SV: Re: SV: Re: SV: Re: [sdiy] Compensating PTC and NTC resistors

[René Schmitz]

karl dalen schrieb:

> Please Rene could you explain the idea of using 0 TC of a MFR as means
> to compensate down the 3900ppm of the PTC? I *gladly* admit (once again)
> i have no clue  how that works? What is it in TC2 that makes PTC TC1 to
> degrade?

Well the reasoning goes like this:

A 1k tempco resistor of 3900ppm/K (measured @25°C) has a slope of 
3.9ohm/K. (3.9ohmK^-1/1000ohm = 0.0039K^-1 or 3900ppm/K)
Now we can't change the material of the resistor afterwards, so lets see 
what happens when we try to change the resistor value instead. Of course 
we can't really do that, but we can put something in series.

Lets try what happens if we put a 100ohm resistor in series, and see how 
the tempco of the series connections turns out.

If we idealize the resistor for a moment we get:

1100ohm at 25°C, but the slope, is still only 3.9ohms/K, because the 
series resistor is ideal, and doesn't contribute to that. How much ppm 
is that? 3.9ohm*K^-1/1100ohm = 0.003545K^-1 or 3545ppm/K.

Well, thats not really what we need, but it is just to show the concept.
Its not the tempco of the series resistor thats doing the work here, its 
the series resistance, because it changes the value of the series 
arrangement without affecting the slope, effectively reducing the 
relative percentage (can you say ppm-age ?!) of change with respect to 
the whole arrangement.

Of course, I left out the TC of the series resistor, first because its 
value is difficult to know exactly. And more importantly because its TC 
can be made relatively small by using MFRs with tight specs. In that 
series arrangement typically the series resistor is way smaller than the 
tempco, and so the influence on the TC of the whole arrangement is way 
down. Besides the tempco of the PTC has tolerances anyway and its 
resistance value has also a tolerance, these are likely to swamp the 
theoretical difference a 100ppm series resistor has over one that has 0ppm.

The tempco we want to arrive at is 3354ppm/K. If the resistance was 
perfectly to scale with absolute temperature it would mean for a 1k 
(@25°C) resistor to have a slope of 1000 ohms / 298.15K -> 3.354ohms/K, 
which for a 1k resistor is the same as stating 3354ppm/K.

That gives us:

(1000ohm * 3900ppmK^-1 / 3354ppmK^-1)-1000ohm =  R2 = 163ohm.

Essentially this is the formula in Elbys datasheet, just with different 
figures, where TC2 is 0, and solved for R2. (Trying to solve this 
equation for both R2 and TC2 it is a little difficult. :-P)

Now we can see how many ppms a resistor of 1163ohm with a slope of 
3.9ohm/K has: 3.9ohmK^-1/1163ohm = 0.003353K^-1 or 3353ppmK^-1, 1ppm off 
due to rounding, not bad eh?

Lets stick in the figures into the equation again, this time we let TC2 
come into the picture, and lets see what happens when the R2 has a TC of 
+100ppm or -100ppm.

(1000ohm * 3900ppmK^-1 + 163ohm * 100ppmK^-1) / (1000ohm + 163ohm)
= 3367ppmK^-1

(1000ohm * 3900ppmK^-1 + 163ohm * 100ppmK^-1) / (1000ohm + 163ohm)
= 3339ppmK^-1

Makes some 15ppm difference. If you happen to have resistors somewhere 
in your input summing (or other CV processing) stage where their 
relative TCs are off by more than 15ppm the effects could easily 
outweigh this.

Now leaning back and watching the mud-fight on SDIY. :(

Cheers,
  René

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