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I have wound a 110uH coil for an antenna system and I want to create a model of the inductor that I can use in a simulation program. In other words, I need to know the inductance, parasitic capacitance and ESR.

Using my NanoVNA-H4 I measured the inductance on a Smith chart at a low frequency (around 70kHz) where the reactance is about 50 ohms. I then measured the self resonant frequency (10.5MHz) and calculated the parasitic capacitance as 2pF.

Is that correct so far?

What about ESR? Is that the ohmic resistance of the coil or is it more complicated than that?

Thanks!
--
Mike

On rf the resistance is higher as dc resistance
Dg9bfc sigi

Am 25.06.2023 22:26 schrieb Mike <mail@...>:

On Sun, Jun 25, 2023 at 01:26 PM, Mike wrote:

I have wound a 110uH coil for an antenna system and I want to create a model
of the inductor that I can use in a simulation program. In other words, I need
to know the inductance, parasitic capacitance and ESR.

Using my NanoVNA-H4 I measured the inductance on a Smith chart at a low
frequency (around 70kHz) where the reactance is about 50 ohms. I then measured
the self resonant frequency (10.5MHz) and calculated the parasitic capacitance
as 2pF.

Is that correct so far?

What about ESR? Is that the ohmic resistance of the coil or is it more
complicated than that?

Yes it is more complicated than that. The inductance will vary with frequency and so will the ESR. In the case of an air wound coil the underlying inductance will slightly change as you increase frequency due to the "skin effect" which forces current to the outer perimeter of the conductor. If the coil is wound on a powdered iron or ferrite core there will be considerable change of inductance with frequency due to the permeability decreasing with frequency. The ESR will increase with frequency due to core losses and the skin effect which increases the RF resistance of the coil windings.

When you try to measure the inductance of an inductor using a VNA the firmware or PC application will calculate the "apparent inductance" by simpling dividing the measured reactance by 2*pi*frequency. This is not the same as the actual inductance L. The reason is that the parasitic capacitance is in parallel with the inductor and you now have capacitor reactance in parallel with the inductor reactance which results in a higher reactance than that of the inductor alone. This is shown in the attached diagram.

So if you tell us what type of inductor you are measuring (air wound, powdered iron or ferrite) more specific information can be provided.

Roger

On 6/25/23 1:26 PM, Mike wrote:

I have wound a 110uH coil for an antenna system and I want to create a model of the inductor that I can use in a simulation program. In other words, I need to know the inductance, parasitic capacitance and ESR.
Using my NanoVNA-H4 I measured the inductance on a Smith chart at a low frequency (around 70kHz) where the reactance is about 50 ohms. I then measured the self resonant frequency (10.5MHz) and calculated the parasitic capacitance as 2pF.
Is that correct so far?
What about ESR? Is that the ohmic resistance of the coil or is it more complicated than that?
Thanks!

ESR is the ohmic resistance *at RF* which will be higher than the DC resistance (skin effect).

What you should be able to do is measure the Z (both X and R) far away from self resonance, and get a rough estimate.

Thank you Roger. The coil is 95 turns of 0.9mm enamelled copper wire close wound on a 36mm PVC former.

--
Mike

On Sun, Jun 25, 2023 at 10:25 PM, Jim Lux wrote:

ESR is the ohmic resistance *at RF* which will be higher than the DC
resistance (skin effect).

What you should be able to do is measure the Z (both X and R) far away
from self resonance, and get a rough estimate.

Thank you Jim.

--
Mike

Mike, measure the inductance and series resistance at the model frequency. I believe recent VNA firmware versions can provide these values directly. Otherwise calculate them from R and X. Then create a simple load with the inductance and resistance in series. This works fine over a single ham band. To create a wideband model, see this:



Brian

On Sun, Jun 25, 2023 at 10:55 PM, Brian Beezley wrote:

Mike, measure the inductance and series resistance at the model frequency. I
believe recent VNA firmware versions can provide these values directly.
Otherwise calculate them from R and X. Then create a simple load with the
inductance and resistance in series. This works fine over a single ham band.
To create a wideband model, see this:



Brian

Thanks for the link Brian.

--
Mike

On Sun, Jun 25, 2023 at 02:27 PM, Mike wrote:

Thank you Roger. The coil is 95 turns of 0.9mm enamelled copper wire close
wound on a 36mm PVC former.

Mike,

Attached is an analysis of your coil using Coil64. The numbers are close to what you measured. For an air wound coil the actual L will not vary much in the frequency range of up to 12 MHz. Note the following:

--> ESR is increasing with frequency and simulation shows .299 ohms at DC, .422 at 1 MHz. and 9.233 ohms at 5 MHz.
--> Self capacitance is calculated at 1.61 pF which is very small. You estimated 2 pF based on your SRF measurement. Any stray capacitance in your test setup will significantly affect your self resonant frequency so you need a good test jig if this is an area of concern.

Note: For air wound coils assuming that apparent inductance at low frequencies is equal to actual inductance L at higher frequencies is a reasonable approximation. Therefore the method of calculating parasitic capacitance based on using this value of L and the SRF to calculate parasitic capacitance gives a decent estimate. BUT this method does not work if the inductor is a ferrite core design.

Roger

On Sun, Jun 25, 2023 at 02:55 PM, Brian Beezley wrote:

Mike, measure the inductance and series resistance at the model frequency. I
believe recent VNA firmware versions can provide these values directly.
Otherwise calculate them from R and X.

The VNA can only measure R + jX or R//jX (with later firmware versions). It calculates inductance by dividing X by 2*pi*frequency and this ONLY gives an estimate of the true coil L if the coil is air wound and the frequency is low enough that the skin effect is not having much effect on underlying inductance. If the coil is wound on a ferrite core you can't use this method to estimate L at higher frequencies.

Roger

On Sun, Jun 25, 2023 at 11:04 PM, Roger Need wrote:

On Sun, Jun 25, 2023 at 02:27 PM, Mike wrote:

Thank you Roger. The coil is 95 turns of 0.9mm enamelled copper wire close
wound on a 36mm PVC former.

Mike,

Attached is an analysis of your coil using Coil64. The numbers are close to
what you measured. For an air wound coil the actual L will not vary much in
the frequency range of up to 12 MHz. Note the following:

--> ESR is increasing with frequency and simulation shows .299 ohms at DC,
.422 at 1 MHz. and 9.233 ohms at 5 MHz.
--> Self capacitance is calculated at 1.61 pF which is very small. You
estimated 2 pF based on your SRF measurement. Any stray capacitance in your
test setup will significantly affect your self resonant frequency so you need
a good test jig if this is an area of concern.

Note: For air wound coils assuming that apparent inductance at low frequencies
is equal to actual inductance L at higher frequencies is a reasonable
approximation. Therefore the method of calculating parasitic capacitance
based on using this value of L and the SRF to calculate parasitic capacitance
gives a decent estimate. BUT this method does not work if the inductor is a
ferrite core design.

Roger

Perfect! Thanks for that explanation Roger.

--
Mike

On Sun, Jun 25, 2023 at 03:15 PM, Roger Need wrote:

The VNA can only measure R + jX or R//jX (with later firmware versions). It
calculates inductance by dividing X by 2*pi*frequency and this ONLY gives an
estimate of the true coil L if the coil is air wound and the frequency is low
enough that the skin effect is not having much effect on underlying
inductance.

Roger, the method I suggested requires inductance calculated this way. It yields an accurate coil model over a narrow frequency range. To my surprise, it seemed good enough over the whole 3.5-4 MHz band. But the wideband model suggested in the writeup noticeably improved accuracy over the somewhat wider 88-108 MHz band.

Brian

This is my test fixture, calibrated at the croc clips. It's not ideal but I'm limited by the length of the coil. Should be OK at my measurement frequency of 70kHz though!

--
Mike

On Mon, Jun 26, 2023 at 01:23 AM, Mike wrote:

This is my test fixture, calibrated at the croc clips. It's not ideal but I'm
limited by the length of the coil. Should be OK at my measurement frequency of
70kHz though!

Calibrating with the crocodile clips will not give you a good reference plane. The reason I say this is if you keep them the same distance apart when you cal with an open, short and load you will have considerable inductance in the short and 50 ohm "cal loads". If you calibrate with the clips close together and then spread them the reference plane has changed. Neither is a good option.

I suggest you calibrate right at the screw terminations on the green block with the alligator clip leads removed. Then attach the leads and make your measurement. From the photo it looks like the leads are about 4" long and each one will add about 100 nH of inductance (total 200 nH or 0.2 uH). That extra .2 uH when you are measuring 110 uH is not significant. However you should get a better estimate of the SRF and be able to calculate the parasitic capacitance to more accuracy.

Try it and see what you find...

Roger

On Mon, Jun 26, 2023 at 05:25 PM, Roger Need wrote:

Calibrating with the crocodile clips will not give you a good reference plane.
The reason I say this is if you keep them the same distance apart when you
cal with an open, short and load you will have considerable inductance in the
short and 50 ohm "cal loads". If you calibrate with the clips close together
and then spread them the reference plane has changed. Neither is a good
option.

I suggest you calibrate right at the screw terminations on the green block
with the alligator clip leads removed. Then attach the leads and make your
measurement. From the photo it looks like the leads are about 4" long and
each one will add about 100 nH of inductance (total 200 nH or 0.2 uH). That
extra .2 uH when you are measuring 110 uH is not significant. However you
should get a better estimate of the SRF and be able to calculate the parasitic
capacitance to more accuracy.

Try it and see what you find...

Roger

Thanks Roger, I will try that tomorrow.

--
Mike

Could you post your .s1p file in shunt on port 0. I would like to reger something.

Have you noticed that when you connect a coil or a trap (finally a dipole) by a single leg on port 0 (the other leg in the air), looking at the ROS, you can see the resonance very well. Ok, it only gives elements at the resonance frequency... but still it's very practical
73
--
F1AMM
Fran?ois

On Mon, Jun 26, 2023 at 05:25 PM, Roger Need wrote:

I suggest you calibrate right at the screw terminations on the green block
with the alligator clip leads removed. Then attach the leads and make your
measurement. From the photo it looks like the leads are about 4" long and
each one will add about 100 nH of inductance (total 200 nH or 0.2 uH). That
extra .2 uH when you are measuring 110 uH is not significant. However you
should get a better estimate of the SRF and be able to calculate the parasitic
capacitance to more accuracy.

Try it and see what you find...

Roger

Roger

I compared both methods of calibration, which I refer to as "screws" and "crocs".

At around 72kHz, where the reactance is approximately 50R, both calibration methods give an inductance of 108uH. However, the SRF was 7.4MHz for "screws" and 12.9MHz for "crocs".

I then repeated the measurement with a different VNA, an FA-VA5. This gave L=110.7uH for "screws" and 110.5uH for "crocs". The SRF was 6.38MHz for "screws" and 6.45MHz for "crocs".

I can accept the difference in L between the two devices but can't decide which one is giving me the most accurate SRF.

--
Mike

On Tue, Jun 27, 2023 at 09:02 AM, Fran?ois wrote:

Could you post your .s1p file in shunt on port 0. I would like to reger
something.

Have you noticed that when you connect a coil or a trap (finally a dipole) by
a single leg on port 0 (the other leg in the air), looking at the ROS, you can
see the resonance very well. Ok, it only gives elements at the resonance
frequency... but still it's very practical
73
--
F1AMM
Fran?ois

-----Message d'origine-----

De la part de Mike
Envoyé : lundi 26 juin 2023 10:23

Hi Fran?ois

Here is the .s1p file for a range of 1 to 20MHz.

--
Mike G8GYW

What I wanted to do is not working.

I have an Excel sheet that allows me from the S11 of an antenna to determine its L and C near the resonance by pressing the curve of a plug to pass through two points.

In your case, it works at resonance but we already know the values involved. Far from resonance the results are not good.
--
Fran?ois

De la part de Mike
Envoyé : mardi 27 juin 2023 15:00

On Tue, Jun 27, 2023 at 05:54 AM, Mike wrote:

I compared both methods of calibration, which I refer to as "screws" and
"crocs".

At around 72kHz, where the reactance is approximately 50R, both calibration
methods give an inductance of 108uH. However, the SRF was 7.4MHz for "screws"
and 12.9MHz for "crocs".

I then repeated the measurement with a different VNA, an FA-VA5. This gave
L=110.7uH for "screws" and 110.5uH for "crocs". The SRF was 6.38MHz for
"screws" and 6.45MHz for "crocs".

I can accept the difference in L between the two devices but can't decide
which one is giving me the most accurate SRF.

With a 110 uH coil it takes 4.2 pF to resonate at 7.4 MHz. and 1.4 pF to resonate at 12.9 MHz. That is a difference of 2.8 pF which is not much.

One way to get to the bottom of this is to short the terminals of the coil together and then "grid dip" it like the old days. You can do this with the NanoVNA by making a pickup coil at the end of a short connecting cable. Calibrate over 5 to 15 MHz. in the usual manner. Set the trace to S11 Log (Return Loss setting) Then attach the pickup coil to the NanoVNA and place the 110 uh coil and the pickup coil in parallel a short distance apart. Look for a dip in the trace. Keep moving the coil further away until the dip has just about disappeared. Now move a marker to the dip and the frequency should be very close to the SRF.

Roger