# JTF Equations for Second Order PLLs

Note that the following equations use the angular frequency, ω (in radians/sec) which is equivalent to 2πf, where f is frequency (in Hertz).

Note also that Hpk is used to represent the unit-less magnitude of H(s) and can be converted from dB to unit-less magnitude using Hpk = |H(s)| = 10^(dB(Hpk)/20). Likewise, Epk is used to represent the unit-less magnitude of E(s) and can be converted from dB to unit-less magnitude using Epk = |E(s)| = 10^(dB(Epk)/20).

The Jitter Transfer Function in terms of the PLL's natural frequency (ωn) and damping factor (ζ):

The JTF -3 dB frequency in terms of the PLL's natural frequency (ωn) and damping factor (ζ):

The natural frequency in terms of the JTF -3 dB frequency (ω3dB) and damping factor (ζ):

The peaking value in terms of the PLL's damping factor (ζ):

The damping factor in terms of the PLL's peaking value (Hpk):