MC9S12Q128_10 Datasheet, PDF (619/644 Pages) Freescale Semiconductor, Inc – HCS12 Microcontrollers

Appendix A Electrical Characteristics
The loop bandwidth f_C should be chosen to fulfill the Gardner’s stability criteria by at least a factor of 10,
typical values are 50. ζ = 0.9 ensures a good transient response.
f_C
<
----------2-----^â‹---^ζ----^â‹---f--^r--^e---^f----------
π
⋅
⎛
⎝
ζ
+
1 + ζ²_⎠⎞
⋅
1^--1-0^--
→
f_C
f_C
<
<
4^---f--r⋅^--e-1^--f-0^{- ;(ζ}
25kHz
=
0.9 )
And finally the frequency relationship is defined as
n = ^f--V-f--_r-^C-_e---^Of--- = 2 ⋅ (synr + 1) = 50
With the above values the resistance can be calculated. The example is shown for a loop bandwidth
f_C=10kHz:
R = ^2-----â‹---^π---K--^â‹--_Φ-n-----^â‹---f--^C-- ^{= 2*π*50*10kHz/(316.7Hz/Ω)=9.9kΩ=~10kΩ}
The capacitance C_s can now be calculated as:
C_s = -_π----2_â‹---f--^â‹_C---^ζ--_â‹-²--R--- ≈ ^0-f--_C-.--5--_â‹-1--R-6--;(ζ = 0.9) ^{= 5.19nF =~ 4.7nF}
The capacitance C_p should be chosen in the range of:
C_s ⁄ 20 ≤ C_p ≤ C_s ⁄ 10 _{Cp = 470pF}
A.4.3.2 Jitter Information
The basic functionality of the PLL is shown in Figure A-3. With each transition of the clock f_cmp, the
deviation from the reference clock f_ref is measured and input voltage to the VCO is adjusted accordingly.
The adjustment is done continuously with no abrupt changes in the clock output frequency. Noise, voltage,
temperature and other factors cause slight variations in the control loop resulting in a clock jitter. This jitter
affects the real minimum and maximum clock periods as illustrated in Figure A-4.
Freescale Semiconductor
MC9S12Q128
619
Rev 1.10