Oscilloscope Things--Bandwidth

Bandwidth determines the basic ability of an oscilloscope to measure signals. As the signal frequency increases, the oscilloscope's ability to accurately display the signal decreases. The bandwidth indicator indicates the frequency range that the oscilloscope can accurately measure.

The bandwidth of an oscilloscope refers to the frequency at which the sinusoidal input signal is attenuated to 70.7% of the actual amplitude of the signal, which is called the -3dB point. As shown in the figure:

Without adequate bandwidth, the oscilloscope will not be able to resolve high frequency changes, amplitudes will be distorted, edges will disappear, and details will be lost. Without adequate bandwidth, all the features and bells and whistles of an oscilloscope mean nothing.

Any signal can be decomposed into the superposition of countless harmonics. From the frequency domain, the general principle of bandwidth selection is: the bandwidth is sufficient if it can cover 99.9% of the energy of each harmonic of the measured signal. The root of bandwidth selection is that we cannot intuitively know what the bandwidth corresponding to 99.9% of the energy of the measured signal is.

The statement "the higher the bandwidth of an oscilloscope, the better" is correct in a sense: the higher the bandwidth, the higher the bandwidth that can accurately measure the measured signal, and the higher the signal reproduction accuracy that can be achieved; the higher the bandwidth of the oscilloscope, the smaller the rise time of the oscilloscope, and the higher the accuracy of the measured rise time. However, the higher the bandwidth, the greater the value and the more valuable it is. In addition, from the perspective of use, the higher the bandwidth is not necessarily better.

When the uncertain signal is decomposed to the Nth harmonic, the energy is attenuated to 99.9%, which can leave enough bandwidth margin when selecting and using an oscilloscope. However, a too high bandwidth will cause a serious problem: the introduced noise energy exceeds the signal's own energy within the same bandwidth range, which will also cause inaccurate measurement results. This is the signal-to-noise ratio (SNR) problem that is repeatedly mentioned in measurements.

If a 500MHz oscilloscope can cover 99.9% of the energy of the measured signal, the measurement accuracy can reach less than 5%, but we insist on using a 1GHz oscilloscope, then the noise energy introduced in the 500MHz~1GHz frequency range is much greater than the remaining 0.1% energy of the measured signal covered in the 500MHz~1GHz range. The measurement result in the time domain is a lot of random noise with high-frequency components superimposed on the waveform, which affects the measurement results of some parameters. Therefore, the measurement result using 500MHz is more accurate! This is why we limit the bandwidth to 20MHz when measuring power supply ripple.

In the digital world, rise time measurements are critical. When it is expected to measure digital signals, such as pulses and steps, rise time may be a more appropriate performance consideration. The oscilloscope must have sufficient rise time to accurately capture the details of rapid transitions. The faster the oscilloscope rise time, the more accurately it can capture the critical details of fast transitions. Rise time describes the useful frequency range of the oscilloscope. In some applications, you may only know the rise time of the signal. There is a constant that can relate the bandwidth of the oscilloscope to the rise time:

Bandwidth = K/rise time

Where K is a value between 0.35 and 0.45, depending on the shape of the oscilloscope's frequency response curve and the shape of the pulse rise time response. Oscilloscopes with bandwidths <1GHz generally have a K value of 0.35, and oscilloscopes with bandwidths >1GHz generally have a K value between 0.40 and 0.45.

In order to determine the existing bandwidth required for the signal amplitude in a specific application, 5 times the law, that is,

Oscilloscope bandwidth ≧ the highest frequency component of the signal X5

An oscilloscope selected using the 5x rule will provide less than ±2% error in measurements, which is generally adequate for current applications. However, as signal speeds increase, this rule of thumb may not hold true.

Some oscilloscopes offer a way to enhance bandwidth through digital signal processing. You can use a DSP arbitrary equalization filter to improve the oscilloscope channel response. This filter expands the bandwidth, flattens the oscilloscope channel frequency response, improves phase linearity, and achieves better matching between channels. It also reduces rise time and improves time domain step response.