DescriptionNEC (Numerical Electromagnetic Code), written by Gerald Burke, is a popular antenna modeling code for wire and surface antennas and scatterers. Models can include wires buried in a homogeneous ground, insulated wires and impedance loads. The code is based on the method of moments solution of the electric field integral equation for thin wires and the magnetic field integral equation for closed, conducting surfaces.LicenseUS Academic: $300US Noncommercial: $300Non-US Academic/Noncommercial: $500US Commercial: $1,100Non-US Commercial: $1,500ID22610Email.
28 shares.AbstractPortrayed below is a complete and self-contained NEC model of one popular form of the end-fed half-wave dipole antenna. Applying a feed to any antenna in NEC or any electromagnetic simulation software is about a simple a task as can be conceived by placing a “source” of near infinitesimal size inline with a dipole element. Use a current source.
Examples and discussions exist,. While perfectly fine for various studies, this leaves the trickiest part out of the equation namely how to change a 50 ohm feed impedance to that appropriate to feed the high impedance end of a half-wave dipole. This study includes the physical model of just such a step-up transformer providing a way to use a 50 ohm source. Electromagnetic simulation toolsI have access to a wide variety of electromagnetic simulation tools. At opposite ends of the software landscape we have. FDTD – method: Actually calculates Maxwell’s equations in time step offering movie like views of the progression of both electric and magnetic fields.
Very slow, often high cost software, but very complete and very cool. NEC – method: Uses technique to calculate steady state currents of each wire segment. Relatively fast, often low cost or free software and offers an easy entry into antenna simulation.Since NEC is available to so many, it got the nod for this project. So now what front end to use.
EZNEC or 4nec2Of the numerous “front ends” available to run NEC, EZNEC and 4nec2 seem to be at the top of the stack.The recent versions of EZNEC include a transformer emulation capability that might be of interest to end-fed experiments. 4nec2 pretty much relies on whatever the underlying NEC can provide. It truly is a front end to the command-line NEC executable programs. This is actually an advantage for 4nec2 since improved or optimized NEC executables instantly upgrade its speed and computational power. Such is the case with the availability of NEC-MP that recompiles NEC into a truly multi-threaded program. This takes advantage of machines with spare threads and speeds up NEC computations enormously.Another advantage of 4nec2 is the ability to parameterize dimensional and RLC values to perform optimization and evolution techniques to play “what if” with great ease.
One disadvantage of 4nec2 it’s buggy as hell and great care must be applied to watch out for issues. Regardless, 4nec2 gets the nod for this effort. How to model the transformer in NECSimulation packages such as EZNEC offer special transformer simulation. Sounds very handy and I look forward to learning how this works someday. However, I wanted to study the behavior of the entire system including the winding of the step-up transformer rather than rely on an idealized version of same.Years ago I took an antenna class from who was kind enough to field questions after the class. At that time I was designing an improvement to the antenna to replace the Franklin stub with a coil.
I knew much could be accomplished in NEC using an inductance inline, but asked him for tips regardless. He said “Why not just simulate the inductor as wires along with the rest of the model?” I did. Of particular significance is the ability of NEC to provide a better realization of a coil than any idealized and perfect inductor.Time to make the model. NEC model of the end-fed half-wave dipole antennaTaking the lessons from the Super J and Dr. Best, I set about to simply design a helical step-up transformer at the end of a half-wave antenna element. It took some trial and error with the tools available in 4nec2, but wound up with this design in figure 1.
Figure 1 – The end-fed half-wave dipole antenna with magnified view of transformer.Features include:. Approximately one half wavelength of straight wire from the antenna top to the top of the transformer winding. 20:3 step-up transformer in the autotransformer configuration. Various ratios were tried until discovering 20:3 produces close to 50 ohms (for this particular situation).
The transformer configuration produces an inductive component at the 3rd tap wire. A reactance, Xs, is in series between the source and the primary winding to provide the means to compensate for this. This is a core-less air transformer (or “air core” if you like) just in case that isn’t obvious.That series reactance is most often a capacitor in series. It’s what one finds in end-fed VHF and UHF antenna systems from Diamond Antenna and others.
One example is the end-fed dual band mobile antenna and companion groundless mount. Numerous web sites reveal the coil and series capacitor of these antennas. No “extra” counterpoise or other conductors required Figure 2 – The transformer converting 50 ohms to the thousands one needs to drive the current node of a dipole.Danger, Danger, Danger!!!I probably am using the term counterpoise incorrectly, but there is so much variation in its use, oh well. Owen Duffy and I cannot disagree, but for the sake of this discussion I’m simply referring to any additional conductor beyond that of the EFHW antenna system (whip, coil, reactance and source).
Alrighty then let’s move along.Figure 2 gives a bit more detail highlighting the location of the source and reminding us eventually something will connect to the feed point and provide a bit of counterpoise. However one point for this particular effort was to prove to myself this can work without need of a purpose-built counterpoise system or other conductors. Hence the wire in light green does not actually exist in the simulations for this article.Okay yeah the little bit of wire coming out from the transformer to meet the source and reactance do provide a little bit of counterpoise, but to what effect. Hint, the effect of the extra wire will be covered in depth in a forthcoming article. The impedance seen by the source Figure 3 – Final impedance after insertion of series capacitor to offset inductive reactance of the end-fed half-wave dipole antenna.Figure 3 shows the resistance and reactance as seen by the source as configured in figure 1. Pretty darn nice if you ask me. The resistance swings quite close to 50 ohms thanks to the “turns ratio” of the autotransformer.
The reactance hovers near zero thanks to the compensating series capacitance.Let’s explore more about that series compensating capacitance. Inductive antenna without a series capacitor Figure 4 – Resulting inductive feed point impedance with no series capacitance.The combination of the transformer with the end-fed dipole results in a positive reactance. This suggests an inductive reactance. The resistance (real) component of the impedance is right where we want it near 50 ohms.
This reveals we only need to compensate for the reactive component. A series capacitance, Xs in figure 1, is the easiest approach for this example. Calculating the value for XsKnowing we need a Capacitive Reactance, we can to take the next steps.
Compensating for +237 ohms merely requires an offsetting -237 ohms from the capacitive reactance. We head to the formulas where Xc stands for Xs.We swap Xc and C and make Xc = 237 ohms and f = 146,000,000.
Solving for C results in a capacitor of value 4.59 pF to provide the -237 ohm reactance to compensate for the antenna/transformer inductive reactance. The effect of series capacitance on resistanceLet’s see what happens to the real value resistance of the antenna system as we dial in the correct capacitance. Figure 5 – How the series capacitor affects the feed point resistance.As one expects, the real value of the inductance changes little with the varying series capacitance.
It is most perturbed with the 1 pF value, but settles in as capacitance gets well beyond the “mere open gap” values. More about 4.56 pF in a moment. The effect of series capacitance on reactance Figure 6 – How the series capacitor affects the feed point reactance.The final reactance presented to the source varies wildly as capacitance increases from 1 pF to our goal. 5 pF overshoots a bit as we expect. Simulation optimizations reveal 4.56 pF brought the net reactance to zero ohms.
This is very close to our predicted value pretty much a bulls eye. There are some parasitic capacitances in play as well, but this result offers good agreement of theory and simulation. Resulting antenna matchThe results speak for themselves. Figure 7 – VSWR of end-fed half-wave dipole antenna. Figure 8 – Return loss of end-fed half-wave dipole antenna. Resulting antenna current Figure 9 – The resulting current distribution of the end-fed half-wave dipole antenna.Nice boring dipole. fed at its end.
with no significant counterpoise system or other extraneous conductors. or “other half” of the antenna to push against.Hallelujah.For those that might be interested, the peak value of current in the middle of the dipole confirms the 100 watts form the source winds up on the element. This assumes the mid point impedance is about 70 ohms. Thus the energy from the source finds its way to the dipole for radiating. Resulting gainThe 0.967 AGT (-0.15 dB) from the NEC4 simulation indicates enough deviation to account for the overly ambitious 2.25 dBi value of the gain shown in figure 10.
Figure 10 – EFHWAntenna Gain in the E-planeThe compensated gain comes to about 2.1 dBi, close to a perfect dipole’s 2.15 dBi gain. Further tweaking of the model can likely improve this, but that’s beyond the larger point of this article. Thanks.I am not familiar with the modeling software and table entries but I understand the structure.The coil wire has a resistance as does the wire making the 1 m section. If I read correctly you've used a 1.25 mm diameter wire for both.I can not see any resistance values in the table.A 1.25 mm copper wire has a resistance at 147 MHz of 0.8 ohms per meter. Aluminum will be 1 ohm per meter.What value did you use in your model?How does the model look (Q and efficiency) when you use a 0.8 ohm per meter value for the wire.-Bob. Yes, absolutely.
4nec2 Vs Eznec
The 'end-fed' moniker does seem to imply a single terminal source, but all power sources are certainly two terminal devices. It's a game of semantics isn't it?
In my mind 'end-fed' refers to the radiator feed, but I could be wrong. The larger question is if point #2 requires 'extra' treatment of ground, lengthly counterpoise or other ideas to get radiation from the dipole radiator. This simulation suggests no as does my experiment with a 10 MHz dipole hereThe problem, of course, is we can never really get a power source infinitely small so even its body will be a bit of electrical 'mass' (or counterpoise if you like) to push against, but the data seems to be suggesting it doesn't have to be electrically large. Put another way, there's nothing about the EFHW that is fighting our ability to energize it so long as we handle the impedance transformation and that's the larger point here. 'IMO, that path attached to Terminal #2 of the source is not correctly thought of, or described as a counterpoise — rather it is one side of a (very) off-center-fed dipole.' I thought this as well especially given the existence of dipoles fed somewhere between mid and end: offset fed.
My simulations and the measurement of the case with extra 0.05 wave wire shown hereseem to suggest the extra wire, while certainly pulling a bit of current, isn't part of the grander sinusoidal current distribution of the primary dipole element. Thus the resonant frequency of the overall system changes little. It's as if the feed point is a demarcation line between independent antennas, each managing their own destiny whereby they draw current if they present a matching HiZ to the feed.I shared your opinion originally, but the evidence just isn't supporting it.