filterfrequencylow pass
A section of a circuit I'm working with makes a sinusoid from a square wave by passing it through an 8th order filter (MAX293). Up until now, everything was ok, but I was told recently that the input (square wave) and output (sinusoid) have to be in phase. Because of the LPF, it adds a phase shift and because the input frequency is variable (0-5khz), the phase shift is also variable.
How can I keep them in phase for the entire frequency region they operate at ? What should I be looking at ?
The -3dB point is your cutoff frequency. It's just standard practice to define it that way. In order to find what your values should be, I'd go with equal element implementation (it's simpler, and you can correct for gain with a simple gain stage later if you need to). Choose R1=R2, C1=C2, and pick a value for either R or C. This yields the following formula for the cutoff frequency: $$f_0=\frac{1}{2\pi RC}$$ I generally choose a value of C initially, as it's easier to find or make a resistor with a strange value, whereas it's more difficult with capacitors. So, set your cutoff frequency equal to f0, and solve for R.
Here's an example: let's say I want a LPF with f0=250 Hz. I'll choose C to be 0.1 micro and solve for R. $$250=\frac{1}{2\pi RC} \rightarrow 250=\frac{1}{2\pi R(0.1x10^{-6})}\rightarrow R\approx6400\Omega.$$
From there, all you need to do is implement your circuit. Once you know what your value for R is supposed to be, you can use a dual-channel potentiometer that has the correct resistance within it's range in place of the two resistors (for the above example, something like a 10k ohm potentiometer would do the trick). This will allow you to change your cutoff frequency, since it's based upon both R and C.
Edit: As Matt Young suggested in the comments, adding a resistor in series with the potentiometer will set the maximum cutoff, and prevent shorts. It's an excellent addition to the circuit, and will keep some sanity when adding the potentiometers.
If you are not very close to the sampling frequency you can assume that the output amplitude from the DAC pretty much represents the input amplitude - this means that the low pass filter you wish to design (if a 1st order) would be based on a resistor feeding a capacitor to ground and the filtered output taken from the capacitor. The 3dB point of the filter is: -
\$f_C = \dfrac{1}{2\pi RC}\$ so...
Plug 20,000 Hz into the formula and maybe 1000 ohms and see what value capacitor you get. For higher order filters I'd use a 2nd order sallen-key calculator like from here - it's a good site and I trust it for coming up with the goods.
You do need to be aware of the problems if the highest frequency you want to produce is greater than a fifth of the sampling frequency - this will cause an amplitude error and you may want to "straighten" this out with a little bit of high pass filtering to. Here is an explanation and below is the formula that you need to worry about when compensating: -
It describes how the amplitude tails off as the input frequency gets closer to the sampling frequency.
Best Answer
You have two options apart from the PLL (which may or may not meet your requirements : there will inevitably be delays between input and output if the frequency changes, while the PLL settles to the new frequency. Given the comments, a PLL capable of tracking down to 0.1Hz will be quite a beast to get right)
1) Delay the input signal in the same manner that the filter delays the output.
This is easier if the filter is a linear phase filter such as a Bessel, or you can use digital filters such as an FIR filter, and a matching digital delay.
It's not impossible otherwise : you can design an "all pass network" aka "group delay equaliser" with the same delay characteristics (phase response) as the filter : however after this, the square wave will generally no longer be a square wave. Whether that matters or not I can't say, I don't know the application.
Given a linear phase filter, the group delay equaliser should be relatively simple and preserve the square wave.
2) Generate one waveform from the other without filtering.
It is possible to generate a triangle waveform from a square by integration (this generates a 90 degree phase shift so you may need to generate two square waves in quadrature). From the triangle, you can use a non-linear network (resistors and diodes, as a "soft clipper) to approximate a sine wave. Better that 2% harmonic content is possible : see the "ICL8038" for an old example of this technique. This only works well if the square wave amplitude is constant.
But it's much simpler to generate a square from a sine, if your application permits...