Lock range: $\Delta f_L=20 \mathrm{MHz}$ (given).
Damping ratio chosen: $\zeta=1$.
From $\Delta \omega_L=4 \pi \zeta \omega_n \rightarrow \omega_n=10 \times 10^6 \mathrm{rad} / \mathrm{s}$ (i.e. $f_n \approx 1.5915 \mathrm{MHz}$ ).
Loop time-constant requirement: $R C_1=200 \mathrm{~ns}$.
Chosen loop-filter components: $C_1=10 \mathrm{pF}, R=20 \mathrm{k} \Omega$.
Secondary capacitor (rule of thumb $C_2=C_1 / 10$ ): $C_2=1 \mathrm{pF}$.
Solve for charge-pump current using the relation in the text:

$$
10 \times 10^6=\sqrt{\frac{I_{\mathrm{pump}} \cdot 1.57 \times 10^9}{2 \pi \cdot 2 \cdot 10 \times 10^{-12}}} \Rightarrow I_{\mathrm{pump}} \approx 8 \mu \mathrm{~A} .
$$


Rounded choice used in the design: $I_{\text {pump }}=10 \mu \mathrm{~A}$.
Corresponding phase-detector (CP) small-signal gain:

$$
K_{P D I}=\frac{I_{\text {pump }}}{2 \pi} \approx \frac{10 \times 10^{-6}}{2 \pi} \approx 1.59 \mu \mathrm{~A} / \mathrm{rad} .
$$