# Helix antennas

New for January 2018! This page was written and contributed by Hadrien from France, so try to read it in a French accent.  Better yet, fire up the Debussy video below as background music, composed around 1890 when he was not yet 30 years old, and think about your many accomplishments (or lack of) during your youth... Learn how to pronounce his name correctly here.

Claude Debussy, "Arabesque"

## Generalities

Helix antennas should not to be confused with spiral antennas.  Planar spiral antennas radiate in both directions. This is not practical for EM warfare: we want to send EM waves to the enemy, not back at ourselves! 3D spiral antennas can radiate in one direction and are broadband, but their gain is low, since only a small part of the antenna is active for a given frequency.

A helix antenna is an antenna consisting of a wire wound in the form of an helix on top of a finite ground plane. The key parameters of helix antennas are :

• r: radius of the helix
• C: circumference
• alpha : angle
• N: number of turs
• S: distance beteen turns
• h: total height
• r_reflector: radius of the reflector
• Left-handed or right-handed

Some parameters are not independent, and are linked by the relationships:

C= 2∙π∙r, S=C ∙tan⁡α, h=N∙S.

Helical antennas have two main modes: the normal mode, when dimensions are small compared to wavelength, and axial mode, when dimensions are similar to the wavelength. Beside these two desired modes, parasitic modes can occur.

## The simulation

The best way to understand helix antennas is to take an existing helix antenna, and simulate it in a very wide bandwidth. This antenna is designed for the 2.4 GHz ISM band, but we’ll see what happens on other frequencies.

Geometrical parameters are r = 20 mm, h = 600 mm, N = 21 turns, and wire_radius = 1.5 mm. Simulation is done using CST Microwave Studio TLM solver, fmax 6 GHz, 10 cells/wavelength, PML (perfectly matched layer) boundary conditions at 10 mm distance, 40 dB energy decrease.

The TLM (transmission line matrix) solver was chosen because not only does it handle wires well, but it will also allow us to simulate deviations from the theoretical structure, for example dielectric supports, in future versions of this page.

## Normal mode helix

 @10 MHz @200 MHz

The normal mode happens when the helix dimensions are small compared to the wavelength: h << lambda and C << lambda. Such antennas behave like straight dipoles, but with an higher effective length, so they are easier to match. They are typically used to make antennas for lower frequencies.

The image below summarizes directivity patterns in this range. From 10 MHz to 100 MHz, the directivity is almost identical to a short dipole, while directivity increases with frequency. Note that this plot doesn’t include radiation and mismatch losses, which are notoriously high in short dipoles. The graph had to be renormalized because the radiation efficiency was so low that it introduced numerical errors!

At 200 MHz (purple, largest trace), the diagram starts to deviate from a pure dipole radiation diagram. This is the sign of the beginning of transition modes.

Normal mode patterns

Rubber ducky antennas operate in normal mode. No, we did not make up that name! Walkie-talkies often use helix antennas in normal mode.

## Distorted modes

In the transition from pure normal mode to pure axial modes, interesting things can happen. At 300 MHz, the antenna as a diabolo shape, with a null on the radial axis. At 1300 MHz, the shape is directive, with an axial peak, but the sidelobes are too strong for practical use.

 300 MHz pattern 1300 MHz pattern

The following picture summarizes radiation patterns in this frequency range. The squiggly line indicates the direction the helix is pointing (it is not some crazy pattern!)

Distorted mode patterns

## Inverse modes

From 1500 MHz to 1700 MHz, the antenna radiates in both directions!

Inverse mode patterns

In this case, this effect shows a dependency to reflector size, as shown by the following pictures.  Which we will post soon!

@ 1500 MHz
r_reflector = 50 mm
@ 1500 MHz
r_reflector = 70 mm
@ 1500 MHz
r_reflector = 100 mm

@ 1600 MHz
r_reflector = 50 mm
@ 1600 MHz
r_reflector = 70 mm
@ 1600 MHz
r_reflector = 100 mm

@ 1700 MHz
r_reflector = 50 mm
@ 1700 MHz
r_reflector = 70 mm
@ 1700 MHz
r_reflector = 100 mm

A closer view on the 1600 MHz / 50 mm case:

In receiving applications, not only do you receive less signal because you have less gain in the main lobe, but you also receive more noise from the back lobe. In SATCOM applications, if your back lobe points towards the ground, with a noise temperature much higher than the sky, you get lots of noise. In transmitting applications, you lose power. In EM warfare applications, not only do you lose power, but you will attack your own systems. Think about it: how would it be practical if it was a gun instead of an antenna?

This effect should be considered as a really dangerous one! Never, ever, use a helix antenna outside of its band without double-checking the actual radiation diagram.

## Axial mode helix

In this mode, the antenna radiates along its main axis. The polarization is circular.

 1800 MHz 1900 MHz

Below is a summary of axial mode across frequencies. Clean radiation diagrams, nothing more to say! This is what you want for directed energy applications such as the UAV Scrambler.

Axial mode patterns

The plot of the directivity in function of the frequency shows that the directivity first increases with frequency and thereafter suddenly decreases, before the antenna abruptly stops working. The directivity decrease at higher frequencies is a clear sign something bad is happening.

Directivity versus frequency in axial mode

Note the ratio between the min and max is roughly 1.7. This is not a coincidence. It’s almost a fundamental law.

### Higher order modes

From ~3100 MHz and up to 6000 MHz, the patterns change from ugly to uglier. We have a complete set of plots every 100 MHz, ask us if you want them.   At 3100 MHz, the sideload is already higher than the main lobe.

3100 MHz. Side lobe is higher than main lobe

5000 MHz. Null on axis.

In higher order modes, the antenna radiates, but not really where you want! Notice that the input impedance is not very far of the value expected for such antennas, so this effect can be surprising if the antenna is tested only on network analyzer.

Impedance versus frequency

### Axial mode design equations

The antenna works well when:

This leads to a fmax/fmin ratio of 1.8, pretty close to the experiment. In this mode, the input impedance is approximately real and approximated by :

Combined with previous equation :

Which is, again, very close to what seen in simulation.

Since the impedance has some dispersion in the operating band and is not purely real, the impedance can be simply approximated as 140 Ω in a first step of the design. You have much more serious problems like mechanical construction.

## Impedance matching a helix antenna

The first and foremost step when dealing with a problem is asking this simple question: “what happens if I do absolutely nothing?”  Let’s calculate the mismatch loss (ML) in a 50 ohm system:

Mismatch loss in 50 ohms

Note that mismatch loss might not tell the full story.  In transmit, if the power amplifer sees a poor match, load-pull effects can make you wish you only had mismatch loss... but you could get around this problem with a ferrite isolator.

In technical terminology, the do-nothing solution sucks, but could be tolerable in some cases. Second question is “what is the simplest solution to solve my probem?" Couldn’t we just match to 140 Ohms?

Mismatch loss in 140 ohms

If you match to 140 Ohms, your mismatch losses are lower than 0.4 dB on the full band. This is perfectly acceptable, so we’ll stick to it. So, let’s write this rule of thumb:

For most practical purposes, an axial mode helix antenna has a 140Ω input impedance. If you need higher precision, don’t forget the imaginary part, and listen to you EM simulator.

Let’s match a helix antenna. First, recall the unmatched S11:

The first try to a simple quarter-wave match to 140 Ω impedance at center frequency (2.,4 GHz, 90°, Zl=84):

Not so bad, but can be slightly improved. After the optimization:

Matching line parameters are f0 = 2.4 GHz, l = 0.2 λ, Zl = 89 Ω. The line is slightly shorter and with an higher impedance, which is typical for capacitive loads.
And with two lines:

Almost perfect. Going further would be milking mouse. Parameters are l1 = 0.27, Zl1 = 78 Ω, l2 = 0.14 , Zl2 = 151 Ω. Here we see a potential problem : 151 Ω is a big impedance, we might have some trouble.

Next step is to implement this in a real circuit, not ideal transmission lines. A way to do this would be to translate the previous electrical values in physical values, but we are lazy. We just run an optimizer. The only precaution was to set the initial length of the lines to approx 90°, so the optimizer converges quickly. The results are shown here:

Note the similarity between the two curves. It’s not a coincidence.

We chose to make this matching circuit on FR4. “Are you crazy ?” No! First, FR4 is not as bad as we usually think, especially at low frequency. Second, it has highly desirable qualities: it’s highly common, easy form manufacturing, and mechanically strong. Substrate parameters are er=4.3, tg_delta=0.013, h=1.6 mm. Optimizer results are: l31 = 18.6 mm, w31 = 1.32 mm, l32 = 10.7 mm, w32 = 0.16 mm. Here we see a potential problem, directly caused by the need of an high impedance: the last line is pretty thin. It won’t handle the power of the new power amplifier you received for Xmas.

The following picture shows the actual power entering the antenna for 1 W available power available at the input. This is the total efficiency of the matching network, including power reflected and power lost in the matching network. Translated in dB, it is -0,4 dB. What did you say about FR4 ?

Efficiency of matched antenna

[TO BE CONTINUED]

## References

http://www.antenna-theory.com/antennas/travelling/helix.php