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E-mail: Jack.Smith@cliftonlaboratories.com
 

Jeff, AC0C, sent me a length of Digiwave coaxial cable, marked DGC-RG58-211000, to verify his measurements. Jeff purchased the cable believing it was an RG-58 variant (foam dielectric, white jacket, foil and drain wire shield) of 50 ohms nominal characteristic impedance.

After some odd results, Jeff measured the cable impedance, (Zo) and found it to be nearly 100 ohms, not the 50 ohms one would expect for an RG-58 type cable. I asked Jeff to send me a section for an independent measurement and I've now confirmed that this is definitely not 50 ohm cable.
 

When a transmission line is  terminated with its characteristic impedance, there is no reflection and the line looks like a pure resistance. To determine the transmission line's Zo with this method, adjust the trimpot for minimum phase angle while observing the impedance (magnitude and phase).

In theory, it should be possible to adjust the trim pot for 0 phase angle over a range of measured frequencies . This isn't actually the case, however, due to a couple of reasons. One is that the trimpot and connecting wire has some residual reactive component. For frequencies in the low MHz range, these imperfections are not too important, however.

But another factor can be at work. We are used to thinking of Zo as being a constant value and resistive only, i.e., the cable impedance is constant with frequency and has no reactive component. In real cables, neither of these are true, and as we shall see, the Digiwave cable is particularly poor in this regard.
 

This data establishes that Zo is certainly not constant over this frequency range and that Zo is not purely resistive.
 

The cable impedance is then: Zo = Sqrt(Zoc*Zsc).

Zo, Zoc and Zsc are all vector quantities, i.e., they have magnitude and phase, or, if you prefer, a real and imaginary component. I'll generally ignore the phase and treat the cables as having only a real component of impedance. This assumption introduces negligible error with high quality cables at normal amateur radio frequencies.

Short circuit and open circuit impedance measurements also used the HP 8752B VNA. To verify my measurement procedure, I made similar measurements on a short length of high quality RG-223 (double shielded, silver plated 50 ohm coaxial cable) and a short length of cheap import RG-58 cable. (These cables are about 9 feet long, and the Digiwave cable is approximately 59 feet long.)

Over the frequency range 300 KHz - 30 MHz, the Digiwave cable Zo varies from 132 ohms to 88 ohms. The cheap RG-58 and  the  RG-223 show much less variation over this frequency range.

There are two apparent anomalies here:

• Elevated Zo at lower frequencies
• At frequencies above 1 MHz, the impedance is nearly twice the expected  50 ohms.
   

Elevated Zo at low frequencies

Let's consider the first apparent anomaly.

Both cables show a considerable increase in Zo at low frequencies, with Zo in this frequency range being an excellent fit to a straight line relationship when Zo and frequency are plotted on a log-log scale.

The difference between the two cables is where they transition from low frequency frequency sensitive Zo to frequency insensitive impedance. The Belden RG-58 makes this transition around 40 KHz, whilst the Digiwave cable does not transition to a (semi) stable impedance until nearly 1 MHz. There is a clue in this plot.

Belden has two useful papers discussing the behavior of coaxial cables at frequencies below those we normally use in amateur radio operations:
http://www.belden.com/pdfs/Techpprs/ciocahalf.htm
http://www.belden.com/pdfs/PDF/Precision%20Video%20Cables%20Part%201.pdf

The commonly stated relationship between a cable's electrical parameters and Zo is:

L is the cable inductance and C is the capacitance as determined in an infinitesimal length of cable. 

This is a useful approximation for a high quality cable, at normal amateur radio frequencies. However, the true relationship is:

R is the series resistance and G is the shunt conductance, representing leakage in the cable dielectric.

If G <<ωC and ωL >> R  then the R and G terms may be neglected and the simplified form of the equation used.

With modern dielectrics (Teflon or polyethylene) G <<ωC is almost always true, but it is not the case that ωL >> R at low frequencies. This is the reason Zo increases at low frequencies; the numerator of the equation increases due to the R component whilst the denominator remains constant.

(In fact, C has some change with frequency and L has a greater relative change in frequency. This is due to skin and proximity effects that alter the current distribution with frequency and hence change the flux linkages and therefore the inductance. The normal consequence of this is that L decreases slightly with frequency and therefore at frequencies where ωL >> R, Zo will drop a bit as the frequency increases.)

To see if the resistive component of Zo explains the Digiwave Zo impedance increase below 1 MHz or so, I measured the DC resistance of the cable, and compared it with a sample of  RG-223.

Why does the Digiwave cable demonstrate so much higher resistance?

The difference in shield resistance can be explained by the cable construction; Digiwave uses a foil shield with a low coverage "drain" braid. RG-223 has two dense shields, both of silver plated copper.

The center conductor resistance almost certainly represents a cost savings measure. Jeff measured the center conductor diameter as 0.5 mm, close to No. 24 AWG, (0.511 mm). No. 24 AWG copper wire has a resistance of 25.7 ohms/1000 ft, or 26 mohms/ft.  The measured resistance is more than five times this value. Steel has an electrical resistance about 10 times that of copper, so my belief is that Digiwave's center conductor is soft steel with a thin copper wash, not enough to make it to the copperweld classification (40% conductivity usually, from what I can find).

Copper-clad center conductors are not unusual in coaxial cable. RG-174 is constructed with it, as is nearly all 75 ohm CATV cable. However, these use a  thicker copper cladding than seems to be the case for the Digiwave cable.
 

Zo is not 50 ohms above 1 MHz.

This is more puzzling. The most likely answer is the one suggested by Jeff; that this cable was mis-manufactured. Either it was intended to be 95 ohm cable (a standard value) and it was mis-labeled, or there was a serious problem in manufacturing. My guess is the former is more probable than the latter.

Loss versus Frequency

The figure below show the loss for the Digiwave cable and the similar length RG-58 over the range 300 KHz - 1 GHz. (59 feet each) (Vertical scale is 2 dB/division) No adjustment is made for mismatch loss.

The results are interesting. Up to 100 MHz, real  RG-58 has lower loss, by 2 dB or so up to 10 MHz, but by 100 MHz, the two cables have similar loss. (The ripples in the Digiwave data is due to the mismatch between the 95 ohm cable impedance and the 50 ohm vector network analyzer source and termination.) However, above 100 MHz, the Digiwave cable shows less loss than real RG-58, amounting to nearly 6 dB less loss at 1 GHz. (Increasing cable loss dampens the ripple amplitude as the frequency increases.)
 

At low frequencies, the Digiwave cable's high resistance increases loss. But above 100 MHz, the difference in loss shifts to favor Digiwave. Some of this loss may be related to the cable impedance; cables with an impedance in the 60-75 ohm range have lower loss than 50 ohm cable. (See http://www.epanorama.net/documents/wiring/cable_impedance.html for a useful discussion of this concept.) Another factor may be related to the cable shield. At VHF/UHF frequencies, the foil used in the Digiwave cable is more homogenous than the woven braid in the classical RG-58, and has less potential for loss. Another factor may be the foam dielectric used by  Digiwave compared with the solid polyethylene found in the Belden RG-58. Finally, to complicate things even more, the Digiwave cable will exhibit increased loss due to the mismatch with the 50 ohm VNA.

The statement "Around 99 per cent coverage is required for a braided conductor in order to avoid excessive loss by radiation and to ensure proper shielding" should be understood in the context - the application discussed is microwave transmission in the range 1 GHz to 10 GHz or more. A lower braid percentage braid coverage is satisfactory for frequencies below 30 MHz.