I've got a 1.8 GHz HP 4291B RF Impedance/Material analyzer but was a bit puzzled to see that the capacitance of the open standard was 82 fF, although it can be changed to any _constant_ value. In other words, it does *not* support the 3rd order polynomial

C(f) = C0 10 ^-15^ + C1 10 ^-27^ f + C2 10 ^-36^ f ^2^ + C3 10 ^-45^ f ^3^

(f in Hz, C in Farads)

The 1.8 GHz 4291B is obsolete, but I checked the online manual for the replacement product (E4991B) and see that again this assumes that the capacitance of the open standard is independent of frequency.

I'm trying to understand why this can be so, despite lower frequency VNAs support a 3 ^rd^ order polynomial.

I don't have one of the very basic opens for my 4291B (P/N 04191-85302), which does not control the exact position of the collet, so are using the better quality open from an 85050B cal kit (85050-80010), where the capacitance is calculated using the following polynomial:

C(f) = 90.4799 10 ^-15^ + 763.303 10 ^-27^ f -63.8176 10 ^-36^ f ^2^ + 6.4337 10 ^-45^ f ^3^

The capacitance is 90.48 fF at 1 MHz and 91.6846 fF at 1.8 GHz. Therefore there's a 1.2 fF variation between 1 MHz and 1.8 GHz. With no way to enter the capacitance as a polynomial, I picked a frequency 75% of the upper limit, on the assumption the capacitance was more critical at high frequencies. I rather arbitrarily picked 91.41 fF, which is the value at 1350 MHz.

As I missing something? Is this far less critical on an impedance analyzer than a VNA?

Dave

Edited by: drkirkby on Jan 6, 2016 2:03 PM

C(f) = C0 10 ^-15^ + C1 10 ^-27^ f + C2 10 ^-36^ f ^2^ + C3 10 ^-45^ f ^3^

(f in Hz, C in Farads)

The 1.8 GHz 4291B is obsolete, but I checked the online manual for the replacement product (E4991B) and see that again this assumes that the capacitance of the open standard is independent of frequency.

I'm trying to understand why this can be so, despite lower frequency VNAs support a 3 ^rd^ order polynomial.

I don't have one of the very basic opens for my 4291B (P/N 04191-85302), which does not control the exact position of the collet, so are using the better quality open from an 85050B cal kit (85050-80010), where the capacitance is calculated using the following polynomial:

C(f) = 90.4799 10 ^-15^ + 763.303 10 ^-27^ f -63.8176 10 ^-36^ f ^2^ + 6.4337 10 ^-45^ f ^3^

The capacitance is 90.48 fF at 1 MHz and 91.6846 fF at 1.8 GHz. Therefore there's a 1.2 fF variation between 1 MHz and 1.8 GHz. With no way to enter the capacitance as a polynomial, I picked a frequency 75% of the upper limit, on the assumption the capacitance was more critical at high frequencies. I rather arbitrarily picked 91.41 fF, which is the value at 1350 MHz.

As I missing something? Is this far less critical on an impedance analyzer than a VNA?

Dave

Edited by: drkirkby on Jan 6, 2016 2:03 PM

> Well, if you are measuring a capacitor, and you see a difference of 1.2 fF from one frequency to another, I guess it bounds your error to approximately, let's see, 1.2 fF... 0.1 percent of 1 pF. Maybe they ignore it as it is such a small effect.

I took the example of my 1.8 GHz analyzer. On a 3 GHz E4991B, the variation of C would be even higher. You obviously felt it desirable on the 8753A to include variation of C with frequency, so it struck me a bit odd the same was not done on the impedance analyzers, as essentially they measure the same sort of parameters, although in a different way.

I'm now starting to doubt if the published coefficients for the 85050B/C/D and 85031B cal kits are screwed up (possibly transposed), but that's another story.

Dave