Old XYL's Tales in Amateur Radio

#2: "A 75m Mobile Loading Coil Can Exhibit a Propagation Delay of Three Nanoseconds"

by Cecil Moore, www.W5DXP.com, Rev. 1.1, Aug. 5, 2017

W8JI's Article: "Inductor Current Time Delay"

Introduction

This myth, described in the above W8JI article, has been around for at least ten years and grew out of a newsgroup discussion at that time regarding how many electrical degrees are occupied by a mobile loading coil. That subject has already been covered in three different articles. [1][2][3] The purpose of this article has a much smaller scope, i.e. to answer the question:

Is it possible for a 75m mobile loading coil to exhibit a three nanosecond propagation delay while transferring appreciable energy from one end of the loading coil to the other end?

Coils have long been used as delay lines for RF signals. It is inconceivable that a humongous 100 uh 75m mobile loading coil, with its considerable self-capacitance, could possibly have a propagation delay of 3 ns. The coil is 10 inches long and has, according to W8JI, the same propagation delay as a 10" piece of RG-213. Of course, such is impossible.

How Should the "S21 Delay" Be Measured?

HP's excellent application note titled, S-Parameter Techniques, is available free for downloading. [4] On page 12, the app-note explains how S21 should be measured:

"S21 - Forward transmission (insertion) gain with the output port terminated in a matched load"

For instance, if one wants to determine the S21 parameter for a length of Z0=600-ohm feedline, one terminates the feedline with a 600-ohm resistor (matched load) and makes the S21 measurement. These same conditions must exist for measuring the S21 Delay. One might ask, why is it necessary to terminate the DUT (device under test) network with a matched load? The answer is that reflected energy must be eliminated from the DUT network to obtain a valid S21 measurement. If reflections are not eliminated during the measurement of S21, then we are measuring group delay in an environment with reflections present and we obtain an erroneous value for S21 unrelated to the energy flow delay through the DUT and that is exactly what W8JI did for his measurement of the S21 Delay. It is a well-known fact that group delay and phase delay can apparently exceed the speed of light which, of course, is physically impossible in the real world.

What Is Wrong with W8JI's S21 Delay Measurement?

Question: Did W8JI terminate the test coil with a matched load? If not, the measured S21 Delay value is in error because of the presence of reflected energy. Since he doesn't tell us what "matched load" he used, it appears from the results that he used a 50-ohm load. As the result of a highly incorrect choice for the matched load impedance, he caused his DUT network to experience an SWR of almost 100:1 rendering any measurement of S21 Delay to be invalid by a large amount.

To find out what load W8JI should have used, i.e. what load would be a match for his test coil, we will use the Hamwaves Inductance Calculator [5]. The calculator accepts metric values and here are those values for the W8JI test coil: 100 turns, coil diameter is 50.8 mm (2 in), coil length is 254 mm (10 in), and the diameter of the #18 wire is 1.024 mm. By entering those values, we discover that the characteristic impedance, Z0, of the W8JI test coil is 4627 ohms and that's the value of the matched load that should have been used in the W8JI S21 Delay measurement.

If W8JI had used a proper 4627 ohm matched load for his S21 Delay measurement, he would have measured approximately 21.5 ns of S21 Delay.

The technical blunder of choosing an incorrect value for the matched load measurement of the DUT test coil for the S21 Delay calls into question the validity of everything that is asserted on that particular W8JI web page. For instance, it is impossible for a large percentage of joules of RF energy to jump from one end of a 10 inch, 100 uh coil to the other end in 3 ns. Such a concept is simply an Old XYL's Tale.

What If We Apply the W8JI S21 Delay Measurement Technique to A Transmission Line?

Let's take a 28-foot-long piece of 600-ohm transmission line and perform W8JI's S21 Delay measurement at 4 MHz. Like W8JI did for his test coil, we terminate the feedline in a 50 ohm load and make the S21 Delay measurement. Surprise, we get a 3-ns result just as W8JI did for his loading coil. Jumping to the same conclusion that W8JI did, we assume that energy is traveling from one end of that 28-foot section of feedline to the other end in 3 ns but now we can see the exact problem with that kind of thinking. 28 feet in 3 ns is 9.33 ft/ns and that presents a problem because the speed of light is 0.983 ft/ns.

Is the signal traveling through that feedline at almost ten times the speed of light or is something wrong with the W8JI measurement setup? And of course, a 50-ohm load is not a matched load for a piece of Z0=600-ohm feedline. We have violated the rules for S21 Delay measurement, just as W8JI did for his coil measurement and are trying to measure S21 Delay in the presence of a 12:1 SWR, an obvious technical blunder.

W8JI made that same above mistake with his S21 coil delay measurement. The only difference is that he made his measurement in the presence of an SWR of 93:1 and that is the same technical blunder. The Hamwaves inductance calculator indicates that the velocity factor for the W8JI test coil is approximately 0.04. Dividing the 10-inch length of the test coil by the 0.04 velocity factor yields an electrical length for the coil of 250 inches. 250 inches in 3 ns is 83 inches per nanosecond which (based on W8JI coil measurement techniques) is 85 times the speed of light and unless W8JI has discovered Warp Drive, seems to this author to be an impossibility.

Of course, the basic technical blunder is considering a humongous 75m mobile loading coil to be a device that is encompassed by the lumped-circuit model in which inductors have no physical length. One should ask oneself: What is the percentage error in considering something that is 10 inches long to have a zero length?

Notes and References

[1] Impedance Measurements on Loading Coils

[2] Degrees of Antenna Occupied by A Loading Coil

[3] 75m Mobile Texas Bugcatcher Loading Coil Lab Measurements

[4] HP's App.Note, "S-Parameter Techniques"

[5] Hamwaves Inductance Calculator