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2016 Extra Class study guide: E8A - waveforms and measurement

Posted: 16 Feb 2016 11:23 AM PST
http://feedproxy.google.com/~r/kb6nu...m_medium=email


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, were
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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