[ARC5] Resistor Excursions

[Tom Lee]

I'm glad you mentioned inductance. I cut the leads close to flush so 
that I'd be measuring the resistor proper to a good approximation. I'd 
been told by many that the spiral-cut film resistors would have a 
"significant" inductance, but they never could quite find a reference 
for me that contained measurements. My measurements confirmed that 
skepticism was warranted. The inductance that was seen was pretty much 
explainable as due to the length of the body itself (order of 0.5 nH per 
mm). With leads, just add another 0.5 nH per mm of total lead length. 
Again, very crude, but fine for the purpose of the exercise.

As you state, surface-mount resistors have quite small inductances. For 
sub-GHz frequencies, calling it zero is a perfectly fine approximation.

I made measurements out to X-band, but I don't trust that I was 
measuring anything at the upper end besides fixturing. ;) But up to 1 
GHz or so, the data seemed fairly reliable (at least repeatable).

-- Cheers,
Tom

-- 
Prof. Thomas H. Lee
Allen Ctr., Rm. 205
420 Via Palou Mall
Stanford University
Stanford, CA 94305-4070
http://www-smirc.stanford.edu

On 4/19/2024 10:49 PM, Richard Knoppow wrote:
>    I am not sure about how resistors are made today, I worked for a 
> company who made precision metal and carbon film resistors about fifty 
> years ago. For very low values, less than the raw resistance of the 
> coated blanks, the coatings could be cut away in strips forming what 
> amounted to parallel resistors on the blank. These would have no 
> inductance beyond lead inductance, and little capacitance.
>    I don't remember the values that were adjusted this way and its 
> probably different now.
>    Remember that when a resistor is spiralled the coiled part is very 
> low Q. Generally, film resistors are good to very high frequencies, 
> again, the inductance being mostly lead inductance. For modern surface 
> mount parts its pretty close to zero.
>     Your network analyzer probably went up to considerably higher 
> frequencies than my RX-Meter (about 250 Mhz).
>
> On 4/19/2024 10:34 PM, Tom Lee wrote:
>> My measurements agree with what Jacques and Richard have said. I once 
>> characterized a junkbox full of CC resistors on a network analyzer in 
>> order to derive the simplest model that would be reasonably valid out 
>> to ~1 GHz and easy for my students to remember when choosing 
>> components. Out of that effort I came up with a crude rule of thumb: 
>> A CC resistor acts very much like a resistor shunted by a capacitance 
>> whose value in pF is numerically equal to the power rating in watts. 
>> So, a half-watt resistor has about a half-pF capacitance, and so on. 
>> It's not a perfect fit, but in terms of "bang for the buck" it serves 
>> well. It satisfied the main goal of the exercise, to come up with 
>> something easy to remember.
>>
>> As I recall, film resistors were quite similar; the inductive nature 
>> that many expect because of the spiral construction didn't really 
>> show up unless the resistances were fairly low (~100 ohms on down). 
>> The capacitance tended to dominate the reactance.
>>
>> The same weekend of experiments yielded another crude rule of thumb: 
>> The shunt capacitance of a surface-mount resistor is (again very 
>> approximately) in pF the size designation of the part, with a leading 
>> decimal point. So, an 0805 resistor has about 0.08pF capacitance 
>> shunting it, etc.
>>
>> These approximations aren't intended for use in circumstances where 
>> high accuracy is needed. They're just for answering questions like, 
>> "Would this resistor likely work in this part of this 1 GHz amplifier?"
>>
>> -- Cheers,
>> Tom
>>
>