Intro - What is RF?

Wireless transfer of data is a staple feature of your Moteino, and often the most misunderstood. In this guide we will try to give you a basic understanding of the variables that come into play for setting up a successful communication path between Moteinos. While these principles are focused towards the sub-Gigahertz band where Moteinos operate, they mostly apply to radio transmission/reception in general.

Moteino supports several types of transceivers:

What is RF?

Radio transmission & electromagnetic propagation

The videos below gives a short and overview of how radio waves get propagated through the medium (atmosphere) and how upper frequency bands quickly lose penetration due to physical constraints.

This also means sub-Gigahertz radio waves are a much better choice than 2.4Ghz/Wifi when you want to maximize range and penetration through dense mediums.

An explanation is also given for ionospheric reflection using the stratosphere to reflect the radio waves – this only works up to 30-40Mhz and does not apply to the 433-915mhz bands, but helps understand how very long range communication works.

Class License and the ISM band

When you ordered your Moteino you had to make the choice which radio frequency the board will work on. This brings us to a great entry point for this guide. The selection of which frequency depends of where you are in the world and which license you use for transmitting with the radio.

“Hang on.. I need a license?”


Yes, but you may already be licensed.

The good news is, governments in most countries have allocated several areas in the radio spectrum that are free to use as long as your transmitting device falls within certain conditions.

The correct jargon for such an arrangement is a ‘Class License’.

Take for example Bluetooth or Wi-Fi. You don’t have to sit for an exam or apply for a license when you buy a Bluetooth headset or a wireless network router or access point. The reason is that these wireless radios adhere strictly to the conditions and restrictions of the appropriate Class License and can therefore be bought and used by everyone even without any prior knowledge of radio theory, antennas or what frequency to operate on.

Class License conditions differ slightly from country to country but generally the following aspects are specifically defined:

  • frequency range

  • maximum output power

  • modulation type

  • width of the signal

  • how long it can stay on one frequency

  • what you can use it for

  • contents of what is being transmitted

The Class Licenses that are of particular interest for using a Moteino are the Class Licenses for the ISM bands. ISM stands for Industrial, Scientific and Medical. In the ISM bands you may encounter lots of industrial radio-frequency noise from heaters, machinery, medical imaging devices and all sorts of other bursts of energy that are either too wide-banded or simply do not fit into any other category.

It is in these ISM frequency ranges that low-power transmitters may be operated. Examples of devices other than the Moteino that share these ISM bands are: garage-door openers, Wi-Fi, Bluetooth, cordless phones, mice and keyboards, small radio controlled planes, cars and boats, RFID tags on clothing, telemetry in domestic electricity meters, etc.

Although the ISM band is Licensed and you are granted the permission to transmit in it, you have no additional rights whatsoever. If you happen to fly your expensive remote-controlled drone over a factory and the factory’s rf noise interferes with your drone’s transceiver (transmitter and receiver) and the drone is damaged you have no legal leg to stand on to recover any damages. In other words, the frequency you use is not protected simply because you were there first.

In most cases however, you will find that the ISM bands are relatively quiet simply because there are not that many Industrial, Scientific and Medical radio transmissions going on in domestic areas and the low-power-like Class License transmissions from garage door openers, remote controlled planes, Moteinos, etc.. are all very limited in how much power they may output.

Now you can understand that if you were hoping to use your Moteino in a big production factory you may have very limited success in achieving a reliable radio link.

Regional considerations

Depending on where you are in the world, this map shows the various Class Licence frequencies that are relevant to choosing your Moteino:

There are many more frequencies that fall within the ISM Band definition but they are not relevant to Moteinos with FSK/LoRa transceivers (e.g. 27MHz, 2.4GHz, 5Ghz).

We will discuss some of the other aspects of the ISM bands a bit later, but based on the information so far you should be able to pick the appropriate Moteino radio module based on where you will use it.

Frequency, Channels and Bands

So what is the difference between a Frequency, a Channel and a Band?

Frequency

To quote a formal definition:

“frequency is the number of occurrences of a repeating event per unit time”.

In the realm of electronics we often refer to these ‘repeating events’ as oscillations. The unit of oscillations per second is called the ‘Hertz’. Kilo-Hertz (or kHz) means a thousand oscillations per second. Mega-Hertz (or MHz) means a million oscillations per second.

Frequencies can be any positive (even fractional) number.

  • The highest frequency humans can hear is around 20,000 Hz (20 kHz)
  • Commercial AM broadcast stations have frequencies like 972, 1233, 1512 kHz
  • Commercial FM broadcast stations have frequencies like 88.1, 96.8, 102.1 MHz
  • Moteinos can transmit on 433, 868 and 915 MHz
  • Bluetooth and Wi-Fi have frequencies of 2.412, 2.442, 2.472 (all in GHz)
  • Visible, red light has a frequency of around 450 THz (that’s TeraHertz)
Radio, like sound or visible light or x-rays, is part of the electro-magnetic spectrum, read more about it here

In reality it is very difficult to transmit on exactly one frequency. There are several reasons for this. Firstly, the hardware itself will be subject to small variations due to the manufacturing process. Secondly, external factors can be a big influence, especially the environmental temperature of the components involved in the oscillator circuit. Lastly, the modulation method (i.e. how we encode the information in the transmission) changes how much ‘around’ the frequency the signals will appear.

Spectrum analyzer plot of transmitting on a ‘single’ frequency

Channels

The concept of channels is made clearer with examples like CB (citizen band) Radios and Wireless Networks. By agreement through international regulatory bodies, fixed frequencies are used to make it as easy as possible for a user of these radios to get access to the various frequencies. In the case of early CB radios these frequencies are achieved by selecting different crystal oscillators with a simple turning knob.

Spectrum analyzer plot of transmitting on a ‘single’ frequency

For a typical HF CB Radio there are about 40 channels between 27.950 MHz and 27.4050 MHz in approximately 25 kHz steps.

In Wi-Fi (wireless networks) there is also the concept of channels. In most cases however, the Wi-Fi device you use (e.g. mobile phone, home router or wireless access point) will automatically select the best (i.e. quietest) channel to work on when it powers up.

802.11 x 2.4GHz Wi-Fi channels

The half-circles you see in the above image indicate that there will be some overlap between adjacent channels. Although this is as per the Wi-Fi specification, it may be of interest to move to a channel ‘further away’ from another nearby Wi-Fi network if you experience any interference from it.

Bands

The concept of Bands is usually understood as a range of frequencies with a certain upper and lower limit. These limits can differ slightly from country to country but some are internationally agreed upon.

Sometimes a band means a general frequency range:

Bandupper/lower limit
HF3MHz – 30MHz
VHF30MHz – 300MHz
UHF300MHz – 3GHz
SHF3GHz – 30GHz

Sometimes the band designates a certain use:

Bandupper/lower limitUsage
AM Broadcast535 – 1700 kHzCommercial Radio Stations
40 metersaround 7MHzAmateur Radio
HF CBaround 27MHzCitizen Band, walkie talkies
2 metersaround 145MHzAmateur Radio
70 cmaround 433MhzAmateur Radio, and ISM
UHF CBaround 477MHzCitizen Band, walkie talkies

There are actually quite lot of bands that are allocated to all sorts of uses. To give you an idea, here is a map of the Canadian radio spectrum and band allocation form 3 kHz (top left) all the way up to 300 GHz (bottom right).

Every little block is an allocated band with specific rules and regulations to adhere to. As you now may appreciate, it is not all that straightforward to just start transmitting somewhere.

Transmitters

To wirelessly send signals from one place to another we use a device called a transmitter. Some transmissions contain some form of intelligence (e.g. Wi-Fi, Broadcast Radio, Walkie-Talkie, GPS) whereas other transmissions are already useful without any additional information (e.g. microwave oven, MRI scanner).

What is RF transmission ?

The term ‘RF’ (Radio Frequency) applies to all these forms of transmissions. RF is any signal, somewhere between 3kHz (most people can easily hear that as a high pitched tone) and 300GHz. RF can be artificially generated (man-made) but RF is also constantly generated by the world around us (lightning, radiation of the sun, cosmic background radiation, etc..).

The frequency (or band) where the transmission happens determines to a large extent how the signal behaves. In general, lower frequencies have a higher level of penetration than higher frequencies. It should be obvious that given the same frequency, more powerful transmissions will reach further than transmissions with less power.

That said, when using radios in the ISM band, most users don’t have much choice in frequency nor power levels. To stay legal, use a Moteino with a radio module operating frequency that matches the ISM band plan in the region where it will be used. The maximum RF power output for these radios is around 100mW (milliWatt) and that is usually also the maximum in the ISM band for these devices.

Power consumption

The radio module on the Moteino is both a receiver and a transmitter (a.k.a. ‘transceiver’). With commands issued from code running in the Moteino’s microcontroller the radio can be set in transmit, receive or sleep mode.

The radio module can only be in one of these modes at one time. It cannot both sleep and receive, nor can it both receive and transmit.

During sleep mode the radio power consumption is minimal (about 0.1 uA @3.3V). Put the radio in sleep mode when you want to save the battery and you don’t need to receive or transmit anything.

During receive mode many of the radio’s circuitry must be turned on and therefore the power consumption is a lot higher than sleep mode (around 15mA @3.3V).

In transmit mode the power consumption is the highest (up to 130mA @3.3V, for RFM69HW/HCW, 45mA for RFM69W/CW). To note that transmission is only on for short bursts while the packet is modulated into the medium, usually a few milliseconds.

Transmission power

Many transmitting devices are not very efficient when it comes to generating RF. The circuitry on the radio module needs to do quite a bit of housekeeping to make sure the transmissions stay on the same frequency, that amplifiers are not exceeding certain levels and that the signal is as clean as possible when it comes out of the final power amplifiers of the radio module chip.

Even the final power amplifiers are not very efficient, simply because they have to work on a relatively high frequency. In some cases you may only get 30% efficiency. Saying that 130mA @3.3V power consumption will generate (according to P = E x I) 429mW of RF power is simply not realistic.

Unless we have precision measuring equipment (e.g. Spectrum Analyzer) we will not be able to tell the exact output power of the radio module and we can only refer to the manufacturer’s datasheet with regards to power levels.

Below is an excerpt of the datasheet for the HopeRF RFM69 radio module:

Without going through all these items, take note of the second last line that indicates the ‘Programmable Pout’ (RF Power Out):

“-18 to +20 dBm in 1dB steps”.

Due to the way the RFM69 modules are implemented in hardware, they make different use of the built in PAs (power amplifiers) on the SX1231h transceiver chip. Hence the RFM69 modules come in two main variants:

  • the RFM69W/CW can output from -18 dBm to +13 dBm
  • the RFM69HW/HCW can output from -2 dBm to +20 dBm

For more details and discussion see this forum thread and this excellent blog article.

 

Decibels

The main things to take away from this topic are that decibels are by far the easiest way to compare power output levels and gain and that calculating the power output coming out of the antenna can be as simple as adding all the gains and subtracting all the attenuation together.

Just the term dB is short for decibel (tenth of a Bell). It is a relative way of comparing the ratio between two values.

Decibel is not power nor loudness nor frequency nor voltage or anything; it is just a comparison between two values with some quantity.

The Bel (named after Alexander Graham Bell) is expressed in base-10 logarithms. Feel free to do a google search for how to use dB and what Logarithms are all about but please come back here when finished.

If we read that a signal is 3dB more powerful we need to instinctively ask ourselves: “more powerful than what?”

This is where the lower-case letter ‘m’ (in dBm) comes into play. The ‘m’ in dBm in the datasheet stands for ‘deciBels in comparison to one milliwatt’.

When we get to the chapter on antennas we’ll use decibels again, but there we use the dBi (ratio in relation to an ‘isotropic radiator’) and dBd (for a dipole).

This means that 0dBm is equal to 1mW (not zero milliWatts!). Yes, 1 mW may not sound like a lot but it is enormous when compared with the very low power levels that your mobile phone antenna picks up. Power levels less than 1mW can be expressed in a negative number, e.g. -10dBm, just as easy as power levels greater than 1mW can be expressed with a positive number, like +20dBm (it is okay to leave out the ‘+’ sign).

Here is a great video that explains decibels and illustrates the concept on a spectrum analyzer:

 

Some Formulas & Math Examples

The formula for calculating the power levels from mW to dBm is as follows:

dBm = 10 x ( log10 (mW) )
(the Log here is the Base-10 Log, not the Natural Log!)

Example 1

5 mW is how many dBm?
PdBm = 10 x Log(5) = 6.98dBm

Example 2:

0.5 mW is how many dBm?
10 x Log(0.5) = -3dBm

To calculate the power level from dBm to mW:

PmW = 10 ^(PdBm / 10)
(^ is the “to the power of“operator)

Example 1:

20dBm is how many milliWatts?
10 to the power of (20/10) = 100mW

Example 2:

13dBm is how many milliWatts?
10 ^ (13/10) = 19.95mW

For easy reference, here is a basic lookup table with the most common values:

After this little excursion into decibels, we come back to the topic of output power and see that the maximum output power of the various Moteino radio modules is:

  • RFM69HW and RFM69HCW: 20dBm (100mW)
  • RFM69W and RFM69CW: 13dBm (20mW)

This output power is only meaningful to us if we can use it to generate a wireless RF signal so we can bridge some distance. In more concrete terms, the device that can turn (most of) this output power into a radio signal is an antenna.

The signal that comes out of the transmitter is an alternating current (AC) at certain frequency.

Antennas

The antenna is the device that transforms the high-frequency signals generated by the transmitter into electromagnetic waves that leave the antenna and travel through the air.

The antenna is also the device that transforms received incoming electromagnetic waves back into Alternating Current electrical energy. For most antennas it holds true that if it can receive well it can also transmit well.

Antennas will pick up incoming radio waves on a broad range of frequencies. However, depending on the specific shape and size of the antenna it can be made very sensitive for a certain frequency. When this happens we say that the antenna is resonant.

Resonance

The resonant length of an antenna for a given frequency is related to the frequency it needs to be resonant for.

To grasp this concept a little better we take a quick dive into Frequency Wavelengths.

The speed of radio waves traveling through air is about as fast as the speed of light. If an oscillator changes polarity of a signal 1 million times per second, the resulting wave form looks something like this:

sine wave at 1MHz on an oscilloscope

The vertical dotted lines are 400 nanoseconds apart, which means that one sine wave (from top to top) takes about 1000ns (or 1 microsecond) to complete.

If we calculate the distance that light travels in 1us we get a length of about 300 meters.

The formula to calculate the wavelength from the frequency is as follows:

Wavelength (in meters)= Speed of light (in 1000’s km/sec) / Frequency (in MHz)
 = 300 / 1
 = 300 meters

For an antenna to work well we commonly use an antenna length of a half-wavelength of the frequency we are interested in. This means that in our 1MHz example, the antenna would be 150 meters long!

Now, let’s crank up the frequency a bit and see what happens at 100MHz (this is the frequency where many commercial FM radio stations are broadcasting).

Wavelength (in meters)= 300 / Frequency (in MHz)
 = 300 / 100
 = 3 meters

As you can see, when the frequency goes up, the wavelength gets shorter.

Quarter Wave Vertical

A common and practical antenna is the quarter-wave (¼ λ) vertical, sometimes called a monopole. It simply uses one leg of the dipole in an upright, vertical position and the other leg of the dipole is replaced with a flat plane or perpendicular radials. Moteinos with transceivers include a monopole wire antenna that you can solder to the “ANT” pinhole for an out-of-box cheap and quite effective antenna.

Examples of quarter-wave verticals, for 1GHz and 2.4GHz respectively:

¼ λ vertical with 4 radials¼ λ vertical with a ground plane
(notice the feedline with SMA connector)

Since the most recognizable part of the original dipole in these antennas is the vertical element sticking up, this antenna is often referred to as a monopole antenna. The term monopole is misleading as this type of antenna needs two elements for proper operation. Even though the ground plane or radials may not look like a ‘pole’, they are essential for making the antenna work.

Another variation of the quarter-wave vertical is the Helical antenna, shown below:

‘Rubber Ducky’ antenna
on a handheld transceiver
Helical on a small radio

The straight vertical element has been coiled up, mainly to make it conveniently short as this is for a handheld radio. The body of the radio acts as the other half of what essentially still is a dipole antenna. By its very nature, the coiling of the radiating element like this creates an inductor and requires a complete re-evaluation of the antenna to ensure optimal performance.

With the PCB (printed circuit board) acting as the ground plane for a quarter-wave vertical antenna, it now becomes clear how the Moteino circuit board acts as the ground plane for the supplied antenna wire:

¼ wave vertical wire antenna on a Moteino
(GarageMote kit)
And here on a MotionMote kit

To further improve the antenna system you could either extend the ground plane or add ground radials (connect to the nearest GND tracks). However, even in this configuration the Moteino antenna system works surprisingly well.

Another way to add an antenna to the Moteino is to make use of a small PCB edge-mounted SMA connector. This allows you to easily interchange antennas without having to de-solder anything. Here is a moteino with PCB edge SMA connector and a small helical antenna:

Moteino also accepts u.FL connectors which are useful to route the signal from inside the enclosure to an external mounted antenna.

 

Half-Wavelength dipole

Another common half-wavelength antenna is the dipole (i.e. two poles) antenna. Here are two examples for 144MHZ and 10MHz respectively:

vertical dipolehorizontal dipole

The dipole antenna is fed in the middle of the two radiating elements. In the middle, where the elements meet, there is a small gap so that the elements don’t touch. For completeness we sometimes refer to these antennas as Center-Fed Dipole.

A simpler, schematic version of the dipole antenna could be drawn as follows:

Where the lower-case letter L is the length representing a half-wavelength of the resonant frequency, and each leg being one-quarter of the wavelength. The two vertical lines are not to scale and indicate the feed line (aka transmission line).

Often, the greek letter λ (pronounced as ‘Lambda’) is used for wavelength. Therefore, when we speak of a half-wavelength dipole antenna we commonly write this as a ½ λ dipole antenna.

Earlier we showed how to calculate the wavelength (in free space; more on that later) of a frequency. Let’s use this to calculate the radiating element lengths of a ½ λ dipole antenna.

Below are the full and half-wavelengths for the common ISM bands:

FrequencyFull Wavelength½ Wavelength
433MHz0.69m34.6cm
868MHz0.34m17.3cm
915MHz0.32m

16.4cm

So is this all the info we need to make a dipole antenna?  Almost. The next section will take velocity factor into consideration.


There is now a wideband PCB Dipole available for 868-915mhz:

Velocity Factor

The conductive material of the radiating elements and the surrounding (insulating) materials around it immediately affects how well the RF propagates through the antenna. These materials actually cause the rf to slow down through the conductor. In free space we use the speed of light as the measure of how fast radio waves are travelling, but in a conductor such as a copper wire, the rf travels at much slower speeds.

The term we use to indicate how much a conductor slows down the propagation of rf is Velocity Factor, often written as VF.

If the radiating elements are made from bare copper copper wire, the velocity factor is around 0.95 (95% the speed of light). We need to take this into account when we cut the wires for our dipole:

Frequency½ λ in free space½ λ in bare copper wire
433MHz34.6cm34.6 x 0.95 = 32.9cm
868MHz17.3cm17.3 x 0.95 = 16.4cm
915MHz16.4cm16.4 x 0.95 = 15.6cm

 

As you can see the differences are not huge, but you would end up with a less than optimal dipole if you didn’t take into account the velocity factor.

Velocity factor also applies to any insulating material that goes over the conductor.

single-insulated solid core copper wire

 

The insulation material will further cause the VF to drop and result in radiating element lengths that need to be made even shorter for resonance on the frequency of interest. The VF for most common insulating materials is between 0.95 – 0.98 (PVC, Polyethylene, Teflon) so be sure to take that into account as well.

Frequency½ λ in free space½ λ in insulated copper wire
433MHz34.6cm34.6 x 0.95 x 0.95 = 31.3cm
868MHz17.3cm17.3 x 0.95 x 0.95 = 15.6cm
915MHz16.4cm16.4 x 0.95 x 0.95 = 14.8cm

 

Note that these figures are an approximation as the Velocity Factor will vary from material to material.

Radiation Patterns

Antennas generally don’t radiate their RF energy in all directions equally. The type and orientation of the antenna determines how well it will radiate in a certain direction.

The radiation pattern shows us the direction where the antenna will be most effective.

The radiation pattern of an antenna is often shown as plots as-seen-from-the side (vertical plane) and as-seen-from-above (horizontal plane) . Here are the plots for a Quarter Wave vertical:

Radiation pattern in the Vertical plane
(as seen from the side)
Radiation pattern in the Horizontal plane
(as seen from the side)

Another way to see the radiation pattern is by modelling the antenna in a 3D view. With some imagination, the radiation pattern for a ¼ λ looks a bit like a doughnut:

Quarter-Wave vertical ratiation pattern in 3DDoughnut

The pink doughnut screenshot above is taken from antenna modelling software called NEC.

We can learn from these radiation pattern plots that for a given height above the horizon this antenna radiates equally well in all wind directions (North – East – South West).

Furthermore, there is almost no radiated power going straight up from the antenna as the Vertical plane plot (the side-view) shows a dip of almost zero power going straight up.

We may also conclude that the maximum power is radiated at an angle of about 30 degrees above the horizon (at the 60 degree point in the plot, where the blue line is furthest away from the middle).

Another aspect to notice is the very little amount of power that is emitted towards the horizon at low angles (i.e. at 90 degrees as shown in the plots). For example, imagine two radios, fitted both with a quarter-wave vertical and separated maybe 2km away but one station is 200m higher than the other. The lower station will be able to ‘see’ the higher station, but the higher station’s antenna does not favour a radiation pattern that extends downwards.

This is where the dipole can make a difference.

Practical Considerations

These principles were adapted from this forum thread, thanks to john k2ox who contributed his antenna/RF knowledge.

1.   Antenna performance is usually referenced to that of a dipole antenna.

  • A dipole antenna is quite often constructed of wire ½ a wavelength long. (one half wavelength of the frequency of operation).  For instance my tuned dipole is trimmed to 5.8 inches for use at 915 MHz.  The antenna is fed at the center, it is cut into two with one side connected to ground and the other to the radio’s ant pin.
  • The dipole antenna has maximum radiation broadside to the wire and nearly zero off the ends.

2. If your antenna design radiates the same power in all directions as a dipole it is said to have zero gain referenced to a dipole antenna. Its gain is 0dbdipole.

3.   Antennas are reciprocal. Their transmit gain is equal to their receive gain.  If the antenna transmits best in one direction it also hears best from that direction.

4.   You cannot get more power out of an antenna than you put into it!

  • You ‘can’ take power radiated in one direction and focus it into another.
  • Say you modify a dipole antenna in some way so that all the power radiated from the back side is redirected to the front.  The two powers get added together in the front which doubles the radiation in the forward direction.  This antenna would be specified as having 3db of gain over a dipole (+3dbdipole).  Although it can’t hear or transmit to anything behind it!
  • This reminds me of the saying “you can’t get something for nothing”.  Kind of like the gambler who tells you about his “gains”, but never mentions his “losses”.
  • Antenna gain is with respect to a reference antenna not to its input power!

5.   So what determines the size antenna? Well now things get complicated.  I’ve spent years devising techniques to explain antenna theory without referring to Maxwell’s equations.  Hopefully, this will get you started.

  • For maximum radiation an antenna must be ‘resonant’.  By the way if you’re new to RF/MW forget about most things you already know about AC and DC circuits.  For instance, when you take a look at a DC circuit, an open or short circuit is quite obvious. A direct metal connection between two conductors is a short at DC but, at RF it can and will result in an open circuit at some frequency.
  • You’ve experienced resonance in musical instruments.  You pluck the string and it radiates sound at its resonant frequency.
  • Dipole antennas are resonated by varying their length.  When they are multiples of ½ wavelength they are resonant.
  • Since the ends of a dipole antenna aren’t connected to anything the current at the very ends are zero. Now picture the amplitude of a sine wave. It starts at zero, goes to a positive maximum at 90 degrees, returns to zero at 180 degrees, then a negative max at 270 and once again to zero amplitude at 360 degrees.  Notice that every 180 degrees or ½ wave the amplitude returns to zero.  When the frequency of an RF signal and the length a conductor are such that the current smoothly goes to zero at its ends it is resonant.
  • Radio waves travel at the speed of light!  That’s because they are Electro-Magnetic waves. Guess what?  So is light, just at a much higher frequency.
  • EM waves travel at 300,000,000 meters/second or 186,000 miles/sec.  These numbers are pretty hard to visualize so I use a more useful number for radio.  If you calculate how many feet/sec that is, you’ll realize it’s a nice round number.  A billion or 1 x 10e9 feet/sec.  When dealing with RF, seconds are way too long.  Let’s use a nanosecond (nS), one billionth of a second.  A radio wave therefore travels about 1 foot per nS!  So if anyone asks “How long is a Nano Second?” tell them: “one foot”. :)
  • My radio operates at 915 MHz, pretty close to 1 GHz.  The period of one cycle or 360 degrees at 1 GHz is 1 divided by 1GHz and that’s 1nS.  At 1 GHZ, one full wavelength is one foot long.

6.   The smallest resonant antenna (1/2 wavelength) is 6 inches at 1000 MHz! Now you have a method of calculating antenna lengths without formulas, calculators, etc.  At 500 MHz, 12 inches (2x).  For the FM radio band (100MHz), 60(10x) inches. All referenced to a Moteino antenna! The lower the frequency the longer the antenna. Real antennas are a little shorter because radio waves are slower in air than in a vacuum.

7.   Why is Moteino’s wire antenna only 3 inches long? It was discovered in the early days of radio that ¼ wave antennas (hundreds of feet tall for the low freq’s used at that time) mounted vertically on the ground acted like full size ½ wave antennas.  Since the earth is so much larger than the missing quarter wavelength it acts like an image of the real quarter wave vertical.  If a conducting object on the ground side of the antenna is a ¼ wavelength or longer in some dimension the antenna will be an effective radiator.  The asymmetry will result in a nonsymmetrical radiation pattern though.  For the 3 inch ¼ wave Moteino antenna to be most efficient it needs a rf conductive mass at least 3 inches long.  The ideal ground plane is a disk with a radius of 3 inches with the 3 inch wire sticking out of its center.  The disk being connected to the Moteino ground terminal and the monopole the ‘ant’ terminal.

8.     What happens if I have a little coin cell mounted in as small of a package as possible? Well, it will certainly be smaller dimensionally than the 3 inches needed for the ground plane.  There are two concerns, it will be an inefficient radiator and something we haven’t discussed yet, it will have an impedance mismatch.

  • Here I will use an analogy:
    Suppose you have a large container you can’t lift.  If it is setting in your driveway you can push against it and it will move in the direction it’s being pushed.  You are delivering power to the load.  Now suppose the container is located on a frozen pond.  When you push, your feet slip and the box doesn’t move.  You can’t deliver any power to the load.  The same goes for your radio.  It needs something to push against.
  • Mismatch reduces the power delivered to the antenna.  The maximum power transfer theorem states, to get the maximum power transferred from a source to the load the source impedance must ‘match’ the load impedance. Feeding a ½ wave dipole in the center yields impedance in the range of 50 to 75 ohms.  A ¼ wave antenna with a good ground plane is ½ that, about 23 ohms.  Moteino’s source impedance is specified as 50 ohms.

9.   Antenna users always wish their antennas were smaller. AM radio stations use ¼ wavelength verticals that are two hundred feet tall.  These are very expensive antennas.  The installation costs, real estate, maintenance, power for aircraft warning lights and on and on.  Moteino users also don’t like dealing with antennas dangling from their projects.  Small antennas do have their down sides.  If they didn’t, AM broadcast stations would be extremely happy to eliminate the expense of those gigantic ¼ wave verticals.

  • Small antennas have lower radiation resistance. The input impedance of an antenna at resonance is the sum of the radiation resistance and the antenna loss resistance.  For antennas very small compared to ½ wavelength the antenna/radiation resistance ratio gets very large and its efficiency goes into the dumpster.
  • Small antennas have narrow bandwidth.  Small changes in frequency yield large changes in impedance.
  • The thinner an antenna is, the narrower the freq range it will operate over, compared with a fatter antenna.
  • Nearby structure has a larger effect on impedance.  Moving your hand in an area of a couple feet from a short antenna can easily change the impedance over a four to one range.
  • Reduced size antennas are often directional.  They work best in one direction.
  • Additional components are required to match the impedance of shortened antennas.  These components add additional loss.
  • Antenna designers are always trying to make a small antenna work as well as a dipole.

10.   The smaller the antenna the more you have to compromise. That doesn’t have to be a bad thing though.

  • In cell phones small antennas are good.  They fit in a small package.  They’re directional. That keeps the radiation away from your head.
  • For Moteino’s, antennas can be downsized to fit in small packages too.  The loss of antenna’s efficiency may have no effect if the distance between radios is short.
  • For greater range orient the antenna to take advantage of directional gain.
  • Interference can be mitigated by positioning a directional antenna so that the interferer is in a null.
  • Directional antennas can put the signal where you want it and they hear best from that direction.

11. Antennas radiate Electro Magnetic waves. The orientation of the electric wave describes its polarization. A dipole antenna positioned with its elements parallel to the ground has horizontal polarization. One pointing up and down is vertically polarized.  The largest signal is received when the received signal has the same polarization as the antenna.  If the polarization of the received signal is opposite of the antenna polarization then no signal will be received!  In this case there may be a lot of signal but it has the wrong orientation to fit through the ‘mail slot’.

  • High frequency signals bounce off things, they are reflected. When this happens they change their polarization.  In your house a transmit signal will reflect off your dishwasher, the leaves on you plants, the walls and on and on.  All of these reflected signals have different polarizations and many of them find their way to your receiver.  That’s why you are able to orient one dipole vertical and another horizontal and it may work just fine.  If you try this in space (satellites) or line of sight in a large open area you will have a very degraded receive signal.

12.   Small printed circuit antennas. Electrically steerable RADAR systems use very small antennas arranged in arrays on a flat surface. These small antennas are built on ceramic substrates and other low loss materials.  Early cellphones had dipole antennas poking from the tops of their cases. Antenna engineers have adapted the RADAR designs for use in modern cellphones.  These are often referred to as patch antennas.  A 915 MHz patch antenna should easily fit on a 2 by 2 inch piece of printed circuit board.