Voltage coefficient in feed back resistor

[SMourareau]

I folks,
It's my first post on this forum I'm very interested in amp design and I would like to submit this subject (kind of mystery) to you.
I recently discovered the concept of voltage coefficient in resistors: The resistor value decreases with voltage applied.
The change in resistor value is small: metal film according to datasheets can have values as small as 1ppm/V in 0.1% range but most metal film have voltage coef much above 5ppm/V.

Now imagine you have designed the perfect 100W/8Ohm audio amp with 0% THD in open loop (!!!).
You introduce your FB loop using your tremendous (for example RC55Y) part that has only 1ppm/V of VCR and then ...
Considering you get approx 40V peak voltage on the FB resistor : your FB resistor is affected of a 40.10-6 fluctuation factor. Which will give a closed loop DHT of around 0.004%.
OK It is small but it is much more than some figures I've often red.

Can some one help understand this strange fact ?

Regards
Stéphane

[h_a]

The NFB resistor fluctuates (max) by 40e-6 ppm, which you forgot to divide by 40 to get the ratio, so it's (40e-6/40)*100 in %=0.0001%

Next, these 40e-6 ppm are the peak value when the sine reaches Vpeak; 99% of the time this value will be smaller or even zero. THD measurement averages these values and will give a further reduced reading.

Last, this number will be reduced by negative feedback just like any other error within the amp as well.

Your example sounds like a low NFB design (or big power amp), but these have still 20-30dB NFB which reduces this number by at least another factor 10.

Have fun, Hannes

[SMourareau]

Hi Hannes,
I not exactly agree with your analysis, I did not forgot to divide by 40 ...
40ppm = 0.004% is the actual fluctuation of NFB resistor (if we consider the voltage on negative input as small against output voltage).

It is not a voltage error against output voltage.
It is the modifcation of NFB resistor during a signal period.

If closed loop gain of the amplifier is G in a non inverting configuration. the simplified NFB loop is a voltage divider made of said NFB resistor plus an other R Resistor. The gain of the amplifier when open loop gain is big against G is:
G = 1 + Rnfb/R
So we clearly see that a 0.004 % modification in Rnfb is almost a 0.004% change in G which means a 0.004% DHT.

This cannot be cancelled by feed back while feed back is the core of the issue.

Regards,
Stéphane

[Samuel Groner]

You forgot to divide by 40 to get the ratio.

I don't understand why you want a factor of 40. I agree that if the amp has 6 dB noise gain (i.e. equal shunt and feedback resistor values) the voltage coefficient will cancel (given resistor value and voltage coefficient match). However for the usual noise gains > 20 dB there is almost no cancellation and voltage coefficient will proportionally affect linearity.

This number will be reduced by negative feedback just like any other error within the amp as well.

By definition imperfections of the feedback network will not be reduced by loop gain. If you put a diode in your feedback network the output will be distorted. Otherwise we couldn't make precision rectifiers and clamps using opamps...

Can some one help understand this strange fact?

Voltage coefficient is extremely difficult to measure down to 1 ppm/V. 1 ppm/V is likely to represent the measurement residual rather than resistor imperfection of decent metal film parts. I've investigated this myself using special distortion measurement techniques and I've not been able to find distortion above -150 dB at +20 dBu. Surprisingly the $20 Vishay bulk metal parts are actually worse with this respect than most standard metal film parts I've measured...

Of course voltage coefficient *is* a serious problem for carbon and thin/thick film resistors. Another issue (for any resistor except those with near-zero tempco) is distortion from thermal self-modulation at low frequencies. I'm doing some research here at the moment but no usuable results yet.

Samuel

[SMourareau]

Samuel,
thank you for your analysis,
Stéphane

[Samuel Groner]

Typo: I should have written -140 dB instead of -150 dB.

Samuel

[AndrewT]

is this why some suggest that peak voltage use <10% of the resistor's power rating for the NFB loop?

[godfrey]

Originally Posted by Samuel Groner

Surprisingly the $20 Vishay bulk metal parts are actually worse with this respect than most standard metal film parts I've measured...

There's another discussion about distortion and excess noise in resistors here: John Curl's Blowtorch preamplifier part II

There's some surprising results with distortion measurements there too.

Originally Posted by AndrewT

is this why some suggest that peak voltage use <10% of the resistor's power rating for the NFB loop?

I expect that's more to do with temperature coefficient - the increase in resistance with self-heating.

To reduce distortion, perhaps one could connect several resistors in series, so that each one has a smaller voltage across it?

(Not that I expect to design a circuit good enough to tell the difference anytime soon)

[Samuel Groner]

There's another discussion about distortion and excess noise in resistors here:

Can't finde the details how these measurements are done; anyone knows the page number..?

Is this why some suggest that peak voltage use <10% of the resistor's power rating for the NFB loop?

Well, that won't address any voltage coefficient issues (rather the opposite: most high-power parts actually have higher voltage coefficient) but at least the thermal self-modulation I mentioned because higher power parts typically have slower thermal time constants which moves the onset of this distortion mechanisms towards lower frequencies.

To reduce distortion, perhaps one could connect several resistors in series, so that each one has a smaller voltage across it?

Sure. But as I said: It ain't a serious issue anyway.

Samuel

[Samuel Groner]

Some literature: http://www.barthelectronics.com/pdf_...lse%20Page.pdf

Samuel