September 2006
Intermediate to advanced
261 pages
7h 38m
English
book
All-Digital Frequency Synthesizer in Deep-Submicron CMOS
by Robert B. Staszewski, Poras T. Balsara
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APPENDIX A
SPURS DUE TO DCO SWITCHING
Let's assume a sinusoidal modulating signal,
For frequency modulation (FM), the instantaneous frequency ωi is the carrier frequency ωc modified by the modulating signal times the FM constant kf :
Defining a new constant called the peak frequency deviation,
we can rewrite Eq. A.2 as
The phase of this FM signal is
where
is a dimensionless ratio of the peak frequency deviation to the modulating frequency.
The resulting signal is
Equation A.7 could be rewritten after some trigonometric expansion:
For small values of β (narrowband FM modulation), we can make the following approximations:
Substituting these into Eq. A.8, we obtain an approximate solution ...
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