On Oscillator Thermal Stability
Oscillators, like most things, are imperfect. A previous page looked
at oscillator linearity
which is important to keep your oscillators in tune across the octaves.
Another important criterion is stability within a changing environment, the dominant effect being temperature. On this page we look at various schemes proposed and
implemented to keep oscillators stable as the ambient temperature changes.
Transistor Exponentiator
The classic circuit for computing logarithms (or exponentials) is based around a
transistor junction and its function:


I_{c} = I_{s} e^{( } 
Vq kT 
) 

Utilising two wellmatched transistors we can eliminate the I_{s} term.
There are two generallyused schemes to compensate for the temperature sensitivity.
Sense and Adjust
The most widelyused scheme is based on a suitable RTD device (typically platinumbased resistor)
to compensate for the T term in the exponent. This approach is fairly intolerant to
temperature changes over a three or so decade (810 octaves) range and is fairly cheap once you
have found a source of the right RTD.
For example, Fritz's DialaTempco design which
provides for scale adjustment, scalefactor tempco and tuning tempco adjustment, and hf tracking adjustment.
The author suggests that drift can be brought down to less than 50ppm/°K.
Keep It Constant
The alternate approach is not compensate for the temperature at all, but simply to keep
the junction at a constant temperature instead. The usual approach is to use some sort of
multijunction part (e.g., LM3046) and utilise two of the junctions to build an onchip
heater (one junction as the heater and one as the thermostat).
Summary
This circuit is appealing, but it has some issues, which may or may not be of concern to
the application:
 The transistors need to be truly matched to cancel out the I_{s} term,
typically done with special logconformance dual transistors (e.g., MAT03, LS318).
 The intrinsic emitter resistance R_{BE} introduces an error voltage which
cannot be cancelled.
 RTDs (or "tempcos") have poor tolerance on both value and temperature coefficient
(typically 10%) so drift between two VCOs are unlikely to match.
 Heating solution requires considerable power and limits the choice of expo transistor.
SSM2164 Paired Compensator
To whet your appetite, here is a deliciously simple scheme based around the
SSM2164
from 1999 devised by
Roman Sowa:
and further developed around 2008 by
Osamu Hoshuyama:
As you can see both schemes are essentially the same, using a second SSM2164 gain cell to compensate for the temperature sensitivity of the first.
One essential difference between the two is the tempco voltage setting of the first gain cell.
Sowa sets it to a nominal 1V, while Hoshuyama sets it to a more specific value of 268mV.
Later, Dixon settled on a compensator voltage of 289.5mV and incorporated the scheme into the Dixie, Rubicon, and Atlantis modules manufactured by
Intellijel.
In 2011 Gratz explored the SSM2164 thermal properties and proposed a compensator
voltage of 284mV.
A similar approach was published by Patchell some time around 2002, but made using traditional OTAs rather than SSM2164.
This scheme has many attractions. It is simple, requiring the addition one
extra gain cell  the SSM2164 has four such cells, so it is not a huge loss to
utilise one for compensation. And with both gain cells on the same silicon
the thermal coupling and silicon properties matching are as good as can be achieved.
However, the scheme is not perfect. As Dixon found out, and borne out by Gratz's calculations, the log conformity
of the SSM2164 is less than ideal, and the value of the compensator voltage
was arrived at by minimising the tuning error across a range of temperature
and CV, with 289.5mV giving the least worst overall performance (other designers
have chosen slightly different priorities, for example Gillet choosing 280mV in the Mutable Instruments Anushri).
The fundamental
issue here is that the SSM2164 is not designed nor specified for high log
conformance  the only mention in the datasheet is related to gain matching
between any two gain cells, and is quoted (typical values only, no indication
of min or max) as 0.07dB at Av=0dB, and 0.24dB at Av=40dB.
A Note on Achievable Accuracy. For ±6 cents tuning accuracy we need
better than 0.043dB (±0.5%) log conformance, and clearly the SSM2164 is guaranteed never
to achieve that. Before you go screaming your little head off, note carefully
what I wrote: "guaranteed". With only typical values in the datasheet the
manufacturer has not specified the worst case that this device is guaranteed
to meet, and so we cannot make any assumptions about it. And that is fair,
given that this device is not targeted at the analogue computing market, but
at the less rigorous audio market, where fractions of a dB here or there are
not of concern. In practice, it is entirely possible for a compensated SSM2164
to be good enough for musical needs.
Log Amp InA Loop
All solutions presented so far are based on discrete components, or components not
designed for the specific purpose of log/antilog computation. However, there are
devices specifically designed and made for this purpose  log amps.
Some examples include the LOG101 from TI, the MAX4206 from Maxim, and the AD8304 from Analog Devices.
Initial view is that these are expensive components! They are typically $5$10 each in volume.
But for your money you get a device that has a usable range of five or more decades (16+ octaves),
has everything integrated in one package, has excellent performance over a wide temperature
range (e.g, 0 to 70°.C) and takes up very little PCB area.
