parasitic capacitance of resistors

[electrolust]

http://www.resistorguide.com/resistor-capacitance/

The explanation lies in the fact that even ideal conductors under ideal conditions have a certain ability to store charge. Metal leads that connect the resistor to the rest of the circuit are an example of such conductors. The longer the leads, the more charge can be stored and the higher the parasitic capacitance. So, the shorter the leads, the less parasitic effects can be seen in a given resistor, which is why SMD resistors have less parasitic effects.

If low capacitance is desired, the resistor should be kept as small and compact as possible. Wire-wound resistors should be avoided because the windings generate inter-coil capacitance, which makes them unusable above 50 kHz. Carbon type resistors are usable up to around 1 MHz. Foil resistors, on the other hand, have superior characteristics for high-frequency use, with the capacitance usually less than 0.05 pF which makes them cope with frequencies up to 100 MHz.

An HP 54006A resistive probe has a parasitic capacitance (due to resistor axial leads) of .250pF.  It is rated up to 6GHz.  How can this rating be so high if a .05pF capacitance is only "good for" 100MHz?

At very small numbers, an extremely exotic Inifinimax III+ probe has 40-some fF capacitance and is good for 30GHz, not 100-odd MHz.

[CatalinaWOW]

The value of the resistance also matters.  Low impedance of high frequency scope probes moves the corner up to around 6GHz.  A 10,000 ohm resistor requires nearly three orders of magnitude less capacitance to reach the same frequencies without significant impact.

This is another case where numbers have been supplied and it looks like technical data, but not all of the numbers required to make a valid comparison are available.  A common practice in marketing products.

[tggzzz]

The quote the OP supplied is a load of horsepuckey written by someone with a superficial "understanding" of the topic. Ignore it.

[CatalinaWOW]

I tried to say that nicely, but I agree.

[tggzzz]

I tried to say that nicely, but I agree.

Sometimes, particularly with things that are so inept they can only aspire to being "wrong", directness is the appropriate way of saving people's time

[T3sl4co1l]

Giving out fixed numbers, in an overview article, is dumb and wrong.

Cutoff frequency depends on application, value, and physical size.

Most important to realize is that capacitance and inductance are proportional to the length dimension of the object in question.

Even more important is to realize that, there are no such things as capacitors or inductors: these are theoretical simplifications that we use only because they are easy.  No real capacitance exists: only equivalent C, ESR, ESL and higher order corrections.  No real inductor, or resistor, exists: only a similar chain of corrections.

You can correct it forever and get a workable RLC model of a "resistor" or "capacitor" or "inductor", up to any frequency you might be concerned with*.  But this is a pretty awful approach, when better methods exist.

(*This is in the 100s of GHz.  Beyond there, the physics of substrates and materials tend to prohibit transmission line design methods entirely, and your approach will more and more resemble a traditional optics system instead.)

Enter the transmission line.  Anywhere you have two conductors spaced apart, you can have an EM wave between them.  Corresponding to that space, you have an equivalent L and C, but it's distributed over the space.  At low frequencies, we approximate these as ideal inductance and capacitance, and say (without stopping to qualify that we really mean "in the LF approximation") that this structure is an inductor, or capacitor.

The simplest, most useful takeaway of this is: whenever you have a transmission line structure (usually a volume with a constant cross section, and length > width, for simplicity's sake), it has a characteristic impedance, velocity of propagation (speed of light or lower, and you can calculate how much lower based on the fill -- dielectric or magnetic), and electrical length (physical length divided by velocity factor).  These properties are true, independent of frequency, even for frequencies much higher than 1/(electrical length).  Which is what gives rise to reflections and standing waves and all that useful (sometimes) stuff.  And, since inductance and capacitance are properties of space, they are proportional to length: if we know the TL properties, we also know its low frequency approximation.

Simple example: without looking at a datasheet, using some important memorized numbers, I can tell you the LF properties of ANY 50 ohm coax cable.  Zo is 377 ohms, so the cable is (377/50) times lower, so has that many times more capacitance, and less inductance, than space.  (These are 8.84 pF/m, and 1.257 uH/m, respectively; note that sqrt(ratio) of these is 377 ohms!).  That's 67 pF/m and 167 nH/m for starters.  But wait, that's if it's air cored, which it isn't: velocity factor is 0.67 (for the most common, solid filled coax; teflon and foamed coaxes have lower e_r than solid polyethylene, so also have higher velocities -- everything else follows proportionally!).  We know this is due to dielectric, and not magnetic loading, so we adjust C up, and L down, by the same factor.  (Think of it this way: Zo in the cable is not 377 ohms, but 377 * 0.67.)  This gives 100 pF/m and 111 nH/m.  You will find very similar numbers (within rounding error, and whatever other simple mistakes I've made here) in the datasheet!

Applied to a resistor: the physical length of, say, an 0805 chip resistor, is much smaller than a 1/4W axial resistor, so its transmission line length is shorter, and you can expect it to have smaller L and C (in the LF limit) as a result.  If the resistor is hanging out in space, relatively distant from any nearby metal, then it will have a high TL impedance, further increasing L and reducing C.

The resistor's terminals also count as a TL, if a short one (electrical length = component width); this mainly becomes significant when the capacitive reactance of that element becomes comparable to the resistor value.

Also, by realizing that capacitance varies with frequency, that there is no comprehensive answer to "stray capacitance" (only that there are reasonable answers in certain situations), you'll see how it can be that the probe capacitance can be strangely small.

Tim