The vast majority of the antennas we use today are fed via coaxial cables. But when modeling antennas, the coaxial feed lines are almost always skipped. Due to this, the common-mode current that may be present in the coax and may influence the antenna operation is never examined.
This page is a shortened and modified version of the article published in the QEX magazine (07/08-2021).
It is a common practice to model the antenna without its matching network and its feed line. If you do it in this way, you assume that the antenna and its feeding system are electrically balanced, and the feeder does not pick up any RF radiation from the antenna elements. The assumption is that only differential currents flow in the coax. In other words, there is no common-mode current in the feeder.
Those who admit that the system is not electrically balanced, are often convinced that a common-mode choke (sometimes called a 1:1 current balun or a line isolator) connected between the antenna feed point and the coaxial cable is a sufficient countermeasure reducing the common-mode current to a negligible value.
Unfortunately, these assumptions are overoptimistic in many cases.
The common-mode current value depends on a number of factors:
the input power (the higher the power, the higher common-mode current)
the feed point impedance (the higher impedance magnitude, the higher the common-mode current at the same input power)
the physical symmetry of the antenna and its coaxial feeder
the symmetry of the antenna current distribution near the feed point (the more symmetrical it is, the lower common-mode current)
the impedance and resistance of the common-mode choke, if used
the length of the coax feed line between the feed point and ground
Fortunately, you can use one of the contemporary antenna simulators and model not only the antenna but also its feed line. In this way, you can calculate the common-mode current in the coax before you actually build your antenna system. If the current is too high, you can modify your design and reduce the common-mode current when you are still in the design phase.
Such modeling is not very simple, but it is not extremely difficult either.
It is not quite obvious how to add a coax feeder to the antenna model in the popular antenna simulators that we use nowadays.
Some simulators (like EZNEC or 4nec2) allow you to use an object called a transmission line. However, this object is an idealized model of a real transmission line. It assumes that the currents in the transmission line are always balanced (exactly equal and opposite in phase). And we know that in the real world, the currents are not necessarily equal.
Fortunately, Roy Lewallen, W7EL, in his help file to the EZNEC program, presented a workaround for this problem. The real coax can be simulated as a combination of two objects: a transmission line and a wire.
Let’s assume that the real system is a simple half-wave dipole antenna fed directly with a coax cable, like shown below.
The transmitter is represented here by a voltage source delivering PSC power. One of the source terminals is grounded. The power delivered to the antenna PIN is smaller than the transmitter output power PSC because of the loss in the real feed line.
As W7EL explained, the real coax can be simulated in EZNEC or 4nec2 simulator as a combination of a transmission line and a wire like in the figure below.
The wire in the model should have the same diameter as the coax shield and the same insulation as the coax jacket. It should be connected to this element of the antenna model, to which the coax shield will be connected in the real antenna. It should be routed in the way the real coax is expected to be routed. The grounding point is the place in which we can consider the coax shield grounded (where it touches the ground for the first time).
The transmission line object can be routed from the antenna feed point to any direction in your antenna system model. In contrast to the wire discussed before, the idealized transmission line does not have to follow the expected position of the real coax. You need to enter the transmission line parameters: characteristic impedance, length and (in case of the EZNEC) velocity factor and attenuation per unit of length.
In the EZNEC simulator, the transmission line length should be entered as the real cable length between the transmitter output and the antenna feed point and the source power PSC should be equal to the transmitter output power. EZNEC will calculate the PIN based on the entered data.
In the 4nec2 simulator, the transmission length should be entered as the real cable length divided by its velocity factor. The most popular coax cables have the velocity factor equal to 0.66, but there are cables with other values too. You should check this parameter in your cable datasheet. However, the 4nec2 simulator does not handle transmission line attenuation, so entering the transmission line lengths makes sense only in the more complex antenna systems with more than one feed point. In such systems, phase differences between the feed point voltages and currents influence the whole system parameters and performance.
If you have just one feed point, the transmission line length does not matter. You may set it even as zero. In the 4nec2, you enter PIN as source power. In order to find out the value of PIN , you need to know what the coax attenuation will be in the real installation. I use the TLDetails program by AC6LA to calculate the PIN.
For example, let’s assume that you enter the following data in the TLDetails:
“Input Watts”: 100
Coax type: Belden 9201 (RG-58/U)
Coax length: 30 m
Frequency: 14.175 MHz
R & X at load 67 and -13 ohms respectively (these values you find by running the 4nec2 simulation)
The program will then calculate the “Power at load” as equal to about 74 W.
And you can enter now the input power in your 4nec2 model as 74 W. So, the process is a little more complex than in the EZNEC.
But that's not all. If your antenna model has only one feed point, the model can be simplified even more – see the drawing below. Such model will work in every simulator: EZNEC, 4nec2 and MMANA-GAL. PIN should be calculated in the external program like explained above.
The source in now moved to the antenna feed point and its input power is reduced due to losses in the coax. In our example, the PIN source should have its power set to 74 W.
As you can see in the drawings above, the wire simulating the coax is grounded. It is usually assumed that the grounding point is the point where the real coax touches the ground for the first time. Due to high capacitance between the shield and ground, it is considered as an equivalent of a galvanic connection to ground. When modeling that, set the ground model to MiniNEC ground and terminate the lower end of the coax at zero height (z=0).
If you use 4nec2 or EZNEC, you may prefer to model the coax running very slightly over the ground. In this way, you will model the reality more faithfully. The picture below shows such a situation and additionally the coax is routed not ideally vertically. The ground model should be set to Real High Accuracy.
After simulating your model at a chosen frequency, you will be able to examine the current flowing through the wire simulating the coax. And this current is just the common-mode current that will flow in the real coax. The common-mode current is not constant at every point over the length of the coax because we have a standing wave here. The antenna simulators allow you to examine the current in various segments of the wire and/or view its magnitude graphically. You should be interested in the common-mode current maximum value. When you modify your system, you observe this maximum and your goal is to make it as low as possible.
Graphical presentation of the common-mode current in the 4nec2 simulator:
Common-mode current calculated on the segments of the wires simulating coax in the 4nec2 simulator:
Graphical presentation of the common-mode current in the EZNEC simulator:
Common-mode current calculated on the segments of the wires simulating coax in the AutoEZ+EZNEC simulator:
Graphical presentation of the common-mode current in the MMANA-GAL simulator:
Please note that in the MMANA-GAL, you must not route horizontal wire close to the ground. That’s because of the limitation of its software engine. You should ground the coax as shown above.
Current on various segments of wire #3 as calculated by MMANA-GAL and exported in the Table of currents:
In the MMANA-GAL example above, the common-mode current seems to be very low. That’s because the input voltage source in the MMANA-GAL was set to just 0.707 V rms (which is the default setting). Please notice that in the EZNEC and the 4nec2 simulators, you can set the PIN in Watts, what is very convenient. You can not do that in MMANA-GAL which support only voltage sources.
It is possible to calculate the voltage corresponding to 74 Watts in our example above. But the calculation is rather complicated. You need to use complex numbers. So, if you are not interested in the exact value of the common-mode current, I would suggest rather to focus on the ratio of the common-mode current in the coax to the maximum current in the antenna driven element. Your goal should be to reduce this ratio to no more than 1/5 for 100 W power input and 1/10 for 1 kW input.
Even in such a simple model as above, you can influence the common-mode current by changing the angle the coax is routed from the feed point and changing its length between the feed point and ground. You can significantly reduce the common-mode current by making the coax length close to the odd number of quarter waves: ¼ wavelength, ¾ wavelength, and so on.
It works even if the coax is not perpendicular to the antenna driven element. But mind that this rule is applicable only for the systems without the common-mode chokes and for low feed point impedance antennas.
The most popular method used to reduce the common-mode current is installing a common-mode choke (also called 1:1 current balun, or line isolator) between the antenna feed point and its coaxial feed line. It is shown in the schematics as two mutually coupled inductors wound on the same core.
Differential currents flowing through the common-mode choke create opposite magnetic fields in the core, so the choke is practically a short-circuit for them. The choke is not a short-circuit though for the common-mode current. Typically, it creates an impedance of a few thousands ohms for the common-mode current. This is the impedance of one of the coils shown in the circuit diagram above.
The less advanced hams may suspect that this common-mode impedance is mainly inductive. But no. The well-designed choke should create mostly resistive impedance for the frequency of interest.
In order to model a common-mode choke, you need to either calculate or measure its parameters. If you use the parameters measured or calculated for a specific frequency, you can use one of the two models: complex impedance Z of the connected in series resistance R and reactance X or a so-called trap circuit consisting of Ls, Rs and Cp as shown below.
You insert a load in the top segment of the wire simulating the coax just below its junction with the antenna. If the simulator does not support loads in the Z=R+jX form, use the trap circuit.
The above models are valid only for one frequency, because Ls and Rs change with frequency. So do Z, X and R.
It is not very convenient when we want to simulate the antenna system in a frequency range rather than on a single frequency. Fortunately, the common-mode choke impedance can be quite well approximated with a parallel RLC circuit or two parallel RLC circuits connected in series – see below.
Such models are valid for wide frequency range (for example 1-100 MHz) and their components are fixed – not frequency dependent. The more complex 2xRLC approximation is a little more accurate than the 1xRLC.
1xRLC approximation:
Red dots show the exact values of choke impedance magnitude |Z|, the continuous cyan line is the |Z| of the 1xRLC circuit and the dashed cyan line is the equivalent serial resistance of the 1xRLC circuit.
2xRLC approximation:
Red dots show the exact values of choke impedance magnitude |Z|, the continuous cyan line is the |Z| of the 2xRLC circuit and the dashed cyan line is the equivalent serial resistance of the 2xRLC circuit.
You can calculate the common-mode choke parameters using TFCI Calculator. The calculator will find the complex impedance Z and trap circuit component values for the entered frequency. It can also calculate the components for the 1xRLC and 2xRLC models.
Once you have the common-mode choke model, you can insert it in the antenna system model in your favorite simulator.
There are generally two types of baluns: the voltage baluns and the current baluns.
A voltage baluns does not reduce the common mode current.
A current balun (Guanella balun) can be simulated in the same way as the common-mode choke. Calculate or measure the impedance of a single winding and insert either the 1xRLC or 2xRLC approximation circuit in your model.
If you use baluns or ununs in your system, the source impedance must be adjusted for their impedance ratio. For example, if you use 4:1 balun, do not use a 50-ohm source but a 200-ohm source. Alternatively, you can use 50-ohm source and a step-up transformer (in EZNEC). But, in my opinion, it is an overkill for a single feed point system.
If the common-mode current is greater than about ¼ of the antenna maximum current, you should expect noticeable distortion of the radiation pattern, and change of the antenna resonance frequency and feed point impedance. So, you’d better keep the common-mode current smaller than that.
Always check the power dissipated in the choke/balun model. For the transmitter power levels of 100 W and higher, it is often the power dissipated in the choke/balun that is the limiting factor. In other words, once you get a small value of the common-mode current in the wire simulating the coax, do not stop there. Check how much power is dissipated in the choke/balun.
By adding additional common-mode chokes in series to the existing one, you can not only reduce the common-mode current, but also reduce the total power dissipated in all chokes together.
Please remember that there are two mechanisms of exciting the common-mode current:
by conduction
by radiation
Excitement by radiation is often referred to as picking up RF energy by the coax from the radiating antenna. This happens when, for example, the coax is not routed vertically from a horizontal dipole. Please mind that you may reduce the excitement by conduction by installing a very high impedance common-mode choke, but still have large common-mode current excited by radiation. Fortunately, all simulators take into account both mechanisms.