Signal Conditioning and Processing

[Stickly Mephisto]

Homework Statement

I've been given a small challenge having been shown a some waveforms and a bit of data. I am very new to this area but I must utilise DSP to condition and process an analogue voltage measurement. I don't know what the waveforms are from and I wasn't told so that I couldn't just search it.

What I'm attemtpting to digitise is a pulsed sinusoid. I'll add a couple of drawings to this post to show what I'm trying to explain. But I have a variable duty ratio, frequency and voltage depending on the impedance of the purely resistive load. These waveforms can also be combined for intermediate effects on the load. However, I'm most interested in the voltage and frequency properties.

I have a voltage range of about 500μV to 1.5V. Combined with a frequency range of 50 Hz to about 12 Mhz. So, I think my teacher want me to apprecciate the difficulties of having such wide ranges of operation. I need to digitise this analogue measurement so that I can find RMS values, peak values and such.

Relevant Equations

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I'm thinking that I am going to need something like a low pass filter around 100 Hz so that low noise disturbances from a nearby PSU and such won't disturb my sampling. However, the unit will have to operate around 50 Hz sometimes. Is it possible to use a Fast Fourier Transform to filter out frequencies below 100 Hz most of the time, but then simply "disable" this when measurements dip below 100 Hz? And if so, assuming the frequency is low and say my voltage is low, what is the optimal way to filter out this gaussian noise when the noise and measurement magnitudes and frequencies are somewhat comparable but signal remains dominant.

Then in terms of my ADC, given the voltage ratio of something like 3000:1, does this just mean that I will need to adjust the number of bits to limit my quantisation error for voltage but if I want something like a max of 1% error, I have to compare this to my minimum measurement and then re-evaluate as necessary? But for low voltage values I think I need to consider minimum voltage for ADC, so I may need to boost the voltage.

Apologies if anything is unclear or simply incorrect. I have only done very basic signal conditioning and processing but I want to learn more. So, if you feel redirecting me to a link on theory will be most beneficial, that is fine. Thank you.

 

[berkeman]

Welcome to the PF.

I have a voltage range of about 500μV to 1.5V. Combined with a frequency range of 50 Hz to about 12 Mhz. So, I think my teacher want me to apprecciate the difficulties of having such wide ranges of operation. I need to digitise this analogue measurement so that I can find RMS values, peak values and such.

So what sampling frequency do you plan on using? And how much memory will you need to use per sampled waveform to span that wide frequency range?

Are you allowed to use variable gain stage ahead of the ADC? If so, how will you know what the amplitude of the incoming signal is? How quickly can the amplitude change? Or is it confined to a narrower range of amplitudes for each waveform that you need to digitize?

Is this a paper exercise, or will you be designing and building the sampling circuit and testing it on waveforms? If you will be testing on real waveforms, will you use an Arbitrary Waveform Generator (AWG) like an HP 33120 to download/generate the waveforms?

https://www.used-line.com/images/11/14111.jpg

 

[Stickly Mephisto]

Hi! Thank you
It's a paper exercise but I think I'm going to need to come up with a block diagram or maybe a basic circuit with specific values. I'll email and ask. Even if not I think it would be good practice.

So what sampling frequency do you plan on using? And how much memory will you need to use per sampled waveform to span that wide frequency range?

Nyquist's theorem dictates that we require a sampling frequency of at least twice that of the signal in order to recover it. So I would need 24 Mhz sampling. Memory wise. If, for example, I had a 12 bit quantisation stage (which I'm pretty sure is not suitable but we can get to that) then that would be 12 bits multiplyed by my sampling frequency of 24 Mhz multiplied by my time period ( 1 / f_wave ). So per time period of my waveform pulse that's about 36MB/s multipled by whatever the time period (s). At least that's my reasoning.

Are you allowed to use variable gain stage ahead of the ADC? If so, how will you know what the amplitude of the incoming signal is? How quickly can the amplitude change? Or is it confined to a narrower range of amplitudes for each waveform that you need to digitize?

I would imagine so. Okay. So, I'll assume I can use a Programmable Gain Amplifier so I ensure it can operate within the correct voltage for the ADC. But this would need to relay the applied gain so that it can be attenuated correctly later. And I'm not sure how I could figure out the gain to be applied. Could you have two measurements or two circuits where one lags the other? Then feed back into the PGA and other components the required gain. Then it can pass through ADC properly before being attenuated back to correct reading.

For the waveform amplitude variabilty, I think I can assume that each pulse varies a little, but successive pulses can vary greatly. So, that gives me approximately the time period to feedback any gain changes I presume

 

[berkeman]

This is a pretty non-trivial system design, IMO. What year EE class is this for?

Most of your initial reasoning seems okay to me. I didn't check the numbers closely, but you seem to be approaching it in a reasonable way. Here are a few things that come to mind...

• Be sure to factor in your anti-alias filter characteristics in your sampling frequency choice. The polynomial that you use for that analog filter and the order of the filter will change how high you want your sample rate. You also need to factor in the accuracy you want (12 bits?) to be sure that aliasing doesn't distort your digitized waveform in a way that impacts your accuracy.

• Another option in choosing the sample rate is to oversample by a significant ratio, and use the extra samples to help you improve the effected number of bits (ENOB) of your digitizing system. We used this trick in a project that I'm currently working on to increase our 8-bit ADC resolution to an effective 12-bit resolution. See this link for related info: https://www.picotech.com/library/oscilloscopes/resolution-enhancement

• If your input signal can vary in amplitude significantly from one packet/waveform to the next, that presents a big challenge in the acquisition circuit design. If you can throw away the first part of the signal to determine the amplitude range, and set your VGA according to that and acquire the rest of the signal and get what you want, that is not too bad. Many radio circuits work like that, where the AGC amp has a fast attack and slow change rate after the start of acquisition. If you truly are being presented with waveform bursts that vary significantly in amplitude and you need to acquire the whole signal, then you might have to consider using several duplicated receive circuits in parallel set to different input gains. You would acquire all of them at once, and then determine which one gave you the best signal amplitude without clipping. Another alternative might be some sort of non-linear amplitude compression circuit outside, and then you un-compress the data digitally in your later processing. (see what I mean about a challenging project?)

• I'd recommend looking through some higher-end oscilloscope datasheets to get a feel for the kind of sample rates, input bandwidths and acquisition memory depths they offer. I know that at my work, for some of the network transceivers that we design and work on, we had to buy some very specialized oscilloscopes to allow us to capture the network waveforms with high fidelity and long acquisition times (our packets can get quite long). Maybe start at this Tektronix web page and then branch out to other brands and models of 'scopes (full disclosure -- I worked for Tek for one summer during my undergrad): https://www.tek.com/choose-tek-scopes