I happened to find an old carbon comp resistor, 680k value hidden away. With carbon composition this is more of a pre-soldered guide than an absolute value. It was more like 688k. I decided to do some DC tests to see how much, if any, it would change over a 210V range against a metal film of the same value.
|Percentage change with applied voltage.|
In the above plot there is a clear change in apparent resistance of the carbon resistor against an applied DC voltage. The measurement contradicts a H/Hill statement that it is really only above 250V where the voltage coefficient becomes apparent. Maybe they meant significant. To put this in prospective, of the original 688k value it represents a drop in resistance of over 20k. The metal film (red plot) is stable at 100.0%.
Having repeated the test and confirmed the behaviour I needed to know if this was something that takes seconds to change or is this change instantaneous and works in real time.
To check this I constructed a potential divider out of two resistors. The bottom resistor was a 62K metal film and the measurement was made across this device. The top resistor was the device under test being either the 688k carbon composition or a 680K metal film resistor. Using a linear ramp source to 210V I could measure the lower reference resistor and determine the behaviour of the top resistor. The tail off at high voltage is the probe capacitance, so linear to +170V.
|Real Time Voltage vs Resistance change.|
In the above plot the carbon (red) is plotted against the metal film (blue) with the left hand scale. You can see that the red line drops slightly more voltage at the 0.0001s (0.1ms) point as it has a slightly higher resistance value. However as the voltage rises it crosses the blue plot and ends up with a lower voltage drop. This is real time compression well within the audio range. To clarify the difference in voltage drop is plotted in green on the right hand scale, -7V to +3V. This shows that at the 0.1ms point the carbon resistor is dropping about 1.3V more than the metal film as to be expected being a higher value resistor. However with ~180V applied at 0.48ms the carbon film resistor is now dropping 4.8V LESS. It has shrunk in real time.
|Piecewise Linear and Poly Curve Fit.|
In a final look at the data you can either view the drop in resistance as a three section piecewise linear (blue, orange & purple lines) with three gradients or curve fit to the equation shown in the title.
The real world effect for valve / tube amplifier designers is that the carbon composition resistor can add some non linearity and compression not normally present in metal film. In my opinion it would be a mistake to consider the use of carbon in the early stages of a cascaded design. When taking the first measurement at DC the digital display would flick around on the carbon resistor but was rock steady with the same value metal film. The noise is really something else. However as an anode resistor in the overdriven /clipping stage, well it may be worth the 30p to someone. I however will probably stick to metal film based on reliability. Is the above effect audible? I will have to say-