Question on sampling rate? - Page 1
Forum section: electronics / beginners

author: rfengg
author_rank: Regular Contributor
timestamp: July 30, 2019, 12:01:31 am
content: My understanding of ADC's can be summarized on the left side of a grain of rice and hence this question.We have receiver chain designed by an external company in which the input frequency can be between 117-119MHz and the sampling frequency of the ADC after a low noise amplifier is 80MHz.I know that this system works fine though the signal is under-sampled.What I am not able to get my head around is, that though the bandwidth of the signal after the LNA is only 2MHz, how can a 80MHz sampling rate, faithfully reproduce a signal which is much higher?If I assume for the sake of argument, the signal is at a constant frequency of 118Mhz, how can a 80MHz sampling rate, correctly reproduce a 118MHz signal?

author: rstofer
author_rank: Super Contributor
timestamp: July 30, 2019, 12:31:06 am
content: Look up equivalent time sampling. As long as the signal is repetitive, the scheme works. It has been used on scopes forever, more or less.

author: radiolistener
author_rank: Super Contributor
timestamp: July 30, 2019, 01:12:34 am
content: when you capture signal with ADC which working at sampling frequency Fs, it can capture just Fs/2 bandwidth. All frequencies above Fs/2 will be folded into 0...Fs/2 range. The border Fs/2 works like mirror, it mirrors all frequencies back into Fs/2 range.So, you can receive images from Fs/2...Fs range as Fs/2...0 range signal. In order to receive signals above Fs/2, you're needs to remove 0...Fs/2 range from the input signal with analog filter placed before ADC. Otherwise it will be merged with Fs/2...Fs signal.In your case, ADC works at 80 MHz, it means that it can capture 40 MHz bandwidth:- Frequency range 40...80 MHz will be mapped on ADC bandwidth as 40...0 MHz- Frequency range 80...120 MHz will be mapped on ADC bandwidth as 0...40 MHz- Frequency range 120...160 MHz will be mapped on ADC bandwidth as 40...0 MHz- etc...Your 117-119 MHz range will be captured by ADC as 37...39 MHz. In order to prevent merging with real 37...39 MHz, the real 37...39 frequencies should be removed from input signal with filter. The same you're needs to remove 43...41 MHz range because it also will be mapped to 37...39 MHz.So, you're needs to put BPF (band pass filter) before ADC. This BPF should pass just 117...119 MHz range and cut off all other frequencies. After that you can get 117...119 MHz range as 37..39 MHz range on 80 MHz ADC output...PS: by the way, 80 MHz is not a good choice for 117...119 MHz, because this frequency range will be mapped to 37...39 MHz, it's too close to the 40 MHz border. It's better to keep frequency of interest at the center of ADC bandwith, it will allows to use bandpass filter with more smooth slopes. 70 MHz will be better choice, because ADC with 70 MHz sample rate will capture 35 MHz bandwidth and 117..119 MHz range will be mapped to 12...14 MHz. So, you can use 0..12 MHz (105...117) and 14...35 MHz (119...140) for slopes of bandpass filter.

author: rfengg
author_rank: Regular Contributor
timestamp: July 30, 2019, 06:53:49 am
content: Quote from: rstofer on July 30, 2019, 12:31:06 amThanks rstofer, but the signal into the LNA is quite random and not periodic as in scopes.

author: oPossum
author_rank: Super Contributor
timestamp: July 30, 2019, 06:58:44 am
content: I think the correct term is sub-nyquist sampling, not equivalent time sampling.

author: David Hess
author_rank: Super Contributor
timestamp: July 30, 2019, 10:47:47 pm
content: The Nyquist frequency relates to the *bandwidth* which can be faithfully reproduced and *not* the maximum frequency. So like radiolistener says, 80 MS/s is plenty to faithfully reproduce a 117 to 119 MHz signal assuming that the analog input bandwidth of the ADC is sufficient.Not all ADCs support under-sampling and in the past, it was common to place a high bandwidth sampler in front of the ADC to extend its bandwidth. This provides a useful model of what is actually going on; the sampling process converts the bandwidth limited signal to the baseband where the ADC can see it just like a mixer would. Some samplers are simply mixers driven from a comb source and the same parts may be used.Another example would be digitizing a 10.7 MHz IF frequency which might have a bandwidth of only 15 or 30 kHz with a 250 kS/s ADC.

author: rfengg
author_rank: Regular Contributor
timestamp: July 31, 2019, 12:29:05 am
content: Another example would be digitizing a 10.7 MHz IF frequency which might have a bandwidth of only 15 or 30 kHz with a 250 kS/s ADC.Thanks David but that's exactly when I get confused when I think of a 10.7MHz signal with a bandwidth of 15 or 30khz being digitized at 250kS/s.If I think in time domain of a sine wave of say 10Mhz , the time period of that is 100ns.250kS/s is 0.25Samples/us or 0.025samples/100ns, right?So if we sample a 10Mhz signal with a period of 100ns at 0.025 samples for one time period, how can we accurately reproduce this waveform?

author: David Hess
author_rank: Super Contributor
timestamp: July 31, 2019, 02:15:12 am
content: That is why I suggested thinking of it in a different way.A sampler really is a special RF mixer and RF mixers can be used as samplers with some minor changes. The difference is that the local oscillator going to the sampler is an impulse instead of an RF sine or square wave. The impulse is an RF comb at the local oscillator frequency and every multiple.So the 250 kS/s "local oscillator" which is a series of impulses at 250 kHz actually contains harmonics of 250 kHz. They are *all* mixed with the 10.7 MHz IF and whatever signals are present show up at the output from DC to the Nyquist frequency. Since the IF filter is narrow, only those signals within the 15 kHz or 30 kHz or whatever bandwidth show up and they are comfortably within the Nyquist frequency so there are no aliasing issues. The sampler down-convertered the IF passband to frequencies below the Nyquist frequency of the ADC.