Reconstruction Filter

[viki2000]

I need to generate a rectified sinewave 1Vpp 100Hz using MCP4725 and lookup table.
The PIC is PIC16F1825 working at 32MHz.

The values for lookup table we can generate either using next page:
http://www.daycounter.com/Calculators/Sine-Generator-Calculator.phtml
or, as I prefer, using next software Smart Sine:
http://tahmidmc.blogspot.de/2012/10/smart-sine-software-to-generate-sine.html
I used next code:

[Ttelmah]

Your basic synthesis is fine. It's just the numbers being used that are wrong.

What you have is the +ve half cycles of a sine wave, going from 0 to 1v being repeated. Your sine wave needs to have your existing data, halved in amplitude, but added to your half level output value, for half a cycle, then subtracted from the same value for the next half cycle.
The step size will then be half what it currently is.
The glitches are almost certainly digital noise, which means you need to improve layout/grounding.

Then I2C above 400KHz, really requires an active terminator. You are 'pushing it' at 600K. Your 'nop' section is pointless. This is why CCS has 'delay_cycles'.

Then just add a little analog filtering.

[asmboy]

a 45 point "1 degree"
or 90 point 1/2 degree
lookup table would do nice enough sine waves
with some analog magic:

[temtronic]

Don Lancaster once wrote about 'Magic Sinewaves', that HAS to be on the Net 'somewhere'.....

[viki2000]

@Ttelmah
I have read your recommendations several times, but I am not sure I understand them all as you meant.
Especially this:

[Ttelmah]

You are actually generating this:

<http://www.kpap.net/notes/item.php?id=RMSSinusoidSegments>

Look at the second diagram down the page. You have the values for a half wave, going from 0 to 1v, and are repeating these.

To generate a full wave the same amplitude, you need to halve the amplitude of your waveform, then offset these values 'up' by half a volt (so these now go from half a volt to one volt), for one half cyle, then use the same value again, but now take them away from the half volt value.

On the pull-ups, do what they say and read the high speed mode documentation. HS mode, actually requires both devices to support it, and has a current source pull-up (not a simple resistor).

<https://www.i2c-bus.org/highspeed/>

The PIC actually has sufficient drive to operate high speed busses up to perhaps 1.5Mb/s, but to get reliability over 400Kb/sec, you do need the active pull-ups.
You also have to re-program the I2C interface to alter how clock stretching is handled, but this works OK with a PIC as master.

[viki2000]

This is where I do understand what do you mean:

[Ttelmah]

OK. I couldn't see why anyone would want to synthesise a rectified waveform. Everything 'using' synthesised waveforms normally want a full wave.
In which case your synthesis is fine, so just add a low pass filter to get rid of the HF.

[viki2000]

I wanted a smaller step size. I had in mind either a good reconstruction filter or to enlarge the lookup table, but that would imply higher speed on I2C.
From here all my questions.

I have tried simple low pass RC filter with R=1K and C=150nF.
The improvement is minimal, almost not observable.
Then I tried a 2 poles low pass Sallen key filter (http://www.calculatoredge.com/electronics/sk%20low%20pass.htm) with Ra=Rb=24K and Ca=10nF and Cb=4.7nF, one after another and works better, still not good enough.
I can provide oscilloscope screenshots with the real device, because simulation software is nice but do not reflect the reality always.
I have 170 points in my look-up table. It should be enough.
For example here he has less points (only 50) and higher frequency:
http://www.romanblack.com/onesec/Sine1kHz.htm
and he uses only RC or RLC filters.
He is then speaking about “natural sampling” instead of “regular sampling” and with that “natural sampling” he says reduces the THD with practically zero 2nd harmonic distortion.
I do not understand how he calculated the numbers in the lookup table to achieve that.

Do you have any idea how to generate the lookup table numbers for any given sine-wave in order to achieve that? If you know how, can you explain it with the waveform above 100Hz full rectified sine?

[RF_Developer]

I'm with Ttelmah in not understanding why you need a rectified sine wave. It creates a lot of problems, and I can see almost no applications where it would be useful.

To synthesize a sine wave, recitfied or ordinary, you only need one quadrant of value - a quarter of a full sine wave, generally the first. The other three can very easily be produced by reading out the first quadrant values in reverse order and/or making them negative.
In your case all you need to do is start at the first point, read out one by one till the end of the first quadrant, then go back again, over and over.

If speed is what you are worried about, it would be best to use a pointer to access the table, incrementing it in the first quadrant, then decrementing it for the second. This saves the overhead that is associated with indexing into arrays.

As to improving the quality of the output; your rectified wave causes a bit of a problem. In the eaxmple you've just given, the RC filter is almost certainly (I've not run the numbers...) arranged to filter out most frequencies above 1kHz, including the second harmonic. This is okay for a fixed frequency, but is no good in the general case in which most DACs work, i.e. with arbitrary waveforms. You might think you've only got 100Hz to deal with, but in fact your rectification means that there is massive amount of harmonics in your desired signal, especially second.

Also, such a filter, as can be seen in that example, has considerable delay, making timing/phase control difficult.

I do not, off hand, know the harmonic/spectral content of a rectified sine wave, but its going to be "fun", to say the least. If you filter as aggressively as in that example, i.e. filtering out everything except the fundamental, then that's what you'll end up with: a sine wave at 100Hz! A typical reconstruction filter for general use is usually arranged to filter out every thing above and including the sampling frequency, i.e. your DAC update frequency, leaving the desired waveshape pretty much intact. Even with a pure nyquist reconstruction filter, i.e. one that cuts out everything above fsamp/2, which is really not practical, your signal will not get down to zero. That null point will get somewhat flattened out.

So, it comes down to why you need this easy to generate, but rather unusual signal, and to what the signal purity requirement really is. Do you have any defined requirements? If not, then you probably don't need it to be all that good, and what you have may met you needs.

[viki2000]

@RF_Developer
Thank you for your thoughts.
I will try to answer to your questions/suggestions

[Ttelmah]

First thing to comment. If this is meant to simulate something receiving rectified mains, this will _not_ be even remotely close to a pure half sine wave. First, unless a precision rectifier is being used, there will be a glitch at the bottom of the waveforms, from the diode offsets. Then mains itself is full of awful spikes and harmonics. The IEEE specifications define that THD should be less than 5% typically at the entry to the property, but inside the building levels will often be far worse, with other types of interference as well. If you are trying to simulate mains behaviour, you should actually be making the signal more noisy, not less...

Put a scope on the 'real' signal....

On the filter, if you look at your signal, there is a fundamental at perhaps 4* the sample frequency (probably digital noise). Look at how the signal is reconstructed from CD's. The good systems use rejection filters at the harmonics of the sampling frequency, to avoid the sort of problems you are seeing.
However I repeat my comment about solving this 'at source'. It's almost certainly a sign of poor layout, with either a digital ground that is drawing current 'across' a section of analog circuitry, or a digital track passing close to analog without a ground between. It looks as if it occurs for each byte in the transmission, so possibly the ACK bit.

[RF_Developer]

[viki2000]

@Ttelmah
I understand your explanation about a real mains, but is not important to me now. I would like to emulate nice sine waves without noise. The real device has been tested according with all the necessary IEC norms and EMC Directive by a accredited test house and passed all the requirements. I only want to provide a rectified sine wave to test certain functionality of the device. I need it clean, I do not care about the dirty reality.
One thing for sure, you are right with the noise. I will try to make a proper layout on a test PCB. Right now I do fast tests, in between other tasks when I have time, and I just tested on a simple breadboard, so no wonder of the noise.

@RF_Developer
After a proper circuit layout, I will try once again some simple RC filters as you suggested, maybe 2-3 stages as Roman Black.
As for “natural sampling” I will dig more in his words, where he provided also an example for Excel. The idea is to choose the numbers in the lookup table in such way to get rid of some harmonics, but you say I need them. Well, I can measure them now, then with a filter and then with some “natural sampling” numbers, then I compare and I see the result.
You say

[Ttelmah]

If you look at the spikes, there are two parts to them. The first is overshoot on the DAC itself. The second is three spikes along each 'flat'. Now the latter I suspect good design will largely remove. The former, you may have to improve with filtering. Your filtering should be on the harmonics of the DAC rate, not the waveform rate. (though they are related, the DAC ones are at much higher frequencies). The odd harmonics of the waveform rate must be left largely unfiltered to give the sharp transition at 9v.