Monday, October 10, 2011

Determining How Much Oscilloscope Bandwidth is Needed to Accurately Capture a Signal

If you input a 100 MHz sine wave with a 1 Vpp amplitude into an oscilloscope with a max frequency of 100 MHz what will you see on the display? You will still see a 100 MHz sine wave, but it will no longer by 1 Vpp. Instead the measured amplitude will be about 700 mVpp. That is because the max frequency rating of a scope is its 3 dB roll off point, just like how a low pass filter is rated. That means any frequency components at the scope's max frequency will be attenuated 3 dB or 30%. For non-sine wave signals used at the a scope's upper frequency limits the result is even worse because entire frequency components can be eliminated. The figures below show a 100 MHz scope and a 500 MHz scope both measuring the same 100 MHz digital clock signal.
100 MHz Scope Measuring 100 MHz Digital Clock
500 MHz Scope Measuring 100 MHz Digital Clock

In the 100 MHz scope screen shot you can see that all frequency components that make up the digital square wave have been attenuated except for the center frequency. In the bottom 500 MHz scope screen shot we get a much better picture of what the clock signal really looks like. The following are good rules of thumb when determining how much scope bandwidth you need to accurately capture a signal:

  • For analog signals choose a scope bandwidth that is at least 3 times larger then the center frequency of the signal.
  • For square or pulse type waveforms choose a scope bandwidth that is at least 5 times larger then the center frequency of the signal. This will ensure you capture up to the 5th harmonic of the signal.
The two most common types of responses that scope's have at their max frequency are Gaussian response and Maximally-Flat response, which are both shown below.
Scopes with frequency ranges 1 GHz or below typically have the Gaussian response and high bandwidth scopes typically have the Maximally-Flat response. With knowledge of the response of your scope there is a much more accurate calculation you can perform to determine the scope bandwidth needed to measure a digital signal. The first step is to determine the maximum practical frequency component within the signal under test. We refer to this frequency component as fknee. Dr. Howard W. Johnson has written a book on this topic titled, “High-speed Digital Design – A Handbook of Black Magic ”. All fast rising edges have an infinite spectrum of frequency components. However, there is an inflection (or “knee”) in the frequency spectrum of fast edges where frequency components higher than fknee are insignificant in determining the shape of the signal. For digital signals with rise time characteristics based on 10% to 90% thresholds, fknee is equal to 0.5 divided by the rise time of the signal: 
fKnee = 0.5/RT (10% - 90%)

The next step is to determine the required bandwidth of the oscilloscope to measure this signal. The table below shows multiplying factors for various degrees of accuracy for scopes with a Gaussian or a Maximally-Flat frequency response.

This calculation has nothing to do with the frequency or clock rate of your signal, just the rise time. Let's walk through an example with a Gaussian Response scope measuring a signal with a 1 ns rise time and we want 3% accuracy or better. Using the "fknee" calculation above, the highest frequency component (fknee) would be 500 MHz. From the table above, to achieve 3% accuracy or better we need a scope with a max range of at least 950 MHz. For the example we just did the clock rate of the digital signal could have been 100 MHz or 500 MHz, it doesn't matter the rise time is what determined the bandwidth needed.

One last note, don't forget to check/consider the bandwidth of the cabling or probe you are using along with the connection method to the signal!


10 comments:

  1. Wow, that means that in order to measure a pentium 4 at 3.2Ghz I would need .... a 16Ghz scope haha. Kind of hard to lay my hands on one of those :S

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  2. Yeah wideband scopes are not cheap!

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  3. On the other hand, the external clock on a Pentium 4 is only 200 MHz (http://www.hardwaresecrets.com/dictionary/term/342). You can't access the internal clock.

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  4. This comment has been removed by the author.

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