Problem Statement:
To convert an analog (Voltage and current) signal into a digital signal using ADC (audio card).
Display it on the MATLAB Simulink environment and perform Spectral Analysis of the resulting
voltage and current signal.
Components Required:
1) Audio card
2) Transformer
3) Resistors for VDR
4) Veroboard
5) Audio jack
Summary:
The project involved converting analog voltage and current signals into digital signals using an ADC
(audio card). The digital signals were displayed in the MATLAB Simulink environment, and spectral
analysis was performed. The Fast Fourier Transform (FFT) was used for its computational
efficiency in real-time signal processing. The analysis revealed a fundamental frequency of 50.2 Hz
with lower magnitudes for odd harmonics, while nonlinear loads exhibited additional frequency
components, correlating with time-domain distortion. No spectral leakage was observed in the
spectrum, validating the use of a rectangular window. Frequency resolution was calculated as
0.0625 Hz, ensuring detailed spectral analysis.
Methodology:
The digital voltage and current signals sampled in PBL 1 are now required to undergo spectral
analysis. To achieve this, the Discrete-Time Fourier Transform (DTFT) is applied as the signal is
periodic. While MATLAB's DFT tool can be used for this purpose, its computational time can be a
limitation. Therefore, the FFT tool is utilized instead, as its efficient algorithm allows for real-time
Fourier transformation.
No spectral leakage was observed in the frequency spectrum, as minimal energy was transferred to
neighbouring bins. Therefore, the default rectangular window is sufficient, and there is no need to
use other windowing techniques such as Hamming or Blackman-Harris to address spectral
leakage. Applying such techniques unnecessarily could disturb or distort the frequency spectrum.
Matlab Code:
The code below can sample signals at 8000 samples/sec and 16 bit resolution. The code can also
perform spectral analysis
Waveforms:
Calculation:
The frequency resolution calculation is stated below
Δf=Fs/N=8192/131072=0.0625
Conclusion:
When the Fourier Transform was applied to the line voltage signal, the spectrum revealed that the
fundamental frequency component was 50.2 Hz, while the magnitudes of the odd harmonic
components were observed to be lower than the fundamental frequency. Similarly, in the case of
nonlinear loads, many frequency components other than the fundamental frequency were present,
which aligned with the distorted waveform observed in the time domain. This distortion could also
be analyzed by performing an Inverse Fourier Transform.It was further observed that no spectral
leakage occurred in the frequency spectrum, confirming that the rectangular window was suitable
for the sampled data.
