Real series resistance calculation of parasitic capacitance of inductors

[sourcecharge]

Hi! 

Been here for awhile,

Doing my bit....

but now, I have ran into a wall....

This seems tricky, so I decided to ask the internet experts.

Let me explain.

I am working on series resonant circuits using halfbridge driver inputs.

My task that I assigned myself, is to measure the series resistance of all relevent real resistance of series resonant circuits.

The total resistant of series resonant circuits can be measured indirectly by measuring the V(p) output of a series resonant circuit accross the capacitor by calculation.

The total resistance of a series resoanat circuit includes:

R(dc) = wire resistance
R(ac) = wire eddy current resistance
R(di) = dielectric resistance [parasitic capacitance]
R(core) = core resistance
R(ESR) = equivilent series resistance of the capacitor in resonance
R(connection) = series resistance of all connecting wires and average of the R(ds)on of the N and P channel mosfets.

R(dc), R(ESR), and R(connection) are easily measured with my mastech MS5308 LCR meter and my mastech  MS8040 digital multimeter(s) which have been calibrated to 10V DC under the DC setting with a voltage reference with an error of 0.002% error at 25 degrees C. 

The MS5308 LCR meter allows me to measure the dissipation factor of the wire insulation by binding up a bundle of wire and using it like a capacitor.  The dissipation of the heavy insulated polyimide wire is about 0.0056 at 10kHz, which follows manufacturing datasheets of dissipation between 0.006 an 0.005 of the most commonly use polyimide at 1 mm thickness between frequencies of 1khz to 10khz.  (As frequency decreases, DF decreases)

I have measured this 2inch 60u MPP inductor that I have hand wraped with 24 sections on my LCR meter, and it is stating a Q between 250 and 300.  The LCR meter's Vpp is 2V.  Althought the range is consistant, the actual value does not seem to be consistant.

When the inductor is used under load within the series resonant circuit, the Q of the inductor is dramatically decreased to about 190.  This can only be explained by either the R(core) or the R(di).

The R(core) is voltage dependent and fits the leggs equation very accurately, which leaves R(di).

My exact question involves these values:

R(dc) = 13.24 ohms
R(ac) = 0 ohms
R(core) = 8.3 ohms
R(ESR) = 2.17 ohms
R(connection) = 2.55 ohms

+/-10V input squarewave

6240    hz RF
374      pF parasistic capacitance
0.0045 DF polyimide wire isulation
128.35 mH MPP inducator
4.694   nF metalized polypropylene capacitor with 0.0004 DF at 10khz

output Vp 1250
ouput I in avg 148.4mA

Unaccounted for resistance = 22.7 ohms

I'm thinking this is parasitic capacitance because these resistance is not voltage dependent.

My question is:

How do I calculate the exact amount of series resisance associated with an inductor from a parasitic capacitance with a certain amount of dissipation from the wire insulation.

BTW, it should equal about 22 to 23 ohms.

[Benta]

You might need to include current displacement in the windings. This reduces the current carrying cross-area of the wires.

[pwlps]

I have measured this 2inch 60u MPP inductor that I have hand wraped with 24 sections on my LCR meter, and it is stating a Q between 250 and 300.  The LCR meter's Vpp is 2V.  Althought the range is consistant, the actual value does not seem to be consistant.

When the inductor is used under load within the series resonant circuit, the Q of the inductor is dramatically decreased to about 190.  This can only be explained by either the R(core) or the R(di).

The R(core) is voltage dependent and fits the leggs equation very accurately, which leaves R(di).

The R(core) is frequency dependent (increases with frequency). Did you use the same frequency with your LCR meter as in the circuit under load ?

[sourcecharge]

You might need to include current displacement in the windings. This reduces the current carrying cross-area of the wires.

At 6000 hz, R(ac) or the eddy current loss of the wire, is non existant.  I think it's up to about 50khz that this resistance is actually measureable.

Under a technical document from arnold's magnetics, it gives equations for this resistance.

I have calculated this resistance using their equation and found the calculation to be less than the measured resistance.  I guessing thats because it is not relavent at low frequencies.  Their equation is in this tech doc is on page 10 of the pdf.

Arnold's MPP_en_2006_Rev2_intro.pdf

Arnold's MPP_en_2006_Rev2_1.57-5.218.pdf

of coarse I can upload them due to their being 4MB size...

[sourcecharge]

I have measured this 2inch 60u MPP inductor that I have hand wraped with 24 sections on my LCR meter, and it is stating a Q between 250 and 300.  The LCR meter's Vpp is 2V.  Althought the range is consistant, the actual value does not seem to be consistant.

When the inductor is used under load within the series resonant circuit, the Q of the inductor is dramatically decreased to about 190.  This can only be explained by either the R(core) or the R(di).

The R(core) is voltage dependent and fits the leggs equation very accurately, which leaves R(di).

The R(core) is frequency dependent (increases with frequency). Did you use the same frequency with your LCR meter as in the circuit under load ?

No but I did measure it at 1khz and at 10khz.  The Q difference is calculated to be due to frequency of measurement.

[emece67]

.

[sourcecharge]

What's the inductor core material? Being it conductive there may be eddy currents on it.

Regards.

It's a MPP type. 60 u

Legg's equation accounts for eddy currents.

R(core) = u(r) x L x (a x B(max) x f + c x f + e x f^2)

a, c, and e are coefficients that are given by the manufacturer arnold's magnetics (they are now owned by someone else I forget who.)

It's either the core or the windings.  If it's the core, a +/-1V squarewave input would have a 10x less resistance, but it doesn't, in facts its about 5% of the difference that the legg's equation predicts.  So right off the start, this 22 or so ohms is there.  That's why I'm thinking its the parasitic capacitance.

The way I'm doing my R(di) calculation is by using (wL)^2/R(p) where R(p) is 1/(w x C(p) x DF) and C(p) is the parasitic capacitance.

This actually calculates to the exact answer as an equation given by the original Legg's research journal.

8 x pi^3 x C x L^2 x f^3 / DF

In order for the series resistance to be calculated to about 22 ohms, the DF of the polyimide wire would have to be 0.055, and not 0.0056.

idk, what if the core is flux walking?

 

[sourcecharge]

So, I reverified that R(ac) is not at play, and it looks like it doesn't under 50khz.

I also verified that the R(p) of the capacitor to R(s) of the inductor calculation is correct by using B2 Spice.

There is a possiblity that polyimide has a voltage dependent dissipation factor, because I can't find any data concerning the voltage dependance.

If it's not the insulation's dissipation changing then that only leaves the core resistance.

The thing is that the manufacturere of the cores gave a, c, and e vaules for gausses of 10 of the 60u type MPP cores.  The calculated B(max) is only 18.88 at a 10V input and only 3.66 gauss at a 2V input.

So does that mean that the core is flux walking?

Does anyone know anything about flux walking and whether it would happen in a series resonant circuit driven by a +/- halfbridge AC squarewave output?

[sourcecharge]

So read up on flux walking and it pertains to half brides.

Here is a good tech doc that explains it:

https://www.ti.com/lit/ml/slup126/slup126.pdf

pg 6

so I'm going to test this by using multiple mosfets in parallel decrease the total R(d)on for the the N an P channel mosfets.

Apparently, it can increase losses without actually saturating the core.