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Let’s start by laying out the requirements for the antenna. Obviously, the first and most important is about the frequency it needs to operate. As I intend to use the antenna for LoRa application, it needs to be tuned for the 433MHz. Another important requirement is that it needs to be easy to build and of relatively contained dimensions. Last, but not least, it needs to radiate as uniformly as possible in all directions (omni-directional).

What is an Antenna?

Fundamentally antennae are transducers, which convert electrical signals (voltage and current) into electromagnetic waves (electric and magnetic fields). In its simplest form, an antenna is a piece of wire (metal), driven by an electrical signal (time-varying current). Such signal generates electric and magnetic fields, that radiates electromagnetic (EM) waves from the wire. Generally, any electronic component or wire, when time-varying currents go through it, generates some EM radiation, but what makes it an antenna is the fact its physical conducting structure is designed to facilitate radiating, while all the other components tend to be designed to suppress it (to reduce EM noise).

I will not go further into electromagnetism theory, it will suffice to say that Maxwell’s equations are used to describe the EM phenomenon, and solving them gives us all the information needed about EM fields and waves. Solving Maxwell’s equations is quite a complex task, involving some tricky maths. Fortunately for us, lots of research has been done on electromagnetism and antennae, so we can use the results already published to work out our antenna’s design instead.

Another way of looking at an antenna is to think of it as a resistive-inductive-capacitive (RLC) network: just like any RLC network, depending on the frequency of the electrical signal applied, the impedance of the network will vary, showing more capacitive or inductive behaviour. At a particular frequency, the antenna will show a purely resistive behaviour, and it is said to be “resonant”. Under resonance condition, it is easier to match the impedance of the antenna with the one of the transmission line feeding it, maximising the power radiated. This is why, when designing antennae, typically the physical dimension is chosen so that it is resonant at the frequency of interest.

For example, for a wire antenna like a dipole, the resonance condition is met for wire length of a wavelength, and also at multiples or fractions of it (the wavelength λ in meters can be calculated using the relation λ = c/f where c is the speed of light (299.7925 km/s) and f is the frequency in MHz). The figure below show a typical dipole.

In my case, for an antenna resonating to the 433MHz frequency, if I were to use a half-wave dipole like the one above, the overall length of the antenna would be λ/2, that is 34.6cm. Although not impractical to build, I was aiming to something a little smaller. Also, the impedance of the half-wave antenna at its feeding point is about 73 ohm, which is less than ideal, considering that it will have to be matched with a 50 ohm line. To help, we can leverage a physical effect, which allows the antenna's dimension to be reduced: the ground effect. It can be demonstrated that, creating a ground plane, we can use a quarter-wave monopole antenna, which radiates with the same characteristics of the dipole, thanks to the fact the ground will mirror the monopole, thus making the antenna equivalent to a dipole, as shown below:

Now, the monopole seems a better choice, with a more compact length of λ/4, that is 17.36cm. Also, because of it's structure, not just the length is halved, but also the feeding point impedance, with a theoretical value of about 37 ohm.

While talking about the dipole and the monopole, I have introduced some of the parameters used to characterise an antenna. Together with the ones already mentioned, it is worth recalling also the following (the list is not exhaustive):

• gain and directivity

• impedance

• bandwidth

I am deferring the description of such parameters till I get to the measurement phase of the project, with the exception of the radiation pattern, because it gives us useful information, needed for the design. The radiation pattern is the distribution of the radiated energy into space, represented as a diagram. Below there is an example of radiation patterns for some antenna types.

Monopole Antenna Design & Build

It is time to design the antenna. For the monopole, we need to design the ground plane. One way to achieve that is to use 4 radials, drooped at 90 degrees respect to the radiating element, and spaced 90 degrees from each other, in a "star" configuration. The lengths of the radials is the same as the radiating element: λ/4 (17.36cm). With this configuration, the antenna looks like:

As seen before, the monopole with ground plane made with radials at 90 degrees from the radiating element will present a 37 ohm impedance at the feeding point. I need to find a way to match the 50 ohm of the feeding transmission line, possibly avoiding building a matching RLC network! One observation comes to the rescue: if we imagine the radials drooped all the way down, forming a 180 degree, the monopole will actually become a "proper" dipole, which means its impedance at the feeding point is going to be about 73 ohm. This suggests increasing the drooping angle of the radials respect to the radiating element, the feeding point impedance should increase. This way, the 50 ohm impedance is reached for a drooping angle of about 135 degrees, as shown below.

So, looks like we worked out the structure of the antenna, including the length of the radials and the radiating element. A quick look to check what I have got available around reveals a bunch of panel mount 4 holes SMA connectors and several pieces of 16 AWG solid copper core wiring cable of different lengths:

First, I need to cut 5 pieces  of wire, making them all the same length: 17.36cm. Actually, I'm cutting the 4 radials a little longer (18cm), to give me a bit of extra length that I can bend to form a sort of hook around the SMA connector holes. The radiating element will likely need to be trimmed a bit, as in my calculations, I didn't take into account the difference of velocity of the EM waves in copper respect to the speed of light in vacuum. For the solid copper wire, I'm assuming a velocity factor of 0.95, which will make the new length 17.36 * 0.95 = 16.49cm (although I will not cut it yet, but I will trim it a bit at time, when tuning the antenna as close as possible to 433MHz).

Once all the wire pieces are ready, secure the 4 radials to the holes of the SMA connector, making sure they are positioned correctly and forming an angle as close as possible to the 135 degrees specified for the design. Using the helping hands, and fitting the largest soldering tip I have got for my soldering iron (and cranking up the temperature of the iron to 350C),  the radials are soldered in place. The little hook around the hole helps making both a more mechanically robust and electrically sound connection.

And now, the tricky bit: soldering the radiating wire to the center conductor of the SMA connector.This is achieved with the help of a little flux, Unlike the radials, for the central conductor there is no way to make any sort of mechanical connection to help strengthen the structure, so I have resorted to using some heat-shrinking tubing for the task. Notice, this tubing, although covering only a small fraction of the radiating element, is likely to influence the velocity factor, with the result that the element might end but needing to be a little shorter than the 16.49cm predicted. Since I have no idea on what the velocity factor is for the heat-shrinking tubing, I will leave it till the trimming at the tuning stage.

It is time to show the final result of this effort!

Tuning the Antenna

And now, lets use the full power of the NanoVNA to help tune this antenna! As mentioned in my first blog, my settings are less than idea for measurements, so I expect also the results to be "tainted" by this, but hopefully they will be good enough.

The NanoVNA is a pocket Vector Network Analyzer, with a working frequency range of 50KHz - 900MHz, and a price tag of merely £35! (If you are interested to know more about it, please check the link in the reference section).

Before taking measurements, the NanoVNA needs to be calibrated, using the calibration kit included (Short, Open and 50 Ohm Load). The instrument comes with a touchscreen, from which you can operate and show the measurements. The screen is nice, but rather tiny, so I preferred to install the NanoVNA Saver, a Python frontend for the NanoVNA that can be installed on my laptop and used to control the instrument (the NAnoVNA can be connected using the USB-C cable included).

The calibration procedure is quite straightforward, and only takes few minutes to complete. The idea behind the calibration is to make sure that the error introduced by the connecting cables are corrected by the software. To minimise the errors, all the measurements are taken under the same conditions, especially minding the position of the cables stays the same (thanks shabaz for the advice!). I have calibrated the NanoVNA for the frequency range 410-450MHz. The video shows how easy is to calibrate the NanoVNA, (this is an example, just to show how it is done).

I have repeated several measurements, for the Return Loss (S11) and the Standing Wave Ratio (SWR). Since the start, the results were surprisingly encouraging: the graphs clearly showed the antenna resonating around the 418MHz. Although already pretty good, I wanted to shift the resonance frequency up by trimming the radiating element, taking off about 2mm at time and repeating the measurement. Iterating this procedure, I managed to get the antenna to resonate at 433MHz. Below you can see the last measurement taken, using the NanoVNA Saver, and the setup for the measurement.

As can be noticed from the setup above, although the monopole has the SMA connector, I connected the antenna using a SMA to IPEX adapter cable connected to an IPEX to SMA connector, which in turn is connected to a SMA to SMA cable and finally to the SMA connector of the NanoVNA. The calibration has been performed at the end of the SMA to SMA cable. This might seems odd, but I have done this way because the antenna will be used with the TTGO board, which only has an IPEX connector, so to connect my antenna to the board I have to use the SMA to IPEX adapter cable. Doing the calibration this way, I am measuring the antenna in the conditions that are the closest to the way it will be used (the only difference is that when in operation, the antenna won't use an IPEX to SMA adapter - adapter shown in the photo above).

With this setup, and with a final length of the radiating element of 16.3cm, those are the measurements taken:

The result seems good so far, even the impedance measured is very close to the expected one (although, being the NanoVNA very close to the antenna, and the whole measurement taken is a small room, where there are reflections, I suspect the reading might not be very reliable...).

Now that the build is complete, the next step is to compare my quarter wave antenna to the others I have, measuring all the other antennae in the same conditions. Finally, the proof will be in the pudding, when I will setup the two TTGO LoRa board and will test the transmission of all the antennae and compare the results.

References

Articles:

Bill Schweber - Understanding Antenna Specifications and Operation, Part 1

What is the purpose of a VNA calibration kit

Books

Constantine E. Balanis - Antenna Theory: Analysis And Design (one of the most comprehensive books around)

Joseph Carr, George Hippsley - Practical Antenna Handbook

NanoVNA:

NanoVNA | Very tiny handheld Vector Network Analyzer

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Other articles of this series:

Building a poor man's quarter-wave 433MHz antenna: Introduction

Building a poor man’s quarter-wave 433MHz antenna: Comparing Antennae