1-23 combined linear and nonlinear impedance circuit, the voltages developed across the impedances are complex waveforms. Figure 1-16.—Sine-wave generators with a combination of impedances. When two sine wave voltages are applied to a circuit, as in figure 1-16, nonlinear impedance Z2 reshapes the two sine-wave inputs and their harmonics, resulting in a very complex waveform. Assume that nonlinear impedance Z2 will allow current to flow only when the sum of the two sine-wave generators (G1 and G2) has the polarity indicated. The waveforms present across the linear impedance will appear as a varying waveform. This will be a complex waveform consisting of: a dc level the two fundamental sine wave frequencies the harmonics of the two fundamental frequencies the sum of the fundamental frequencies the difference between frequencies The sum and difference frequencies occur because the phase angles of the two fundamentals are constantly changing. If generator G1 produces a 10-hertz voltage and generator G2 produces an 11-hertz voltage, the waveforms produced because of the nonlinear impedance will be as shown in the following list: a 10-hertz voltage an 11-hertz voltage harmonics of 10 hertz and 11 hertz (the higher the harmonic, the lower its strength) the sum of 10 hertz and 11 hertz (21 hertz) the difference between 10 hertz and 11 hertz (1 hertz)

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