A general purpose bb loop simulator was written to numerically simulate a BB loops with various non-idealities.
The program is written in C and runs under UNIX, producing time domain output suitable for driving a plotting package. A description of the program is available here and the C source is here. .
A paper describing the theoretical foundations of the simulator is Walker, R.C., Designing Bang-bang PLLs for Clock and Data Recovery in Serial Data Transmission Systems , pp. 34-45, a chapter appearing in "Phase-Locking in High-Performance Sytems - From Devices to Architectures", edited by Behzad Razavi, IEEE Press, 2003, ISBN 0-471-44727-7.
A "traditional" BB loop requires both an integral and proportional loop control to manage the very wide tuning range of an on-chip VCO.
The charge pump required for proportional control is expensive, needing 4 bond pads plus an external capacitor.
To economically allow multiple channels on a high-speed transceiver, several authors have used only one charge pump per chip. For a multiple transceiver, it is possible to use only one second-order TX PLL, and to use first-order PLLs for all the RX channels. The RX PLLs may be run with proportional (BB) only if their VCO center frequency can be held accurate to a fraction of the BB-deltaF by using a replica of the TX tune voltage.
Here is an example 1.25G Quad receiver, with a measured BB delta T of 11 ps. This corresponds to a BB delta F of (11p/800p)*1.25GHz = 11 MHz. We simulate a VCO frequency error of 4 MHz. This is a VCO mismatch of 36% BB delta F.
Here is this loop simulated with 100% transition density and no-tristate:
(click on image for larger view) The green trace is the simulated data jitter, and the red trace is the loop phase trajectory which is attempting to track the data.
Same loop with "1111100000" data.
Notice that the peak/peak jitter is about 5x the first simulation. This is a characteristic problem of a non-tristated loop with long run lengths.
Now lets look at the performance with tristating. First with 100% transition density:
And then with "1111100000" data.
The complete loss of lock here is caused by the steady state vco mismatch. When the runlength is 5, the effective VCO BB delta F is 20% of normal. This is insufficient to track out the 25% VCO mismatch relative to BB delta F. The next plot shows a VCO mismatch of 19%, which will just be within the 20% allowed by the run-length.
The resulting loop is stable, but has a very tiny slew rate in the vertical direction (20%-19% = 1% of BB delta T/update time). This causes the funny behavior that the loop tracks to outer edge of the input jitter. This is because a very slowly approaching edge will be repelled by very rare excursions before it ever gets to the center of the distribution.