Fundamentals

Bob Harper

Issue 16, October 2018

Radio is more than just ‘ac’, or radiation of Electromagnetic Energy. Radio is a communications system that conveys intelligence far beyond the range of any human being, or wire-bound technology. Radio communicates human intelligence beyond this Solar System, and we in turn receive radio waves from beyond this Galaxy.

In issue 14 we looked at transmission lines, open wire and coaxial cables, characteristic impedance and velocity factor. The transmission line was described as an “untuned circuit” which would carry RF energy to infinity if the transmission line only had pure inductance and capacitance. We looked at how the characteristic impedance can be calculated, if you ever need to, but understanding the relationship between transmission line dimensions may help you understand antennae, without doing the calculations.

This month we will look at the signal path in greater detail with an aim to estimate how far a signal can carry or how much signal is required to achieve a link. Secondly, we take a look at how antennae are created on a PCB, greatly reducing the manufacturing costs, size, and weight of a complete transceiver.

# Signal Paths and Decibels

First, let me review a diagram we used two issues ago, explaining that the radio circuit consists of the Antennae and Cables, plus the signal path which in our simplified form, should be more correctly called the Free Space Signal Path. The circuit must also have a transmitter to create and modulate the signal and a receiver to demodulate the signal, i.e. get the data or voice back.

# Free Space Signal Path Losses

While there are losses as the signal passes through the atmosphere, the main issue with the signal path through the atmosphere is a result of the RF energy spreading out as the distance from the transmitting antenna increases. Remember the RF wave is the surface of a sphere ever expanding at the speed of light from it’s origin. Area = 4πr2, where r is the distance from the transmitting antenna.

This is compounded as the wavelength decreases, or the scale of wavelength to distance from the origin (radius) increases, meaning that higher frequencies experience greater losses at the same distance.

Antennae have a parameter known as “Antennae Aperture” that is a circular area proportional to the wavelength, squared. To cut a long story short, the formula for the free space path loss becomes:

FSPL = (4πd/λ)2, or FSPL = (4πdf/c)2

where:

• d = distance between the two antennae
• λ= wavelength
• f = frequency
• c = Speed of Light (˜300m/s)

Note: These formulae remain true as long as all dimensions are in the same units, including speed of light.

Path losses are easier to calculate in decibels, so for frequency (f) in MHz and distance (d) in km, the formula becomes:

FSPL(dB) = 20log(d) + 20log(f) + 32.44

• All logs are base 10
• 32.44 tidies up all of the constants including Speed of Light, and MHz and km conversions.

For example, a WiFi link (2.45GHz) between two antennae 1km apart would have a loss of:

FSPL(dB) = 20log(1km) + 20log(2450MHz) + 32.44 = 100.2dB.

# Gain vs. Loss

This is a good time to confirm the difference between gain and loss, in dB numbers. Taking the figure above, rounded to 100; as a loss of 100dB we should write it as a gain of -100dB. The minus (-) simply indicates the output is less than the input.

As a ratio gain value, 100dB = 10(100/20) = 100,000, but -100dB = 10(-100/20)= 0.00001.

For science students, with a little assistance from your science teacher, and anybody else wanting an example, calculate the path losses between a transmitter (using 2400MHz) on Earth, and a spacecraft about to land on Mars, at the greatest separation between Earth and Mars. How does NASA communicate over that distance?

# Complications

The FSPL figure is based on “free space” meaning there are no obstructions, mountains, foliage, cities of glass and steel, crowds of people cheering, etc. to add to the losses. (Not even any atmosphere but thankfully that’s not usually a major loss).

Therefore the FSPL is a base line estimating the minimum losses or a clear path.

We have mentioned that transmission lines have losses, which is to be expected, but to put the losses in perspective, let us consider a popular coaxial cable type, of a standard of construction known as ‘RG-58’ as you would find it in most Electronics Catalogues.

It is important to know that there is good RG-58, and really bad RG-58. That is because a cable that fits the connectors and has an impedance of almost 50 Ohms can be sold as RG-58, even if it doesn’t fit all of the specifications.

My best advice is to avoid using the cheapest cable unless you intend doing the cheapest job! All cables have tables for losses on a data sheet just as you expect from all electronic components.

Briefly, a sample of RG-58 loss figures include, 0.35dB/m @ 450MHz, 1.06dB/m @ 2.4GHz, 1.69dB/m @ 5.8GHz.

These figures tell you two important facts. The loss is proportional to the length of the cable, and increases as a function of the frequency of use. It doesn’t tell you that losses result from resistance of the conductors, type and dimension of the dielectric insulation, and radiation losses due to ‘thin’ braiding.

It also doesn’t tell you that the losses change over time as the cable ages, dielectric chemistry changes, conductors corrode, water gets into the cable, mechanical damage to the cable, etc. New coax is the best it can ever be! The image below shows new versus old coax braid.

# Connectors

Yes connectors do have losses, which are minimal as long as they are kept dry and don’t become corroded. In fact the losses are typically 0.01dB per connector, and even better for better connectors. So we’re not ignoring them but simply saying they are typically less than rounding off other values. There will be at least eight plugs and sockets in the typical path, so all up still less than 1dB.

# Antenna Gain

Antenna gain was explained last issue, though we have only looked at low gain antennae up to now. For a two way link, typically the antennae would be of the same type, meaning that their gains would be identical. In the GHz region, dish antennae are popular, though anything from a “Rubber Ducky” (or worse) can be used, with the transmission and reception efficiency very low. (A 'Rubber Ducky' is a type of antenna made from a spring inside a rubber hose often seen in Police TV shows. Though compact and robust, it is quite innefficient.)

The efficiency of an antenna is a combination of Gain, and Aperture, sometimes called the window. As the wavelength gets smaller with increasing frequency, so does the Antenna Aperture, unless the antenna uses multiple antenna elements, called phased elements, or reflectors, such as a dish antenna has. A dish increases both gain and aperture.

# Isotropic Source

Remember, antenna gain is a measure of how much stronger the signal is at the measured point than what would be expected from an Isotropic Source, so Antenna Gain is often given as a gain over the isotropic equivalent source, and in dB is labelled as ‘dBi’. A dipole gain is about 1.7dBi at the strongest signal direction.

# Transmitters

Similarly, transmitters can be specified by the power they transmit, or the gain the transmitter has over a standard value, usually compared to a standard such as 1 Watt or 1 milliwatt. For example, a 1 Watt transmitter transmits 1000mW, or has a gain of 0dBW, meaning it has zero gain over 1 Watt or 30dBm, meaning it has a gain of 30dB over 1mW, or 1000 times 1mW.

Conversion between dBm and dBW is deceptively easy, dBm = dBW + 30.

Also easy, now that you have digested dBm and dBW, receiver specifications usually state the minimum signal they can detect, either as microVolts, or dBm. This measurement is the Receiver Sensitivity – the lowest value radio signal that the receiver can be expected to receive.

A reasonable receiver, depending on your expectations might have a 1µV minimum signal, which on 50Ω cable is the same as -107dBm, so any receiver that can receive -100dBm or less is pretty good. (e.g. -110dBm is better than -100dBm.)

Based on the figures we have gathered thus far, we can begin to calculate our Link Budget, the calculations to set up a 1km link between two WiFi, eh, let’s just say two 2.4GHz transceivers. Note that the principle is the same for any radio link, including your up-coming hobby moon-landing next year! Well somebody has to make the first private moon-landing.

Engineers must recognise one vital fact – “There are things we can control and things over which we have no control.”

With that in mind, the path losses (FSPL) will be 100.2dB as calculated above. The connector losses we consider to be less than 1dB in total. The transmission lines can be kept short, but how short and what type of coax? Assuming the antennae are outside and with a little elevation, say 3m of RG-58 for each end, or 6m total with 1.69dB losses/m = 10.14dB. (NB: I wouldn’t really use RG-58 for 2.4GHz, but for an example it will do nicely).

That’s 100.2 + 1 + 10.14 = 111.3dB, as total losses between transmitter and receiver, but not including antenna gain.

If the receiver sensitivity is -107dBm, and the transmitter is permitted up to 200mW or 23dBm, the affordable loss would be 23dBm -(-107dBm) = 130dB. (Note that the sum of two dBm or dBW values becomes a dB value).

Whew! We have ˜20dB more than we need even without antenna gain. BUT! What if we don’t actually have as much power or sensitivity as we expected. What if there is more loss than expected in the cable and connectors? What if the antennas are actually -8dB each instead of having a gain? I know, unlikely, but let’s look at what to do if we don’t have enough gain to overcome the losses.

Let’s do the calcs again with a little more skepticism about our system performance. Try it with 100mW transmitter, -100dBm receiver, path losses of 120dB due to trees and buildings in the way, and we get 20dBm -(-100dBm) = 120dB. Now the losses are 120dB + 1 + 10.14 = 131.14dB. Total path gain (without the antenna gain) = 120dB – 131.14dB = -11.14dB.

To correct this the two antennae need to add at least 11.14dB gain to the system, and as they might be the same design antennae, they would require 5.57dB each. Remember that is 5.57dBi; i.e. gain over an isotropic source. A dipole is 1.7dBi, so a small beam antenna, even just four elements should manage 6 to perhaps 7dBi. In fact, there are many simple antennae that would manage 5.7dBi.

The important matter at this moment in time, was to show you a method of using dB figures in calculating what you need for your radio circuit. Knowing how to do so allows LoRa technology to be made much more reliable. Drone antennae can be chosen for the range requirements. Country folk may even get some WiFi between out buildings!

Amateur Radio Operators not only listened in to the 1969 Moon Mission, but have calculated the distance to the moon using radio waves bounced off the moon from a home transmitter. Radio Amateurs have communicated between continents by bouncing Morse Coded Signals off the moon in a method named EME, ‘Earth Moon Earth’ communications.

# PCB Antennae

You will probably not have seen mobile phones with external antennae, though they had them not too long ago. However, makers out there may be familiar with WiFi/Bluetooth/2.4GHz dongles that plug into Arduino boards for communications.

They come in two types; those with an antenna socket, and those without. The later have an onboard PCB antenna that may not even be recognisable as an antenna.

Any single plane antenna can probably be adapted to work on a printed circuit board (PCB). There is a simplicity of manufacture resulting in lower cost per unit, smaller size and lower weight. However, efficiency may suffer as the PCB materials absorb some of the energy, and the designs may force the antenna to be squeezed into a smaller space, often too close to other electronics, and always encapsulated within the case of the device.

The PCB material causes a transmission line effect which we have discussed before, known as velocity factor. RF, and light, travel at different speeds in different media. The speed is slower than the speed of light, and getting slower as the dielectric material becomes more dense (in simple terms). The velocity factor changes the scale of the antenna allowing the antenna to be smaller than the same design in open air.

The easiest PCB antennae to recognise are the dipole which we have spent most of out time on, and the monopole, being half a dipole with a ground reflector to behave as the other half of the dipole. The ‘ground’ plane for the monopole is the ground of the PCB.

When the dipole and monopole are used, they are typically used straight, as they should be in open air, but to squeeze them even smaller the ‘wire’ track may be turned back and forth, or ‘Meandered’ as shown here.

While a meandered antenna looks fancy, and takes up less space, it is always less efficient than a straight conductor.

Some meandered antennae are given as less that 60% efficient, so they may be good for smaller spaces but they should be avoided if you are looking for better performance. In fact, where antennae are concerned, bigger really is usually better.

# Other Options

One option for a larger antenna is a loop antenna usually somewhere between a half wave and a wavelength, with a half wave to be avoided if possible, and a full wave being a good choice if possible. All loops other than an exact full wavelength require matching via capacitors or inductors, but a full wave loop on 2.4GHz would be a square with 31mm sides, (less for velocity factor), or if a circle, having a circumference equal to one wavelength ˜116mm at 2450MHz or about 38mm diameter. They are used but not when space is the main factor.

# Inverted-F or Lazy-F

An antenna popular on fast aircraft was a blade antenna, due to it’s low drag and almost omnidirectional pattern. The antenna is a quarter wave laid over parallel to the ground, aircraft skin, and grounded at the leading end. The impedance at the grounded end therefore is zero Ohms, and the (RF) impedance at the other end is very high, maybe thousands of Ohms. The feed point is connected along the quarter wave at the appropriate position for a good match, e.g. 50Ω. Along came a need for PCB antennae and the Lazy-F or Inverted-F became a good choice.

Note the grounded end, the free end, and the feed point presumably at the 50 Ohms impedance point. As a quarter wave antenna, the Lazy-F is relatively efficient yet small, with a good radiation pattern, and they are very popular amongst board designers.

There are meandered versions which attempt to be smaller, but at some loss in efficiency; although advertising claims won’t mention it.

# Bow Tie

When a wider bandwidth is required, the options are still good, but a common solution is called the Bow Tie Dipole, because it has a shape like a Bow Tie. The two halves are triangular in shape with one corner of each as the feed point.

Whereas a dipole is designed to be a certain length, the Bow Tie is designed to be a certain angle, which will effect the impedance. The angle at the feed points and the area of each side of the bow tie creates a lot of capacitance to the free space, and between the two halves of the antenna.

The end result is a much broader tolerance to frequency, with the lower frequency limit resulting from the limited length between the ends of the Bow Tie, and the upper frequency resulting from the construction at the feed points.

The antenna calculator design software found here, https://www.changpuak.ch/electronics/Microstrip_Patch_Antenna_Calculator.php is meant for an open air antenna, but on a PCB, the lower frequency limit will simply be even lower. The impedance will change due to the PCB material which may require a different angle.

In electronics, radio, and especially antenna work, you never get anything for free. Wider bandwidth comes with lower efficiency and higher noise levels, but that’s how we get bandwidth when we need it.

# Patch Antenna

One last PCB antenna for now, mainly to continue on from the Bow Tie in replacing a length of wire, or PCB track with a shape. This antenna is known as a Patch Antenna, another antenna from an aviation background where a patch of aluminium is attached, usually completely insulated, to a surface on the aircraft, thus the name ‘Patch’. A feed point is chosen by mathematical design as a point of suitable impedance and radiation pattern.

We are not here to teach you how to design this antenna, however you might note that the sum of these four sides adds to the wavelength of the desired frequency, with some adjustment no doubt for the dielectric of the PCB material.

The Patch is connected to the coax inner conductor, and the outer conductor is attached to the adjacent ground plane. On an aircraft that would be the fuselage, but on a PCB, the ground is the ground plane on the opposite side of the PCB. The board here shows this with a Patch Antenna driven by a track.

You might note that there appears to be a second patch on the PCB in the figure, and in some cases, there is an array of patches connected to make a specific radiation pattern, either a narrow beam or a wide beam depending upon the lengths of the feed lines to the various patches.

# PCB Yagi ANTENNA

The Yagi antenna is a collection of dipoles carefully placed, and of graduated lengths designed to enhance the radiation pattern in one direction while reducing the radiation in other directions.

It does this by using the transformer effect. Each element receives the energy from the powered element, called the 'Driven Element' and re-radiates that energy. The element behind the Driven Element is called the 'Reflector' which pretty much describes what it does. The Reflector (RE) is longer than the Driven Element (DE) by about 5%.

One or more elements in front of the DE known as Director Elements (DI) are shorter than the DE by about 5%, and may each be ~5% shorter than the previous although not always designed that way.

The spacing between the elements is about a quarter (0.25) wavelength, but a value of 0.22 wavelength is a common "estimate" figure. In fact, there is a lot of compromise and argument over what works best and there is no "one design" for any particular frequency or band.

The Yagi is one example of what we call a single plane antenna, which makes it ideal as a PCB antenna, as the example presented here shows. The directors are simply isolated strips having no electrical connection to each other or the other elements.

The reflector can be an isolated strip as shown here, or may be the ground plane of the PCB. Either option can be required depending upon the engineer's requirements and application.

The driven element can be a simple dipole fed by two striplines, the term of an RF track on a PCB, or one of many "sneaky tricks" used to simplify PCB production. The PCB Yagi shown uses a 'Half Folded Dipole' fed by a single track, which matches, balances and feeds the RF to the driven element all in one.

The resulting antenna can be used to direct all of the transmitter energy toward the receiver, or used to feed a Dish!

# In Summary

A radio link can be designed using a ‘Link Budget’ to calculate whether sufficient power is transferred to ensure a reliable radio link. The link budget lists all of the gains and losses in the RF circuit. When estimating gains and losses worst cases should be used and some degradation should be catered for.

PCB Antennae are not magic, though there is always some maths involved. They are in most cases simply a Printed Antenna, in the same way that a printed circuit is a normal circuit adapted to a different material.

PCB Antennae can be very simple, reliable, and effective, as long as they are thought out, and not placed deep in amongst the other components. The losses incurred by the dielectric material of the PCB may be offset by requiring no coaxial transmission line, connectors or mechanical mounting.