How to Determine the Optimum Bandwidth for Your Oscilloscope

Choosing the right oscilloscope for your testing and analysis needs is crucial. Oscilloscopes are one of the most used pieces of equipment in electric and electronic applications that involve testing, measurement, analysis, troubleshooting, characterization, and debugging. If chosen correctly, they can deliver outstanding performance and be extremely reliable. There are various types of digital oscilloscopes such as: 

  • Analog Oscilloscopes 
  • Digital Oscilloscopes
  • Digital Storage Oscilloscopes
  • Digital Phosphor Oscilloscopes
  • Mixed Domain Oscilloscopes
  • Mixed Signal Oscilloscopes
  • Digital Sampling Oscilloscopes
  • Handheld Oscilloscopes
  • Computer-Based Oscilloscopes

While comparing these, the first and most important factor taken into consideration is the oscilloscope’s bandwidth. Bandwidth is one of the key indicators of how well your oscilloscope can reproduce the actual nature of your waveforms. Optimum scope bandwidth means accurate and reliable measurement results, less operational costs, high efficiency, and hence, excellent performance. 

Optimum Bandwidth for Your Oscilloscope

The Importance of Oscilloscope Bandwidth – Why Does It Matter?

The lowest frequency at which the measured amplitude of a sine wave is 3 dB lower than the actual sine wave amplitude is considered as an oscilloscope’s bandwidth. At this frequency, the signal has roughly about 30% amplitude error. The combined effects of inductive reactance and capacitive reactance increase the impedance as the frequency increases, and this phenomenon limits the bandwidth. 

So, an oscilloscope with a bandwidth equal to the original signal frequency will produce inaccurate results. Hence, your scope bandwidth should be greater than the highest signal frequency to be measured. 

But that’s not it. Your oscilloscope probe’s maximum bandwidth should also match that of your oscilloscope because the same phenomenon applies to the probes as well. An oscilloscope with the right bandwidth and a probe with the wrong bandwidth will ultimately produce inaccurate results. In order to effectively capture signal frequencies and amplitude, it is critical to have optimum bandwidth for both the oscilloscope and its probes.  

How to Choose the Right Bandwidth for Analog and Digital Applications

Analog Applications

  • For testing and analysis in analog applications, remember the “3x rule”. Your oscilloscope’s bandwidth should be at least three times higher than the maximum signal frequency. 
  • The oscilloscope can measure analog signals accurately in the portion of the frequency band where it is still relatively flat with minimal attenuation. A well-designed oscilloscope should have virtually no attenuation (0 dB) at approximately one-third of the oscilloscope’s bandwidth. 
  • However, this bandwidth specification (3-dB attenuation frequency) may not necessarily be the same for the attenuation or amplification at other frequencies. So, before buying an oscilloscope, check its response flatness or run a swept frequency response test.

Digital Applications

  • For measuring digital signals, keep in mind the “5x rule”. Your oscilloscope’s bandwidth should be at least five times higher than the fastest digital clock rate in your device under test. 
  • An oscilloscope with this bandwidth can capture up to the fifth harmonic of your signal with minimum signal attenuation. The fifth harmonic is an important component because it helps determine the overall shape of your digital signals.
  • However, bandwidth is not the only parameter; other specifications such as the rise and fall times need to be considered while making accurate measurements on high-speed rising and falling edges. 

How to Calculate Oscilloscope Bandwidth

All oscilloscopes exhibit a low-pass frequency response that rolls off at higher frequencies. The frequency responses of oscilloscopes can be categorized into two types, namely the Gaussian response and the maximally-flat frequency response. 

Gaussian Response

Oscilloscopes with a Gaussian response exhibit a slow roll-off characteristic beginning at roughly one-third the -3dB frequency. 

Typically, oscilloscopes with bandwidth specifications of 1GHz and below shows a Gaussian-type response. 

Maximally-Flat Response

  • Oscilloscopes with maximally-flat frequency response usually exhibit a flatter in-band response with a sharper roll-off characteristic near the -3dB frequency.
  • Generally, oscilloscopes with bandwidth specifications greater than 1GHz have a maximally-flat frequency response. 

Whether your oscilloscope has a Gaussian response, maximally-flat response, or somewhere in between, the bandwidth can be calculated with the help of the rise time. Rise time is defined as the amount of time it takes for the signal to go from 10% to 90% of its maximum value. So, the first step is to know the rise time. 

For oscilloscopes with a Gaussian-type response, the rise time and bandwidth are related as:

Rise time = 0.35 / oscilloscope bandwidth (based on a 10- to 90-percent criterion)

For oscilloscopes with a maximally-flat response, the rise time and bandwidth are related as:

Rise time = 0.4 / oscilloscope bandwidth (based on the sharpness of the frequency roll-off characteristic)

The next step is to calculate the measurement error. Say you want to measure a signal of 100 MHz bandwidth, 3.5 ns rise time square wave with a 100 MHz bandwidth oscilloscope.

Rise time of the 100 MHz oscilloscope = 0.35/100 MHz = 3.5 ns

The rise time of input signal =  = 4.95 ns

Measurement error = (4.95 ns – 3.5 ns) / 3.5 ns = 0.414 = 41.4%

Now, on choosing an oscilloscope with a bandwidth 5 times higher than the signal frequency, the calculations are as follows:

Rise time of 500 MHZ oscilloscope = 0.35/500 MHz = 0.7 ns

Displayed signal rise time =  = 3.569 ns

Measurement error = (3.569 ns – 3.5 ns) / 3.5 ns = 0.0198 = 2%

From this, a formula can be generalized for determining the oscilloscope bandwidth.

Required oscilloscope bandwidth = the highest frequency component of the measured signal x 5

The measurement error of an oscilloscope using this formula is typically less than ± 2%, which is enough for most measurements.

BONUS: 3 Best Oscilloscopes Based on Their Bandwidth 

Siglent Technologies SDS1202X-E Digital Oscilloscope 

This is a 200 MHz digital oscilloscope with 2 channels and a sampling rate of 1 GSa/sec, and can store 14 million measurement points. 

Tektronix 1052B Digital Oscilloscope

This digital storage oscilloscope has a measurement bandwidth of 50 MHz. With 2 channels and an acquisition rate of up to 2GS/s, this oscilloscope can efficiently capture intermittent faults and monitor power supply stability over time.

Tektronix MDO3104 Mixed Domain Oscilloscope and Spectrum Analyzer

This Tektronix MDO3104 mixed domain oscilloscope has a bandwidth of 1 GHz and 4 analog channels. It also offers the functionalities of a spectrum analyzer, a waveform generator, a logic analyzer, a protocol analyzer, and a digital voltmeter/counter. 

Summary

In conclusion, the bandwidth of an oscilloscope is a significant figure of merit. Though not the only specification to be considered, it is one of the most important factors that contribute directly to the performance and measurement accuracy of the scope. 

Remember to choose the right bandwidth for both the oscilloscope and its probes. If your budget is flexible, investing in an oscilloscope with a little extra bandwidth can go a long way in ensuring both the accuracy and relevance of your scope for future test requirements. 

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