A
Anthony William Sloman
Guest
It strikes me that John Larkin\'s original idea of synthesising trapezoids can be made to work.
You would still use a fast 14- or 16 bit DAC, but the waveform you fed into your comparator would be made up of four sequential components - all coming out of the DAC - high segment of arbitrary length, a falling edge, a low segment, and a risng edge
With a 14-bit DAC - the LTC2000 comes to mind
https://www.analog.com/media/en/technical-documentation/data-sheets/2000fb.pdf
you\'d synthisese the rising and falling edges of the trapezia as 16-successive steps of a staircase waveform.
The LTC2000 can be clocked at 2.5GHz, so the rising and falling edges could be just 6.4nsec wide, and your maximum full amplitude output frequency would be a 78MHz triangular wave.
The trick is that you could have 1024 different rising or falling edges, with all the steps moved up or down in in steps of 0.1% of the full scale swing.
Only the first and last steps of the staircase would look different.
If you low pass filtered the waveform the zero crossing point would move across the 0.4nsec clock period in steps of 0.4psec.
The trick would be to use a Bessel - linear phase - filter which has a little bit of output ripple (figure 2.58 in Williams and Taylor) where the impulse response crosses the zero line, and put that point at the 3.2 nsec zero-crossing point ( picking the filter time constant to be about 0.64nsec, depending on the filter order) which would stop the odd first step from having much effect on the zero crossing point.
You could get any frequency less than 78.125 MHz, and you could step the period up in increments of 0.4.psec. 78.123 MHz would be the next one down
Because your filter only deals with rising an falling edges, you don\'t need to change it when you are synthesising much slower square waves.
It should work. I\'d hate to build it - the LTC2000 comes in a ball grid array package.
--
Bill Sloman, Sydney
You would still use a fast 14- or 16 bit DAC, but the waveform you fed into your comparator would be made up of four sequential components - all coming out of the DAC - high segment of arbitrary length, a falling edge, a low segment, and a risng edge
With a 14-bit DAC - the LTC2000 comes to mind
https://www.analog.com/media/en/technical-documentation/data-sheets/2000fb.pdf
you\'d synthisese the rising and falling edges of the trapezia as 16-successive steps of a staircase waveform.
The LTC2000 can be clocked at 2.5GHz, so the rising and falling edges could be just 6.4nsec wide, and your maximum full amplitude output frequency would be a 78MHz triangular wave.
The trick is that you could have 1024 different rising or falling edges, with all the steps moved up or down in in steps of 0.1% of the full scale swing.
Only the first and last steps of the staircase would look different.
If you low pass filtered the waveform the zero crossing point would move across the 0.4nsec clock period in steps of 0.4psec.
The trick would be to use a Bessel - linear phase - filter which has a little bit of output ripple (figure 2.58 in Williams and Taylor) where the impulse response crosses the zero line, and put that point at the 3.2 nsec zero-crossing point ( picking the filter time constant to be about 0.64nsec, depending on the filter order) which would stop the odd first step from having much effect on the zero crossing point.
You could get any frequency less than 78.125 MHz, and you could step the period up in increments of 0.4.psec. 78.123 MHz would be the next one down
Because your filter only deals with rising an falling edges, you don\'t need to change it when you are synthesising much slower square waves.
It should work. I\'d hate to build it - the LTC2000 comes in a ball grid array package.
--
Bill Sloman, Sydney