Currents in Standing-Wave Antennas

How can the current "flowing" out of the top of a mobile loading coil be greater than the
current "flowing" into the bottom of the coil? Scroll down to the bottom of this page.

Current Distribution on a Trapped Dipole

The above graphic was copied from Antennas For All Applications, Third Edition, by John D. Kraus and Ronald J. Marhefka. It is from page 824, Figure 23-21(a). The accompanying quote is: "At the frequency for which the dipole is 1/2WL long, the traps introduce some inductance so that the resonant length of the dipole is reduced." So on 75M, the 40M traps introduce inductance and function as loading coils. It is clear from the diagram that there exists a current drop at the location of the inductance on 75m.

Four In-Phase 1/2WL Elements with Phase-Reversing Coils

This graphic was copied from the same reference above. It is also from page 824, Figure 23-21(b). The accompanying quote is: "A coil can also act as a 180 degree phase shifter as in the (above) collinear array ... Here the elements present a high impedance to the coil which may be resonated without an external capacitance due to its distributed capacitance. The coil may also be thought of as a coiled-up 1/2WL element." In a phase-reversing coil, the current is flowing into both ends of the coil at the same time (which doesn't violate Kirchhoff's laws). It just means that a lumped circuit analysis is not valid for a distributed network problem.

What EZNEC Says About Current Distribution Using Inductive Loading Stubs

There's not a lot of difference between inductive loading stubs and loading coils. The EZNEC current distribution is virtually identical to the current distribution illustrated by Kraus in the example above, i.e. there is a current drop across the inductance.

Why the Net Current is not Constant Through a Loading Coil

Some say that the current through a loading coil must be constant according to Kirchhoff's laws. What they are missing is that there are two currents flowing through a loading coil in a standing-wave antenna, a forward current and a reflected current. Speaking on standing-wave antennas, Kraus says (page 187 in the above reference): "A sinusoidal current distribution may be regarded as the standing wave produced by two uniform (unattenuated) traveling waves of equal amplitude moving in opposite directions along the antenna." Balanis, in Antenna Theory, second edition, page 489, agrees: "Standing wave antennas, such as the dipole, can be analyzed as traveling wave antennas with waves propagating in opposite directions (forward and backward) and represented by traveling wave currents, If and Ib, in Figure 10.1(a)."

A transmission line has a distributed inductance and distributed capacitance that causes a delay through it. A real-world loading coil has a distributed inductance and distributed capacitance that causes a delay through it. At a single frequency, this delay can be specified in degrees. Let's use the same assumptions as Kraus. Consider the following loading coil with all four currents having equal magnitudes, i.e. |If1|=|If2|=|Ir1|=|Ir2|.

Let's assume the coil is located at the base of a mobile antenna and that If1 and Ir1 are in phase at zero degrees. The net current on the left side of the coil will equal 2*|If1| or 2*|Ir1| at a phase angle of zero degrees. Also assume that the coil causes a 45 degree delay at the resonant frequency. It follows that If2 will lag If1 by 45 degrees and that Ir2 will lead Ir1 by 45 degrees. The following phasor diagram shows what happens.
It is obvious that the net current on the right side of the coil will equal 1.414*|If2| or 1.414*|Ir2|. The phase angle of the net current hasn't changed through the coil but the magnitude certainly has. In fact, the delay in degrees through the coil can be had from the angle whose cosine is I2net/I1net = 1.414/2 = 0.707.

In reality, the magnitudes of If1, If2, Ir1, and Ir2 are not equal so this exercise is completely accurate only for thin-wire antennas. However, the ballpark conclusions from that assumption are apparently good enough for John D. Kraus.

The moral to this exercise is to avoid using a lumped circuit analysis on a distributed network problem. That includes all problems where forward and reflected waves exist as they do on standing-wave antennas and transmission lines with an SWR greater than 1:1.

The following graphic explains why the current is different at the top and bottom of a loading coil. The magnitudes and phases of the currents at each end of the coil depend simply upon its physical location within the standing wave environment.

What Does EZNEC® Have To Say About Currents Through a Coil?

The following graphic (on the left) is of a base-loaded mobile antenna for ~60m operation. It is 8 feet tall from the feedpoint to the tip and contains a loading coil occupying the space between one foot and two feet from the base. The loading coil was generated using the "Wires - Create - Helix" option available within EZNEC. The antenna is resonant on 5.89 MHz and shows a typical current distribution at that frequency with a greater magnitude of standing wave current at the bottom than at the top of the loading coil. Some might say it is logical for more current to be "flowing" into the bottom of the coil than out the top. Let's question that logic by adding 1/4 wavelength of wire to the top of the antenna on the left to obtain the antenna on the right.
Observe what happens to the currents between the two antennas. In the antenna on the right, is it possible to have 1.29 amps of current "flowing" into the bottom of the coil and 2.068 amps "flowing" out of the top? Of course not! The technical facts are that standing wave current doesn't flow in the normal sense of current flow. The equation for a normal traveling wave current is K*Func(kz ± ωt). The equation for standing wave current is K*Func(kz)*Func(ωt). These two currents are quite different in form and function. EZNEC displays the net standing wave current, not the underlying forward current and reflected current. Both antennas illustrated above are Standing Wave Antennas!

Moral: There is no useful phase information contained in the standing wave current phase measurement. Therefore, the standing wave current phase measurement alone cannot be used to determine the percentage of a wavelength that is occupied by the loading coil. Loading coils occupy tens of degrees of a wavelength but measuring that length is quite a technical challenge. The estimated number of degrees occupied by the coil in the above examples is estimated to be ~60 degrees since the self-resonant frequency of the coil is approximately 9 MHz. A very rough estimate of the electrical length of the coil can be obtained using an arc-cosine function on the standing wave current amplitudes. Hint: The only phase information in a standing wave is embedded in its amplitude, not in its phase.

Download the EZNEC files for the above antennas:       Download zipped test316.EZ.       Download zipped test316c.EZ.

There are two very interesting web pages that shed light on this issue. Please pay close attention to the limitations of the lumped circuit model when applied to large loading coils:

RF Coils, Helical Resonators and Voltage Magnification by Coherent Spactial Modes

Class Notes: Tesla Coils and the Failure of Lumped-Element Circuit Theory

What Does EZNEC® Have To Say About Traveling-Wave Antennas?

We have seen above that standing-wave current phase cannot be used to measure delays through a coil because that phase is virtually unchanging over the entire length of an antenna, whether a coil is present or not. Therefore, the phase measurements reported using standing wave current phase are meaningless. One way to actually measure the delay through a coil would be to eliminate reflections and measure the forward traveling wave delay through the coil. Such an antenna is called a "traveling wave antenna". Following is what EZNEC tells us about such an antenna.
The coil, which models out to be self-resonant around 13.7 MHz, is being used at 5.89 MHz, just as in the above earlier example. EZNEC says the delay through the coil is 15.68 degrees at 5.89 MHz. This configuration could be easily duplicated and measured in the real-world by anyone so equipped.

Download the EZNEC file for the above antenna:       Download zipped test316y.EZ.

A free demo version of EZNEC is available at