What is RF and Microwave Engineering?

RF and microwave engineering is a specialist area of electronics engineering which addresses alternating current (AC) stimuli and responses, intentionally and unintentionally generated, operating at frequencies typically ranging from approximately 20 kHz to 300 GHz [1]. Within this range, RF is generally understood to be up to about 1 GHz and microwave above that. For the sake of brevity, we will assume RF and microwaves to be synonymous. There is no sudden change in electrical properties at 1 GHz but the wavelength (λ) at this frequency is 0.3 m or about one foot. In the early days of what we would consider to be bulky radar equipment, when they were exploring higher frequencies, component sizes and cable lengths were becoming significant fractions of a wavelength around this frequency. It was known that the smaller the wavelength in relationship to the dimensions of a typical target, such as an aircraft, the better would be the quality of the reflection, with fewer distortions due to diffraction and other noise. However, the higher frequency sources required new, expensive and unreliable technologies for that time and presented extra challenges simply in handling the frequencies involved.

RF applies to both circuit currents and voltages and to (propagated) electromagnetic waves. The transition between these is achieved with an antenna. A purpose-built antenna should be designed to either transmit or receive RF energy, or it may be an inherent property of a circuit, desirable or otherwise.

As RF engineering has evolved, we have developed a better understanding of the properties across the various frequency bands. For example, we tend to talk about audio frequencies separately from RF and microwaves separately from high-speed digital. That is just a convenient shorthand method. Perhaps it is wrong. They are all AC just like RF. They all have well understood properties including, for example, propagation. In fact electromagnetic waves have been successfully transmitted using antennas well down into the audio frequency range. Confusion may have arisen because audio frequencies, by definition, are those we are capable of hearing, but only when they are converted into acoustic waves using some type of transducer such as a loudspeaker. There are a couple of challenges using low RF frequencies however: antennas and bandwidth.

An antenna with good directionality (the ability to radiate energy efficiently in one direction) needs to have dimensions of at least several wavelengths. A simple, but popular and electrically small antenna with a radiation pattern close to omni-directional in the H field is the half wave dipole. As its name implies, it has a length of half a free-space wavelength (λ/2). An audio frequency of, for example, 1 kHz, has a wavelength of 300 km, so it would be quite a challenge to build a 150 km half wave dipole for a 1 kHz transmitter or receiver.

Taking this argument further, to a step lower in frequency, 50 Hz or 60 Hz are almost universally used frequencies for the transmission of power over long distances, sometimes across countries and continents. Many people will know one of the reasons why AC was originally chosen over DC for power transmission: the convenience of being able to easily change AC voltages using transformers. Another consequence of using AC is that transmission line properties may be relevant when the transmission line distances become significant electrical lengths. So 50 Hz is a wavelength of 6000 km. That would be a very long power transmission line for a full wavelength but some longer lines might be significant portions of a wavelength and their transmission line properties cannot be ignored.

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Is High Speed Digital Related to RF

Most definitely yes! Why?

'High speed digital' refers to a digital data signaling rate which is expressed in bits per second (bit/s). The adjective 'digital' is used because it describes a technology used for communicating using discrete voltages which may be achieved in many different ways. In most cases signaling rates will be measured in many megabits per second (Mbit/s) or even gigabits per second (Gbit/s). Bits are, by definition, binary digits for which we know that there are 2 possible states, commonly referred to as 0 and 1. Depending on the type of coding used these might represent nominal voltages of say 0 V and 1 V, or it might be a more sophisticated form involving intermediate voltages. The transitions between states are not of course instantaneous in practice as this would require 'infinite' bandwidth. More realistically, to describe the waveform, minimum and maximum values of rise and fall times should be specified. If either is too fast there is a risk that the spectrum of the waveform will exceed the allocated bandwidth. If either is too slow, the bandwidth might be too limited and there may be excessive errors caused by inter-symbol interference (ISI), which would degrade the bit error rate (BER).

As an example, for a 1 Mbit/s signaling or information rate, the bit period will be 1 μs, and the rise and fall times might be in the order of a few tens of nanoseconds. Now we must think about the data itself represented as a voltage against time waveform. The actual data passing through can be any combinations of 1s and 0s unless there is some coding algorithm at work limiting the bit patterns. Depending on the coding used, there might even be some long strings of 1s or 0s or rapidly changing alternate states, a repeating 1010 pattern. The bandwidth necessary will be determined by the highest frequency content of this waveform, when there are the maximum possible number of 01 and 10 transitions per unit time. That is usually the 1010 condition which is also the type of waveform often used for high speed, non-sinusoidal, clocks. However, in this case the clock period would actually be two bit widths, making the square wave clock frequency not 1 MHz but 500 kHz. Three such bits from a string like this are shown in Figure 2-1, in this case with a 50 ns rise and fall time.

Figure 2-2 and Figure 2-3 show the log magnitude spectra of the waveform in Figure 2-1 for rising and falling edges of 400 ns and 40 ns respectively. In each case, the vertical scale is in logarithmic amplitude units of dBμV (dB relative to 1 μV). These were obtained using simulations with the Matlab® 2021B fast Fourier transform (fft) function.

Noting that Figure 2-2 and Figure 2-3 have logarithmic vertical scaling, it is still clear that the bandwidth occupied in each case is equivalent to many times the 'frequency' of the 1010 waveform. So for this relatively slow data rate by today's standards, of 1 Mbit/s, we can clearly see that the spectrum extends to many megahertz. Furthermore, for the 40 ns slope case, the amplitudes of the higher frequency components are greater than for the 400 ns slope case.

Another way of looking at the 101010 waveform with very short rising and falling edges would be as a pulse waveform with a pulse width of 1 μs, a pulse repetition frequency of 2 μs and therefore a duty ratio of 50%. If this was used as a square wave clock waveform, its frequency would be 500 kHz, but that would be the frequency of the square wave and not of the (sinusoidal or cosinusoidal) component frequencies in its spectrum.

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What Are HF, VHF, UHF and Similar Designations?

These are examples of widely adopted shorthand acronyms for frequency bands: high frequency, very high frequency and ultra high frequency. Using these makes it convenient for anybody to talk informally about the frequencies they are referring to without needing to remember the frequency detail. Formal documents would normally specify the frequency detail when is was required. Table 3-1 and Table 3-2 summarise some of the commonly used frequency band designations and their frequency ranges [17] [18].

Table 3-1 IEEE frequency designations

Designation	Meaning	Start	Stop	Unit
VLF	Very Low Frequency	3	30	kHz
LF	Low Frequency	30	300	kHz
MF	Medium Frequency	300	3000	kHz
HF	High Frequency	3	30	MHz
VHF	Very High Frequency	30	300	MHz
UHF	Ultra High Frequency	300	3000	MHz
SHF	Super High Frequency	3	30	GHz

Table 3-2 Radar band frequency designations

Designation	Meaning	Start	Stop	Unit
L	L-Band	1	2	GHz
S	S-Band	2	4	GHz
C	C-Band	4	8	GHz
X	X-Band	8	12	GHz
Ku	Ku-Band	12	18	GHz
K	K-Band	18	27	GHz
Ka	Ka-Band	27	40	GHz

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Why Do You Talk About Smith Charts So Much?

Familiarity and understanding of transmission lines and the Smith Chart are strongly recommended in RF and microwave engineering. An example of a blank impedance (Z) Smith Chart is shown in Figure 4-1. There are also admittance (Y) Smith Charts and mixed impedance and admittance (ZY) Smith Charts.

A good understanding of transmission line theory which is behind the Smith Chart is a fundamental and essential RF and microwave engineering skill. It relates to how waves, which are passing along a transmission line, react and interact when they meet a discontinuity. A discontinuity is an impedance (or admittance) differing from the characteristic impedance of the transmission line itself. When this happens, a reflected wave is set up, moving in the opposite direction to the incident or forward wave. This creates a standing wave, also known as a total or resultant wave, which is made up of contributions from the forward and reflected waves. The instantaneous (spatial) voltage on the standing wave is a function of the position at which it is measured on the transmission line. As a visual graphical alternative to the calculations, these effects can be analysed on the Smith Chart with the help the included scaling.

Components can be designed which rely solely on the relative positioning of deliberate mismatches, either short stubs of precise dimensions (distributed components) or discrete (lumped) reactive components. Distributed components will only be effective for a relatively narrow band of frequencies. Smith Charts can also be used for matching and analysis problems using only lumped components, or a combination of lumped and distributed components.

Some experience with the Smith Chart allows the user to quickly observe the behaviour of an imperfectly matched transmission line just by examining the locus of points across a range of frequencies. The scalar quality of the match, either return loss or voltage standing wave ratio (VSWR), may be determined by how much the locus deviates from the center of the Smith Chart. The center corresponds to a perfect match or, alternatively, a reflection coefficient magnitude of zero, effectively a circle with zero radius or a point.

Smith Charts are mostly used in the unity radius region. That means within the circular region between a radius of zero (perfect match, no reflection) and unity (short or open mismatch with 100% reflection). This corresponds to a region in which the magnitude of the reflection coefficient is between zero and 1, irrespective of phase. This should occur on any component that is passive. If we were measuring something which is active, such as an amplifier, sometimes the magnitude of the reflection coefficient may actually appear to be greater than 1. This is not a true measurement and indicates that an instability or possible oscillation is present, distorting the results. Sometimes it may be possible to stop such instabilities with carefully designed reactive matching, which presents frequency dependent loading. An amplifier which is designed in this way would be known as unconditionally stable if it showed no instabilities across the specified frequency range.

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What Is Skin Depth and Why is it Important?

Analyses of plane waves incident on real conductor boundaries with air using Maxwell's equations tells us that a perfect conductor will not support an electric field [2] [3]. However, a perfect conductor has infinite conductivity. We know that copper for example is a good conductor but far from being a perfect one. For comparison purposes, some conductivities of common metals used as conductors in electronics are shown in Table 5-1.

Table 5-1 Conductivities of Some Common Metals

Metal	Chemical Symbol	Conductivity (σ) (S/m)	Relative Permeability (μr)	Skin Depth (m)			Density (kg/m3)	Metal Market Price Cash 02/12/2020 (USD/tonne)
				50 Hz	100 MHz	1 GHz
Silver	Ag	6.173×107	1	9.059×10-3	6.406×10-6	2.026×10-6	10.49×103	Expensive
Aluminium	Al	3.816×107	1	1.152×10-2	8.147×10-6	2.576×10-6	2.70×103	2051.50
Gold	Au	4.098×107	1	9.335×10-3	6.601×10-6	2.486×10-6	19.30×103	Expensive
Copper	Cu	5.813×107	1	1.112×10-2	7.862×10-6	2.987×10-6	8.96×103	7616.50

The result of the analysis is that the magnitude of an incident electric (E) field or magnetic (H) field, as it penetrates the conductor, will reduce exponentially with depth from its value at the air/metal boundary. The depth at which it reaches 1/e times its value at the surface is known as the skin depth (δ), given by (5-1).

$$\delta =\frac{1}{\sqrt{\sigma \pi f{\mu }_0{\mu }_r}}$$

In (5-1), f is the frequency (Hz), σ is the conductivity of the metal (S/m), μ is the permeability of the metal (H/m). Also, remember that μ = μ₀μ_r, where μ₀ is the absolute permeability, 4π×10^-7 H/m and μ_r is the relative permeability which is unitless. The relative permeability for a non-magnetic metal such as copper is 1.

The full current penetrates further than the skin depth itself and the general rule of thumb is that 5 skin depths will contain very close to 100% of the alternating current [2]. Therefore, for AC conductors, any thickness in excess of about 5 skin depths would be wasted and unnecessary. If the thickness is less than 5 skin depths, we could have either of 2 problems depending on the application. We will look at two situations where we need to consider skin depth: power transmission and screening.

The conductors used in power transmission are nearly always either copper or aluminium. Power frequencies used throughout the World are almost universally either 50 Hz or 60 Hz. If the full penetration depth is less than 5 skin depths there may be a tradeoff between the metal cost itself (and the cost of the maintenance of the overhead structures carrying the cables) compared to wasted energy in the form of heat. To some extent we may be able to tolerate some extra heat loss if there is a significant cost saving otherwise. Overhead transmission lines have the advantage in cooler climates that they allow better heat dissipation and can safely run quite hot, limited only by the maximum safe levels of thermal expansion. With underground transmission lines, heat dissipation may be more limited because of the restricted convection available.

Electrical screening, often referred to as the 'Faraday cage' principle, is another important application in which to consider skin depth. In this case we wish to attenuate the penetrating wave as fully as possible. Therefore we need to choose the metal and its thickness correctly, assuming that otherwise the screen is correctly constructed. From the formula for skin depth in (5-1), it is clear that the skin depth reduces for increasing frequency. Therefore we must base the screening design on the lowest frequency which it is required to attenuate, that with the deepest skin depth. About five skin depths would be the starting point and if the metal is mechanically too thin, its thickness may be increased as necessary which would only improve the screening. (5-1) also shows that one way of reducing the skin depth even further is to use a magnetic metal (one with a higher μ_r) such as mu-metal. This has a relative permeability of 20000 to 50000 compared to 1 for non-magnetic metals. Although this is offset slightly by its conductivity being less than copper or aluminium, it reduces the skin depth to about 1% of its value for a non-magnetic metal.

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What is EMC?

EMC stands for electromagnetic compatibility. That is all about how well all electrical equipment exists together in our environment without causing undue interference to other electrical equipment.

There are two categories of electrical equipment:

1. The electrical equipment we are responsible for.
2. All other electrical equipment.

In summary, our equipment must not cause undue interference to other equipment and we have the right to expect that no other equipment will cause undue interference to our equipment.

We have to address:

• Emissions

All electrical equipment generate emissions at some level but they must be sufficiently small to have minimal affect on other electrical equipment.

• Susceptibility (or Immunity)

Susceptibility and immunity are essentially reciprocals of each other; they are different ways of referring to the same property: how easily our equipment will be affected by emissions from other equipment.

What are the mechanisms which cause interference between electrical equipment?

• Conducted

The interference path is via physical conductor connections between the electrical equipment causing the interference to the 'victim' electrical equipment.

• Radiated

The interference path is by propagation mechanism(s) through the atmosphere or free space from the interfering source equipment to the victim equipment.

Unfortunately, many EMC problems are not simple 'conducted' or 'radiated' issues, they are often combinations of both. For example, a cable connected to the victim equipment may be acting like an antenna and collecting interference radiated from the source equipment. One of the interesting challenges in solving EMC issues is that many of the problems do not have simple solutions, for example, improving screening or filtering.

EMC has become such an important requirement for the military that several government departments of defence across the World have written EMC requirement specifications for their own military equipment. In some cases they have been released under an accessible liberal licence to the public and the requirements have been specified for civilian equipment. Releasing an EMC specification to such a huge and potentially critical audience has exposed it over the years to many suggestions for improvements. Provided the resources are available to consider these in sufficient technical depth and to revise and implement some of them, the result is a widely respected 'industry standard' specification document. One example from the USA Department of Defense (DOD) is known by its original document number, appended by a letter representing it's issue, 'E' in this case or MIL-STD-461E (7). This is full of comprehensive EMC requirements and detailed supporting information, including test equipment diagrams, anechoic chamber configurations, data recording methods and full explanations.

Perhaps the most commonly quoted requirements from MIL-STD-461E relate to radiated emissions, conducted emissions, radiated susceptibility and conducted susceptibility. Each of these is numbered starting with the letters RE, CE, RS or CS respectively. Each of these has a whole family of specifications.

Some examples of the graphical requirements for these are shown in Figure 8-1. and Figure 8-2.

Figure 8-1 shows a graphical limit for conducted emissions used in CE101. The frequency range over a horizontal logarithmic scale is from 10 Hz to 100 kHz. Although scaled linearly, the vertical scale is also logarithmic as it is in a dB current unit, dBμA, that is dB relative to 1 μA. As the emission currents are AC, the units are root mean square (RMS).

Figure 8-2. is an example of a radiated emissions limit graph. In this case the vertical scaling is again logarithmic, dBμV per metre (dBμV/m). Again, the field is AC so the units are RMS.

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What About Fourier and Laplace Transforms?

One of the Matlab® add-on applications, DSP System Toolbox, includes many built-in functions for performing these. For example, the Fourier transform may be performed using the Matlab built in 'fft()' function using the 'fast' algorithm. Some basic Matlab scripts need to be written initially to create an input array representing the real voltage against time waveform which is the argument of the fft() function. The output comprises an array of complex numbers which represent the contents of the frequency 'bins' in amplitude and phase. The frequency spacing of these is a function of the sampling frequency chosen for the input waveform. Most of the challenges of using the Matlab fft() function are in choosing an appropriate sampling frequency and performing the correct normalisation and scaling. The outputs may be plotted in amplitude and phase against complex frequency.

Another use of Laplace transforms has been in the analysis of negative feedback loops with a second order transfer function, such as those often used in phase locked loop circuits [14] [15].

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How is Wireless Related to RF and Microwave?

It is good to see the renaissance of the word 'wireless' in recent years. The name was originally adopted for radio receivers, in those days using valves or vacuum tubes. These were wireless in the sense of 'no wires'. They received and demodulated radio waves 'over the air' so there were no wires to carry the signal from the studio to the home, rather like a telephone line. Most of them still actually required a power cable so, in the strict sense of the word, they were not completely wireless. Truly wireless, or fully portable, radios did exist but they were in substantial boxes which included heavy high tension (HT) and low tension (LT) batteries necessary for the vacuum tubes. In recent years the name 'wireless' has been adopted again for communications not using wires. Although they may not always be completely wireless, if for example you have plugged your smartphone in to a charger, they are readily capable of being truly wireless. Battery technology now is so good that small devices with appreciable processing power can be powered truly wireless for several hours after the battery has been charged. In the days of the vacuum tube portable wireless the HT battery was often about 90 V and horrendously expensive, being constructed of about 60 zinc carbon cells in series. The LT battery, which powered the tube filaments was either another expensive zinc carbon battery or possibly a lead acid accumulator which had to be re-charged periodically.

Recently, we have heard many references to the 'internet of things' (IOT). This is one of the areas where the true potential of wireless devices may be exploited. Smartphones, for example require appreciable processing power even in standby mode and need to be regularly transmitting 'I am here' signals to the local cell tower so the battery drain is significant. Many IOT devices may be attached to sensors in remote areas well away from power and telecommunications infrastructure, and will only need to report data infrequently. Although this still requires a short periodic transmission, the data capacity is small and, for a well designed IOT device, the battery drain will also be very small.

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Why Are Transmission Lines So Important?

They are so important because they are so widespread and need to be understood in detail to be used and exploited correctly. For the time-being we will consider loss free single ended transmission lines to avoid complications.

Let us start with a little background information. By definition, a transmission line is a device (possibly a very long device) to transmit intelligence (information) or energy from one location to another. In transmission line theory we are considering the AC case only: alternating currents conducted along the transmission line. Information cannot be transmitted using DC. That is because the DC would need to be modulated in some way to carry the information. Modulated DC is no longer DC, it is DC with an AC component. We can of course carry energy along a transmission line using DC and that is done in many parts of the world, often to avoid needing to synchronise the power frequencies in different areas. Another way of looking at one of these would be a transmission line with zero frequency and therefore infinite wavelength. That is just DC and the normal DC rules would apply.

A simple source and load circuit schematic, based on the Thevenin equivalent circuit is shown in Figure 9-1

We know that we are expected to consider this as an AC circuit because:

• The Thevenin equivalent circuit symbol includes a frequency (f).
• The source and load are represented by impedances, not resistances.
• The source and load reflection coefficients (ρ_S and ρ_L respectively) are included.

However, we are not expected to consider any transmission line behaviour because there is no spatial information. The implication is that the frequencies considered are such that the shortest wavelength (highest frequency) is much greater than the circuit dimensions. This also is known as a lumped element approach, not quite like DC because we still have reactive components. There still are reactive components whose impedances are functions of frequency and we could calculate the reflection coefficients ρ_S and ρ_L, as shown in (9-1) and (9-2) respectively, provided we define a system impedance Z₀.

$${\rho }_L=\frac{Z_S-Z_0}{Z_S+Z_0}$$

$${\rho }_L=\frac{Z_L-Z_0}{Z_L+Z_0}$$

The next schematic in Figure 9-2 shows a similar circuit but with an explicit transmission line shown symbolically, connecting the source and the load.

Taking this a step further, we can simplify our symbol for the transmission line to a 2-port network like shown in Figure 9-3.

A 2-port network such as this is typical of what we might measure with a vector network analyzer (VNA) to yield a result in the form of S parameters across frequency.

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How Are Optical Fibers Used?

Over the last 30 to 40 years, thanks to the growth of the Internet and the provision of faster data services, such capacity is almost wholly served by optical fiber cables, a major part of the telecommunications infrastructure. However, most countries do also have considerable copper telecommunications cables. Where used, these are mostly in the areas relatively local to small customers' domestic premises. In telecommunications jargon, this is often known as the last mile (or first mile) of the telecommunications path between the server and client. It is a very approximate average of the distance between most customers premises (where the telecommunications services are consumed) and the first (or last) point in the telecommunications infrastructure where the signals enter or leave the (high capacity) optical fiber part of the network.

There are essentially two types of optical fiber transmission mode: single mode (or monomode) and multimode. Single mode allows a much larger bandwidth and has the smallest transmission loss but is much more expensive to manufacture and install as the components are much more expensive. Multimode fiber and components are much cheaper but they have a more limited capacity and range. For most optical fibers, the wavelengths concerned are around 850 nm, 1310 nm and 1500 nm. 850 nm tends to be used for multimode and the others for monomode. The equipment, especially connector technologies, for multimode do not require tolerances as small as those required for monomode. That is because the optical fiber core diameter for monomode is approximately 8 μm and that for multimode is approximately 60 μm.

Optical fibers also have advantages related to electromagnetic compatibility (EMC). The fiber materials are insulators and therefore cannot conduct currents so will not couple in any way to or from sources of radiated or conducted interference. This suggests they are a good choice for when it is required to transmit data through an environment with significant electric or magnetic fields.

One may reasonably assume that optical fibers are designed to carry optical wavelengths. The visible wavelength range is actually from about 400 nm to 700 nm but the shortest wavelength currently used for most optical fibers is 850 nm, which is actually at the short wavelength end of the infrared range. Probably for historical reasons, optical fibers were named as such in the early days when they literally used optical wavelengths and before it was fully discovered what the optimum wavelengths would plan out to be allowing for the limitations of optical amplification, attenuation windows, fiber manufacture and optical components.

Telecommunications service providers (TSPs) have to maintain minimum quality of service (QOS) commitments to their customers. That is because the information capacities necessary in the optical domain, deep within the infrastructure, are extremely high. My service provider claims that the 'broadband cable' to my house meets the Data Over Cable Service Interface Specification (DOCSIS) at something like 30 Mbit/s, by today's standards relatively slow. However adding up my service with those of my street, my neighbourhood and my town quickly gets up to many gigabit/s (Gbit/s).

With such a high information rate comes high revenue earning capacity. The TSPs design their equipment with many types of redundancy built in and at great expense. No customer is going to pay for a disconnected service or one which has a high bit error rate (BER). The less reliable a digital connection is, the more likely the customer will move to a competitor's service.

Most specialists in RF and microwave will be familiar with how optical fibers work by means of guiding electromagnetic waves along cylindrical dielectric (high purity glass) waveguides and the principles of single mode (or monomode) and multimode operation. .

Since telecommunications de-regulation, few TSPs actually manufacture their own equipment except perhaps for a few very specialised and small quantity applications. They place huge manufacturing contracts with telecommunications equipment manufacturers. So these are the places where most RF and microwave engineers will be found.

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CAD and Other Applications

Some are listed below.

• Microsoft Office Professional: Excel, Word, Access, Powerpoint, Outlook
• Matlab (R2019b)
• Matlab Toolboxes:
• Simulink 10.0
• Antenna Toolbox 4.1
• Communications Toolbox 7.2
• DSP System Toolbox 9.9
• Instrument Control Toolbox 4.1
• Control System Toolbox 10.7
• Data Acquisition Toolbox 4.0.1
• Parallel Computing Toolbox 7.1
• Phased Array System Toolbox 4.2
• RF Blockset 7.3
• RF Toolbox 3.7
• Signal Processing Toolbox 8.3
• Simscape 4.7
• Simscape Electrical 7.2
• Simulink Control Design 5.4
• Spreadsheet Link 3.4.2
• Symbolic Math Toolbox 8.4
• Altium Designer 2.2.0
• Cadence Allegro 16.6
• Simetrix 8.20
• Advanced Design System (ADS)
• Microwave Office
• HTML/CSS
• Ansoft Designer 2.2.0
• Visual Studio 2015 Express (C/C++)
• Visual Basic 2010 Express
• Excel Visual Basic Applications
• LT Spice XVII
• MPLAB XIDE 3.65 (Microchip C/C++ embedded firmware)
• TextPad 7.3.0
• MCUXpresso 11.1.1 (ARM Cortex range)

For several applications, viewer only versions can be downloaded free complete with documentation. Documentation is generally very comprehensive and accessible. For example the Matlab® licence with my choice of 'toolboxes' provides access to more than 100000 pages of documentation in searchable PDF form with many references.

Visual Studio 2015 Express was a free download with Visual Basic and C/C++ and just required registering for a Microsoft account, and also includes extensive documentation.

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