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Below are concepts and explanation of apps that support Lab. VI.

The objective of this lab is to study the amplitude and phase relationship of harmonic input and output of simple linear circuits. You may or may not have learned Fourier analysis. But here is the basic idea:



A signal s[t] can be expressed as a sum of many (infinite) sinusoidal functions. To analyze the output of s[t] through a circuit, it is simpler to find out what happens to each component sinusoidal function rather than the whole complicated signal s[t]. Each sinusoidal function is called a harmonic. For most circuits, which are linear, the output of a harmonic is also a harmonic of the same frequency, with a change in amplitude and phase. This is referred to as a phasor.

If we know the output of each harmonic component of signal s[t], we can add all of them up and get the output of s[t].

In this lab, you will measure the phasor output of an input harmonic signal, which is the change in amplitude and phase relative to the input. The oscilloscope you use has nice built-in functions to do this.


Old Lab VI



Some basic illustration of complex number representation of harmonics


   
A simple introductory illustration of phasors for an RCL circuit


     


Fun things with sinusoidal signals (learn Fourier synthesis)



   



Harmonic signal basic

Phasor basic

Second-order filters (both passive and active)


   



Illustration of Fourier analysis of signal through a simple (single-pole) RC filter.