Odd results using DE-5000(LCR) to measure characteristic impedance of coax

[bitslip]

Hi all,

tldr: For short coax cables, I can use DE-5000 readings as-is and calculated Z0 is close to 50-ohms, for long cables I have to scale my Ls (shorted inductance) by ~0.5 to ~0.6 and then I calculate close to 50-ohms.  Not sure if this is user-error, wrong technique, wrong math or bad equipment. 

My goal is to measure Z0, L/ft and C/ft for some unknown 4m coxial cable, so I thought I'd use my new DE-5000 for the job and start by measuring some KNOWN 3m long 50-ohm SMA-to-SMA cables from two different brands/vendors, one RG-174 the other RGS-316.

DE-5000 gives VERY consistent reads between measurements and I've performed the calibration in the unit (open/short) before taking any measurements, using supplied TL-21 alligator clip assembly, measurements @ 100 kHz.

Approach:  Hooking DE-5000 via TL-21 alligator clips to an un-soldered SMA connector, attaching coax to SMA connector, taking readings of the coax cable with far end "open", writing down Cs_open/Ls_open and then shorting the far-end with an SMA short, noting C_short, L_short.

Using equation 1 to compute Z0 with equation 2 ideally to verify / validate.  Weirdly, if I scale both Ls values by ~0.5 to 0.6, EQ1 and EQ2 give me nearly identical (and correct results), if I don't scale Ls, the computed Z0 is off by ~25-30 ohms by both EQ1 & EQ2.

Equations:

1.  Z0 = SQRT(L_short / C_open)
2.  Z0 = SQRT(Z0_open*Z0_short) where Z0_open = SQRT(L_open/C_open), Z0_short = SQRT(L_short/C_short)

Actual data:

COAX_1 (3m):

[open]: cs: 309.0 pF, ls: 8.223 mH
[short]: cs: 1649.6 nF, ls: 1.534 uH

Z0(EQ1): 70.46 ohms
Z0(EQ1, 0.5*Lshort): 49.82 ohms

Z0(EQ2): 70.53 ohms
Z0(EQ2, 0.5*Ls): 49.873 ohms

COAX_2 (3m):

[open]: cs: 294.0 pF, ls: 8.614 mH
[short]: cs: 2.05 uF, ls: 1.239 uH

Z0(EQ1): 64.92 ohms
Z0(EQ1, 0.6*Lshort): 50.29 ohms

Z0(EQ2): 64.87 ohms
Z0(EQ2, 0.6*Ls): 50.25 ohms

Any insights or help would be appreciated.  I've tried to read all the literature I can find on using an LCR meter for these measurements and I've repeated the measurements numerous times and remain very confused.

[bitslip]

I should add,

Looking at the IETLabs manual for the DE-6000 (https://ietlabs.com/pdf/Manuals/DE_6000_im.pdf) they do mention something about using the disspiation reading -- is this my missing factor?


Adjustment to accuracy (Z) based on dissipation (D) reading:
D > 0.1: Z * √(1+D2)

In capacitance mode, D ≤ 0.1: ZC = 1÷(2πƒC)
In inductance mode, D ≤ 0.1: ZL = 2πƒL

Secondary Parameters Accuracy:
AZ = impedance (Z) accuracy
Definition: Q = 1/D & Rp = ESR * (1+1/D2)
D value accuracy: DZ = ± AZ *(1+D)
ESR accuracy: RZ= ± ZM * AZ (Ω)
ie., ZM = impedance calculated by 1÷(2πƒC) or 2πƒL

[G0HZU]

If you just plan to measure C per unit length at 100kHz and L per unit length at 100kHz and then try and predict Zo for higher frequencies using the simplified equation for Zo of Zo = sqrt(L/C) then I think you will get confusing results due to the increased inductance per unit length at low frequencies due to skin effect in the cable conductors.

So I'd expect you to get a different result for L per unit length at 100kHz compared to 10kHz or 1MHz. This will obviously affect the results from your equation for Zo.

It's also worth mentioning that the characteristic impedance of coax tends to increase (and become complex) as the test frequency is reduced. This is because the resistive losses (per unit length) in the conductors become much more significant at lower frequencies compared to the magnitude of the reactance (per unit length).

Look up the Telegrapher's Equations to see the relevant equation for Zo at a given frequency. This includes the resistive loss in the equation and this gives a better result for Zo at lower frequencies.

I'd expect the magnitude of the Zo to be about 80 ohms for RG316 cable at 100kHz for example.