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# Sensor bandwidth vs sampling rate

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#### VirusX2

##### Member level 4
Say i have a (current) sensor with 50kHz bandwidth, i think that means that the maximum freq of the input that can pass to the output is 50kHz? Am i right?

Secondly, lets say i want to drive the output of the sensor to an ADC. How does the sampling rate (ksps) be connected with the bandwidth of the sensor? Can i use a sampling rate of 50kSPS, less, more? Can anyone explain please?

#### KlausST

##### Super Moderator
Staff member
Hi,

bandwith often is defined by the -3dB limit.
Means the sensor may ouput higher frequencies but with reduced amplitude.
A detailed reading of the datasheet is important.

Sampling frequency vs signal frequency is well documented and very often discussed. Read about "nyquist criterion".
If you violate nyquist criterion you risk to get "alias frequencies" which can not be suppressed on the digital side.

Klaus

You can always consider equivalent time sampling depending on what you
are looking for in the sample set. If you care about trend over time, called
equivalent time sampling, repetitive signals only, can be used to get around
Nyquist.

If on the other hand what you care about is each and every individual sample, eg.
some specific per sample measurement, you have to meet Nyquist.

Regards, Dana.

### VirusX2

Points: 2

#### crutschow

Say i have a (current) sensor with 50kHz bandwidth, i think that means that the maximum freq of the input that can pass to the output is 50kHz?
It's not a brick wall frequency, it is generally the frequency where the response drops by -3dB.
i want to drive the output of the sensor to an ADC. How does the sampling rate (ksps) be connected with the bandwidth of the sensor? Can i use a sampling rate of 50kSPS, less, more?
The sampling rate is determined by the highest signal frequency you want to capture by the ADC.
If you want the full 50kHz of the sensor response, then the Nyquist sampling criteria states that the sampling rate needs to be a least double the highest frequency of interest or 100kHz here (in practice more than double is used to minimize filtering requirements and aliasing).

To minimize any aliased signal and noise, the signal into the ADC should be well low-pass filtered above the desired maximum.

### VirusX2

Points: 2

#### VirusX2

##### Member level 4
Alright so if i dont want to use the full 50khz bandwidth but i want to monitor an input signal say 1khz, i have to use a sampling rate of >=3ksps?

What test are you making on each sample ? What do you care about, its peak value,
or RMS, or what ? What type of signal is it, random, or continuous.....?

Regards, Dana.

#### KlausST

##### Super Moderator
Staff member
Hi,

some pedantic details:
The sampling frequency needs to be higher than 2 * signal frequency.
* Signal 1kHz, sampling frequency 2kHz --> no meaningful results
* Signal 1kHz, sampling frequency 2001Hz --> you need to perform an RMS calculation over 2000 samples to get meaningful result
* Signal 1kHz, sampling frequency 2010Hz -->you need to perform an RMS calculation over 200 samples to get meaningful result

If you´re interested in frequencies up to 1kHz you may use 3kHz sampling frequency. So far so good.
(only 3 samples are sufficient to perfectly reproduce the 1kHz amplitude)
But you additionally need to suppress all frequencies above 1500Hz in a way that their amplitudes are very low.
All frequencies above 1500Hz will create alias frequencies with the same amplitude as the original frequencies.
Example: Original 2500Hz, 0.1V amplitude will cause an alias frequency of 500Hz with 0.1V amplitude.
Thus you need to suppress this 2500Hz signal.

The closer you get to the nyquist criterion the more complicated it becomes. Complicated (high order) filters which cause amplitude variations, phase shift...

The higher the sampling frequency referenced to the max. frequency of interest, the more relaxed.

Klaus

#### crutschow

The higher the sampling frequency referenced to the max. frequency of interest, the more relaxed.
Also, a high sample frequency relative to the highest signal frequency of interest allows you to digital filter any noise that isn't aliased.
Thus sigma-delta converters, that use a very high sample frequency, generally need only a simple (one-pole) anti-alias filter at the input.

VirusX2

### KlausST

Points: 2

#### VirusX2

##### Member level 4
The sampling frequency needs to be higher than 2 * signal frequency.
* Signal 1kHz, sampling frequency 2kHz --> no meaningful results
* Signal 1kHz, sampling frequency 2001Hz --> you need to perform an RMS calculation over 2000 samples to get meaningful result
* Signal 1kHz, sampling frequency 2010Hz -->you need to perform an RMS calculation over 200 samples to get meaningful result

If you´re interested in frequencies up to 1kHz you may use 3kHz sampling frequency. So far so good.
(only 3 samples are sufficient to perfectly reproduce the 1kHz amplitude)
But you additionally need to suppress all frequencies above 1500Hz in a way that their amplitudes are very low.
All frequencies above 1500Hz will create alias frequencies with the same amplitude as the original frequencies.
Example: Original 2500Hz, 0.1V amplitude will cause an alias frequency of 500Hz with 0.1V amplitude.
Thus you need to suppress this 2500Hz signal.

I need to data log and reproduce the waveform, not the rms value. Also while the freq of the signal i am logging say be 1khz, transients may occur at high freq and i want to capture those transients.

#### KlausST

##### Super Moderator
Staff member
Hi,

If you are interested in the high frequency of transients, then this is belongs to the "frequency range of interest".

Klaus

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