Design Of Fourier Decomposition Synthesis Experimental Instrument Based On RLC Series Circuit

With the wide application of Fourier analysis,the application of Fourier series to the decomposition and synthesis of periodic functions is gradually included in major universities as a required experiment for students majoring in science and engineering.However,there are many discrete components and no comparison waveforms about the Fourier decomposition and synthesis experiment instrument.In response to the above problems,this subject proposes the design of a Fourier decomposition and synthesis experimental instrument based on RLC series circuit.In view of the problem of multiple discrete components and no waveform comparison,this design focuses on solving the problem of waveform comparison.This topic presents two methods for obtaining a sine wave:one is to decompose the periodic waveform into a sine wave on the basis of the resonant circuit;the second is to use a filter circuit to filter the periodic waveform into a sine wave,and finally the two methods are obtained to compare the sine wave.This design uses the chip ICL8038 to generate the excitation signal,and then divides the signal into two channels after the inverter circuit and the emitter follower designed by LF353;one channel is input to the RLC series circuit to decompose into a sine wave,and the other channel is to use the chip LM324 Obtained by the designed filter.According to the principle of Fourier analysis and RLC series resonant circuit,a design wave of 1kHz square wave is used as the excitation signal sine wave.By changing the capacitance value at different frequencies to make the RLC circuit reach the resonance point,the harmonics of different frequencies can be seperate.According to the principles of various filters,the 1kHz square wave as the excitation signal is filtered by different filter circuits to obtain sine waves of various frequencies.The two designed methods for obtaining sine wave can get sine wave better.The filtered sine waves of different frequencies are input to the oscilloscope after passing through the phase shift amplitude modulation circuits of 1kHz,3kHz,5kHz and 7kHz,respectively,and compared with the sine waves of various frequencies decomposed by the RLC resonant circuit,which can quickly determine the waveform decomposition.Right or wrong,measuring relative amplitude can basically reach 1:1/3:1/5:1/7.Finally,the sine waves of different frequencies obtained by filtering are input into the adder,and the square wave is synthesized by adjusting the phase and amplitude.Through testing,this design realizes the decomposition and synthesis of periodic waveforms and also solves the problem of comparing waveforms;it achieves the expected results and can be fully applied in experimental teaching.