A question asked online about measuring terminated coax cable loss with an RF voltmeter and whether to condemn it based on comparison with specs raises an interesting case to discuss.
The subject raises some immediate concerns:
- the accuracy of the termination;
- the accuracy of the voltmeter;
- the extent to which the voltmeter disturbs the thing being measured; and
- assumptions about matched conditions.
Lets take an example to explore the theoretical answer. We will use 10m of Belden 8359 (RG58A/U) @ 3.6MHz.
Lets model the scenario in TLLC. We will select the “Use Lint” switch for a better model of this specific cable at 3.6MHz and take the “Long” output.
Above is the input form.
RF Transmission Line Loss Calculator
|Transmission Line||Belden 8259 (RG58A/U)|
|Length||67.357 °, 0.187104 λ, 10.000000 m, 5.197e+4 ps|
|Line Loss (matched)||0.284 dB|
|Line Loss||0.282 dB|
|R, L, G, C||3.247376e-1, 2.670566e-7, 4.548358e-6, 1.010800e-10|
|Γ, ρ∠θ, RL, VSWR, MismatchLoss (source end)||1.795e-2+j9.163e-4, 0.018∠2.9°, 34.909 dB, 1.04, 0.001 dB|
|Γ, ρ∠θ, RL, VSWR, MismatchLoss (load end)||-1.418e-2+j1.293e-2, 0.019∠137.6°, 34.341 dB, 1.04, 0.002 dB|
|S11, S21||3.212e-2-j1.200e-2, 3.730e-1-j8.927e-1|
|Y11, Y21||9.562e-4-j8.077e-3, -8.316e-4+j2.103e-2|
|NEC NT||NT t s t s 9.562e-4 -8.077e-3 -8.316e-4 2.103e-2 9.562e-4 -8.077e-3 ‘B8259, 10.000 m, 3.600 MHz|
|k1, k2||1.487e-5, 2.744e-10|
|C1, C2||4.701e-1, 2.744e-1|
|Mhf1, Mhf2||4.531e-1, 8.362e-3|
|dB/m @1MHz: cond, diel||0.014866, 0.000274|
|Loss model source data frequency range||1.000 MHz – 1000.000 MHz|
|Correlation coefficient (r)||0.999924|
Now the ratio of the magnitudes of correct voltage readings from output to input is given by the figure |Vout/Vin|=0.9373=-0.562dB so loss appears to be 0.562dB.
I say appears to be because the load impedance for Vout is 50+j0Ω, and for Vin is 53.30-j1.281Ω. There is some impedance transformation because Zo is not 50+j0Ω, but 51.42-j1.33Ω so there is a very slight standing wave (VSWR=1.04 at the load end).
So, the spec tells us MLL=0.284dB and we measured 0.562dB under mismatch, albeit slight and a configuration chosen to reveal the problem.
If a physical measurement is taken to test a sample of cable, there are further uncertainties (errors) that might compromise the measurement.
You might ask why the published specification is not subject to the problems discussed here. The manufacturers choose a longer sample and they smooth the measurement curve.
Origin of the theory
The theory behind this is well over 100 years old, it comes from a self educated mathematician, Oliver Heaviside who built on the work of James Clerk Maxwell.