# inductor tc

Started by November 15, 2023
```I'm used to an air core inductor having a positive tempco of
inductance around +120 PPM/k or so, just from the physical expansion
of the copper increasing the diameter.

But this Coilcraft midi-spring part

https://www.dropbox.com/scl/fi/mfplgwzorhsh5sodxz5cu/Coilcraft_150n_Midi.jpg?rlkey=nrhwa9j64swuz7bmo1hiyjr9j&raw=1

is much less, maybe +30 PPM. I wonder if the plastic expansion changes
the geometry or something. Lengthens the solenoid?

Well, it makes it easier to temperature compensate my oscillator. Out
on my bench, it's measured 49.9944 MHz, exactly the same, for 3 hours.

```
```On Wednesday, 15 November 2023 at 23:55:30 UTC+1, john larkin wrote:
> I'm used to an air core inductor having a positive tempco of
> inductance around +120 PPM/k or so, just from the physical expansion
> of the copper increasing the diameter.
>
> But this Coilcraft midi-spring part
>
> https://www.dropbox.com/scl/fi/mfplgwzorhsh5sodxz5cu/Coilcraft_150n_Midi.jpg?rlkey=nrhwa9j64swuz7bmo1hiyjr9j&raw=1
>
> is much less, maybe +30 PPM. I wonder if the plastic expansion changes
> the geometry or something. Lengthens the solenoid?
>
> Well, it makes it easier to temperature compensate my oscillator. Out
> on my bench, it's measured 49.9944 MHz, exactly the same, for 3 hours.
Just a question, what about the permeability of the enclosing material?  Could it be that it would have minute permeability that is affected from temperature?

You could heat it above the curie point, if the inductance decreased suddenly...
```
```On Wed, 15 Nov 2023 17:59:16 -0800 (PST), Klaus Kragelund
<klaus.kragelund@gmail.com> wrote:

>On Wednesday, 15 November 2023 at 23:55:30 UTC+1, john larkin wrote:
>> I'm used to an air core inductor having a positive tempco of
>> inductance around +120 PPM/k or so, just from the physical expansion
>> of the copper increasing the diameter.
>>
>> But this Coilcraft midi-spring part
>>
>> https://www.dropbox.com/scl/fi/mfplgwzorhsh5sodxz5cu/Coilcraft_150n_Midi.jpg?rlkey=nrhwa9j64swuz7bmo1hiyjr9j&raw=1
>>
>> is much less, maybe +30 PPM. I wonder if the plastic expansion changes
>> the geometry or something. Lengthens the solenoid?
>>
>> Well, it makes it easier to temperature compensate my oscillator. Out
>> on my bench, it's measured 49.9944 MHz, exactly the same, for 3 hours.
>Just a question, what about the permeability of the enclosing material?  Could it be that it would have minute permeability that is affected from temperature?

It's plastic so Ur=1. It does have a dielectric constant >1, which has
some tempco.

But I'm guessing it has a positive mechanical effect, stretching out
the solenoid length as temp rises, and that has the opposite tempco as
the diameter expanding.

The bare-naked spring coil inductors are stretched by the tempco of
the PCB. 370HR is 14 ppm/degc.

Almost everything in this oscillator contributes a negative frequency
TC. The PCB capacitance is especially terrible, around +900 PPM/K. We
just cut some big reliefs through several plane layers under the
critical nodes, to reduce that capacitance. That will reduce the mag
field of the coil from bouncing off the copper planes too.

>
>You could heat it above the curie point, if the inductance decreased suddenly...

There probably isn't a curie point, being basically an air core
inductor.

```
```On 2023-11-15 20:59, Klaus Kragelund wrote:
> On Wednesday, 15 November 2023 at 23:55:30 UTC+1, john larkin wrote:
>> I'm used to an air core inductor having a positive tempco of
>> inductance around +120 PPM/k or so, just from the physical expansion
>> of the copper increasing the diameter.
>>
>> But this Coilcraft midi-spring part
>>
>> https://www.dropbox.com/scl/fi/mfplgwzorhsh5sodxz5cu/Coilcraft_150n_Midi.jpg?rlkey=nrhwa9j64swuz7bmo1hiyjr9j&raw=1
>>
>> is much less, maybe +30 PPM. I wonder if the plastic expansion changes
>> the geometry or something. Lengthens the solenoid?
>>
>> Well, it makes it easier to temperature compensate my oscillator. Out
>> on my bench, it's measured 49.9944 MHz, exactly the same, for 3 hours.
> Just a question, what about the permeability of the enclosing material?  Could it be that it would have minute permeability that is affected from temperature?
>
> You could heat it above the curie point, if the inductance decreased suddenly...
>

You can make the longitudinal expansion of the plastic compensate for
the circumferential expansion of the copper.

To within a couple of percent, L(uH) = (a**2 N**2)/(9a + 10 b), where
a is the mean radius of the coil,
b is the length of the winding (both in inches), and
N is the number of turns.

CTE(a) is controlled by the copper,  CTE(b) by the plastic.

so we get

dL/dT = 2 N**2 a da/dT/ (denom)
- N**2 a**2 *( 9 da/dT + 10 db/dT) / denom**2

da/dT = a*CTE(Cu)
db/dT = b*CTE(plastic)

Dividing by L and collecting terms, we get

TCL = (dL/dT)/L  = (2 CTE(Cu) - (9a CTE(Cu) + 10b CTE(plastic))/(9a + 10b).

With CTE(Cu) = 17 ppm/K and CTE(plastic) probably 100 ppm/K, you get
zero TC somewhere about a/b = 4.5, i.e. diameter ~ 9 x length. (That is,
unless I've made a blunder, which is a definite possibility at 1 AM.)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

```
```On Thu, 16 Nov 2023 01:21:45 -0500, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

>On 2023-11-15 20:59, Klaus Kragelund wrote:
>> On Wednesday, 15 November 2023 at 23:55:30 UTC+1, john larkin wrote:
>>> I'm used to an air core inductor having a positive tempco of
>>> inductance around +120 PPM/k or so, just from the physical expansion
>>> of the copper increasing the diameter.
>>>
>>> But this Coilcraft midi-spring part
>>>
>>> https://www.dropbox.com/scl/fi/mfplgwzorhsh5sodxz5cu/Coilcraft_150n_Midi.jpg?rlkey=nrhwa9j64swuz7bmo1hiyjr9j&raw=1
>>>
>>> is much less, maybe +30 PPM. I wonder if the plastic expansion changes
>>> the geometry or something. Lengthens the solenoid?
>>>
>>> Well, it makes it easier to temperature compensate my oscillator. Out
>>> on my bench, it's measured 49.9944 MHz, exactly the same, for 3 hours.
>> Just a question, what about the permeability of the enclosing material?  Could it be that it would have minute permeability that is affected from temperature?
>>
>> You could heat it above the curie point, if the inductance decreased suddenly...
>>
>
>You can make the longitudinal expansion of the plastic compensate for
>the circumferential expansion of the copper.
>
>To within a couple of percent, L(uH) = (a**2 N**2)/(9a + 10 b), where
>a is the mean radius of the coil,
>b is the length of the winding (both in inches), and
>N is the number of turns.

We can measure frequency to PPBs, so a spring as the inductor in an
oscillator could be a position/elongation sensor to PPBs.

There must be a use for that.

(I've been playing with the microinch-sensitive LVDTs that are used
for machine shop metrology. They are expensive.)

>
>CTE(a) is controlled by the copper,  CTE(b) by the plastic.
>
>so we get
>
>dL/dT = 2 N**2 a da/dT/ (denom)
>        - N**2 a**2 *( 9 da/dT + 10 db/dT) / denom**2
>
>da/dT = a*CTE(Cu)
>db/dT = b*CTE(plastic)
>
>Dividing by L and collecting terms, we get
>
>TCL = (dL/dT)/L  = (2 CTE(Cu) - (9a CTE(Cu) + 10b CTE(plastic))/(9a + 10b).
>
>With CTE(Cu) = 17 ppm/K and CTE(plastic) probably 100 ppm/K, you get
>zero TC somewhere about a/b = 4.5, i.e. diameter ~ 9 x length. (That is,
>unless I've made a blunder, which is a definite possibility at 1 AM.)

Right, the plastic can reduce the TC.

We did once have a traumatic experience with some copper+plastic
inductors where the plastic cold-flowed and changed L enough to kick
us out of phase-lock after some weeks or months in the field. The fix
was to bake them overnight to remove the stresses. I still suffer PTSD
from that experience.

>
>Cheers
>
>Phil Hobbs
```