On Sat, Sep 28, 2019 at 03:49 PM, Dr. David Kirkby from Kirkby Microwave Ltd wrote:
I don¡¯t think your simple model is really suitable for the following
reasons
1) The variation of C with homemade standards is likely to exceed that of
commercial standards - this is from experience measuring them.
2) The inductance of shorts is likely to be more with homemade standards
than commercial ones - again this is based on experience measuring them.
3) People may well want to make measurements in a 75 ohm system.
4) it is possible to improve upon the accuracy of loads at low frequencies
by using a DC resistance measurement.
5) In the case of a female N, a simple standard can be made by just leaving
the connector open. This will create a higher impedance transmission line
than 50 ohms as the centre conductor sits in a cylindrical section with a
greater diameter than when its mated.
6) The loss of homemade standards is likely to be greater than commercial
ones from Keysight - again this is based on actual measurements I have
performed.
Dave, thanks for taking the time to reply. I appreciate your comments, and I agree with you on all these points -- but I wasn't really concerning myself with homemade standards, which I assume are almost always uncharacterized.
Instead (and I should have made this clearer), I was wondering what the impact was of the Capacitance and Inductance terms of characterized Open and Short standards. Ditto for their Delay, Loss and Offset Zo terms.
For the HP Open and Short standards I looked at, Delay has the largest impact on Gamma (which was the reason I never set this term to 0 in my calculations), followed by the Open's C0 term. The other terms have an effect, but that effect is much smaller than the effect of Delay or C0.
As for homemade standards, probably the best one can do to characterize them is verify that the load is as close to 50 ohms as possible (using a 4-terminal ohms measurement) and determine the Delays of the Short and Open using an *already-calibrated* VNA (although I did come across a web page where the author actually derived C0-C3 (and perhaps L0-L3? I don't recall any longer).
I see your notes that the
phase variation up to 1500 MHz is smaller than the uncertainty in the
calibration standards. I can¡¯t square that circle.
I was quite surprised to see this result, which is one reason why I originally posted the results here with my question wondering if there were a math error.
Running through the numbers again, they look good to me. Here's an example of the effect of the capacitance terms of an 85032F Male-N Open at 900 MHz. Note that C0-C3 are spec'd as follows (all values in Farads):
C0 = 89.939e-15;
C1 = 2536.8e-27;
C2 = -264.99e-36;
C3 = 13.4e-45;
First, calculating the Open's Gamma using C0-C4. The equations are:
divisor = (2*pi*f * (C0 + C1*f + C2*f^2 + C3*f^3))
Zopen = -j / divisor
GammaOpen = ((Zopen/50) - 1) / ((Zopen/50) + 1)
If the frequency (f) is 900MHz, then GammaOpen equals 0.9962 - j0.0877 (i.e. magnitude of 1, angle of -5.0292 degrees).
Let's now calculate Gamma for the C0-only model. The equations now are:
divisor = (2*pi*f * C0)
Zopen = -j / divisor
GammaOpen = ((Zopen/50) - 1) / ((Zopen/50) + 1)
Gamma now is 0.9964 - j0.08461 (i.e. magnitude of 1, angle of -4.8538 degrees).
From this I draw a couple of conclusions:
1. At 900 MHz this standard's C0 has a significant impact on the angle of Gamma (about -4.9 degrees).
2. Adding in the additional C1-C3 terms only changes the Open's angle of Gamma by about 0.18 degrees, which is significantly smaller than this Standard's spec'd "Deviation from Nominal Phase" of +/- 0.65 degrees (from DC to 3 GHz).
(By the way -- should any one else like to verify the results, the equations and C0-C3 terms are above.)
Thanks again for your comments and insights,
- Jeff, k6jca
