Quote:A PFD is likely to have a dead-zone problem if it produces very narrow pulses for small phase errors.
That's what you'd think, but it's not what happens. Consider the case of an ECL PFD with an RC response and a negative phase error at the inputs. The UP output will rise to Vp(-1+2(1-exp(-(Tw+Tp)/tau))) then decay with time constant tau. The DN output will begin Tp later and will charge to Vp(-1+2(1-exp(-Tw/tau))) before beginning to discharge. Tw is the time UP and DN are both on, tau is the RC time constant, Tp is the phase error, and Vp is the peak output voltage. This is a resonably good model for an ECL PFD.
By choosing Tw and Tp to be small values, the PFD output can be given any desired peak amplitude. For example, choosing tau=1ns, Tw=300ps, and Tp=100ps, the peak values of the UP and DN outputs are limited to approximately -72mV. Assuming the thermal voltage of a diff pair, Vt, is 25mV, the diff pair in a charge pump input will only have switched 5.3% of its current, yet the charge pump output is still linear.
Here are the results of a Mathcad model of these equations. For each Tp, I integrate the charge pump output to get the total charge transferred to the loop filter.
Tp (ns) | Charge Transferred (fC) |
--------- | -------------------------- |
0.00001 | 0.00019364 |
0.00003 | 0.00058096 |
0.0001 | 0.001937 |
0.0003 | 0.005814 |
0.001 | 0.019 |
0.003 | 0.059 |
0.01 | 0.2 |
0.03 | 0.636 |
0.1 | 2.617 |
0.3 | 13.676 |
1 | 98.066 |
3 | 322.108 |
If you plot this data on a log-log plot, you'll find that it's remarkably linear, even down at 10ps phase error, and even though only 5.3% of the current is being switched at 10ps phase error. There's little point in going to smaller phase errors, since the charge transferred at 10ps is only 1.2 electrons. I suppose an argument could be made that there's a dead zone for phase errors that result in less than 1 electron transferred, but I think that's different than what we're discussing here.
Some nonlinearity shows up for errors larger than 1ns, but that's a different effect.
The primary problem with this example is that the UP and DOWN pulses are unlikely to only reach -72mV. They have to stay on long enough to generate the flip-flop reset pulse - the 0.3ns width used here, with the resulting -72mV maximum output, isn't wide enough to acomplish that goal. As Tw is made wider, the maximum output gets wider, and linearity should improve, although there's not much room for improvement. There isn't any practical possibility that Tw could be smaller. Of course, scaling the values to reflect a faster or slower process doesn't change the fundamental result.
I have simulated similar results on real circuits, and measured real PFDs in the lab, all with similar results.
-- Mike --