# Amateur Radio Manual/Sinusoidal Waveforms

As mentioned in the previous chapter, an alternating current is a current that changes with time. A specific class of current, and voltage for that matter, is the sinusoidal waveform. Sinusoidal waveforms are fundamental to radio. A Morse code signal, for example, is generated from a sinusoidal waveform. Sinusoidal waveforms are the basis behind AM, FM, and television signals as well.

## Basic Characteristics of Sinusoidal Waveforms

There are three basic characteristics of sinusoidal waveforms (hereafter sinusoids): amplitude, frequency, and phase.

As shown in the diagram, the amplitude is the difference between the high value and the low value. The waveform may have different units, depending upon what the waveform is. If the waveform is measuring a voltage as a function of time, then the amplitude will be in Volts; if it were current as a function of time, amplitude would be in Amps. The frequency is equal to ${\displaystyle {\frac {1}{\lambda }}}$  and is a measure of how quickly the waveform cycles. If the waveform is a function of time, then frequency will usually be measured in Hertz (Hz). Since frequency is a measure of how rapidly the waveform cycles, frequency is sometimes (usually in older texts) given as cycles. One cycle is equal to one Hertz. λ is the inverse of frequency and is referred to as the period (usually a "T" is used to indicate the period.) Phase is a measure of how "offset" the signal is from some reference signal. Phase only makes sense when comparing signal of the same frequency, as otherwise phase will change as a function of time.

In the second plot, red is a sine wave and green is a cosine wave. As can be seen, these waveforms are identical save that one is a shifted version of the other. Notice how the cosine function reaches a peak at 0, while the sine function reaches a peak at ${\displaystyle {\frac {\pi }{2}}.}$  The cosine function reaches the peak sooner and is said to lead the sine function by ${\displaystyle {\frac {\pi }{2}},}$  or 90°.