[time-nuts] need example frequency vs temp equation

Bernd Neubig bneubig at t-online.de
Thu Oct 13 01:10:29 EDT 2011

Hi Jim,

There are different types of TCXO compensation techniques on the market.
Each of them generating a different style of f(T) characterisitcs.
Furthermore the f(T) response varies from unit to unit, because each TCXO is
usually uindividually compensated (or sometimes in groups of similar quartz
f(T) characteristics.
To name a few compensation types:
The classical types can be broken down in direct and indirect compensation:
1. the first one using a thermistor/capacitor/resistor network connected in
series to the quartz crystal resonator. This network represents a temprature
dependenta load caopacitants to the crystal.
2. the indirect ones using a thermistor/resistor network which generates a
temperature-dependent DC voltage, which is fed to a varactor diode (in
series to the crystal) and thus changing f over T. Sometimes the passive
network is combined with an op-amp to realize a higher voltage swing. 
3. The modern TCXO (all these small ceramic packaged SMD units) use IC-based
compensation techniques. There are different TCO on the market which differ
in their working principle slightly. But in general, most of those IC's
contain a temperature sensor, from which a DC voltage represented by
polynomial of 3rd or higher order is generated by analog techniqes:
The coefficients for the polynomial are 
- a0 = reference voltage
- a1 = outoput from temperature sensor
- a2 = output from temperature sensor multiplied by the same with an
analogue multiplier
- a3 = output of a2 multiplied with temp sensor output  etc.
These components are fed into an analogue summing amplifier through analogue
potentiometers, which are setting the magnitude of each coefficient.
This summed-up voltage ploynomial feeds one or two varactor diodes in series
to the crystal.
In the (still individual, but highly automated)compensation process, the
coefficient potentiometers are set set through a serial data line such, that
the f(T) characteristic shows minimum deviation over temperature. This
process runs through the whole operating temperture range in small
temperature steps, mostly in both directíons to take into account some of
the hysteresis of the crystal's f(T) characteristic.
4. Besides these techniques there are some other approaches, such like the
first generation of digitally compensated TCXO, which were using loo-up
tables for eacht temperature increment (bit), which contains the digital
word for the necessary compensation voltage. The disadvantage of this method
are the discontinuities between eacht temperature bit, causing small
frequency jumps and/or jitter

To conclude: Because of the individual process, TCXO do not show any uniform
f(T) characteristic. You can fit it by a higher order polynomial, but the
responses are looking different for each individual unit.

Best regards

Bernd, DK1AG


-----Ursprüngliche Nachricht-----
Von: time-nuts-bounces at febo.com [mailto:time-nuts-bounces at febo.com] Im
Auftrag von Jim Lux
Gesendet: Donnerstag, 13. Oktober 2011 02:13
An: Discussion of precise time and frequency measurement
Betreff: [time-nuts] need example frequency vs temp equation

I'm putting together some examples of oscillator behavior vs temperature and
I'm looking for some plausible coefficients and simple equations to use to
generate nice looking curves.

oscillators are TCXO and run of the mill whatever they use for computer
clock oscillators (AT cut?).

Something that gives me decent PPM vs degrees C for a range from cold (-50
to -40) to hot (say +70 to +80)

I've got tons of measured data, but before I spent the time to try and do a
curve fit (implying that I can actually read the data and not have to copy
it by hand from a table or translate some oddball log file)

I've got Vig's tutorial: If you look at page 2-7, it's those curves I want
to generate.

(or if you look at 4-43 in the tutorial)

Maybe the Army book by Bennett?

Even better if I can replicate the hysteresis with a simple model.

I've got Frerking's equation
delta F/F = A1* deltaT + A2*deltaT^2 + A3*deltaT^3

deltaT = T - 25C

but what's some good numbers for A1, A2, and A3..  I found one reference
that cites Gerber and Ballato
A1 = -5.08E-6 * angle of cut relative to 35.25 degrees
A2 = -0.45E-9
A3 = 108.6E-12

that gets me a generic AT cut..

But what about TCXOs (which have more lumps in the curve...)

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