# E-8

E8A – AC waveforms: sine, square, sawtooth and irregular waveforms; AC measurements; average and PEP of RF signals; Fourier analysis; Analog to digital conversion: Digital to Analog conversion

We use all different kinds of waveforms in amateur radio. It is, therefore, important to know about the different types of waveforms and how to measure their parameters. One parameter of an AC waveform that you need to know is its root mean square, or RMS, value. The root-mean-square value of an AC voltage is the DC voltage causing the same amount of heating in a resistor as the corresponding RMS AC voltage. Because of this, the most accurate way of measuring the RMS voltage of a complex waveform would be measuring the heating effect in a known resistor. (E8A05)

If the waveform is regular, it’s relatively easy to calculate the RMS value. In the case of a sine wave, the RMS value is 0.707 times the peak value. You use the RMS voltage value to calculate the power of a wave.

The type of waveform produced by human speech is, however, irregular. For irregular waveforms, such as that of a single-sideband phone signal, we’re most interested in the peak envelope power (PEP). The characteristics of the modulating signal determine the PEP-to-average power ratio of a single-sideband phone signal. (E8A07) This makes calculating or measuring the average power more difficult.

If you know the peak envelope power (PEP), though, you can make a pretty good guess at the average power. The approximate ratio of PEP-to-average power in a typical single-sideband phone signal is 2.5 to 1. (E8A06) Put another way, the average power of an SSB signal is about 40% of the peak power.

It used to be that all the waveforms we used in amateur radio were analog waveforms, but nowadays digital waveforms may be even more important than analog waveforms. An advantage of using digital signals instead of analog signals to convey the same information is that digital signals can be regenerated multiple times without error. (E8A12) All of these choices are correct when talking about the types of information that can be conveyed using digital waveforms (E8A11):

• Human speech
• Video signals
• Data

Perhaps the most common digital wave form is the square wave. An ideal square wave alternates regularly and instantaneously between two different values. An interesting fact is that a square wave is the type of wave that is made up of a sine wave plus all of its odd harmonics. (E8A01)

Another type of wave used in amateur radio is the sawtooth wave. A sawtooth wave is the type of wave that has a rise time significantly faster than its fall time (or vice versa). (E8A02) The type of wave made up of sine waves of a given fundamental frequency plus all its harmonics is a sawtooth wave. (E8A03)

To make use of digital techniques in amateur radio, such as digital signal processing or DSP, we must convert analog signals to digital signals and vice-versa. To do this we use an analog-to-digital converter (ADC).

ADCs sample a signal at a particular point in time and convert that sample into a digital number that is proportional to the amplitude at that time. The number of bits in the digital number is called the resolution of the ADC. An analog-to-digital converter with 8 bit resolution can encode 256 levels. (E8A09)

To convert radio signals to digital streams used in software-defined radios, you need to sample the signal at a very high rate in order to preserve signal integrity. A direct or flash conversion analog-to-digital converter would, therefore, be useful for a software defined radio because its very high speed allows digitizing high frequencies. (E8A08)

Sequential sampling is one of the methods commonly used to convert analog signals to digital signals. (E8A13) Sequential sampling allows you to sample a signal only once per cycle, thereby allowing you to use a slower, and less expensive ADC, and still preserve signal integrity. Sequential sampling only works, however, when the waveform is a regular waveform.

Sometimes signals are passed through a low pass filter before being digitized. The purpose of a low pass filter used in conjunction with a digital-to-analog converter is to remove harmonics from the output caused by the discrete analog levels generated. (E8A10)

The differential nonlinearity in the ADC’s encoder transfer function can be reduced by the proper use of dither. With respect to analog to digital converters, dither is a small amount of noise added to the input signal to allow more precise representation of a signal over time. (E8A04)

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E8B – Modulation and demodulation: modulation methods; modulation index and deviation ratio; frequency and time division multiplexing; Orthogonal Frequency Division Multiplexing

In FM modulation, the two primary parameters of interest are deviation ratio and modulation index. Deviation ratio is the ratio of the maximum carrier frequency deviation to the highest audio modulating frequency. (E8B09) 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 is 1.67. (E8B05)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 is 2.14. (E8B06)

The term for the ratio between the frequency deviation of an RF carrier wave, and the modulating frequency of its corresponding FM-phone signal is modulation index. (E8B01) The modulation index is equal to the ratio of the frequency deviation to the modulating frequency. The modulation index of a phase-modulated emission does not depend on the RF carrier frequency. (E8B02)

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 is 3. (E8B03) 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 is 3. (E8B04)

Some communications systems use multiplexing techniques to combine several separate analog information streams into a single analog radio frequency signal. When a system uses frequency division multiplexing, two or more information streams are merged into a “base band,” which then modulates the transmitter. (E8B10). When a system uses digital time division multiplexing, two or more signals are arranged to share discrete time slots of a data transmission. (E8B11)

Orthogonal Frequency Division Multiplexing is a digital modulation technique using subcarriers at frequencies chosen to avoid inter symbol interference. (E8B08) Orthogonal Frequency Division Multiplexing is a technique used for high speed digital modes. (E8B07)

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E8C – Digital signals: digital communications modes; information rate vs. bandwidth; error correction

Digital modes have become very popular in amateur radio lately, but Morse Code, the type of modulation that has been around the longest, is the original digital mode. One advantage of using Morse Code is that it has a very narrow bandwidth. The bandwidth necessary for a 13-WPM international Morse code transmission is approximately 52 Hz. (E8C05)

The bandwidth needed for digital transmissions increases as the data rate increases. The bandwidth necessary for a 170-hertz shift, 300-baud ASCII transmission is 0.5 kHz. (E8C06) The bandwidth necessary for a 4800-Hz frequency shift, 9600-baud ASCII FM transmission is 15.36 kHz. (E8C07)

PSK has become a very popular digital mode. One reason for this is that it occupies a very narrow bandwidth – only 31 Hz. One technique used to minimize the bandwidth requirements of a PSK31 signal is the use of sinusoidal data pulses. (E8C04) When performing phase shift keying, it is also advantageous to shift phase precisely at the zero crossing of the RF carrier because this results in the least possible transmitted bandwidth for the particular mode. (E8C03)

When digital communication systems were first developed, data was sent one bit at a time. As the need for faster data transmission grew, engineers figured out how to send multiple bit simultaneously. Instead of sending single bits, these systems send and receive “symbols,” which stand for multiple bits. The definition of symbol rate in a digital transmission is the rate at which the waveform of a transmitted signal changes to convey information. (E8C02) The relationship between symbol rate and baud is they are the same. (E8C11)

Whenever digital data is sent over a radio channel, it is encoded. Gray codes are often used for this purpose. Gray code is the name of a digital code where each preceding or following character changes by only one bit. (E8C09) An advantage of Gray code in digital communications where symbols are transmitted as multiple bits is that it facilitates error detection. (E8C10)

There are many things that can cause errors in a data stream. For example, an interfering signal might cause a receiver to interpret a transmitted symbol incorrectly. When these errors are not allowable, digital communications systems implement some form of error detection and correction.

One way to achieve reliable data communication is to use the Automatic Repeat ReQuest, or ARQ, protocol. In systems that use ARQ error control, if errors are detected, a retransmission is requested. (E8C08) Senders will also re-transmit a data packet if they do not receive an acknowledgement from the receiver that it has correctly received a packet.

Another way to correct errors is a technique called forward error correction. Forward Error Correction is implemented by transmitting extra data that may be used to detect and correct transmission errors. (E8C01) When a receiver receives erroneous data, it can correct the errors itself.

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E8D – Keying defects and over modulation of digital signals; digital codes; spread spectrum

It is good amateur practice to ensure that the CW and digital signals you transmit are high quality. Perhaps the biggest problem that you’ll have when sending CW signals is key clicks. Key clicks are spurious signals that cause interference to other stations operating near your frequency. The generation of key clicks is the primary effect of extremely short rise or fall time on a CW signal. (E8D04) It follows, then that the most common method of reducing key clicks is to increase keying waveform rise and fall times. (E8D05) Fortunately, most modern transceivers allow you to set the rise and fall times of the CW signal, so this is an easy fix.

To ensure high-quality digital signals, such as when transmitting audio frequency shift signals, such as PSK31, you need to set the audio input level properly. A common cause of over modulation of AFSK signals is excessive transmit audio levels. (E8D07). Strong ALC action indicates likely over modulation of an AFSK signal such as PSK or MFSK. (E8D06)

Intermodulation Distortion (IMD) is a parameter that you can measure that might indicate that excessively high input levels are causing distortion in an AFSK signal. (E8D08) A good minimum IMD level for an idling PSK signal is -30 dB. (E8D09)

Digital codes

Although ASCII and Unicode have now become standard codes for sending textual information, we still use the Baudot code when sending and receiving RTTY. Some of the differences between the Baudot digital code and ASCII are that Baudot uses 5 data bits per character, ASCII uses 7 or 8; Baudot uses 2 characters as letters/figures shift codes, ASCII has no letters/figures shift code. (E8D10)

Even though it uses more bits per character, ASCII does have some advantages over Baudot. For example, one advantage of using ASCII code for data communications is that it is possible to transmit both upper and lower case text. (E8D11)

In an eight-bit ASCII character, the eighth bit is the partity bit. In systems that use even parity, the parity bit is set to either a one or a zero, so that the number of ones in the character is equal to an even number. In systems that use odd parity, the parity bit is set to either a one or a zero, so that the number of ones in the character is equal to an odd number. The advantage of including a parity bit with an ASCII character stream is that some types of errors can be detected. (E8D12)

Amateurs can now use spread-spectrum techniques on all bands above 420 MHz. The reason these bands are used is because spread-spectrum signals require more bandwidth than is available on the lower frequency bands.

Spread spectrum transmissions generally change frequency during a transmission. This is called frequency hopping. The way the spread spectrum technique of frequency hopping works is that the frequency of the transmitted signal is changed very rapidly according to a particular sequence also used by the receiving station. (E8D03) Direct sequence is a spread spectrum communications technique that uses a high speed binary bit stream to shift the phase of an RF carrier. (E8D02)

Because transmission and reception occur over a wide band of frequencies, spread spectrum communications are less susceptable to interference on a single frequency than are more conventional systems. Received spread spectrum signals are resistant to interference because signals not using the spread spectrum algorithm are suppressed in the receiver. (E8D01)

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