## Comparing Transmission Media

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## Comparing Transmission Media

I would like to know, for a given frequency, assuming the length (12") is the same, which of these transmission lines has the worst signal loss: coaxial cable, waveguide, microstrip, or stripline?

I think that microstrip and stripline have the worse signal loss, then coaxial cable, and then waveguide. Is that correct? What is the explanation behind it?

Dr. Johnson replies:

Marwan, perhaps I can improve your understanding of the causes of signal loss in those types of media.  There are two primary causes: resistive, and dielectric.  Resistive losses arise due to the effective series resistance of the conductors.  Dielectric losses arise due to intrinsic properties of the insulating medium between the conductors.

In the limit, by making the conductors out of superconducting materials and separating them with a near-perfect vacuum, you could theoretically make the losses approach zero for any of the structures you mentioned.  In that sense, they are all equivalent. There's nothing particularly special about any one form of transmission pathway. What matters is simply the series resistance and the dielectric quality.

Unfortunately, that answer doesn't provide much useful guidance in the selection of transmission media. You asked for a more practical, and useful, result. Towards that goal please let me expand my answer.

I shall begin by examining dielectric loss. That is a property of the insulating (dielectric) medium and little else. For a given dielectric material in a coaxial or stripline configuration it does not matter whether the conductors are large or small, or whether the conductors are made square (stripline) or round (coaxial), or if the coaxial cable is squished into an ellispoidal shape—in all cases the dielectric loss in units of dB/m remains precisely the same.

That astonishing behavior results from the way signals propagate in a dielectric medium. The E&M field pattern within a coaxial or stripline configuration propagates much like a simple plane wave in free space. The wave is guided by the signal and return conductors, but the signal power actually flows in the dielectric space between the conductors. The dielectric loss for a guided wave, in units of dB/m, is the same as you would experience for unguided plane waves traveling in an infinite universe filled with the same dielectric material. The shape of the transmitting cavity (round, square, or otherwise) does not affect the result.  Similarly, the size of the structure does not affect the result, either. If you shrink the structure by a factor of two all the fields become twice as intense, but as long as the dielectric material behaves in a linear fashion (i.e., it does not break down and develop arcs) the same dB/m attenuation results.

Microstrips are slightly different. They carry a small portion of their signal power in the air above the trace, as opposed to the main body of their signal power which remains trapped in the dielectric media between the trace and the underlying reference plane. The small portion of signal power flowing in the air suffers almost no loss. Therefore, microstrips always have slightly lower overall dielectric losses than striplines made from the same dielectric material. I have in the past intentionally designed resonant structures on the microstrip layer to take advantage of that property. Waveguides have a reputation for very low dielectric loss because their power-carrying region is generally filled with air (or pressurized gas). Low dielectric loss is not an intrinsic property of the waveguide geometry. If you stuffed the waveguide full of polyethelyne, for example, the waveguide would have the same dielectric loss as a polyethelyne-insulated coaxial cable.

[ED. NOTE: A waveguide stuffed with polyethelyne would actually have *more* dielectric loss than an equivalent coaxial cable, because the propagating modes within a waveguide do not move straight down the conduit. Waveguide modes bounce around from side to side in a way that actually increases their effective electromagnetic path length beyond the straight-line length of the conduit. Any waves that endure a longer propagating path suffer additional dielectric loss. The mode of propagation in a coaxial cable, called the TEM mode, moves straight down the cable, so its effective electrical path length is the same as the straight-line length.]

Now let's consider resistive loss. Start by ruling out superconductors for this discussion, because they are expensive, unreliable, and balky. Besides, for superconductors the resistive loss is near-zero, so there isn't anything interesting to talk about. Focus your attention exclusively on copper, the world's most popular conductor. It has two properties that account for its popularity: (1) It has the lowest resistance of all the non-precious metals, and (2) It has good mechanical properties that make it easy to form wires or deposit with electroplating.

Suppose you showed me two copper-based transmission structures made using the same dielectric material. Just looking at them, I can tell you which will have the least loss. It is the one with the larger cross-sectional area. That happens because, quite simply, the larger you make the cross section, the less series resistance you have in the conductors. Since series resistance translates directly into resistive power loss, the bigger cross-section enjoys the least resistive loss. I don't have to consider dielectric loss in this example, because by the construction of the example, the dielectric materials are the same, so the dielectric losses remain the same, regardless of the physical scale or shape of the conductors.

In practice, such simplistic comparisons may be complicated by various geometrical factors, but ignoring that for a moment, if you just remember that BIGGER conductors have LESS resistive loss you will have gone a long way towards understanding transmission line losses.

I am now in a good position to dissect Marwan's assertions.

From a resistive-loss perspective, microstrips and striplines are much smaller than the coaxial cables found around a typical digital lab, and waveguides are larger still. Therefore, the resistive-loss hierarchy (from most to least) goes like this: microstrips and striplines, then coaxial cables, then waveguides.

From a dielectric-loss perspective, microstrips and striplines built from FR-4 board materials suffer greater dielectric loss than polyethelyne coaxial cables, which suffer more than air-filled waveguides. Under those assumptions the dielectric-loss hierarchy (from most to least) goes the same way as the resistive-loss hierarchy: microstrips and striplines, then coaxial cables, then waveguides.

Adding together the two loss types, I conclude that, with the typical dimensions and materials most often encountered in laboratory situations (and I've seen a BUNCH of labs), Marwan's assertions stand correct.

Next let's look at a counter-example to the ordinary hierarchy. Suppose you made a coaxial cable ten times bigger than a waveguide and used air as the dielectric. That construction requires that you insert tiny plastic spacers into the coaxial structure to hold the center conductor in place, preventing it from falling to one side and shorting out. Once complete, your giant coaxial cable might have significantly less loss than the waveguide.

For example, here are the specs on the HCA900-50T Series 9-inch air coax:

Outer diameter of shield:  9 inches
Dielectric: Air or pressurized gas
Attenuation at 100 MHz: 0.0479 dB per 100 feet
Power handling capacity at 100MHz: 611 KW
Main application: RF transmitter to antenna

When thinking about series resistance, you must take into account the resistance of the signal conductor and also the resistance of the return (or shield, or reference-plane) conductor. Current traverses both paths, engendering skin-effect resistive losses on both surfaces. In a typical mictrostrip or offset stripline, expect resistive losses on the return conductor on the order of 30% as great as the resistive losses on the signal conductor. Coaxial cables exhibit a similar ratio.

The waveguide is most interesting in this regard, as it has no signal conductor. It is just a hollow pipe that supports various guided modes of signal propagation. Given the same outer diameter, and filled with the same dielectric material (let's assume air in both cases), a waveguide should therefore have substantially less resistive loss than a coaxial cable. That sounds good in theory, but in order to achieve that improvement you must take great care in launching signals into and recovering signals from the waveguide. The launch and recovery operations are done with structures that resemble tiny antennas. Once established, the launch and recovery structures work properly only over a narrow range of frequencies. If you change the carrier frequency, the system must be "re-tuned". That accounts for the popularity of coaxial cable, which is easily connected and works uniformly well over a broad range from DC to RF.

I hope this brief note gives you more insight into the physics behind Marwan's assertions, and some of the exceptions to the rules.

Best Regards,
Dr. Howard Johnson