Tuesday, March 31, 2020

HASviolet: Antenna Math

full wave loop antenna math


The math behind antenna design can be a complex and somewhat divisive topic.  Our goal with the HASviolet antenna was to create something that would be a great educational tool to easily illustrate certain antenna design characteristics.

This article will explore things like wavelength calculations, impedance and passive elements to name just a few concepts to get you excited about antenna math!

The Speed of YOU !

Everybody will learn at a different pace and many antenna theory books seems to get overly complicated to the general hobbyist or someone studying for an amateur radio license.

The first thing to understand is the relationship between frequencies and wavelengths.  This general concept is a cornerstone of the HASviolet antenna.

Light waves travel at 299,792,458 meters per second in a vacuum, like outer space.   Here on planet Earth,  our atmosphere slows both light and radio waves just a little to 299,704,644.54 meters per second.  This 87,813.46 difference in speed reduction is referred to as the byproduct of the refractive index of 1.000293.

To adjust these speeds to United States standard measurements, this means a radio wave would travel at 670,480,189,13 miles per hour here on Earth!


full wave loop antenna math
For many reasons, metric is a better standard of measurement because radio waves are often referred to by the length of a full wavelength in meters and not feet.

In the case of 911.250 MHz, which is the HASviolet project design frequency, the wavelength would be 32.88 centimeters. 

A simple equation is 300/F, with F being the frequency in Megahertz.   The value of 300 is a nice round number that is "close enough" to the reduced decimal value of the speed of light.  So, if we use 300 divided by 911.250 MHz the result would be 32.92 centimeters.

As you can see, its easy to get lost in the math and these values will change when making a real antenna because radio waves travel in free atmosphere much quicker than they do within copper wire.

Every metal has its own resistive properties which makes them appear to travel around 306/F.   Silver, copper and brass are some of the lowest cost metals that are the best conductors or heat or electricity.

If you are still following the math,  the way to calculate the actual length of a piece of phosphorous bronze rod 1.2 mm in diameter would work out to about 335.8 millimeters.

Now that we have that out of the way, lets go have some fun!


Full wave loop matching

The interesting thing about a full wave loop is that the feed line connection point impedance will change depending on where that is connected.

Many articles talk about using a full wave loop as a great antenna on much lower frequencies, such as the 3.5 MHz "80m" amateur radio band, but that is hard to experiment with unless you have a really big back yard and tall trees!

We can easily experiment with a 900 MHz full wave loop antenna because they are small.

full wave loop antenna math 900 Mhz K2GOG



















If we connected a feed line at the corner, the impedance would be roughly 80 to 150 ohms, but trying to figure out how to make an easy to build antenna becomes harder.

Instead, HVDN chose to "squash" the full wave loop to resemble a rectangle but this increased the impedance almost up to 300 Ohms if we decided to connect the feed line on one of its longer sides.

HVDN HASviolet 900 MHz K2GOG



















We used a 1/4 wavelength section of 75 Ohm coaxial cable to help us match the higher impedance antenna "driven" element to our transmitter. This allows our HASviolet LoRa radio to have a more efficient way of transferring RF energy to or from the antenna.

Reflector Business

To further change the antenna impedance, we also used a passive reflector directly behind the driven element. This simple antenna element not only gives us the directivity we need to project the main antenna signal forward, but it also has an effect on the antenna impedance too!

A reflector or "parasitic" element is not electrically connected at all to the driven element or the feed-line.  Moving it further backwards or forwards will change the way the antenna works.  We have decided to not share the distance we are using to promote experimentation with our design.

Our upcoming HASviolet V2 antenna uses a really easy way to move the reflector up or down and we think its pretty special.  Also, our V2 antenna also allows the user to build it for either 900 MHz or 1.2 GHz so we expect that many people will find this as a useful antenna for different applications for amateur radio or some other applications that share the same spectrum.

More Technical Details

Please have a look at our detailed technical manual on the hvdn.org/violet landing page or even on our Git Hub page for more information.


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