulations of a FT240-31 inductor with 11 and 14 turns.

In the video he states:

It turns out that the heating effects in the coil are related to the voltage across the coil only, not the current through the it or anything else.

In fact, there is current flowing through the inductor and that develops a voltage difference across the ends. When we are talking about the self inductance properties, then we are talking about the voltage induced in the inductor as a direct result of the current flowing through the inductance.

Let's look at his own figures to demonstrate,

Above is his Simsmith model. Let us focus on just the left hand two elements L and R1 (for the 11t inductor) as it is a quite complicated model. L was derived from a measurement of the inductor in a fixture, and to some extent the fixture is captured.

The voltage applied to both L and R is given as 272.2V, this is around the voltage that would be applied to a 50+j0Ω load at 1500W, so his experiment to to simulate the conditions if that inductor was the 50Ω winding of a 50Ω transformer at 1500W.

The impedance of R1 is given as 4134-j328.1Ω (interpolated possibly) from his measurement of Z.

From V and Z, we can calculate $$Y=\frac1Z$$ and $$I=\frac{V}Z$$, and powers $$P_i=I^2R$$ and $$P_v=V^2G$$ (R and G being the real parts of Z and Y respectively).

Let's use Python as a complex number calculator to make the maths easy.

>>> import math
>>> import cmath
>>> z=4134-328.1j
>>> y=1/z
>>> y
(0.00024038230052189223+1.907823725235434e-05j)
>>> v=272.2
>>> v
272.2
>>> p50=v**2/50
>>> p50
1481.8568
>>> pv=v**2*y.real
>>> pv
17.810607331400476
>>> i=v/z
>>> i
(0.06543206220205906+0.005193096180090851j)
>>> pi=abs(i)**2*z.real
>>> pi
17.81060733140048

We can see there is current flowing, and that calculated pv and pi reconcile (and they reconcile with Simsmith)… so the power dissipated (ie converted to heat) in the inductor can be calculated from current or voltage, his statement quoted earlier is plainly wrong.

So, if either current or voltage can be used, is one better?

This is more a question of whether voltage or current can be measured reasonably accurately and conveniently.

Whilst in W0QE's test configuration it is fairly easy to make a valid voltage measurement of the inductor shunted by the 50Ω dummy load at the T (the test was designed for that), measurement of a ‘floating' common mode choke is not so easy as the instrument may significantly disturb the thing being measured (it doesn't have the 50Ω shunt load, circuit impedance is now much higher and the effect of the instrument leads etc is much greater).

A better approach for the common mode choke might be to use a clamp on RF ammeter and use measured Z of the choke to obtain $$P_{choke}=I^2 \mathbb{R}(Z_{choke})$$ or $$P_{choke}=I^2 Real(Z_{choke})$$.

I make the observation that many hams write about common mode current, but it is rare to see valid measurement of common mode current.

Another question that arises is the accuracy of measurement of Z. In this instance, the choke in fixture is very close to self resonant (evidenced by the smallish magnitude of X) and the real part of Z is quite sensitive to layout and shunt capacitance such as the fixture… giving rise to significant uncertainty or R around the resonant frequency. You might question whether the fixture actually represents the intended deployment scenario.

He also calculates the expected flux level as 50.7 gauss and mutters that they are rated for 57 gauss… yes, rated for 57 gauss.

Above is from the Fair-rite datasheet for #31 material. It is easy to see that saturation flux density is of the order of 1000 gauss (0.1T), so operating at 50 gauss is way way below saturation. Like many if not most ferrite ham applications at HF, loss becomes a problem way before saturation.

Nothing in the Fair-rite #31 datasheet relates core loss to flux density.

I could not see where he used this magic 57 or 50.7 gauss in any power calculation, all of his power calculation is based on a small signal measurement of the inductor magnetising impedance. 57 gauss may have been sourced from Amidon… but keep in mind that Amidon is not a manufacturer, Fair-rite is a manufacturer. So much for the claim that loss is dependent on voltage and not current.

## Conclusions

In this application, the power dissipated in an inductor can be calculated from Z and either current through it, or voltage across it.

If you want to estimate the core loss in a common mode choke, carefully measure the common mode impedance and the common mode current and calculate the core loss.

Uncertainty in Z can be significant, especially near the inductor's self resonant frequency.