Greetings,
I'm putting together an amp with 300V across the anode resistors. I read on Tubecad it is better to use multiple resistors than one.
"There is a voltage distortion mechanism in many resistors that is so small at low voltages that it is usually disregarded, but in a high voltage circuit, such as this one, the distortion becomes an issue. Using six resistors in series reduces the resistor distortion by six fold."
I'm ordering parts, and I must say I'd much rather use one big high power resistor than six smaller ones. Would it be much worse?
Thanks.
The Tube CAD Journal, Electrostatic Headphones
I'm putting together an amp with 300V across the anode resistors. I read on Tubecad it is better to use multiple resistors than one.
"There is a voltage distortion mechanism in many resistors that is so small at low voltages that it is usually disregarded, but in a high voltage circuit, such as this one, the distortion becomes an issue. Using six resistors in series reduces the resistor distortion by six fold."
I'm ordering parts, and I must say I'd much rather use one big high power resistor than six smaller ones. Would it be much worse?
Thanks.
The Tube CAD Journal, Electrostatic Headphones
Carbon composition resistors do have this issue.
Pretty much every other type doesn't (as long as you're in the voltage/power spec range).
Pretty much every other type doesn't (as long as you're in the voltage/power spec range).
Various types of resistors exhibit this effect of varying resistance with applied voltage. In one of Douglas Self's books, he takes measurements of various types of resistors and shows the amount of distortion they generate.
Funny story, I remembered that thick film resistors were one of the worst types of resistors for having a changing resistance with applied voltage, so I replaced a thick film feedback resistor with a wirewound resistor, which should have been much better.
I got more distortion out of the circuit with the better resistor. All I can figure was that the 2nd harmonic distortion generated by the thick film resistor was in opposite phase to the 2nd harmonic distortion of the circuit and was cancelling some of it. Improving a component doesn't always make the system better.
Funny story, I remembered that thick film resistors were one of the worst types of resistors for having a changing resistance with applied voltage, so I replaced a thick film feedback resistor with a wirewound resistor, which should have been much better.
I got more distortion out of the circuit with the better resistor. All I can figure was that the 2nd harmonic distortion generated by the thick film resistor was in opposite phase to the 2nd harmonic distortion of the circuit and was cancelling some of it. Improving a component doesn't always make the system better.
Resistor distortion is basically 3rd order. As the resistor current changes, it heats and cools in the rhythm of the signal. That causes distortion due to what is called temperature coefficient, generally expressed in parts per million.
If you have a resistor with 100ppm tempco, it's value changes 100ppm which is 0.01%, per degree change in temperature, and that can happen in the signal rhythm.
Doesn't sound like much, but as an anode resistor, or a feedback resistor with lots of AC voltage, it can have an effect. The cure is using a resistor with low tempco in those positions. Tempco is normally in the data sheet. But you probably are not surprised to learn that the lower the tempco, the higher the price ;-)
Or a higher wattage resistor, or multiple Rs in series or parallel.
Jan
If you have a resistor with 100ppm tempco, it's value changes 100ppm which is 0.01%, per degree change in temperature, and that can happen in the signal rhythm.
Doesn't sound like much, but as an anode resistor, or a feedback resistor with lots of AC voltage, it can have an effect. The cure is using a resistor with low tempco in those positions. Tempco is normally in the data sheet. But you probably are not surprised to learn that the lower the tempco, the higher the price ;-)
Or a higher wattage resistor, or multiple Rs in series or parallel.
Jan
I don't really think resistors have such a low thermal inertia that they can heat up and cool down tens, hundreds or thousands times per second.
Its not a matter of faith. Its well documented. And yes, you are right, it is frequency dependent.
If I send you an article, will you read it?
Jan
If I send you an article, will you read it?
Jan
Yes more resistors or higher power resistors means less heat cycling and less temp. dependent distortion.
It probably becomes predominantly second order when you have a large DC bias voltage across the resistor. Pretending the third-order term is instantaneous to keep the mathematics simple, when D is the DC bias and x the signal, (D + x)^3 = D^3 + 3 D^2 x + 3 D x^2 + x^3. The distortion term 3 D x^2 >> x^3 when D >> x.
Of course I'll do. I'd appreciate that.
Maybe just post the article here? I'm sure I'm not the only one that is interested.
The thermal inertia is not a brick-wall filter, so they heat up and cool down a little bit every period. That is, the temperature variations are much smaller than they would be with a 0.001 Hz signal, but they are not zero. Whether they are large enough to matter depends on the circumstances and requirements; in most cases the effect is negligible.
That's exactly what I'm talking about - sorry for not being 100% clear.
Another thing is that with the given application (plate load) the resistors are "preheated" by the quiescent current, and the current is changing maybe +/-50% at most. Given that tube's nonlinearity is probably several orders higher with that kind of current swing, I don't feel there's a reason to investigate further, apart from purely academical interest.
Still it'll be nice to see the measured numbers just to be sure.
Different types of resistors have different mechanisms of voltage-dependent non-linearity. Carbon and MOX because their materials are semiconductors. Metal film have flicker effect: increasing conductance at sintered metal grains with increased voltage. Wirewound have self-inductance or self-capacitance. Only bulk foil are virtually free from these non-linearities. They also have very low temperature coefficient.
Last edited:
Interesting read, thanks Jan. From the numbers found therein I deduct that nonlinearity even of the carbon composite resistors is negliblibe compared to non linearity of any tube stage. Not neglible may be their current noise that increases with voltage differential applied. I remember a noisy tube amp that I significantly "de-noised" by replacing all carbon anode resistors by metal-film types. So yes, composite carbon is the worst choice audio resistor imho.
I think that strictly speaking the article does not prove that it is the heating. It shows it depends on frequency and resistor make and model.
I think we can agree that a more powerful engine in a car increases its top speed. An increase in top speed does not proof a more powerful engine is put in. It could also be a tail wind or because it's going downhill.
I think we can agree that a more powerful engine in a car increases its top speed. An increase in top speed does not proof a more powerful engine is put in. It could also be a tail wind or because it's going downhill.
Perhaps check out the other more recent threads on this forum about resistor related distortion and the effort that some posters have put in to try and quantitatively define the issue.
Of course, the article was not meant to prove that, we already knew that ;-). And it also depends on the power dissipation to a very large extend, which you will see if you look carefully at the various test conditions. It's a ton of work Ed did.
There is an interesting resistor from Vishay, one of the nude ones. They recognized that heating expands the body, modulating the resistance and thus causing distortion. So they mounted the resistor on a substrate that has the same thermal expansion rate, but with opposite polarity - it shrinks when heated.
The idea being to cancel the thermal distortion. Ed did some unpublished work that shows fascination stuff: the thermal mass of the resistor body and the substrate is different, so the cancellation works very good in some frequency ranges, and less good or not in others.
That's physics for you!
Jan
It will get worse with a big DC bias, although it will probably remain negligible in most cases. Looking at the power dissipation variations when subjected to a sine wave with peak value Vp:
No DC bias:
Voltage across the resistor: Vp sin(2 pi f t)
Highest momentary dissipation: Vp^2/R
Lowest momentary dissipation: 0
Peak-peak variation: Vp^2/R
Frequency of the variation: 2 f
Large DC bias VDC >> Vp:
Voltage across the resistor: VDC + Vp sin(2 pi f t)
Highest momentary dissipation: (VDC + Vp)^2/R
Lowest momentary dissipation: (VDC - Vp)^2/R
Peak-peak variation: 4 VDC Vp/R
Frequency of the variation: f
The variations in the momentary power dissipation get worse by a factor of 4 VDC/Vp and the frequency halves, so the thermal inertia helps less (and the distortion of the current through the resistor becomes mainly second order, or when you drive it with current, the distortion of the voltage across the resistor becomes mainly second order).
No DC bias:
Voltage across the resistor: Vp sin(2 pi f t)
Highest momentary dissipation: Vp^2/R
Lowest momentary dissipation: 0
Peak-peak variation: Vp^2/R
Frequency of the variation: 2 f
Large DC bias VDC >> Vp:
Voltage across the resistor: VDC + Vp sin(2 pi f t)
Highest momentary dissipation: (VDC + Vp)^2/R
Lowest momentary dissipation: (VDC - Vp)^2/R
Peak-peak variation: 4 VDC Vp/R
Frequency of the variation: f
The variations in the momentary power dissipation get worse by a factor of 4 VDC/Vp and the frequency halves, so the thermal inertia helps less (and the distortion of the current through the resistor becomes mainly second order, or when you drive it with current, the distortion of the voltage across the resistor becomes mainly second order).
Last edited: