The purpose of this article is to present some actual laboratory measurements made on the author's 75m mobile Texas Bugcatcher loading coil and offer an explanation of the relationship between the measured phase delay, calculated time delay, and the number of real-world electrical degrees occupied by the loading coil based on accepted transmission line theory. A number of personal conclusions will be drawn by the author as this paper proceeds.

This article is NOT meant to achieve the quality level of a peer-reviewed IEEE white paper. It is what it is - the results of some simple university laboratory measurements. Others are encouraged to run their own measurements and draw their own conclusions.

__Test Setup__

The Texas Bugcatcher 75m loading coil has 26 turns of #14 solid wire at four turns per inch with a coil diameter of six inches. W5DXP loaned his 75m Bugcatcher Loading Coil to Louisiana Tech University where EE graduate students ran some simple measurements. The current magnitude and phase at each end of the coil were measured with Tektronix CT2 current probes at 4 MHz under various resistive loads. Here is a simple diagram (based on an EZNEC graphic) and a picture of the test setup.

__Measured Phase Shift Results__

Keeping the source frequency constant at 4 MHz, for four different load resistances, 50 ohms, 1200 ohms, 1930 ohms, and 3170 ohms, __the phase shift between the current into the coil and the current out of the coil was measured.__

The following graph shows the phase shift results.

The answer is that the net current phase shift is primarily the result of the superposition of forward and reflected current. If the current is 100% standing wave current, the phase shift through the loading coil is zero degrees. At 4 MHz, an EM traveling wave travels at 1.44 degrees/nanosecond.[1] But for the loading coil, only if the current is 100% traveling wave current is the current time delay through the loading coil directly proportional to the current phase shift through the coil. An earlier article presents the mathematical difference between standing waves and traveling waves.[2]

What we are looking for is the valid calculated delay through the loading coil. In this paper, we will present the boundary conditions necessary to ensure that the calculated delay through the coil is valid which __occurs only when reflected energy is absent__.

Note that if we did not know the Z0 of a piece of coax, we could vary the load resistance until the current magnitude into the coax was equal to the current magnitude out of the coax and that value of load resistance would be a close approximation to the Z0 of the coax. We can do the same thing for the 75m mobile Texas Bugcatcher coil (assuming that the I^{2}R losses in and radiation from the coil are small compared to the load resistor).

For a high-Q coil, that traveling-wave-only condition is very close to being true when the current magnitude into the loading coil is equal to the current magnitude out of the loading coil. There is a small error due to I^{2}R losses in and radiation from the coil but, like lossless transmission lines, we will consider that error to be small enough to ignore during this conceptual discussion.[4] In fact, these measurements indicate that a 75m loading coil can be modeled as a transmission line with a high characteristic impedance (Z0=~1930 ohms) and a very low velocity factor (VF=~0.0193).

__Current-In vs Current-Out Measurements__

The following graph indicates what happens to the Current-Out/Current-In ratio for the loading coil for the four load resistances used for the measurements.

The point at which the Current-Out/Current-In ratio equals 1.0, i.e. Current-Out=Current-In, indicates the approximate value of the characteristic impedance (Z0) of the coil which is ~1930 ohms. From Fig. 2, the phase shift through the coil when the load resistance is 1930 ohms is 41 degrees. __This is the only phase shift that will yield valid results in the calculation of the actual delay through the coil and the number of electrical degrees occupied by the coil in a 75m mobile installation.__

Note that at 4 MHz the ratio of degrees/nanosecond = 360^{o}/250ns = 1.44 deg/ns.[1] Therefore, a phase shift of 41 degrees means a current time delay of 41^{o}/1.44 = 28.47 ns (but only for traveling waves).

__What Happens If We Choose a 50 Ohm Load for Our Coil Measurements?__

With a 50 ohm load, the total current is primarily standing wave current with an SWR of 1930/50 = ~40:1. The phase shift through the coil measures 4.3 degrees on the 75m mobile Texas Bugcatcher coil. To calculate the apparent "delay", we divide the phase shift by 1.44 deg/ns and get a "delay" of 3 nanoseconds. Of course, 3 ns is NOT the actual real-world delay through the coil and is an erroneous calculation based on a __false concept__ which is: ** Under all conditions, the time delay through the coil is related to the phase shift through the coil by some constant multiplier** - an obviously false statement as can be inferred from Fig. 2.[5]

__Notes and References__

[1] For any fixed frequency, the ratio of (degrees of signal passing a certain point) to (the time it takes for that to happen) is a constant. For HF frequencies, simply divide the 360 degrees (in one cycle) by the number of nanoseconds in a cycle. For instance, 360 degrees/cycle divided by the 250 ns/cycle in one 4 MHz cycle equals 1.44 deg/ns.

[2] Current Through a 75m Bugcatcher Loading Coil

The equation for a pure standing wave is of the form: I(x,t)=[Imax*cos(kx)]sin(wt) where the term within brackets is the amplitude term which yields the amplitude envelope of the standing wave. __Note that the phase of a standing wave changes only with time (t) and not with position (x)__ - for -90^{o} < kx < +90^{o}, the length of a 1/2WL dipole.

[3] Analysis of an 80m Base-Loaded Mobile Antenna

[4] Zipped EZNEC file for a 75m Bugcatcher Coil

Considering the I^{2}R losses in and radiation from the coil to be negligible is based on EZNEC modeling. Using copper wire for the coil, the source power was 25.74 watts and the load power was 25.72 watts indicating that I^{2}R losses in and radiation from the coil amounted to only 0.08% of the total power.

[5] That same erroneous 3 ns delay based on that same false concept still exists on a well known ham radio web page as of the date of this article. Exactly the same errors in delay measurements exist there as would happen if we mistakenly took only the measurement data from the Texas Bugcatcher coil using a 50 ohm load. Inductor Current Time Delay