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Some of the important waveforms are the "pure" sine, such as RF carriers and control tones. Square waved transition between two levels rapidly, and are the most usual signals in digital circuits. Sawtooth waves are of use in scanning traces across CRO and CRT TV screens. Voice and musical sounds are irregular waveforms.
Fourier analysis tells us that a squarewave can be thought of being made up of a the fundamental and odd harmonics, at progressively reducing levels.
Off the exam, this explains why if an amplifier is overdrive, and the sinewave become flat-topped, harmonic distortion become evident.
If all (odd and even) harmonics are present, the waveform becomes a sawtooth wave. These are not symmetrical triangular waves, but either start at a negative level before rising to a linearly positive one, then dropping back to negative; or start positive, and decline to a negative one, before jumping back to positive.
There are range of analogue to digital conversion methods, each suitable for different uses. Successive approximation is an example. This works by having in internal D-to-A generate a voltage at half the reference voltage to compare to the incoming signal. Depending if it is higher or lower comparison is them made to a ¼ or ¾ reference level, then by eighths, sixteenths, etc until a a full evaluation is made, with each step generating a bit.
The number of levels which can be measured by a system is dependent dependant on number of bits used. The formula is N = 2n, so an 8 bit system can have 256 levels.
Total Harmonic Distortion (TDM) is a widely used measure of audio quality. It is measured in percent, with a lower figure being better. A clean sinewave oscillator is fed into an audio circuit, and signal components which are not part of a pure sine wave appearing at the output are measured. This can be used on amplifiers, broadcast systems, and analog-to-digital and digital-to-analog converters.
Flash digitisation uses a very large number of comparators to evaluate the level in a single step. This speed allows direct digitisation of RF signals. They are also used in instruments such as Digital Storage Oscilloscopes.
Low cost multimeters are sensitive to the average level of an AC signal, and factor the display to RMS, based on the assumption that the measured signal is a sine wave. If the signal is a squarewave, or has a high crest factor, the reading will not be accurate. To obtain a true RMS reading for any waveform, a meter containing an IC which converts the signal to an accurate representation of the RMS value is used.
These do not have to be expensive, with the multicompPRO MP730835 under A$34 at the moment. The multicompPRO MP730026 EU-UK is under A$55.
In SSB systems power is measured using Peak Envelope Power. The amount of energy is in a 2.5 watt PEP signal is equivalent to that in a 1 watt AM or CW one.
The modulation index of an FM signal is the deviation of the transmitted signal divided by the modulating signal frequency.
If a 2200 Hz tone from a packet modem is causing a deviation of plus and minus 4.4 kHz (4400 Hz), then the modulation index at that moment is 2.
Deviation ratio is the ratio of maximum permitted deviation to maximum permitted audio input frequency. The formula is the same.
If the maximum input frequency is 4 kHz, and the maximum deviation is ±5 kHz, then the deviation index is 5 / 4 = 1.25.
Sometims we need to combine signals onto a single bearer or carrier. This can be anything from 2 to hundreds or more.
One method is frequency based, with signal modulated using different carriers. Before optical fibre, an example using SSB to modulate multiple telephone calls one a single thick coaxial cable running between cities, each at a different (supressed) carrier frequency.
Time division multiplexing combines multiple slower digital streams into a faster one. Telex used to run at 50 baud, far slower than the data carrying capacity of a single pair. Thus at a local exchange the 20 or so Telex signals from a district could be combined onto a single pair to send into the city centre Telex exchange by sampling each Telex line in turn 50 times per second. Thus a 1000 bit per second signal can carry 20 Telex messages at once.
Orthogonal Frequency Division Multiplexing is a modulation method for transferring large amounts of data wirelessly. It is used in various cellular / mobile telephone systems, and in Wi-Fi. It uses multiple sub-carriers across the channel.
These are the actual questions from the Extra licence exam pool, as published by the NCVEC.
E8A01
What is the name of the process that shows that a square wave is made up of a sine wave plus all of its odd harmonics?
A. Fourier analysis
B. Vector analysis
C. Numerical analysis
D. Differential analysis
This is Fourier analysis, answer A.
E8A02
Which of the following is a type of analog-to-digital conversion?
A. Successive approximation
B. Harmonic regeneration
C. Level shifting
D. Phase reversal
This is Successive approximation, answer A.
E8A03
What type of wave does a Fourier analysis show to be made up of sine waves of a given fundamental frequency plus all of its harmonics?
A. A sawtooth wave
B. A square wave
C. A sine wave
D. A cosine wave
This is the sawtooth wave, answer A.
E8A04
What is "dither" with respect to analog to digital converters?
A. An abnormal condition where the converter cannot settle on a value to represent the signal
B. A small amount of noise added to the input signal to allow more precise representation of a signal over time
C. An error caused by irregular quantization step size
D. A method of decimation by randomly skipping samples
Dithering means adding noise to a signal, so answer B.
E8A05
What of the following instruments would be the most accurate for measuring the RMS voltage of a complex waveform?
A. A grid dip meter
B. A D'Arsonval meter
C. An absorption wave meter
D. A true-RMS calculating meter
This is the true-RMS meter, answer D.
E8A06
What is the approximate ratio of PEP-to-average power in a typical single-sideband phone signal?
A. 2.5 to 1
B. 25 to 1
C. 1 to 1
D. 100 to 1
This is 2.5:1, meaning that if we have an SSB transmitter which is 12.5 watts PEP, the energy is about the same as a 5 W CW or AM transmitter, answer A.
This does vary with the amount of "processing" applied to the signal.
E8A07
What determines the PEP-to-average power ratio of a single-sideband phone signal?
A. The frequency of the modulating signal
B. Speech characteristics
C. The degree of carrier suppression
D. The amplifier gain
This is the characteristics of the speech presented to the radio, answer B.
E8A08
Why would a direct or flash conversion analog-to-digital converter be useful for a software defined radio?
A. Very low power consumption decreases frequency drift
B. Immunity to out-of-sequence coding reduces spurious responses
C. Very high speed allows digitizing high frequencies
D. All of these choices are correct
Its high speed allows digitising of radio frequency signals, answer C.
E8A09
How many different input levels can be encoded by an analog-to-digital converter with 8-bit resolution?
A. 8
B. 8 multiplied by the gain of the input amplifier
C. 256 divided by the gain of the input amplifier
D. 256
Simples! 28 = 256, answer D.
E8A10
What is the purpose of a low pass filter used in conjunction with a digital-to-analog converter?
A. Lower the input bandwidth to increase the effective resolution
B. Improve accuracy by removing out-of-sequence codes from the input
C. Remove harmonics from the output caused by the discrete analog levels generated
D. All of these choices are correct
The steps between samples may cause unpleasant harmonics in the audio stream, which this filter removes, answer C.
E8A11
Which of the following is a measure of the quality of an analog-to-digital converter?
A. Total harmonic distortion
B. Peak envelope power
C. Reciprocal mixing
D. Power factor
Any audio system, including an A-to-D, can be assessed in terms of its Total Harmonic Distortion, answer A.
E8B01
What is the modulation index of an FM signal?
A. The ratio of frequency deviation to modulating signal frequency
B. The ratio of modulating signal amplitude to frequency deviation
C. The type of modulation used by the transmitter
D. The bandwidth of the transmitted signal divided by the modulating signal frequency
This is the ratio of frequency deviation to modulating signal frequency, answer A.
E8B02
How does the modulation index of a phase-modulated emission vary with RF carrier frequency (the modulated frequency)?
A. It increases as the RF carrier frequency increases
B. It decreases as the RF carrier frequency increases
C. It varies with the square root of the RF carrier frequency
D. It does not depend on the RF carrier frequency
The modulation index relates to deviation, not carrier frequency, answer D.
E8B03
What is the modulation index of an FM-phone signal having a maximum frequency deviation of 3000 Hz either side of the carrier frequency when the modulating frequency is 1000 Hz?
A. 3
B. 0.3
C. 3000
D. 1000
3000 / 1000 = 3, answer A.
E8B04
What is the modulation index of an FM-phone signal having a maximum carrier deviation of plus or minus 6 kHz when modulated with a 2 kHz modulating frequency?
A. 6000
B. 3
C. 2000
D. 1/3
6 / 2 = 3, answer B.
E8B05
What is the deviation ratio of an FM-phone signal having a maximum frequency swing of plus-or-minus 5 kHz when the maximum modulation frequency is 3 kHz?
A. 60
B. 0.167
C. 0.6
D. 1.67
5 / 3 = 1.666667, answer D.
E8B06
What is the deviation ratio of an FM-phone signal having a maximum frequency swing of plus or minus 7.5 kHz when the maximum modulation frequency is 3.5 kHz?
A. 2.14
B. 0.214
C. 0.47
D. 47
7.5 / 3.5 = 2.14, answer A.
E8B07
Orthogonal Frequency Division Multiplexing is a technique used for which type of amateur communication?
A. High speed digital modes
B. Extremely low-power contacts
C. EME
D. OFDM signals are not allowed on amateur bands
OFDM is used in high-sped digital modes, answer A.
E8B08
What describes Orthogonal Frequency Division Multiplexing?
A. A frequency modulation technique which uses non-harmonically related frequencies
B. A bandwidth compression technique using Fourier transforms
C. A digital mode for narrow band, slow speed transmissions
D. A digital modulation technique using subcarriers at frequencies chosen to avoid intersymbol interference
This is the digital modulation method used in Wi-Fi, including when used on Amateur microwave frequencies. It uses multiple subcarriers, answer D.
E8B09
What is meant by deviation ratio?
A. The ratio of the audio modulating frequency to the center carrier frequency
B. The ratio of the maximum carrier frequency deviation to the highest audio modulating frequency
C. The ratio of the carrier center frequency to the audio modulating frequency
D. The ratio of the highest audio modulating frequency to the average audio modulating frequency
This is the ratio of the maximum deviation to the highest audio frequency, answer B.
E8B10
What describes frequency division multiplexing?
A. The transmitted signal jumps from band to band at a predetermined rate
B. Two or more information streams are merged into a baseband, which then modulates the transmitter
C. The transmitted signal is divided into packets of information
D. Two or more information streams are merged into a digital combiner, which then pulse position modulates the transmitter
Information streams can be modulated onto subcarriers, and then modulated into a radio signal, answer B.
E8B11
What is digital time division multiplexing?
A. Two or more data streams are assigned to discrete sub-carriers on an FM transmitter
B. Two or more signals are arranged to share discrete time slots of a data transmission
C. Two or more data streams share the same channel by transmitting time of transmission as the sub-carrier
D. Two or more signals are quadrature modulated to increase bandwidth efficiency
TDM has packets from two or more data streams sent in different timeslots, such as in GSM or DMR, answer B.
On to: Signals & Emissions 2 - Digital
You can find links to lots more on the Learning Material page.
Written by Julian Sortland, VK2YJS & AG6LE, June 2022.
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