YRabbit's notes - Radio

Making an antenna for a 4G modem

2020-07-29T12:55:00+10:00

After calculation, I proceed to the manufacture of antenna parts. Special care is needed when bending the antenna wire itself and making the balun.

Bending the wire

I never doubted for a second that I couldn't just take and bend the wire in compliance with all radii and distances, so on my CNC3018 I made a template where the finished antenna wire should go without effort:

Antenna template

Practice has shown that this thing is useful for the final alignment of the antenna, but it does little to help bend it. It made sense to make one separate corner to bend the wire only on it, but now this is no longer relevant to me :)

I'll see how long the copper wire I need:

octave:2> quad_size*8
ans =  224.38

I'll mark this distance in a notepad and put a simple 22AWG into the template:

22AWG in antenna template

The mark must match the drawing in the notebook:

Notepad segment

22AWG next to segment in notebook

Bend the copper wire carefully:

Bending copper wire

Almost finished antenna

I solder the antenna straight away.

Antenna solder

Balun

The RG174 cable will be connected directly to the antenna (the diameter of the first shield is 1.98mm, the diameter of the jacket is 2.79mm). I considered using a bazooka balun, but two considerations made me abandon this idea:

I do not have a tube with a diameter of mm, namely with this ratio of diameters this type of balun becomes effective;
the bazooka balun is connected around the circumference of the coaxial cable screen at a certain distance ( or less if the balun is folded) from the vibrator, I very much doubt that I can do this accurately and evenly around the entire circumference of such a small wire. I have seen and read about options when the balun is connected directly to the vibrator, but I think that with such a connection the balun turns into an additional vibrator, and I really do not want to repeat the calculation of the antenna taking into account this vibrator surface.

So I decided to implement a less efficient, but easier to manufacture balun from a piece of wire.

In addition to careful manipulation of the outer sheath of the coaxial cable, it is advisable not to overheat the shield: the internal dielectric may melt and the characteristics of the cable may deteriorate.

Remove only minimum isolation from the end

Isolation removed

Finished balun

Reflector

Now I can move on to other structural details. This is what the antenna looks like in FreeCAD:

Video

The two vibrators are positioned at an angle of to each other and at to the horizon.

The antenna was conceived as hanged from the ceiling on a wire loop - two triangular combs at the top of the reflector allow you to choose the antenna angle in the horizontal plane. The modem cradle has a cutout for the USB cable and there are also two hooks to gently secure the top of the modem.

Few details should be placed on the face of the reflector to minimize disturbance to the reflective surface, which, by the way, is an ordinary foil for baking all sorts of delicious things.

The most important part of the reflector is the vibrator posts. They perform an important function of maintaining the calculated shape of the vibrators and the distance between the vibrators and the reflective surface of the reflector.

Now I will say about the material of the posts. While all other parts of the antenna can be made from almost anything, the vibrator posts must be radio transparent at the antenna frequency. My frequency is close to the radiation inside the microwave, so heating a piece of plastic for a couple of minutes showed its suitability (there is no charring and other unpleasant manifestations of interaction with radiation). It is believed that at the points of zero potential, you can use any material for the posts, up to metal, sometimes the posts are even soldered to the reflector. I don't do this for the following reasons:

I doubt that I will ideally make vibrators, so the point of zero potential will not be such;
I calculated the antenna based on the air insulation between the vibrators and the reflector. If you use metal posts, then you need to calculate and simulate with these additional vibrators.

I don't have a 3D printer, so making posts is a fun task. I had to make an auxiliary clamp to accurately cut the grooves on the ends of the posts:smile: Here's the first clamp, unsuccessful:

Bad version of the auxiliary clamp

Second clamp with reinforced rigidity:

Second clamp

The reflector is much larger than my CNC3018, but this can be solved:

Large reflector sheet on CNC

Soldering cables and baluns to vibrators, the last step before exciting antenna testing:

Soldering cables to vibrators

Testing

Rear view will not receive design awards :)

Build and function test

Huawei modems have a convenient mechanism for assessing signal quality on the page at http://192.168.8.1/html/antennapointing.html

So just a modem without an antenna:

Signal parameters without antenna

Modem with antenna:

Signal parameters with antenna connected

Excellent! The receiving conditions changed and went into a completely green area. LTE Signal Parameters Reference.

Antenna for 4G Modem

2020-06-29T13:02:00+10:00

Current reading: SINR/RSRP: 20 dB / -95 dBm. Do I need an antenna? Not sure. Would it be fun to make an antenna? Certainly! So let's get started:)

Simulation accuracy

First, I want to make sure that openEMS (the modeling system I plan to use) is calculating correctly. Let's take the antenna impedance data from the book 1.

Impedance versus antenna perimeter

I am interested in the graph on the right, namely the fact that with the perimeter of one square equal to , the reactance .

Let's draw only the top square of the antenna, the feed gap is on the left:

Top half of the antenna

The antenna is a square wire with a side of , effective radius, the length of the full side of the square is , the feed gap is equal to . Thus, the perimeter of the antenna is .

After simulation EndCriteria = 1.e-6, OverSampling = 10 I get the resonant frequency :

directivity: Dmax = 3.0867 dBi
Minimum SWR frequency:
 2840000000
Resonant frequency (jX=0):
 2865000000
Impedance at minimum SWR:
 129.502 -  13.569i
Impedance at resonant frequency:
 133.07147 -   0.41565i
Minimum SWR:
 2.6234

From the frequency I find the wavelength: and the theoretical perimeter: .

Hence the discrepancy between theory and simulation: . The source code of the simulation can be downloaded here.

Given the artisanal nature of production, this accuracy suits me:)

Antenna geometry

In theory, an antenna is two squares connected by "vertices", where the connection point is the feed point of the antenna. But I will be dealing with a real copper wire (there is a height and thickness), which bends with a certain radius, as well as with a real soldering iron, so that the geometric model will look like this:

Graphic model of Kharchenko antenna

The dotted lines are auxiliary geometry, the red curve is the center of the wire from which the antenna is made, the radii of all arcs are equal to (here means the center).

At this point, I will need the characteristics of my copper wire. It just so happened that I had a lot of rectangular copper wire at hand, so I will be guided by this type of wire.

My copper wire

The rectangular cross-section of the wire is described by the width and the height , , hence it is clear how the wire will bend --- I can ignore in the geometric model, but will play an important role in describing the feed gap.

Feedpoint model

Here is the radius of the inner surface of the wire, is the radius of the outer surface of the wire. As you know, the angle between the radius of the circle and the tangent to the circle at this point is equal to , all angles in the models are equal to or .

I took the gap between the wires for powering equal to 1mm, from here:

Because of the need to have the feed gap, I slightly moved the "squares" apart, the measure of the "extension" is 2:

All arcs have length . The choice of a name for the variable is not really appropriate, but as it is :) Let's compose a system of equations describing the relationship between the elements of the structure:

The first equation of the system reflects the fact that the perimeter of one "square" should be related to the "quarters" of the wavelength. The second equation introduces the relationship between the lengths of the sides of the "square", it is not as obvious as the first equation, but it is derived quite simply.

I solve the system in Maxima:

(%i1) eq0:2*delta_port + quad_small + quad_big = 2*quad_size;
(%o1)         quad_small + quad_big + 2 delta_port = 2 quad_size
(%i2) eq1:quad_small = quad_big - dR*sqrt(2);
(%o2)                 quad_small = quad_big - sqrt(2) dR
(%i3) solve([eq0, eq1], [quad_small, quad_big]);
                     2 quad_size - 2 delta_port - sqrt(2) dR
(%o3) [[quad_small = ---------------------------------------,
                                        2
                         2 quad_size - 2 delta_port + sqrt(2) dR
              quad_big = ---------------------------------------]]
                                            2

The and unambiguously set the antenna model (as a function of wire parameters, radius of curvature and wavelength), now I can proceed to simulation.

Simulation

After I got my hands on modeling simple dipole antennas and a simple loop antennas, creating a model for Kharchenko's antenna was not too difficult (full text of the model). The mathematical model was described above, I chose the parameters based on common sense and materials available:

, - my wire,
Ohm - coaxial wire resistance,
- I think this is a more or less normal rounding radius,
- must be at least wavelength.

But the size of the side of the "square" I selected by running the simulation and achieving the minimum at my frequency of 2.6 GHz. And after that, I selected the distance from the middle of the wire to the reflector , achieving a resistance of 50Ohm (, ).

To reduce the calculation time while maintaining accuracy, I took advantage of the ability to specify an uneven mesh:

Mesh for antenna calculation

I tried to do so that as many surfaces as possible coincided with the grid lines: these are the wire planes along the axis, the reflector plane and the antenna feed gap.

Here are some more snapshots of the mesh and model:

General view of the model

Antenna close-up

Feed line

1.: ^ Antenna Theory and Design. Warren L. Stutzman, Gary A. Thiele
2.: ^ These appear due to the aspect ratio in a right triangle with angles of : and

The actual simulation results:

Input impedance of Zin_real antenna

Input impedance of Zin_imag antenna

S11

Antenna directivity simulation video

directivity: Dmax = 10.6344 dBi I will count on this result.