Frequency Synthesizer PLL (Digital Type)
Unlocked
VCO OUTPUT (fout)
--
FEEDBACK FREQ
--
fin →
PFD
→ LPF
→ VCO
→ fout
↑ ───
÷ N Counter
─── ┘
PLL Frequency Synthesizer Analysis
Step 1: PFD Equilibrium
The PFD compares $f_{in}$ and the feedback signal $f_{fb}$. At lock:
fin = ffb
Step 2: Frequency Division
The signal $f_{out}$ passes through the ÷N counter before returning:
ffb = fout / N
Step 3: Final Synthesis Solution
Substituting Step 2 into Step 1:
fout = fin × N