Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Richard (Rick) Karlquist]

On 11/24/2016 5:16 AM, Bob Camp wrote:


The biggest challenge is to take out the “early stuff”. One approach is to fit
the same equation twice with the time constant restricted to a range on each.
For most OCXO’s (90%) the equation when fit early represents an upper limit
to the drift. You might get a another element that comes in and is apparent
after a year or two. It might be replaced by another element after five or ten 
years.
They generally (~80%) represent a change in sign (negative drift vs positive).

If you look at the “other 10%” some have really poor aging and are not shipped.
Some are very erratic and simply can not be fit. Some of the 90% are fit with a
“upper limit” because they exhibit no measurable aging over the 30 days (or 
whatever)
of testing.

If you take the bad aging (out of spec) parts out of the pile, those are the 
ones
with the best fit. They have very pretty curves and they stick to those curves
for a *long* time. They have a single dominant cause for their aging ( = the 
defect).
The rest of the parts have all of the causes bashed down by the process so that
over a 20 or 30 year span, there probably is no single dominant cause.

Bob




This excellent response channels what Jack Kusters used to say.  The
idea that aging follows any predicable pattern might have been true
decades ago.  For example, I remember being told in 1974 that
everyone knew that metal crystals aged downward and glass crystals
aged upward.  It was true at the time, but those aging processes
have been beat down.  According to Jack, 10811/E1938A aging is
primarily "stress relaxation".  It could be either direction and
a given crystal can change direction over time.  On top of that,
crystals have frequency "jumps" at unpredictable intervals.  At
HP, we had an "aging system" that watched crystals to try to reject
bad actors and find the well behaved ones.  The problem was that the
longer you watched an oscillator, the better chance of catching
it in the act of jumping.  They didn't necessarily get better
over time (over many months).  No matter how many crystals we
looked at, we never found one that had atomic like aging.

My observation is that the systematic (therefore predictable)
aging processes have been eliminated by improved manufacturing
techniques, leaving the true random (unpredictable) aging
processes.

The one thing I can say is that it is good to keep the crystal
ovenized at all times.  Even a momentary oven outage tends to
reboot aging.

Rick
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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Bob Camp]

Hi


> On Nov 23, 2016, at 11:21 PM, Scott Stobbe  wrote:
> 
> Hi Lars,
> 
> There are a few other pieces I have yet to fully appreciate. One of which
> is that Aln(Bt+1) isn't a time-invariant model. In the most common case
> (for the mfg) the time scale aligns with infancy of the OCXO, when it's hot
> off the line. However after pre-aging, perhaps some service life, what time
> reference is best? Sometime I will try adding an additional parameter for
> infancy time and see how that goes.


The biggest challenge is to take out the “early stuff”. One approach is to fit 
the same equation twice with the time constant restricted to a range on each.
For most OCXO’s (90%) the equation when fit early represents an upper limit
to the drift. You might get a another element that comes in and is apparent 
after a year or two. It might be replaced by another element after five or ten 
years.
They generally (~80%) represent a change in sign (negative drift vs positive). 

If you look at the “other 10%” some have really poor aging and are not shipped. 
Some are very erratic and simply can not be fit. Some of the 90% are fit with a
“upper limit” because they exhibit no measurable aging over the 30 days (or 
whatever)
of testing. 

If you take the bad aging (out of spec) parts out of the pile, those are the 
ones
with the best fit. They have very pretty curves and they stick to those curves
for a *long* time. They have a single dominant cause for their aging ( = the 
defect). 
The rest of the parts have all of the causes bashed down by the process so that
over a 20 or 30 year span, there probably is no single dominant cause. 

Bob

> 
> A fit of the full ten year data-set, attached in the two plots
> "Lars_10Year.png", "Lars_10Year_45Day.png".
> 
> I would agree to your description of 1/sqrt(t) aging for the first 1000
> days, but sometime after, it follows 1/t. Attached is plot of age rate
> "Lars_AgeRate.png". You can see during the first 1000 days the age rate
> declines at 1 decade for 2 decades time indicating t^(-1/2), but eventually
> it follows 1/t.
> 
> On Wed, Nov 23, 2016 at 3:57 PM, Lars Walenius 
> wrote:
> 
>> Hi Scott.
>> 
>> 
>> 
>> Here is a textfile with data for the 10 years (As in the graph 2001-2011).
>> 
>> 
>> 
>> Also the ln(bt+1) fit, as Magnus said, has the derivate b/(b*t+1) that
>> with b*t >>1 is 1/t. But my data has the aging between 1 and 10 years more
>> like 1/sqrt(t) If I just have a brief look on the aging graph.
>> 
>> 
>> 
>> Lars
>> 
>> 
>> 
>> *Från: *Scott Stobbe 
>> *Skickat: *den 19 november 2016 04:11
>> 
>> Hi Lars,
>> 
>> 
>> 
>> I agree with you, that if there is data out there, it isn't easy to find,
>> 
>> many thanks for sharing!
>> 
>> 
>> 
>> Fitting to the full model had limited improvements, the b coefficient was
>> 
>> quite large making it essentially equal to the ln(x) function you fitted in
>> 
>> excel. It is attached as "Lars_FitToMil55310.png".
>> 
>> 
>> 
>> So on further thought, the B term can't model a device aging even faster
>> 
>> than it should shortly after infancy. In the two extreme cases either B is
>> 
>> large and (Bt)>>1 so the be B term ends up just being an additive bias, or
>> 
>> B is small, and ln(x) is linearized (or slowed down) during the first bit
>> 
>> of time.
>> 
>> 
>> 
>> You can approximated the MIL 55310 between two points in time as
>> 
>> 
>> 
>> f(t2) - f(t1) = Aln(t2/t1)
>> 
>> 
>> 
>> A = ( f(t2) - f(t1) )/ln(t2/t1)
>> 
>> 
>> 
>> Looking at some of your plots it looks like between the end of year 1 and
>> 
>> year 10 you age from 20 ppb to 65 ppb,
>> 
>> 
>> 
>> A ~ 20
>> 
>> 
>> 
>> The next plot "Lars_ForceAcoef", is a fit with the A coefficient forced to
>> 
>> be 2 and 20. The 20 doesn't end-up fitting well on this time scale.
>> 
>> 
>> 
>> Looking at the data a little more, I wondered if the first 10 day are going
>> 
>> through some behavior that isn't representative of long-term aging, like
>> 
>> warm-up, retrace (I'm sure bob could name half a dozen more examples). So
>> 
>> the next two plots are fits of the 4 data points after day10, and seem to
>> 
>> fit well, "Lars_FitAfterDay10.png", "Lars_1Year.png".
>> 
>> 
>> 
>> If you are willing to share the next month, we can add that to the fit.
>> 
>> 
>> 
>> Cheers,
>> 
>> 
>> 
>> On Fri, Nov 18, 2016 at 1:26 PM, Lars Walenius 
>> 
>> wrote:
>> 
>>> 
>> 
>>> Hopefully someone can find the correct a and b for a*ln(bt+1) with
>> 
>> stable32 or matlab for this data set:
>> 
>>> Days ppb
>> 
>>> 2   2
>> 
>>> 4   3.5
>> 
>>> 7   4.65
>> 
>>> 8   5.05
>> 
>>> 9   5.22
>> 
>>> 12 6.11
>> 
>>> 13 6.19
>> 
>>> 25 7.26
>> 
>>> 32 7.92
>> 
>> 
>> 
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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Scott Stobbe]

Hi Lars,

There are a few other pieces I have yet to fully appreciate. One of which
is that Aln(Bt+1) isn't a time-invariant model. In the most common case
(for the mfg) the time scale aligns with infancy of the OCXO, when it's hot
off the line. However after pre-aging, perhaps some service life, what time
reference is best? Sometime I will try adding an additional parameter for
infancy time and see how that goes.

A fit of the full ten year data-set, attached in the two plots
"Lars_10Year.png", "Lars_10Year_45Day.png".

I would agree to your description of 1/sqrt(t) aging for the first 1000
days, but sometime after, it follows 1/t. Attached is plot of age rate
"Lars_AgeRate.png". You can see during the first 1000 days the age rate
declines at 1 decade for 2 decades time indicating t^(-1/2), but eventually
it follows 1/t.

On Wed, Nov 23, 2016 at 3:57 PM, Lars Walenius 
wrote:

> Hi Scott.
>
>
>
> Here is a textfile with data for the 10 years (As in the graph 2001-2011).
>
>
>
> Also the ln(bt+1) fit, as Magnus said, has the derivate b/(b*t+1) that
> with b*t >>1 is 1/t. But my data has the aging between 1 and 10 years more
> like 1/sqrt(t) If I just have a brief look on the aging graph.
>
>
>
> Lars
>
>
>
> *Från: *Scott Stobbe 
> *Skickat: *den 19 november 2016 04:11
>
> Hi Lars,
>
>
>
> I agree with you, that if there is data out there, it isn't easy to find,
>
> many thanks for sharing!
>
>
>
> Fitting to the full model had limited improvements, the b coefficient was
>
> quite large making it essentially equal to the ln(x) function you fitted in
>
> excel. It is attached as "Lars_FitToMil55310.png".
>
>
>
> So on further thought, the B term can't model a device aging even faster
>
> than it should shortly after infancy. In the two extreme cases either B is
>
> large and (Bt)>>1 so the be B term ends up just being an additive bias, or
>
> B is small, and ln(x) is linearized (or slowed down) during the first bit
>
> of time.
>
>
>
> You can approximated the MIL 55310 between two points in time as
>
>
>
> f(t2) - f(t1) = Aln(t2/t1)
>
>
>
> A = ( f(t2) - f(t1) )/ln(t2/t1)
>
>
>
> Looking at some of your plots it looks like between the end of year 1 and
>
> year 10 you age from 20 ppb to 65 ppb,
>
>
>
> A ~ 20
>
>
>
> The next plot "Lars_ForceAcoef", is a fit with the A coefficient forced to
>
> be 2 and 20. The 20 doesn't end-up fitting well on this time scale.
>
>
>
> Looking at the data a little more, I wondered if the first 10 day are going
>
> through some behavior that isn't representative of long-term aging, like
>
> warm-up, retrace (I'm sure bob could name half a dozen more examples). So
>
> the next two plots are fits of the 4 data points after day10, and seem to
>
> fit well, "Lars_FitAfterDay10.png", "Lars_1Year.png".
>
>
>
> If you are willing to share the next month, we can add that to the fit.
>
>
>
> Cheers,
>
>
>
> On Fri, Nov 18, 2016 at 1:26 PM, Lars Walenius 
>
> wrote:
>
> >
>
> > Hopefully someone can find the correct a and b for a*ln(bt+1) with
>
> stable32 or matlab for this data set:
>
> > Days ppb
>
> > 2   2
>
> > 4   3.5
>
> > 7   4.65
>
> > 8   5.05
>
> > 9   5.22
>
> > 12 6.11
>
> > 13 6.19
>
> > 25 7.26
>
> > 32 7.92
>
>
>
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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Magnus Danielson]

It really means that B will be harder to get a qualitative value for.

Also, you need to have "clean" data or else you will be far off.
Plot the estimated variant and also plot the difference.
As Jim Barnes used to teach, always check the whiteness of matching 
residues!


Cheers,
Magnus

On 11/23/2016 09:58 PM, Lars Walenius wrote:

Bob,
I have to ask about the B-term. In the paper that Scott started this with I see that 
B was 4.45. But if I understand you correct Bt<1 even at 30days is normal? That 
would mean a B of <0.033?

Lars


Bob wrote:
In a conventional fit situation, you have < 30 days worth of data and the “time 
constant”

is > 30 days. Put another way bt <= 1 in the normal case. It is only when you 
go out to years
that bt gets large.

Bob


On Nov 18, 2016, at 9:58 PM, Scott Stobbe  wrote:


Hi Lars,

I agree with you, that if there is data out there, it isn't easy to find,
many thanks for sharing!

Fitting to the full model had limited improvements, the b coefficient was
quite large making it essentially equal to the ln(x) function you fitted in
excel. It is attached as "Lars_FitToMil55310.png".

So on further thought, the B term can't model a device aging even faster
than it should shortly after infancy. In the two extreme cases either B is
large and (Bt)>>1 so the be B term ends up just being an additive bias, or
B is small, and ln(x) is linearized (or slowed down) during the first bit
of time.

You can approximated the MIL 55310 between two points in time as

f(t2) - f(t1) = Aln(t2/t1)

A = ( f(t2) - f(t1) )/ln(t2/t1)

Looking at some of your plots it looks like between the end of year 1 and
year 10 you age from 20 ppb to 65 ppb,

A ~ 20

The next plot "Lars_ForceAcoef", is a fit with the A coefficient forced to
be 2 and 20. The 20 doesn't end-up fitting well on this time scale.

Looking at the data a little more, I wondered if the first 10 day are going
through some behavior that isn't representative of long-term aging, like
warm-up, retrace (I'm sure bob could name half a dozen more examples). So
the next two plots are fits of the 4 data points after day10, and seem to
fit well, "Lars_FitAfterDay10.png", "Lars_1Year.png".

If you are willing to share the next month, we can add that to the fit.

Cheers,

On Fri, Nov 18, 2016 at 1:26 PM, Lars Walenius 
wrote:


Hopefully someone can find the correct a and b for a*ln(bt+1) with

stable32 or matlab for this data set:

Days ppb
2   2
4   3.5
7   4.65
8   5.05
9   5.22
12 6.11
13 6.19
25 7.26
32 7.92

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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Lars Walenius]

Hi Scott.

Here is a textfile with data for the 10 years (As in the graph 2001-2011).

Also the ln(bt+1) fit, as Magnus said, has the derivate b/(b*t+1) that with b*t 
>>1 is 1/t. But my data has the aging between 1 and 10 years more like 
1/sqrt(t) If I just have a brief look on the aging graph.

Lars

Från: Scott Stobbe
Skickat: den 19 november 2016 04:11

Hi Lars,

I agree with you, that if there is data out there, it isn't easy to find,
many thanks for sharing!

Fitting to the full model had limited improvements, the b coefficient was
quite large making it essentially equal to the ln(x) function you fitted in
excel. It is attached as "Lars_FitToMil55310.png".

So on further thought, the B term can't model a device aging even faster
than it should shortly after infancy. In the two extreme cases either B is
large and (Bt)>>1 so the be B term ends up just being an additive bias, or
B is small, and ln(x) is linearized (or slowed down) during the first bit
of time.

You can approximated the MIL 55310 between two points in time as

f(t2) - f(t1) = Aln(t2/t1)

A = ( f(t2) - f(t1) )/ln(t2/t1)

Looking at some of your plots it looks like between the end of year 1 and
year 10 you age from 20 ppb to 65 ppb,

A ~ 20

The next plot "Lars_ForceAcoef", is a fit with the A coefficient forced to
be 2 and 20. The 20 doesn't end-up fitting well on this time scale.

Looking at the data a little more, I wondered if the first 10 day are going
through some behavior that isn't representative of long-term aging, like
warm-up, retrace (I'm sure bob could name half a dozen more examples). So
the next two plots are fits of the 4 data points after day10, and seem to
fit well, "Lars_FitAfterDay10.png", "Lars_1Year.png".

If you are willing to share the next month, we can add that to the fit.

Cheers,

On Fri, Nov 18, 2016 at 1:26 PM, Lars Walenius 
wrote:
>
> Hopefully someone can find the correct a and b for a*ln(bt+1) with
stable32 or matlab for this data set:
> Days ppb
> 2   2
> 4   3.5
> 7   4.65
> 8   5.05
> 9   5.22
> 12 6.11
> 13 6.19
> 25 7.26
> 32 7.92

daysppb
2   2
4   3.5
7   4.65
8   5.05
9   5.22
12  6.11
13  6.19
25  7.26
32  7.92
33  8.15
39  8.42
46  8.92
46  9.18
47  9.02
54  9.51
60  9.78
74  10.45
83  11.36
92  11.78
97  12.08
110 12.8
128 13.6
158 14.7
193 15.9
224 16.9
254 18
284 19.01
314 20
343 21.1
375 22.3
417 23.7
445 24.8
476 25.7
515 26.7
545 27.7
586 28.8
615 29.4
646 30.2
672 30.7
703 31.4
743 32.2
787 33.5
826 34.6
861 35.3
904 36.2
940 37
976 37.7
101038.5
104639.1
107239.5
108138.3
112438.6
116339.6
120140.5
123941.2
128542.2
132043
135743.6
139844.4
143245
146745.7
150146.3
153447.1
156047.7
159748.4
162848.9
165949.3
168749.9
171850.35
174850.7
177951.2
180951.5
185052
188652.6
191453
194753.45
198453.9
201954.3
204554.5
207154.7
211655.11
213254.97
216555.27
219855.63
223056
226556.5
230957
234657.4
238957.85
243458.35
247358.7
251359
255059.3
258759.65
262560
266460.35
269660.6
272960.85
276461.15
279661.4
282961.6
286361.85
289862.1
293562.4
297262.8
300763.12
304363.47
307863.73
311464.05
314964.3
318464.5
322464.75
325964.96
329565.23
333265.54
336865.82
340666.09
344166.33
348266.55
351966.72
356367.01
360467.22
364767.59
369268.02
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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Lars Walenius]

Bob,
I have to ask about the B-term. In the paper that Scott started this with I see 
that B was 4.45. But if I understand you correct Bt<1 even at 30days is normal? 
That would mean a B of <0.033?

Lars

>Bob wrote:
>In a conventional fit situation, you have < 30 days worth of data and the 
>“time constant”
is > 30 days. Put another way bt <= 1 in the normal case. It is only when you 
go out to years
that bt gets large.

Bob

>> On Nov 18, 2016, at 9:58 PM, Scott Stobbe  wrote:
>
> Hi Lars,
>
> I agree with you, that if there is data out there, it isn't easy to find,
> many thanks for sharing!
>
> Fitting to the full model had limited improvements, the b coefficient was
> quite large making it essentially equal to the ln(x) function you fitted in
> excel. It is attached as "Lars_FitToMil55310.png".
>
> So on further thought, the B term can't model a device aging even faster
> than it should shortly after infancy. In the two extreme cases either B is
> large and (Bt)>>1 so the be B term ends up just being an additive bias, or
> B is small, and ln(x) is linearized (or slowed down) during the first bit
> of time.
>
> You can approximated the MIL 55310 between two points in time as
>
> f(t2) - f(t1) = Aln(t2/t1)
>
> A = ( f(t2) - f(t1) )/ln(t2/t1)
>
> Looking at some of your plots it looks like between the end of year 1 and
> year 10 you age from 20 ppb to 65 ppb,
>
> A ~ 20
>
> The next plot "Lars_ForceAcoef", is a fit with the A coefficient forced to
> be 2 and 20. The 20 doesn't end-up fitting well on this time scale.
>
> Looking at the data a little more, I wondered if the first 10 day are going
> through some behavior that isn't representative of long-term aging, like
> warm-up, retrace (I'm sure bob could name half a dozen more examples). So
> the next two plots are fits of the 4 data points after day10, and seem to
> fit well, "Lars_FitAfterDay10.png", "Lars_1Year.png".
>
> If you are willing to share the next month, we can add that to the fit.
>
> Cheers,
>
> On Fri, Nov 18, 2016 at 1:26 PM, Lars Walenius 
> wrote:
>>
>> Hopefully someone can find the correct a and b for a*ln(bt+1) with
> stable32 or matlab for this data set:
>> Days ppb
>> 2   2
>> 4   3.5
>> 7   4.65
>> 8   5.05
>> 9   5.22
>> 12 6.11
>> 13 6.19
>> 25 7.26
>> 32 7.92
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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Bob Camp]

Hi

In a conventional fit situation, you have < 30 days worth of data and the “time 
constant”
is > 30 days. Put another way bt <= 1 in the normal case. It is only when you 
go out to years
that bt gets large.

Bob

> On Nov 18, 2016, at 9:58 PM, Scott Stobbe  wrote:
> 
> Hi Lars,
> 
> I agree with you, that if there is data out there, it isn't easy to find,
> many thanks for sharing!
> 
> Fitting to the full model had limited improvements, the b coefficient was
> quite large making it essentially equal to the ln(x) function you fitted in
> excel. It is attached as "Lars_FitToMil55310.png".
> 
> So on further thought, the B term can't model a device aging even faster
> than it should shortly after infancy. In the two extreme cases either B is
> large and (Bt)>>1 so the be B term ends up just being an additive bias, or
> B is small, and ln(x) is linearized (or slowed down) during the first bit
> of time.
> 
> You can approximated the MIL 55310 between two points in time as
> 
> f(t2) - f(t1) = Aln(t2/t1)
> 
> A = ( f(t2) - f(t1) )/ln(t2/t1)
> 
> Looking at some of your plots it looks like between the end of year 1 and
> year 10 you age from 20 ppb to 65 ppb,
> 
> A ~ 20
> 
> The next plot "Lars_ForceAcoef", is a fit with the A coefficient forced to
> be 2 and 20. The 20 doesn't end-up fitting well on this time scale.
> 
> Looking at the data a little more, I wondered if the first 10 day are going
> through some behavior that isn't representative of long-term aging, like
> warm-up, retrace (I'm sure bob could name half a dozen more examples). So
> the next two plots are fits of the 4 data points after day10, and seem to
> fit well, "Lars_FitAfterDay10.png", "Lars_1Year.png".
> 
> If you are willing to share the next month, we can add that to the fit.
> 
> Cheers,
> 
> On Fri, Nov 18, 2016 at 1:26 PM, Lars Walenius 
> wrote:
>> 
>> Hopefully someone can find the correct a and b for a*ln(bt+1) with
> stable32 or matlab for this data set:
>> Days ppb
>> 2   2
>> 4   3.5
>> 7   4.65
>> 8   5.05
>> 9   5.22
>> 12 6.11
>> 13 6.19
>> 25 7.26
>> 32 7.92
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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Scott Stobbe]

Hi Lars,

I agree with you, that if there is data out there, it isn't easy to find,
many thanks for sharing!

Fitting to the full model had limited improvements, the b coefficient was
quite large making it essentially equal to the ln(x) function you fitted in
excel. It is attached as "Lars_FitToMil55310.png".

So on further thought, the B term can't model a device aging even faster
than it should shortly after infancy. In the two extreme cases either B is
large and (Bt)>>1 so the be B term ends up just being an additive bias, or
B is small, and ln(x) is linearized (or slowed down) during the first bit
of time.

You can approximated the MIL 55310 between two points in time as

f(t2) - f(t1) = Aln(t2/t1)

A = ( f(t2) - f(t1) )/ln(t2/t1)

Looking at some of your plots it looks like between the end of year 1 and
year 10 you age from 20 ppb to 65 ppb,

A ~ 20

The next plot "Lars_ForceAcoef", is a fit with the A coefficient forced to
be 2 and 20. The 20 doesn't end-up fitting well on this time scale.

Looking at the data a little more, I wondered if the first 10 day are going
through some behavior that isn't representative of long-term aging, like
warm-up, retrace (I'm sure bob could name half a dozen more examples). So
the next two plots are fits of the 4 data points after day10, and seem to
fit well, "Lars_FitAfterDay10.png", "Lars_1Year.png".

If you are willing to share the next month, we can add that to the fit.

Cheers,

On Fri, Nov 18, 2016 at 1:26 PM, Lars Walenius 
wrote:
>
> Hopefully someone can find the correct a and b for a*ln(bt+1) with
stable32 or matlab for this data set:
> Days ppb
> 2   2
> 4   3.5
> 7   4.65
> 8   5.05
> 9   5.22
> 12 6.11
> 13 6.19
> 25 7.26
> 32 7.92
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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Bob Camp]

Hi


> On Nov 18, 2016, at 4:36 PM, Magnus Danielson  
> wrote:
> 
> Hi Lars,
> 
> Now, consider f(t) = a*log(b*t+1), then the derivate is a*b/(b*t+1) and 
> second derivate - a * b^2 / (b*t + 1)^2.
> 
> Forming first f'(t) and second f"(t) derivate estimates from data is trivial. 
> Given that we can estimate a and b using
> 
> a = - f('t)^2 / f"(t)
> 
> b = - f'(t) / (f'(t) * t - a)
> 
>  = - f"(t) / (f("t) * t - f'(t))
> 
> A bit of paper and pen work or you get Maxima to do some work for you.
> I haven't seen how any real estimator of this drift function is implemented,


By far the most common implementation of the equation as an estimator is in 
factory test of OCXO’s that
are built to the 55310 spec. It also is fairly common to use it on commercial 
OCXO’s as well. Put another way:
It’s how you answer “Does it meet the 20 year aging spec?” in less than 20 
years. 

Bob


> but I wanted to provide some notes from note-book of stuff being unfinished.
> 
> Cheers,
> Magnus
> 
> On 11/18/2016 07:26 PM, Lars Walenius wrote:
>> Bob wrote:
>>> As mentioned earlier in this thread. The function that has been used in 
>>> several posts
>>> isn’t the right log function. The proper fit is to ln(bt+1)
>> 
>> You are absolutely right. It was my mistake to use the ln(t) in the graph. 
>> As that was what I know in Excel and I don´t have Stable32 or MatLab. In 
>> Excel I actually double checked that (a*ln(bt+1)) with b 5 to 1000 gave 
>> about the same as (a*ln(t)) for my data set (only the offset was largely 
>> different).
>> 
>> Hopefully someone can find the correct a and b for a*ln(bt+1) with stable32 
>> or matlab for this data set:
>> Days ppb
>> 2   2
>> 4   3.5
>> 7   4.65
>> 8   5.05
>> 9   5.22
>> 12 6.11
>> 13 6.19
>> 25 7.26
>> 32 7.92
>> 
>> It would also be interesting if I could get the drift after 10 years to see 
>> if it is about 6E-13/day as with the ln(t).
>> 
>> 
>> Peter wrote:
 I'm not very good with Excel, but this curve-fitting function sounds very
 useful.  Could you please tell me how it's done?
>> 
>> In the graph I only right-clicked the curve and selected ”add trendline” 
>> here I checked the logarithmic and show equation.
>> 
>> Lars
>> 
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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Magnus Danielson]

Hi Lars,

Now, consider f(t) = a*log(b*t+1), then the derivate is a*b/(b*t+1) and 
second derivate - a * b^2 / (b*t + 1)^2.


Forming first f'(t) and second f"(t) derivate estimates from data is 
trivial. Given that we can estimate a and b using


a = - f('t)^2 / f"(t)

b = - f'(t) / (f'(t) * t - a)

  = - f"(t) / (f("t) * t - f'(t))

A bit of paper and pen work or you get Maxima to do some work for you.
I haven't seen how any real estimator of this drift function is 
implemented, but I wanted to provide some notes from note-book of stuff 
being unfinished.


Cheers,
Magnus

On 11/18/2016 07:26 PM, Lars Walenius wrote:

Bob wrote:

As mentioned earlier in this thread. The function that has been used in several 
posts
isn’t the right log function. The proper fit is to ln(bt+1)


You are absolutely right. It was my mistake to use the ln(t) in the graph. As 
that was what I know in Excel and I don´t have Stable32 or MatLab. In Excel I 
actually double checked that (a*ln(bt+1)) with b 5 to 1000 gave about the same 
as (a*ln(t)) for my data set (only the offset was largely different).

Hopefully someone can find the correct a and b for a*ln(bt+1) with stable32 or 
matlab for this data set:
Days ppb
2   2
4   3.5
7   4.65
8   5.05
9   5.22
12 6.11
13 6.19
25 7.26
32 7.92

It would also be interesting if I could get the drift after 10 years to see if 
it is about 6E-13/day as with the ln(t).


Peter wrote:

I'm not very good with Excel, but this curve-fitting function sounds very
useful.  Could you please tell me how it's done?


In the graph I only right-clicked the curve and selected ”add trendline” here I 
checked the logarithmic and show equation.

Lars

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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Lars Walenius]

Bob wrote:
>As mentioned earlier in this thread. The function that has been used in 
>several posts
>isn’t the right log function. The proper fit is to ln(bt+1)

You are absolutely right. It was my mistake to use the ln(t) in the graph. As 
that was what I know in Excel and I don´t have Stable32 or MatLab. In Excel I 
actually double checked that (a*ln(bt+1)) with b 5 to 1000 gave about the same 
as (a*ln(t)) for my data set (only the offset was largely different).

Hopefully someone can find the correct a and b for a*ln(bt+1) with stable32 or 
matlab for this data set:
Days ppb
2   2
4   3.5
7   4.65
8   5.05
9   5.22
12 6.11
13 6.19
25 7.26
32 7.92

It would also be interesting if I could get the drift after 10 years to see if 
it is about 6E-13/day as with the ln(t).


Peter wrote:
>> I'm not very good with Excel, but this curve-fitting function sounds very
>> useful.  Could you please tell me how it's done?

In the graph I only right-clicked the curve and selected ”add trendline” here I 
checked the logarithmic and show equation.

Lars

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Re: [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Bob Camp]

Hi

As mentioned earlier in this thread. The function that has been used in several 
posts
isn’t the right log function. The proper fit is to ln(bt+1)

Bob

> On Nov 16, 2016, at 4:36 PM, Peter Vince  wrote:
> 
> Hello Lars,
> 
> Just out of curiosity I yesterday put just the first thirty days (like in
>> the pdf mentioned below) and let Excel calculate the logarithmic function.
>> If I extrapolate that to 10 years it seems that the drift would be
>> 6E-13/day but as can be seen in the aging graph it was more like ten times
>> higher.
>> 
> 
> I'm not very good with Excel, but this curve-fitting function sounds very
> useful.  Could you please tell me how it's done?
> 
> Thank you,
> 
>  Peter
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[time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

[Peter Vince]

Hello Lars,

Just out of curiosity I yesterday put just the first thirty days (like in
> the pdf mentioned below) and let Excel calculate the logarithmic function.
> If I extrapolate that to 10 years it seems that the drift would be
> 6E-13/day but as can be seen in the aging graph it was more like ten times
> higher.
>

I'm not very good with Excel, but this curve-fitting function sounds very
useful.  Could you please tell me how it's done?

 Thank you,

  Peter
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