I am trying to work out the likely phase lag for a lowpass filter whose job is to take out the notches from a DAC.
The DAC is 12 bit and will be generating a 400Hz sinewave. It will be driven at around 250x i.e. 100kHz. So the fundamental to filter out will be 100kHz.
I am not good at maths but doing some digging around, it looks like a simple RC has a 45 deg phase shift at the 1/2piRC point, and somewhere around 1 degree when a factor of 100 away from that (40kHz).
I am happy with 1-2 degrees of lag, but more importantly it needs to be fairly constant from 400Hz to 500Hz, or at least quantifiable, because the table feeding the DAC can be shifted to compensate.
What about a 2nd order filter? The filter performance should be better for a given phase lag, no?
Obviously perfection is impossible to achieve but I think a 10kHz rolloff frequency would produce a really clean result. The Q is what delay can be achieved at that rolloff.
There is a huge amount of stuff online but a lot of it is the audio stuff, which is full of BS :)
On a sunny day (Thu, 11 Nov 2021 16:13:52 +0000) it happened Peter snipped-for-privacy@nospam9876.com wrote in <smjfg7$alv$ snipped-for-privacy@dont-email.me:
Thank you. That looks like both a 1st order and a 2nd order passive lowpass, with 40kHz values (10k/400pF etc) will achieve ~ 0.5 degree of phase shift.
Getting 1/2 of one LSB of 12 bits worth of rejection at 100kHz, -75dB, and meanwhile just 1 degree of phase lag at 400 Hz, is going to be a real challenge with only 2 poles I think, if I'm understanding their requirements correct.
So I think OP needs to specify how much fundamental rejection is acceptable or I think higher order than that will be needed.
My bad, neglect that, I'm thinking of PWM DACs! Just need to attenuate the sinc-weighted component of the switching frequency which will be pretty low, already.
Given a 12-bit DAC making a 500 Hz sine wave at 100K samples/second, it will look perfect on a scope, with no filter. It would look awfully good on a spectrum analyzer too. It doesn't need much filtering.
Good thing to Spice. I have a quantizer block around here somewhere.
In fact if you can clock at 250x but only need 400 Hz question is why you need a 12 bit DAC in the first place, you could do pretty good just by selectively knocking out harmonics before you even go analog e.g. this old chestnut:
What you want is a linear phase low pass filter. Williams and Taylor are a full bottle on the subject.
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This means that you get a smooth and monotonic transition between voltage steps. It doesn't roll off the high frequency content of the step edge all that fast - a higher order linear phase filter will do that better, but you need more precise reactance values to keep close enough to linear phase.
The two amplifier version of the Sallen-Keys 2-pole low pass filter lets you use the same value of capacitance in both the capacitors, and you can use E92 resistors to get very close to the linear-phase characteristic.
Why not use the signal to drive an AC motor and resistor to ground? The flywheel effect in the motor means the HF is blocked, so the resistor gets the LF signal relatively pure. Or use an iron wire instead of the motor, the skin effect at 100 kHz makes a cylinder resistance that of a .15mm tube, but at 400 Hz gets 2.5mm of skin depth... so the 1mm soft wire that wraps my Romaine does a 6:1 resistance rise between 400 Hz and 100 kHz.
John Larkin <jlarkin@highland_atwork_technology.com> wrote
Indeed - the 12 bits is plenty. But I won't have 4k samples per cycle. So there will be steps larger steps than 4k/cycle.
I can see that removing the steps is not difficult, because of the huge "oversampling". They will need to be removed however, as far as possible, for EMC reasons.
07:38 (0 minutes ago) to sci.electronics.design You don't need 4k filtering (-72 dB) on DAC transitions, but you DO need to define PASS and STOP band accuracy needed ( eg. 0.05 dB, <1 deg) ( >-40 dB @ 100kHz and harmonics)
Something like this but in an active twin-T notch filter with a 60 kHz LPF.
I believe Analog Devices has a pdf titled "Basic Linear Design" which has a lot of filter coefficients and a bit of writeup on how to implement those. supposedly gaussian and bessel are (kinda) linear phase.
I've played a bit with those in maxima. trying to calculate component values. you may keep any mistakes you find. As always you have to be careful with the scaling. plotting the actual transfer function with the parasitic Rs included will be necessary.
/*the pole locations in the analog book Basic Linear Design are absolute values*/ s1:-0.8075+%i*0.9973; s2:-0.8075-%i*0.9973; s3:-0.7153+%i*0.2053; s4:-0.7153-%i*0.2053; s5:-0.8131;
/* [L1 = 1.786926598348852E-4, C1 = 9.43803114632655E-11, L2 = 6.250769103578177E-5, C2 = 3.951204204467418E-11, L3 = 1.378438412673788E-5] the values i have on board are a little different used those for R(s)
Also, 1 deg of 40kHz is around 70 nS. I don't think this is relevant at all as it's well below your sampling period. you could not compensate this with your 100kHz.
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