While I was studying for my exam I saw this question where he's given me a bunch of ADCs asking me which would work and which wouldn't He's given me the Minimum required Precision for the ADC and I don't really know what to do with it, to convert it into a value that I can compare it with something else
For resolution and accuracy defined by %x the Vref does not matter as the signal may be scaled from +/-10V to match Vref for bipolar and Vref/2 for unipolar.
Sampling rate must be > 2x fmax. This rules out (1),(2) next (3),4) at 1kHz
For sampling rate fs= 1kHz and fmax-478Hz fmax/fs = 0.478
- attenuation at 478 Hz must be <4% = -28dB
- or >0.96 of flat response or 0.35dB error in passband
- and bandstop at 1/2 of fs must be > -28dB for 4% accuracy Since 500Hz/478 = 1.046 the stop band is >-28dB @ 500Hz with < -0.35dB at 478Hz which is possible a 10th order filter.
Yet the resolution needed is 1% or 100:1 and 7 bit has a quantization error of 1/128 makes it possible yet harder to design a brick wall filter that has no group delay at 0.96 of the f-3dB breakpoint unless you have more resolution.
That rules out (4) as practical
But with extra resolution , of 9 bits then allowance for filter accuracy with have an N order LPF to reject aliasing noise that affects accuracy.
This so-called Nyquist filter may have a Bessel Filter for a maximally group delay or a linear phase response to say -12dB so that signals at fmax are not distorted by phase. In order to reject the alias below x% the filter order N must be such that at N*-3dB per half octave.
- An octave is 2f or 20log2=6dB/oct per order
- And this is 500/478Hz= 1.046 f is 4.6% of an octave implying something on the order of 1/0.046 = a 20th order filter ballpark or better with FIR methods.
This makes (3) the only possible but not easy solution.
Sampling at less than twice the highest frequency will cause aliasing therefore 1 and 2 can be discounted. The signal has a peak amplitude of 10 volts and this means that the remaining ADC that should successfully work is item 4 because it has a Vref of 10 volts.
Having said that I've come across ADC's whose maximum range is twice the ADC reference voltage.
Also, because the input signal falls below 0 volts you have to assume that the ADC can handle fully bipolar signal inputs.
I want to add some information as per my experience.
As you need the minimum resolution of 1% which can only be achieved by using the 1st option with 10bit. Now as per the nyquist criteria to prevent aliasing of sampled signal your sampling frequency is less than the twice of signal frequency.
So I would suggest you to use the 4th option which is SAR ADC by which you can achieve the required sampling freqency. But as the 4th option has lower bit i.e 7 bit which can you you the resolution of 7.8%. Now to achieve the higher resolution you need to do the oversampling and averaging.
Which means you have to take more samples at the same point and then average them.