Oscilloscope Signal Reconstruction Explained
An oscilloscope is a powerful tool that allows us to visualize electrical signals.
By showing these signals as waveforms on a screen, oscilloscopes help engineers and technicians understand the behaviour of circuits.
However, simply displaying a waveform is only part of the story.
The real magic happens in signal reconstruction, where the oscilloscope accurately reproduces the original signal from the data it captures.
In this post, we will explore how oscilloscopes reconstruct signals, why this process is important, and the key concepts behind it.
What is Signal Reconstruction?
Signal reconstruction is the process of converting the sampled data back into a continuous signal that closely resembles the original waveform.
When an oscilloscope captures a signal, it takes multiple samples of the voltage over time.
These samples are just data points, not a continuous curve.
To make sense of this data, the oscilloscope reconstructs the signal, connecting these dots to form a waveform that represents the original signal as closely as possible.
Sampling: The First Step in Signal Reconstruction
Sampling is the process where the oscilloscope measures the signal’s voltage at regular intervals.
The speed at which these samples are taken is called the sampling rate, usually measured in samples per second or Hertz (Hz).
The higher the sampling rate, the more data points the oscilloscope collects, leading to a more accurate reconstruction.
However, if the sampling rate is too low, important details of the signal may be lost.
This is where the Nyquist Theorem comes into play.
According to this theorem, the sampling rate must be at least twice the highest frequency present in the signal to accurately reconstruct it.
If the sampling rate is too low, it can lead to a problem known as aliasing, where different signals become indistinguishable from each other.
In an oscilloscope, a low-pass filter removes any frequencies that are higher than half of the sampling frequency.
Even though the sampling theorem is followed, the signal still isn’t accurately reconstructed.
This happens because the signal is reconstructed by simply connecting the sampled points with straight lines.
When the signal’s frequency is close to half the sampling frequency, the sinusoidal signal is only captured with a few points.
Using the simulator, you can see a problem at high frequencies that causes the measurement signal to be shown incorrectly.
A 20kHz signal is sampled internally at around 100kHz.
According to the sampling theorem, this 100kHz sampling frequency is well above the signal frequency.
The figure above illustrates the effect. In each sine wave period (black line), the signal is sampled at 6 points.
When you connect these sampled points with lines, the resulting points differ from those of the original sine wave (red line).
This creates an amplitude modulation, and the black signal is not accurately represented by the red lines.
The issue arises because simply connecting the points with lines doesn’t provide a correct reconstruction of the original signal.
When there are many sampling points, this approximation works well.
However, if the sampling frequency is close to the Nyquist-Shannon limit, problems can occur.
Bandwidth Effect on Signal Reconstruction
The oscilloscope’s bandwidth is another critical factor in signal reconstruction.
Bandwidth refers to the range of frequencies the oscilloscope can accurately capture.
If the signal contains frequencies higher than the oscilloscope’s bandwidth, those high-frequency components will be lost or distorted in the reconstruction process.
This can lead to an inaccurate representation of the original signal.
To avoid this, it’s important to use an oscilloscope with a bandwidth higher than the highest frequency present in your signal.
This ensures that all components of the signal are captured and accurately reconstructed.
In Short…
Signal reconstruction is a crucial process that transforms sampled data into a visual representation of the original signal.
By understanding how sampling, interpolation, and bandwidth affect signal reconstruction, you can use an oscilloscope more effectively.
Accurate signal reconstruction ensures that the waveform displayed on the oscilloscope screen truly represents the signal being measured.
This accuracy is vital for diagnosing and analyzing circuits, leading to better designs and more reliable electronic systems.