[sdiy] Tempco adjuster idea

[Ian Fritz]

Hi ASSI --

Rebuttals inline.  :-)

At 05:24 AM 4/27/2003, ASSI wrote:
>On Sunday 27 April 2003 07:27, Ian Fritz wrote:
> > The ideal tempco resistor (for compensating exponential current
> > generators) has what's called a PTAT (proportional to absolute
> > temperature) response. This means that the resistance is of the form
> > R = AT, where A is a constant and T is absolute temperature.  This
> > dependence cancels the 1/T factor in the exponential of the
> > transistor I-V response function. The corresponding temperature
> > coefficient (1/R)(dR/dT) is just 1/T, or 3350ppm/K at room
> > temperature.
>
>Keep in mind that this is already an approximation for the temperature
>dependence of an idealized pn junction.

Yes it is, but it is a very good approximation.  Otherwise we would not be 
able to make accurately scaled VCOs.

>Once you get the diffusion
>resitances and other second order stuff in, things start to look
>different again.

The most important deviation for our applications is the emitter bulk 
resistance contribution, which can be quite accurately eliminated by 
standard compensation techniques and/or by using high-conformance 
transistors.  Other deviations only occur at very low currents, which we 
either avoid by not working there or we ignore because the frequencies 
involved are so low that the deviations don't matter (can't hear the beats).

>The rest of the circuit will have it's own idea about
>temperature dependence as well, especially noticeable if you're not
>careful with the type of resistors.

Of course. Generally, though, you can break the errors into two kinds: 
errors in the scale factor, which come from the exp(a Vb / kT) term in the 
converter and errors that are more or less linear, such as from the linear 
temperature coefficient of the integrating cap.  Please see the VCO pages 
at my website for discussion of how to separately compensate these and for 
examples of highly stable compensated oscillators.
http://home.earthlink.net/~ijfritz/sy_circ.htm

> > So what if you buy some tempcos and their coefficients are different
> > from this?  Since they are normally made of metals, their resistance
> > will still have a linear T dependence, but they will not be PTAT.  In
> > other words, their resistance can be well approximated as R = AT + B,
> > where the constant B is the resistance extrapolated back to T = 0.
> > If B is positive then the coefficient is too low, and conversely if B
> > is negative then it is too high.
>
>The TKR is defined as 1/Ro*(R(T)-Ro)/(T-To), which is why you always
>need to know what Ro and To is.

This is how manufacturers usually spec their tempcos, true, and you need to 
understand this and look very carefully at the specs to decide if a 
particular unit is suitable for your needs.  For example, I found one 
manufacturer who specifies two tempcos, one for a large range above room 
temperature and another for a large range below.  I actually had to look at 
their tabulated data to figure out the tempco for variation near 25 C.

>This is different from the above
>differential definition except around To and also different from
>(dR/dT) except for linear temperature dependence.

Yes, but, we are interested in small variations around room temperature. 
Therefore, it is the coefficient at room temperature (25 C) that matters to 
us. This coefficient should be 1/298.15 K^-1 = 3550 ppm/K.

> > So to correct for an incorrect coefficient one just needs to make a
> > circuit that cancels the B term.  This looks easy to do, at least on
> > paper, and the only drawback is that it takes several amplifiers
> > instead of just one to condition the control voltage inputs.
>
>No, you still have to fight both coefficients. The offsets introduced
>by B can be canceled by trimming at a single temperature. Then when
>you find that the compensation fades as you go away from that
>temperature, that means that A is incorrect.

Nonsense.  If B=0, then compensation is exact for any A  (ignoring 
nonlinearities).  AT/T = constant.  You seem not to understand the idea of 
multiplicative correction.  The converter response is proportional to exp[a 
(AT+B)/kT], where a is the constant factor needed to obtain 1V/oct 
response. When B=0 the T factors cancel. This is how converters are 
compensated.

>You can trim A towards
>zero rather easily with passive components, but not the other way
>around.

Why on earth do you think A should be zero?

All VCOs already have a trimpot to adjust the frequency scaling.  This is 
what gives the correct A coefficient.  So that's already in the 
circuit.  As B is tuned out, it will be necessary to adjust A to 
compensate, i.e. the two adjustments will interact a bit.  But I wouldn't 
call it a "fight".

>[...quad opamp circuit...]
>Also make sure that the damn circuit does not oscillate with the the
>gains so low...

Well, it is common to use an input circuit with 100 k summing resistors and 
a 2 k tempco for feedback.  This is a much smaller gain (.02).  There have 
been reported problems with oscillations with certain tempco resistors, 
possibly due to them not having a non-inductive winding. But you are right, 
this is one of the (many) factors one has to watch for.

>The tempco resistor compensates the actual converter,
>what you are trying equates to compensating the CV itself if I
>understood correctly.

No! Again, you seem not understand at all!  What I am suggesting is a 
circuit to electronically adjust the tempco to exactly 3550 ppm/K for 
proper compensation of the converter.

>If so, I'd suggest it's far easier to produce a
>PTAT signal with a bandgap and then mix that with the VC in the usual
>way.

In what sense is this "usual"?  I've never seen it done for a VCO. The main 
temperature effect is multiplicative -- an additive correction won't work 
at all.

> > I hope to try this idea out in the near future so that I can use
> > the  3200ppm/K units that KRL sold me.
>
>Heat up your expo converter to 40°C for the trim and save the opamps
>for something more useful. :-)

I have no fundamental objection to the brute-force thermostating 
approach.  But, of course, you don't just abra-cadabra heat something 
up.  It takes heating and temperature control circuitry to do this, it eats 
up quite a bit of power, stray heat can effect other circuit elements, you 
usually end up using low-performance array transistors for the converter -- 
we've been over all this many times before.  Op amps are cheap, even 
high-quality ones.

Best regards,

   Ian