The article Measuring coaxial cable loss with a voltmeter discussed some pitfalls of that measurement method, starting with the influence of theoretical error in actual Zo at lower frequencies.
You might expect that using a directional wattmeter has exactly the same problems because as many online experts advise, at the end of the day they are just a voltmeter.
They are wrong, a Bird 43 might use a half wave detector driving a d’Arsonval meter and you might regard that to be a voltmeter, but the RF signal it measures is a combination of samples of forward and reflected waves wrt to its calibration impedance (usually 50+j0Ω) and we will see that makes a difference.
Where a directional wattmeter is calibrated for a purely real impedance (ie X=0), then the relationship \(P=P_{fwd}-P_{ref}\) holds true (On the concept of that P=Pfwd-Prev).
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
Parameters | |
Transmission Line | Belden 8259 (RG58A/U) |
Code | B8259 |
Data source | Belden |
Frequency | 3.600 MHz |
Length | 10.000 m |
Zload | 50.00+j0.00 Ω |
Yload | 0.020000+j0.000000 S |
Results | |
Zo | 51.42-j1.33 Ω |
Length | 67.357 °, 0.187104 λ, 10.000000 m, 5.197e+4 ps |
VF | 0.642 |
Line Loss (matched) | 0.284 dB |
Line Loss | 0.282 dB |
Efficiency | 93.71 % |
Zin | 5.330e+1-j1.281e+0 Ω |
Yin | 1.875e-2+j4.506e-4 S |
VSWR(50)in | 1.07 |
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 |
Vout/Vin | 3.714e-1-j8.606e-1, 9.373e-1∠-66.7° |
Iout/Iin | 3.739e-1-j9.270e-1, 9.995e-1∠-68.0° |
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 |
γ | 3.275e-3+j1.176e-1 |
Loss model source data frequency range | 1.000 MHz – 1000.000 MHz |
Correlation coefficient (r) | 0.999924 |
We can calculate the expected (or theoretical) readings on Bird 43 wattmeters or the like placed at both ends of the line.
Source: \(P_{fwd}=80.00000,P_{ref}=0.02583,\)
\(P_{source}=P_{fwd}-P_{ref}=80.00000-0.02583=79.97417\);
Load: \(P_{fwd}=74.97381,P_{ref}=0.02759,\)
\(P_{load}=P_{fwd}-P_{ref}=74.97381-0.02759=74.94622\);
Overall: \(Loss=10\cdot log_{10}(\frac{P_{load}}{P_{source}})=0.28200dB\).
Readers will note that the reflected power values are very small and in practice it would be a challenge to read forward and reflected power to this resolution. For this type of test scenario with a nominal load, it should usually be the case the reflected power is very small and mostly the result of imperfection of the nominal load that the difference between theoretical Zo and nominal Zo.
So, in this case if we ignored reflected power in the calcs we would obtain \(Loss=0.28180dB\), but practical measurement with great care of forward power would make it difficult to achieve tenth dB accuracy for low loss cable sections. So, with care, one might measure this section to be 0.3dB and that would be sufficient to indicate whether it was likely to be faulty when compared to the MLL specification (0.284dB).
Note that measurement using a poor load means you are measuring loss under standing waves and it may be significantly higher than MLL.
The objective in this type of test is to use a load that produces insignificant reflected power, and then do the full calculation of forward minus reverse if the reverse power observed is significant, otherwise calculation based on forward power at both ends will be sufficient.
Measuring short low loss sections risks measurement uncertainty dominating the result.