What bandwidth should your scope and scope probe have? When do you have to worry about “high frequency” effects? This is basic theory relating the time and frequency domains, but too often people quote rules of thumb that, while strictly accurate, are very misleading. Typical misleading statements are:
- the scope’s bandwidth should be at least 5 times the frequency, so you can see a reasonable waveform
- I only have a 1kHz (i.e. 1ms period) signal, which isn’t high frequency (certainly not RF), and an audio frequency scope is sufficient
This post is a basic illustration of the “maximum frequency” in a 1kHz signal, to help dispel some misconceptions.
The “5* frequency” statement is vaguely true, but only for square waves with a 50% duty cycle. However, digital signals rarely have a 50% duty cycle.
The “1kHz isn’t high frequency” is simply wrong. The digital circuits only “care” about the time domain relationships between various signals, principally expressed in the form of maximum frequencies, minimum setup/hold time (typically ns). Basically the circuits neither “know” nor “care” when the next transition will occur, provided the setup/hold times are observed; that intuitively implies:
- the frequency/period is not very important
- the rise/fall times are important, since they are closely related to the setup and hold times
and it is the rise and fall times that determine the high frequency content. For further information, including measurements of a signal from modern jellybean logic, see my earlier post Measuring Digital Signal Edge Speeds Without An Oscilloscope. The useful rule of thumb is that the required bandwidth is BW=0.35/t, where t is the rise/fall time.
So, what is the “maximum frequency” in a 1kHz signal? Three different 1kHz signals are illustrated below:
- a 1kHz square wave with 120μs rise and fall times – the baseline for comparisons
- a 1kHz square wave with 120ns rise and fall times – representative of a 1kHz digital clock signal
- a 1kHz signal with a width of 10μs (1% duty cycle), 120ns rise and fall times – representative of a general digital signal
Those parameters were chosen simply so they could be conveniently generated by a Tektronix 115 pulse generator, and measured with a Digilent Analog Discovery scope and spectrum analyser. The latter, although not fast, does have a 14bit ADC which enables lower signal levels to be measured.
This first “baseline” waveform could be reasonably approximated on a scope with a 5kHz bandwidth, since it has very slow rise and fall times. The frequency domain graph shows the power in the fundamental is ~4dBV, and nothing measurable above 100kHz: the horizontal line above 100kHz is simply the noise floor of the analyser at ~-72dBV.
This “digital clock” waveform is identical except that the rise/fall times are 120ns, not 120μs. There is the same power in the fundamental, but importantly there is much larger (i.e. measurable) power above 100kHz, ~-58dBV at 1MHz.
This “digital signal” waveform also has 120ns rise/fall times but the duty cycle is low. There is the much less power in the fundamental, ~-27dBV, but importantly there is the same power above 100kHz.
That is a simple frequency domain illustration of why the period is unimportant, the “5* frequency” statement is usually wrong, and digital signal are really RF signals