Its a not-particularly-intituitive property of 1/f noise that it is theoretically infinite - after all its commonplace in nature, noise that looks very like 1/f at some timescales, but usually careful measurement will show the 1/f property breaks down on longer timescales.
1/f^2 noise, aka Brownian motion, is similarly infinite, but that's more intuitive as random walks are expected to keep growing.
The idea with the Vishay Zfoils is that their expansion with heating is cancelled by the substrate contracting with temperature, that's how they get their low tempco.
The problem is that those expansion and contraction rates are not the same, so at some frequency range there is a phase shift in tempco between the resistive element and the substrate. It is of course irrelevant at DC, and also disappears at high enough frequency.
Jan
Although not a direct input to Jan's aim for this thread, EEVblog has a long but interesting thread in the Metrology section on resistor tempco, including some history on removing problems with resistance wire to lead terminations (especially by Pettit), and on the variability of resistance material tempco.
T.C. measurements on precision resistors - Page 1
T.C. measurements on precision resistors - Page 1
> what difference does it really make?
Sanders(?) ran into high THD on the NFB resistors for an electrostat driver. I ferget the numbers, but like the amp was good for 0.01% yet gave 0.1% until he re-designed the NFB resistor network.
In this case Jan is looking to see 160+dB down, and certainly resistor linearity is one fog he will run into.
Sanders(?) ran into high THD on the NFB resistors for an electrostat driver. I ferget the numbers, but like the amp was good for 0.01% yet gave 0.1% until he re-designed the NFB resistor network.
In this case Jan is looking to see 160+dB down, and certainly resistor linearity is one fog he will run into.
Thin film resistor kits dont even exist > 0805 (at least not at digikey). Then again it aint normal designing for <120dB noise and THD.
What are the relative implications if only resistor size is varied? Say using the same Susumu thin films, but going from 1206 - 0805 - 0402 - 0201, all else being equal (layout as well). That would be an interesting experiment. Are there formulae that include the film dimensions so the differences can readily be estimated?
What are the relative implications if only resistor size is varied? Say using the same Susumu thin films, but going from 1206 - 0805 - 0402 - 0201, all else being equal (layout as well). That would be an interesting experiment. Are there formulae that include the film dimensions so the differences can readily be estimated?
Another question, regarding thru hole resistors. I tend to make circuits as small as possible, shortest signal path and smallest loops etc. But this requires bending the leads very close to the resistor body. Is that inducing mechanical stress at the joints/connections that affect the resistor performance?
I think I AM trying to design the atomic clock equivalent for audio ;-)
You could also ask yourself who is buying all those $30k Audio Precision machines?
Jan
Yes, leads should ideally be bent without imposing stress on the component body. Its a reliability issue with epoxy-encapsulated semiconductors where stress in the leads coupled with thermal cycling pulls the bond-wire off the lead frame. Lead-frames often have a wide section to ensure bending of the pin doesn't occur inside the epoxy for this reason - for instance DIP IC's.
Of course for hobby use people seldom care about this, its not usually a problem, but if you want the best reliability you treat components with more respect...
A further test might be acquiring some VHP or similar foil resistors in hermetically sealed oil-filled packages which might provide a quicker thermal response. I wouldn't use these because of size and likely substantial cost, but it might more clearly point to extremely low level tempco behavior. Or it might just further confuse the picture. A 'naked' foil resistor with no packaging at all could behave a bit differenty, too. Too fragile-looking for me, but I've read some favorable comments over conventional packaging.
Yet another variant are voltage divider foil resistors; are those two matched foils on separate substrates, or a purpose-made variant of a single-foil on a common substrate? I see some of these on Ebay claiming .001% matching (not absolute value) Testing one side while monitoring the other might be interesting, too.
I watched Bruce Hofer’s testing a while ago with interest.
I then built 3 preamp boards, changing only the resistors
The circuit is Erno Borbely’s all jfet/fet preamp with Dale RN, Caddock Mk132, and Vishay TX 2575 bulk foil resistors. After Bruce’s testing I was skeptical of the bulk foil’s reputation and had a negative bias before listening.
To me the bulk foil version was the cleanest sounding, with a level of resolution, smoothness, and low level detail I don’t get with the other 2 boards. I listened for the defects in areas like the low end that Bruce pointed out, but I don’t hear them. The system was full range electrostatics with JL audio subwoofers with 24/96 and 192khz HD tracks. I’m puzzled as to why I preferrred the buk foils over the Dales, the science ( testing) was against it, but thats what I heard. I need a new hobby.....
I then built 3 preamp boards, changing only the resistors
The circuit is Erno Borbely’s all jfet/fet preamp with Dale RN, Caddock Mk132, and Vishay TX 2575 bulk foil resistors. After Bruce’s testing I was skeptical of the bulk foil’s reputation and had a negative bias before listening.
To me the bulk foil version was the cleanest sounding, with a level of resolution, smoothness, and low level detail I don’t get with the other 2 boards. I listened for the defects in areas like the low end that Bruce pointed out, but I don’t hear them. The system was full range electrostatics with JL audio subwoofers with 24/96 and 192khz HD tracks. I’m puzzled as to why I preferrred the buk foils over the Dales, the science ( testing) was against it, but thats what I heard. I need a new hobby.....
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Question about how to calculate distortion due to TC.
So lets say I have a 0805 SMD resistor, it has therm resistance of 440K/W. Say it is 10kohm, and TC of 200ppm/K.
If I have a +-10Vp signal over this 10kohm the power diss in the resistor is ca 5mW. The resistor temp increases by 5mW*440K/W=2.2K and the change in resistance is 2.2K*200ppm/K=4.4ohm.
So the change is from 10 000 to 10 004.4.
Does this mean the distortion due to resistance change is 20log(4.4/10000) = -67dB?
Or do I get the max linearity out of this: 20log(10004.4/10000) = 0.004dB which is about no change in linearity.
Btw I cannot find therm resistance of 0201. Vishay has a table that goes down to 0402...
So lets say I have a 0805 SMD resistor, it has therm resistance of 440K/W. Say it is 10kohm, and TC of 200ppm/K.
If I have a +-10Vp signal over this 10kohm the power diss in the resistor is ca 5mW. The resistor temp increases by 5mW*440K/W=2.2K and the change in resistance is 2.2K*200ppm/K=4.4ohm.
So the change is from 10 000 to 10 004.4.
Does this mean the distortion due to resistance change is 20log(4.4/10000) = -67dB?
Or do I get the max linearity out of this: 20log(10004.4/10000) = 0.004dB which is about no change in linearity.
Btw I cannot find therm resistance of 0201. Vishay has a table that goes down to 0402...
Actually for static nonlinearities and predominantly second- and third-order distortion, there are equations to estimate harmonic distortion from differential gain and they have a factor in the denominator that helps, especially for third-order distortion. Nordholt mentions them in his book Design of high-performance negative-feedback amplifiers and I believe he got them from Cherry and Hooper, Amplifying devices and low-pass amplifier design.
If I remember well:
Determine the gain in the bias point
Determine the gain in the positive signal peak
Determine the gain in the negative signal peak
Calculate epsilon+ = gain in the positive signal peak/gain in the bias point - 1
Calculate epsilon- = gain in the negative signal peak/gain in the bias point - 1
The second and third harmonic distortion are given by:
D2 = abs(epsilon+ - epsilon-)/8
D3 = abs(epsilon+ + epsilon-)/24
So in SemperFi's example, at extremely low signal frequencies, the power in the peaks is 10 mW, causing an 8.8 ohm resistance increase, both in the positive and the negative peaks.
The distortion in the voltage across the resistor when it is driven by a sinewave current is then:
epsilon+ = 10008.8/10000 - 1 = 0.00088
epsilon- = 10008.8/10000 - 1 = 0.00088
D2 = abs(0.00088 - 0.00088)/8 = 0
D3 = abs(0.00088 + 0.00088)/24 = 73.3333...E-6, about -82.69 dB
When you look at the distortion of the current when driven by a sinewave voltage, you get practically the same result.
So all in all, even at 0 Hz, it is not as bad as -67 dB.
If I remember well:
Determine the gain in the bias point
Determine the gain in the positive signal peak
Determine the gain in the negative signal peak
Calculate epsilon+ = gain in the positive signal peak/gain in the bias point - 1
Calculate epsilon- = gain in the negative signal peak/gain in the bias point - 1
The second and third harmonic distortion are given by:
D2 = abs(epsilon+ - epsilon-)/8
D3 = abs(epsilon+ + epsilon-)/24
So in SemperFi's example, at extremely low signal frequencies, the power in the peaks is 10 mW, causing an 8.8 ohm resistance increase, both in the positive and the negative peaks.
The distortion in the voltage across the resistor when it is driven by a sinewave current is then:
epsilon+ = 10008.8/10000 - 1 = 0.00088
epsilon- = 10008.8/10000 - 1 = 0.00088
D2 = abs(0.00088 - 0.00088)/8 = 0
D3 = abs(0.00088 + 0.00088)/24 = 73.3333...E-6, about -82.69 dB
When you look at the distortion of the current when driven by a sinewave voltage, you get practically the same result.
So all in all, even at 0 Hz, it is not as bad as -67 dB.
And the details of the PCB pads at low enough frequencies where the pads and tracks become heatsinks
It depends on how that resistor is in the circuit. If you have a resistive divider of say 10k series and 10k to ground, your instantaneous attenuation varies between 1:1 (10k - 10k) and 1: 0.9996 (10k - 10.004k).
That determines your distortion, which here is 0.04% if I did my sums correctly.
But if a resistor is used to, say, bias a current source, the effect probably is zero.
Edit: I see Marcel and VovK Z make a similar point.
Jan
Ok thanks. So for resistors with same TC, the size will determine limits of linearity since the size gives a certain therm resistance.
0402 has therm res of ca 800K/W
0805 ca 400K/W
1206 ca 200K/W
In addition to the increase in current noise as size gets smaller.
But it really only matters with farely large voltage swings since you need pretty large temp change to see the effect. ?
Then again -120dB is only 0.0001%!
It really isnt easy bettering that. So I see how the tiniest details matter...
The tiny circuits used in cell phones and bluetooth receivers etc must have a physically limited thd... then again the signal levels in those things are small.
0402 has therm res of ca 800K/W
0805 ca 400K/W
1206 ca 200K/W
In addition to the increase in current noise as size gets smaller.
But it really only matters with farely large voltage swings since you need pretty large temp change to see the effect. ?
Then again -120dB is only 0.0001%!
It really isnt easy bettering that. So I see how the tiniest details matter...
The tiny circuits used in cell phones and bluetooth receivers etc must have a physically limited thd... then again the signal levels in those things are small.
I think my and VovK's points are very different from yours, although all three of them lead to a reduction of distortion.
By the way, having a DC bias across the resistor that is not negligible compared to the peak signal voltage aggravates its thermal distortion. The power excursions will be greater and as epsilon+ and epsilon- will be different, you get even-order distortion, which has a relatively small factor in the denominator of the equation relating differential gain to distortion.
Besides, unlike what I wrote in my earlier post, the equations relating differential gain to distortion are not in Nordholt's book.