Understanding Signal Measurement Bandwidth

In electronic test and measurement, how to capture a complete and true signal is a key concern for engineers. However, in high-frequency measurement, the completeness of the measured waveform is closely related to the bandwidth of the test instrument.

When a signal passes through a bandwidth-limited transmission line, if the line bandwidth is less than the signal bandwidth, the high-frequency components of the signal will be attenuated or completely filtered out. This attenuation causes signal distortion; especially in digital signals, the sharp edges of a square wave (high-frequency components) become blurred, deforming the signal and affecting correct data transmission.

Bandwidth requirements for measuring different waveforms

In general, to measure a waveform accurately, the instrument bandwidth must exceed the bandwidth contained in the waveform. For example, when measuring a sine wave, the instrument bandwidth must be at least approximately equal to the sine-wave frequency. Because if the sine-wave frequency equals the instrument's 3 dB bandwidth, the measured value is necessarily reduced by 3 dB, so an instrument with wider bandwidth is required. The required bandwidth margin depends on how fast the response curve rolls off near 3 dB.

For sine-wave measurement, a known input signal can be used to record the response at these frequencies in order to calibrate the frequency response near the 3 dB bandwidth. By reproducing the response curve and applying the error caused by bandwidth limitation to correct the measured value, the actual value can be obtained.

For an instrument that measures only AC voltage, its response curve rolls off at both low and high frequencies. When using such an instrument, both the high-frequency and low-frequency bandwidth limits must be considered.

For non-sinusoidal waveforms, their harmonics must be considered. If a harmonic exceeds the instrument bandwidth, its effect on the waveform cannot be measured. However, it is permissible if the harmonic exceeds a frequency range that must be ignored. Strictly speaking, a waveform with infinite harmonics would require an instrument with infinite bandwidth to measure the complete waveform. In practice, however, higher-order harmonics contain very little energy and can be neglected, as long as the error in the measurement caused by ignoring them is properly accounted for.

Effect of rise time on bandwidth

Among the many factors affecting digital signals, the bandwidth of a digital signal is strongly related to its rise time. The rise and fall times of a digital signal (that is, the transition time of the signal from low level to high level) have a direct effect on bandwidth. The shorter the rise time, the faster the signal changes; therefore, the more high-frequency components it contains, the greater the bandwidth requirement. If the rise and fall times are longer, the signal changes more slowly, and the bandwidth requirement is relatively smaller.

The probe rise time Tr is defined as the rise time measured when using an ideal instantaneous rising pulse. To achieve reasonable accuracy when measuring pulse rise time or fall time, the combined rise time of the probe and oscilloscope should be faster than the pulse under test by 3-5 times.

The figure above shows measurement error versus rise-time ratio. An oscilloscope/probe combination with a rise time three times faster than the pulse under test (3:1 ratio) is expected to measure the pulse rise time within 5%; a 5:1 ratio will result in only 2% error.When no rise time is specified,The relationship between rise time and bandwidth yields the following formula based on summarized experience:

Formula explanation 

 Rise time: 1. Rise time T_rusually refers to the time required for a digital signal to rise from low level (typically 10% of the maximum voltage value) to high level (typically 90% of the maximum voltage value), in nanoseconds (ns). 2. It is an indicator of the speed of signal change. The shorter the rise time, the faster the signal changes.

Bandwidth: 1. Bandwidth BW is the frequency range contained in the signal, in GHz. 2. The greater the bandwidth, the more information the signal can carry, which also means a broader signal spectrum range.

Meaning of the formula: If the signal rise time is shorter (that is, the signal changes faster), the bandwidth required by the signal is larger. This is because faster signal changes mean that a wider frequency range is needed in the frequency domain to accurately represent the signal; conversely, if the rise time is longer, the bandwidth is smaller.

For example, if a square-wave signal with a rise time of 10 ns needs to be measured, the signal transmission line bandwidth must be above 35 MHz (1G=1000M) to ensure signal integrity.

From the above article, we can understand the relationship between rise time and bandwidth, which can help with subsequent test equipment selection.

Probe bandwidth VS system bandwidth

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• In oscilloscope measurements, the probe is essential, so probe bandwidth also affects the measurement result; the formula for its impact on rise time is as follows:

  

• From this it can also be seen that the wider the bandwidth of the oscilloscope and probe, the smaller the impact on measurement bandwidth; that is, the closer the measurement bandwidth is to the signal bandwidth.

The bandwidth of the entire system is limited and determined by the device with the lowest bandwidth.

How should the appropriate probe bandwidth be selected?

Five-times ruleGenerally, for accurate amplitude measurement, the oscilloscope bandwidth should be five times the frequency of the waveform under test.

Selecting equipment with appropriate bandwidth is very important for measurement results and directly affects measurement accuracy.

If the frequency of the signal under test exceeds the probe bandwidth, the signal cannot be transmitted correctly, and the measured data will be distorted.Higher probe bandwidth is usually accompanied by better measurement accuracy and is suitable for measurements that need to capture details such as subtle changes in high-frequency signals or ripple noise.However,A larger probe bandwidth is not always better，One reason is that the output is limited by the oscilloscope bandwidth.

For example: a high-frequency non-inductive coaxial shunt commonly used in double-pulse testing applications has a bandwidth as high as 2G. But if a 2G-bandwidth shunt is selected while the oscilloscope has only 500M, then this probe's 2G does not mean much; it is mostly limited by the oscilloscope's 500M, and the actual result does not even reach 500M. This is also a point worth noting.

Another effect is that the higher the probe bandwidth,the more noise and error will be introduced, and resolution will also be affected.

Different application scenarios require selecting different probe bandwidths.

When testing digital signals, a probe with high bandwidth and short rise time should be selected, whereas when testing high-speed analog signals, a probe with higher bandwidth is required.

As is well known, double-pulse testing is currently the best means of characterizing the dynamic parameters of third-generation semiconductor SiC/GaN devices, in which the optically isolated probe is the best solution for voltage measurement, and its most prominent feature is high bandwidth. Currently, PMK optically isolated probes achieve bandwidths of 1 GHz and even 1.5 GHz to meet the measurement requirements of high-speed signals.。

 In summary, when selecting probe bandwidth, the frequency range of the signal under test, measurement accuracy requirements, cost budget, and actual application scenario should be comprehensively considered to achieve the best measurement results and cost control.

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