E8: Signals and Emissions

This first group covers the raw nature of a waveform: what it is made of, how to honestly measure its power, and how to convert a smooth analog wiggle into the numbers a computer or software defined radio can work with.

What a square wave is really made of

Start with the headline fact. A square wave (a signal that snaps between two levels, like a light switched fully on, fully off, on, off) is not a single frequency at all. It is built from a sine wave at the base frequency plus that sine wave's odd harmonics, the 3rd, 5th, 7th, and so on. ("Odd harmonics" means odd-numbered multiples: 3 times, 5 times, 7 times the base frequency.) The technique that demonstrates this, that breaks any waveform into its component sine waves, is Fourier analysis. If a question asks what shows a square wave is a sine wave plus its odd harmonics, the answer is Fourier analysis, not "vector," "numerical," or "differential" analysis.

Two ways to look at the same signal: time domain and frequency domain

You can describe a signal in two completely different but equally valid pictures.

• The time domain describes the signal as amplitude at different times, that is, how big the wiggle is, moment by moment, as the clock ticks. This is the view an oscilloscope gives you: voltage going up and down across the screen as time scrolls by. ("Amplitude" just means the size or height of the wiggle.)
• The frequency domain (the view a spectrum analyzer gives) shows the same signal as how much energy sits at each frequency, which is exactly the Fourier picture, a bar chart of "how much of each sine wave is in here."

So when the exam asks which choice describes a signal in the time domain, the answer is "amplitude at different times."

Measuring power honestly: true-RMS

How do you put a single number on the "size" of a wiggling AC voltage? The fair, physics-correct answer is the RMS value. RMS stands for root mean square, and the only thing you need to feel about it is this: the RMS value of an AC signal is the steady DC voltage that would deliver the same heating power to a resistor. It is the "effective" value, the honest measure of how much work the signal can do.

Here is the catch. Cheap meters cheat: they measure a simple average and then just assume the signal is a clean sine wave to calculate RMS from it. That assumption falls apart on lumpy, non-sine signals. A true-RMS meter does the real root-mean-square math directly. So the benefit of a true-RMS calculating meter is that RMS is measured correctly for both sinusoidal and non-sinusoidal signals, sine waves and weird-shaped waves alike. That is the answer the exam wants.

Average power versus peak envelope power (PEP)

A voice signal is constantly changing strength, loud syllables, quiet pauses. So we describe it with two different power numbers. Average power is the average over time. Peak envelope power (PEP) is the power at the strongest peaks of the modulation. ("Envelope" means the outline traced by the tips of the waveform; PEP is the power at the very top of that outline.)

For an unprocessed single-sideband (SSB) phone signal (an SSB voice signal with no compression or processing added), the typical ratio of PEP to average power is about 2.5 to 1. In other words, the peaks are roughly two and a half times the average. And what sets that ratio? The characteristics of the speech, how peaky or smooth your particular voice and speaking style are. Different voices give different ratios, which is exactly why it depends on speech characteristics.

Turning analog into digital: the ADC

A microphone or antenna produces a smooth, continuous analog wiggle, but computers and software defined radios think in numbers. The device that converts the wiggle into a stream of numbers is an analog-to-digital converter (ADC). A few facts the exam tests:

• One common conversion method is "successive approximation." The name describes the trick: the converter guesses, checks whether the true voltage is higher or lower, then guesses again with a finer step, closing in on the answer one halving at a time, like the high-low number-guessing game.
• Resolution is how many distinct levels the converter can output, set by its number of bits. An 8-bit converter can encode 256 different input levels (because 2 to the 8th power is 256). More bits means more levels means finer detail.
• Flash (also called direct) conversion compares the input against many reference levels all at once, so it is extremely fast. That very high speed is exactly why flash converters are used in software defined radios: their speed lets them digitize high frequencies directly.
• Dither sounds backwards but is real: it is a small amount of noise deliberately added to the input before conversion. That tiny added noise smooths out the harsh stair-step rounding error (called quantization noise) and actually makes the result cleaner. So dither reduces quantization noise.
• Total harmonic distortion is one measure of how good an ADC is, it tells you how much false harmonic content the conversion adds. (Notice harmonics showing up again as a quality yardstick.)

Turning digital back into analog: the DAC and its clean-up filter

Going the other direction, a digital-to-analog converter (DAC) turns numbers back into a smooth wiggle. But the raw DAC output is a stair-step that contains unwanted high-frequency junk left over from the sampling process. So we put a low-pass filter on the DAC output. (A low-pass filter passes low frequencies and blocks high ones.) Its purpose is to remove spurious sampling artifacts from the output signal, that is, to smooth away the stair-step leftovers and leave the clean intended waveform. "Spurious" just means unwanted and not supposed to be there.

Modulation is the act of taking a plain radio carrier (a steady sine wave at your operating frequency) and varying one of its properties in step with your information. There are only three properties to vary, amplitude, frequency, or phase, and most modes are just one of those three done in a particular way. This group also covers a little friendly arithmetic and the idea of packing several signals into one channel (multiplexing).

FM and the modulation index

In frequency modulation (FM) you push the carrier's frequency up and down in step with the audio. How far it swings from center is the deviation. A key measure is the modulation index, defined as the ratio of the frequency deviation to the frequency of the modulating signal. In plain words:

modulation index = deviation ÷ modulating frequency

Notice both numbers must be in the same units. Two worked examples straight from the exam:

• Deviation of 3000 Hz, highest modulating frequency 1000 Hz: 3000 ÷ 1000 = 3.
• Deviation of plus or minus 6 kHz, highest modulating frequency 2 kHz: 6 ÷ 2 = 3.

A subtle but important fact: the modulation index of a phase-modulated signal does not depend on the RF carrier frequency at all. You can move the same modulated signal to a different band and the index is unchanged, it is set by the modulation, not by where you transmit it.

Deviation ratio: the worst-case version

The deviation ratio looks almost identical to modulation index, but it uses the maximums: it is the ratio of the maximum carrier frequency deviation to the highest audio modulating frequency. So it is the worst-case, design-limit version of the same fraction.

deviation ratio = maximum deviation ÷ highest modulating frequency

• Maximum swing plus or minus 5 kHz, highest modulating frequency 3 kHz: 5 ÷ 3 = 1.67.
• Maximum swing plus or minus 7.5 kHz, highest modulating frequency 3.5 kHz: 7.5 ÷ 3.5 = 2.14.

Memory trick: both formulas are just deviation on top divided by audio frequency on the bottom. Modulation index uses the actual numbers in a given moment; deviation ratio uses the maximum allowed deviation and the highest audio frequency.

Multiplexing: sharing one channel among many signals

Multiplexing means carrying several separate data streams over one transmission. There are two classic ways and one modern way.

• Frequency division multiplexing (FDM) splits the job by frequency: you divide the transmitted signal into separate frequency bands, each carrying a different data stream. Picture several lanes side by side, each lane a slightly different frequency.
• Time division multiplexing (TDM) splits the job by time instead: two or more signals take turns using discrete time slots of the transmission. Picture one lane, with each signal allowed to send only during its assigned tick of the clock.

OFDM: the modern workhorse

Orthogonal frequency-division multiplexing (OFDM) is used for digital modes. It is a digital modulation technique using many subcarriers at frequencies chosen so they do not interfere with one another (no intersymbol interference). The word "orthogonal" here means the subcarriers are spaced so cleverly that even though they overlap, each one sits exactly at the points where its neighbors contribute nothing, so they stay independent. ("Subcarriers" are many small carriers packed within the channel; "intersymbol interference" is when one data symbol smears into the next.) OFDM is what makes fast, robust digital modes possible.

This group is about purely digital signaling: how data is impressed on a carrier, how much bandwidth a given data rate needs, how errors get caught and fixed, and how to read a constellation diagram.

Symbols, baud, and symbol rate

A digital signal carries information by changing the waveform into recognizable states. Each distinct state is a symbol. The symbol rate is the rate at which the waveform changes to convey information, how many times per second the signal switches to a new state. The unit for this is the baud, and here is a fact the exam likes to confirm: symbol rate and baud are the same thing. One baud means one symbol change per second.

Note that symbol rate is not always the same as bit rate. If each symbol can represent several bits (by using more states), you move more bits per symbol, which leads to the next idea.

Getting more data into the same bandwidth

You cannot break physics, but you can be clever. To increase the data rate without increasing the bandwidth, you use a more efficient digital code, one that packs more bits into each symbol or wastes fewer of them. More information per symbol means more data through the same-width channel.

QAM, PSK, and constellation diagrams

• Quadrature Amplitude Modulation (QAM) is transmitting data by modulating the amplitude of two carriers that are at the same frequency but 90 degrees out of phase with each other. ("Quadrature" means 90 degrees apart.) By independently adjusting the amplitude of those two phase-shifted carriers, you can land on many distinct combined states, carrying several bits per symbol.
• A constellation diagram is a map of those states. For a QAM or QPSK signal it shows the possible phase and amplitude states for each symbol, plotted as a pattern of dots. A clean, tight pattern means a clean signal; smeared dots mean trouble.

PSK and keeping it narrow

PSK (phase-shift keying) carries data by shifting the carrier's phase. Two narrowness tricks the exam tests:

• You should change the phase of a PSK signal at the zero crossing of the RF signal (the instant the waveform passes through zero). Changing phase right at that smooth crossover point keeps the transition gentle, which minimizes bandwidth. Sharp, abrupt changes splatter energy outward; smooth ones stay narrow.
• For PSK31 specifically, the bandwidth is minimized by using sinusoidal data pulses, gently rounded pulse shapes rather than hard square edges. (Remember E8A: square edges mean lots of harmonics, which means a wide signal.)

Bandwidth of specific modes

A handful of numbers to know:

• A 13-WPM Morse code (CW) transmission is about 52 Hz wide. ("WPM" is words per minute.)
• An FT8 signal is about 50 Hz wide. (FT8 is a very popular weak-signal digital mode.)
• A 4800 Hz shift, 9600 baud ASCII FM transmission is about 15.36 kHz wide.

And what affects the bandwidth of a CW signal in the first place? The keying speed and the shape factor, that is, the rise and fall time of the keying. Faster keying and sharper, more abrupt on/off edges both widen the signal. (Again: sharp edges, more harmonics, more bandwidth.)

Error correction and the Gray code

• ARQ (Automatic Repeat reQuest) handles errors the simple, reliable way: if errors are detected, a retransmission is requested. The receiver basically says "I did not get that cleanly, send it again."
• Gray code is a clever way of numbering states so that only one bit changes between consecutive values. Because neighbors differ by just one bit, a small slip into an adjacent state causes only a single-bit error instead of a big jump, which keeps errors small and easy to manage.

Mesh networks

A mesh network is a web of radio nodes that relay for each other so data can hop from point to point. Two facts:

• Nodes in a mesh network use Internet Protocol (IP) addresses, the same kind of addressing the internet uses.
• Nodes form the mesh using discovery and link establishment protocols, automatic routines by which each node finds its neighbors and sets up connections, so the network builds and heals itself without manual wiring.

This last group is about signal quality: the defects that make a signal splatter or distort, the digital codes used for text, and the special techniques of spread spectrum. The recurring theme from all of E8 pays off here, abrupt edges and overdriven levels create unwanted harmonics and intermodulation that widen and dirty your signal.

Key clicks: the price of sharp edges

When you send Morse code, the transmitter switches on and off. If those on/off transitions are too abrupt (extremely short rise and fall times), the result is key clicks, sharp little splatters of energy that spread well outside your intended frequency and annoy nearby operators. (Recall from E8A that a sharp, square edge is full of harmonics; that is literally where the click energy comes from.)

The cure is simple and is exactly the opposite of the cause: increase the rise and fall times of the keying waveform. Softening the edges, rounding the on and off transitions, is the most common method of reducing key clicks. ("Rise time" is how long the signal takes to come up to full power; "fall time" is how long it takes to drop back down.)

Overmodulation of digital (AFSK) signals

Many digital modes are sent as AFSK (audio frequency-shift keying), audio tones fed into an SSB transmitter. The most common cause of overmodulation here is excessive transmit audio levels, simply driving the radio with too much audio, which overdrives it into distortion.

How do you measure that distortion? The parameter is intermodulation distortion (IMD). ("Intermodulation" is when an overdriven stage mixes signals together and produces new, unwanted products.) For an idling PSK signal (a PSK transmitter sending its steady idle pattern), an acceptable maximum IMD level is about -30 dB. The more negative the dB number, the cleaner the signal, so -30 dB means the distortion products are well below the wanted signal.

Digital text codes: Baudot versus ASCII

Two codes for sending text come up:

• Baudot uses 5 data bits per character. Five bits is not enough room for all letters, numbers, and symbols, so Baudot uses two special characters as shift codes, a "letters shift" and a "figures shift," to switch between two sets of meanings, much like the Shift key on a keyboard.
• ASCII uses 7 or 8 data bits per character. With more bits it has no need for a letters/figures shift, and crucially, ASCII can represent both uppercase and lowercase text, which is one of its main advantages over Baudot.

Parity: a cheap error check

A parity bit is one extra bit added to a character to make its total count of 1-bits come out even (or odd) as agreed. The advantage of including parity bits in ASCII characters is that some types of errors can be detected, if a single bit flips in transit, the parity no longer matches and the receiver knows something went wrong. It is a simple, low-cost error check (it detects, though it does not by itself fix).

Spread spectrum: hiding in plain sight

Spread spectrum deliberately smears a signal across a wide range of frequencies using a secret-looking pattern, then de-spreads it at the receiver. This gives it remarkable toughness.

• Why it resists interference: at the receiver, the de-spreading process concentrates the wanted signal but scatters everything else, so signals that do not use the same spread spectrum algorithm are suppressed in the receiver. Interference that does not share the secret pattern just gets spread out into the noise and ignored.
• Direct sequence spread spectrum uses a high-speed binary bit stream to shift the phase of the RF carrier, rapidly multiplying the data by a fast pseudorandom code to smear it across the band.
• Frequency hopping spread spectrum works differently: it rapidly varies the transmitted frequency according to a pseudorandom sequence, hopping from frequency to frequency on a pattern both ends know in advance. ("Pseudorandom" means it looks random but is actually a repeatable, agreed-upon pattern, so the receiver can follow along.)