Hi JPV,
I was able to download the presentations by Bruce Hofer and review them. I’m still trying to get my arms around it, but here are some thoughts and observations.
Bruce states that the voltage coefficient ranges from 0.1 to 1 ppm/V for metal film and from 1 to 10 ppm/V for thick film, so for purposes here I’m going to use 1 ppm/V. Resistance merely goes down by the ppm/V (Kv) times the applied voltage. So a 1 ppm/V resistor’s value will go down by 100 ppm at 100V, or by 0.01%.
When used as a feedback resistor in an amplifier, this means that the distortion effect will be compressive, and mainly third order, since the feedback resistance falls with increasing output voltage and thus gain falls with increasing output voltage. This is a soft odd-order nonlinearity.
Where it gets tricky is when he tries to relate the actual third harmonic number to the voltage nonlinearity, noting that the change in resistance is a function of the absolute value of the voltage across it. This suggests that the resistance modulation is by a full-wave-rectified sinewave in the case of a sinewave voltage applied. In using a Fourier analysis instead of a Taylor series (which he indicates is not applicable because of the absolute value function of resistance modulation), he arrives at the formula H3 = Kv * Vs/5.9.
This is very non-intuitive, at least for me, because we have the amplitude of the third harmonic increasing linearly as the voltage, rather than as the square of the voltage. I have always been taught the latter – and that I guess derives from the Taylor series analysis that is usually applicable to any nonlinearity. This non-intuitive part has me scratching my head.
As an estimate of real-world consequences, consider a 1 ppm/V feedback resistor in an amp operating at 100w 8 ohms. 1 ppm corresponds to –120dB. 1/5.9 corresponds to about –16dB. This means that at 1V across the resistor we have H3 at –136dB. 100W corresponds to about +29 dBV, so we then have H3 = -107dB, or about 0.00045% at 100W. This seems to be different than the number that you quoted in your earlier post. I may be wrong. Check my reasoning here.
Bruce further notes that 5HD also goes up linearly with voltage level, and presumably higher harmonics have a linear relationship as well. This means that the resistor voltage distortion is VERY soft, which is a good thing.
Finally, if the distortion goes up linearly with voltage, it seems to imply that putting resistors in series will not change the outcome. Each of two series-connected resistors of half the value will have half the voltage and will create half the distortion; when the distortions are added together, we are back where we started. There is thus no improvement in distortion. This is also non-intuitive. Thus, using a series string of resistors helps with the thermal distortion but not with the voltage distortion.
Cheers,
Bob
Hi Bob,
Happy birthday!
Cheers, Edmond.
You remembered!! What a guy!
Thanks,
Bob
Google : " Bruce Hofer designing for ultra low distortion " and you will get the link to a PPoint presentation. at the AES
If you add ax to the sentence you will get a pdf of an Audio Express article
Both are addressing the same subject with different détails/explanations
JPV
Thanks! Just got back from dinner at a nice restaurant courtesy of my lovely wife Angela.
Cheers,
Bob
Here are a couple of further thoughts.
Bruce mentions that the voltage coefficient of metal film resistors can range from 0.1ppm/V to 1ppm/V. This is a full 10:1 range, suggesting that different ways of making them, or materials used, can have a very big influence on Kv. This also means there likely is a big influence of manufacturer and packaging style. Herein may be a significant issue with SMT vs through-hole metal film resistors. I'm not sure which type it might favor, but if I had to guess I would think it might favor through-hole because of the larger physical size for a given wattage rating. Bruce's recommendation of SMT resistors of the larger 1206 size makes a lot of sense from the thermal point of view, but may also be applicable to the Kv issue.
The larger physical size of the through-hole part may give the manufacturer more options in resistance material to choose a better one.
Does anyone know the physical mechanism responsible for Kv in a metal film resistor?
Cheers,
Bob
I suppose you mean the voltage coefficient as measured using very short high voltage pulses that do not change the temperature of the resistor.
Thin film resistors are usually deposited on ceramic substrates. A section in such a resistor shows an usually very rough ceramic surface, covered with a conformal very thin film of metal. The aspect ratio (the ratio between the ceramic ridges and the metal film thickness) of such a resistor can be surprisingly high.
The voltage coefficient in such resistor is attributed to current tunneling through the ceramic walls. Of course, the rougher the ceramic, the larger the voltage coefficient. This mechanism explains the resistance dependence of the voltage coefficient (the higher, the worst, since the voltage drop between adjacent ceramic walls is higher) and also why metal foil resistors have a virtually zero voltage coefficient.
I think that the voltage distortion in a string is decreasing because the voltage drop is divided but also the resistor value. With two résistors in serie with half the value, each resistor contributes now 1/4 so the total distortion is divided by 2
A better view is to consider the gain of an amp which is 1+Rf/R1;
The gain is now a non linear function of ~Vout; if we divide Rf in n resistors of value Rf/n = r and apply the formula we have:
gain for one large nl resistor Rf and with R1 linear and small
Vo/Vi =1+ Rf/R1 . (1-k|Vo|) with k the Voltage coef
if we split in n small resistors r
Vo/Vi = 1+ 1/R1 . n .r(1-k|Vo| / n) = 1+Rf/R1 . (1-k|Vo| / n)
this is a Voltage coefficient k/n instead of k
Regards
JP
Thanks, Waly. This seems to make sense.
Might this imply that a lower-value resistor constructed on the same roughness of substrate and thickness of film would have lower voltage sensitivity (Kv), since the tunneling resistance might then be higher in comparison to the physical resistance (I'm assuming the lower resistance was achieved with wider spiral tracks of metal, and realize this all may be a strong function of geometry).
If this is the mechanism, might it follow that there may be some differences attributable to construction between SMT and through-hole? For example, deposition on a smaller rectangular substrate as opposed to deposition on a larger cylindrical substrate. I'm wondering if we can draw a broad-brush conclusion that SMT resistors may tend to have a higher Kv.
Cheers,
Bob
Hi Bob,
> I'm wondering if we can draw a broad-brush conclusion that SMT resistors may tend to have a higher Kv.
YES! I've replaced some smd resistors (apparently of bad quality) on one of my sound cards, by precision MELF (cylindrical) resistors and that made a significant difference. It was a long time ago, so I don't know how much exactly, but I got about 3dB less distortion, well worth the modification.
Cheers, E.
> I'm wondering if we can draw a broad-brush conclusion that SMT resistors may tend to have a higher Kv.
YES! I've replaced some smd resistors (apparently of bad quality) on one of my sound cards, by precision MELF (cylindrical) resistors and that made a significant difference. It was a long time ago, so I don't know how much exactly, but I got about 3dB less distortion, well worth the modification.
Cheers, E.
Hi JPV,
I think you are right and that I goofed.
If we have a single resistor with 1ppm/V and we put 100V across it, its value decreases by 100ppm.
If we have two resistors of half the value in series and put 50V across each one, each one's value decreases by 50ppm. Then, obviously, the value of the series-connected pair will also decrease by 50ppm.
Thanks for the correction.
Cheers,
Bob
I don't think so. Both models can be built on poor (rough) or good (smooth) ceramic substrates. As usual, you get what you pay for: a through hole or MELF device, that doesn't spec the voltage coefficient) can cost as less as 10p, while a top class 0805 SMD can cost over 4 quid a pop, in 100's, but has a 0.1ppm/V Kv guaranteed.
I believe the SMD bad rap among non professionals is coming from their very limited power handling capability. They are able to take much less abuse compared to their through hole counterparts.
Following this discussion with interest...
Personally, have been designing for SMD components. (Ensuring that power dissipation is low).
With SMDs obviously the layout can be more compact but is this voltage distortion significant enough to swamp the gains from reduced PCB parasitics?
Or is the issue more likely to be cost rather than the short comings of some SMD components?
Paul
If surface leakage matters, you don't use through hole components, but switch to better PCB materials, use guarding, or don't use a PCB at all.
The fringing field and parasitics in SMD is a red herring. It either doesn't matter, or it's unavoidable and compensated through other methods. E.g. there's a whole theory of compensating a coplanar microstrip line geometry for the fringing field at a termination (that may include a SMD cap and/or a SMD resistor). Such methods are working to over 100GHz, where thinking about through hole components is not even funny.