## Extra Class question of the day: AC waveforms: sine, square, sawtooth and irregular waveforms; AC measurements; average and PEP of RF signals; pulse and digital signal waveforms

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 of the most important parameters of a waveform is its period. The period of a wave is the time required to complete one cycle. (E8A08) The frequency is the inverse of the period. For example, if the period of a wave is 1 msec, or .001 s, the frequency of that wave is 1 / .001s, or 1000 Hz.

Another parameter that we need to know about a waveform is it 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. (E8A04) 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. (E8A09), and  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 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. (E8A13) All of these choices are correct when talking about the types of information that can be conveyed using digital waveforms (E8A12):

• 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 is. (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)

Digital data transmission is one use for a pulse modulated signal. (E8A11) Narrow bursts of energy separated by periods of no signal is a distinguishing characteristic of a pulse waveform. (E8A10) The waveform of a stream of digital data bits would look like a series of pulses with varying patterns on a conventional oscilloscope. (E8A15)

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. Sequential sampling is one of the methods commonly used to convert analog signals to digital signals. (E8A14) When converting an analog signal to digital values, an analog to digital converter measures, or samples, the value of the analog signal at different points, and converts that measurement to a numeric value. Those numbers are then input to a processor or directly into memory.