[SOLVED] Question about unit for phase detector and NCO gain in a PLL design

Hi,

This question is about digital PLL design. I post my question here because I do not find another appropriate forum on digital PLL. The DPLL is in fact a software PLL according to some PLL's definition. It calculates the phase error with hardware. This phase error passes through a typical digital PI filter, arrives at a NCO. I want to design a similar PLL. Before implementation, I would like to simulate this PLL in Matlab. The questions are about the phase detector unit and NCO unit.

The phase detector gain Kd is shown as: 1 unit/rad

The NCO gain is 20 MHz/unit.


This DPLL is in fixed point number. What does 1 unit mean in above two lines? Is it the whole digital range, or the least bit (LSB)? Or it is something else?


Here are the original data:

Parameter Value
Lock-in Range ΔωL 7.5 KHz
Damping Factor ξ 0.707
Natural Frequency ωn 3.3 x 10^4 rad/s
Phase Detector Gain Kd 1 unit/rad
NCO Gain Ko 20 MHz/unit
PI Filter Coefficient C1 2^-11
PI Filter Coefficient C2 2^-14



Thanks for help me.

In a hardware (electronic) PLL, the output of the PD is usually a voltage (it could be a current). The "gain" if the PD is the slope of its characteristic Vout/ΔΦin, and is measured in Volts/rad.
The input to the VCO is a voltage ("V" of VCO), and its "gain" is the slopa of the characteristic Δfout/Vin, and is measured in Hz/Volt .

In a numerical PLL we have numbers instead of voltages. The VCO becomes an NCO ("N" of number).
So, instead of Volts as unit of voltage we must consider the unit of real numbers. This is simply "unit".

For example:
if a VCO has Ko=20 MHz/V, that means that the output frequency changes 1 MHz when the input voltage changes 0.05 V .
if a NCO has Ko=20 MHz/unit, that means that the output frequency changes 1 MHz when the input number changes 0.05 .

The same concept applies to de PD.

As PD and VCO are connected in cascade (with the loop filter between them), the association of PD-filter-VCO has a transfer funcion whose units are:
Analog: V/rad * V/V * Hz/V = Hz/rad
Digital: unit/rad * unit/unit * Hz/unit = Hz/rad

Regards

Z