On Friday, November 12, 2021 at 3:59:25 AM UTC+11, Jan Panteltje wrote:> On a sunny day (Thu, 11 Nov 2021 16:13:52 +0000) it happened Peter > <nos...@nospam9876.com> wrote in <smjfg7$alv$1...@dont-email.me>: > > >Hi All, > > > >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 :) > > http://sim.okawa-denshi.jp/en/CRCRkeisan.htmWhat you want is a linear phase low pass filter. Williams and Taylor are a full bottle on the subject. https://www.amazon.com/Electronic-Filter-Handbook-McGraw-Hill-Handbooks/dp/0071471715 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. -- Bill Sloman, Sydney
A lowpass filter for a DAC
Started by ●November 11, 2021
Reply by ●November 11, 20212021-11-11
Reply by ●November 11, 20212021-11-11
John Larkin wrote: ===============>> > >> 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. > > > >** Not on good analog one, with a sharp trace. > I'd expect that if the sine wave fits on the screen, you wouldn't see > the stairsteps. > > How many spot diameters fit on one screen? Surely not 4000.** That is not the criterion. A small displacement of a trace line is visible, much less than its width. On a 10x8 cm screen, one can see a step displacement of as little as 0.04 mm. With only a 2x overscan ratio, steps would be seen. ....... Phil
Reply by ●November 12, 20212021-11-12
On Thursday, November 11, 2021 at 8:59:25 AM UTC-8, Jan Panteltje wrote:> On a sunny day (Thu, 11 Nov 2021 16:13:52 +0000) it happened Peter > <nos...@nospam9876.com> wrote in <smjfg7$alv$1...@dont-email.me>:> >... 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.> >What about a 2nd order filter?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.
Reply by ●November 12, 20212021-11-12
John Larkin <jlarkin@highland_atwork_technology.com> wrote>On Thu, 11 Nov 2021 15:12:58 -0800 (PST), Phil Allison ><pallison49@gmail.com> wrote: > >> John Larkin wrote: >>=================== >>> >>> >>> 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. >> >>** Not on good analog one, with a sharp trace. > >I'd expect that if the sine wave fits on the screen, you wouldn't see >the stairsteps. > >How many spot diameters fit on one screen? Surely not 4000.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.
Reply by ●November 12, 20212021-11-12
>What you want is a linear phase low pass filter. Williams and Taylor are a full bottle on the subject. > >https://www.amazon.com/Electronic-Filter-Handbook-McGraw-Hill-Handbooks/dp/0071471715 > >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.Do you mean the one here https://www.electronics-tutorials.ws/filter/second-order-filters.html but two of them cascaded?
Reply by ●November 12, 20212021-11-12
Anthony Stewart 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. https://www.dropbox.com/s/ztqgxc8n4wnagg7/inverse%20chebychev.png?dl=0 Cheers, Tony D. Anthony Stewart
Reply by ●November 12, 20212021-11-12
On 11/11/2021 05:13 PM, Peter wrote:> Hi All, > > 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 :) >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. parallel(a,b):=1/(1/a+1/b); series(a,b):=a+b; ZL1:s*L1; ZC1:1/(s*C1); ZL2:s*L2; ZC2:1/(s*C2); ZL3:s*L3; ZR3:R3; /* Vi L1 *V1 L2 *V2 L3 *Vo C1 C2 R3 */ IR1:Vi/series(ZL1,parallel(series(ZL2,(parallel(series(ZL3,ZR3),ZC2))),ZC1)); V1:IR1*parallel(series(ZL2,(parallel(series(ZL3,ZR3),ZC2))),ZC1); IL2:V1/series(ZL2,(parallel(series(ZL3,ZR3),ZC2))); V2:IL2*parallel(series(ZL3,ZR3),ZC2); IL3:V2/series(ZL3,ZR3); Vo:IL3*ZR3; T(L1,C1,L2,C2,L3,R3,s):=''(ratsimp(Vo/Vi)); /*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; X(s):=1/((s-s1)*(s-s2)*(s-s3)*(s-s4)*(s-s5)); P1:ev(ratexpand(1/(T(L1, C1, L2, C2, L3, R3, s))),R3=1e3); P2:ratexpand(1/(X(s))); M:[ coeff(P1,s,0)=coeff(P2,s,0)/coeff(P2,s,0), coeff(P1,s,1)=coeff(P2,s,1)/coeff(P2,s,0), coeff(P1,s,2)=coeff(P2,s,2)/coeff(P2,s,0), coeff(P1,s,3)=coeff(P2,s,3)/coeff(P2,s,0), coeff(P1,s,4)=coeff(P2,s,4)/coeff(P2,s,0), coeff(P1,s,5)=coeff(P2,s,5)/coeff(P2,s,0)]; res:solve(M,[L1,C1,L2,C2,L3]),numer; /* scale freq to 1.65 MHz it seems the whole prototype filter(X(s)) is not centered around the -3db freq -25db at f=1.54 place at:4.608MHz XXX should've put at 7.68MHz and -48db -10db at w=1.0 -48db at w=3.0 (**) +2.4db at w=0.1 (??) */ scalef(x):=(lhs(x)=rhs(x)*1.54/(2*%pi*4.608e6)); f_res:map(scalef,res[1]); parts:ev(f_res,numer); /* [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) */ load(bode); R(s):=''(T(180e-6,100e-12,68e-6,33e-12,15e-6,1000,s)); bode_gain(R(s),[w,2*%pi*1e6,2*%pi*4.608e6]); 20*log(cabs(R(%i*2*%pi*4.608e6)))/log(10),numer; /* yields - 26.31120206227737dB and - 44.04870603874216dB at 7.68MHz - 3dB at 1.3MHz */ /* properly scaled */ scalef(x):=(lhs(x)=rhs(x)*3.0/(2*%pi*7.68e6)); f_res:map(scalef,res[1]); parts:ev(f_res,numer); /* [L1 = 2.088615504563594E-4, C1 = 1.103146497622583E-10, L2 = 7.306093757429039E-5, C2 = 4.618290628598281E-11, L3 = 1.611161781047285E-5] */ R(s):=''(T(209e-6,110e-12,73e-6,46e-12,16e-6,1000,s)); bode_gain(R(s),[w,2*%pi*1e6,2*%pi*7.68e6]); 20*log(cabs(R(%i*2*%pi*7.68e6)))/log(10),numer; /* yields - 50.78836988946069 dB at 7.68M - 3dB at 1.1MHz */ /* if I compromise on accuracy (4 bit) and choose -24db at 7.68M */ scalef(x):=(lhs(x)=rhs(x)*1.5/(2*%pi*7.68e6)); f_res:map(scalef,res[1]); parts:ev(f_res,numer); /* -24dB at 7.68M -3dB at 2.1M */
Reply by ●November 12, 20212021-11-12
Altho, if it's slow stuff like a 400Hz sine, slowly varying, you may just have to measure the zero crossing and guess the delay from that.
Reply by ●November 12, 20212021-11-12
On 11/12/2021 03:06 PM, Johann Klammer wrote:> Altho, if it's slow stuff like a 400Hz sine, slowly varying, you may just have to measure the zero crossing > and guess the delay from that. > >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.
Reply by ●November 12, 20212021-11-12
Johann Klammer <klammerj@NOSPAM.a1.net> wrote:>On 11/12/2021 03:06 PM, Johann Klammer wrote: >> Altho, if it's slow stuff like a 400Hz sine, slowly varying, you may just have to measure the zero crossing >> and guess the delay from that. >> >> >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.1 degree of *400Hz* (which is what I am generating) is 7us, which is about 1 DAC sample period. So despite the misunderstanding, you are still very right; there won't be any realistic way to compensate for the phase shift by shifting the table. I could have 360 samples per cycle and then 1 sample shift would be exactly 1 degree. Or the sample rate could be tweaked to exactly equal the filter delay, and then I could just delay by one sample :)
