Scilab Function
fr - eng

calcul_3eme_ordre - return the zeros and the pole of a third order digital PLL type 2

Library

• modnum_pll - Phase Locked Loop utility functions

Description

The computation of the poles and the zero of a third order PLL type 2 are made with the open loop transfert function of the loop :

$$\begin{eqnarray} A\left(s\right)&=&G\left(s\right)H\left(s\right), \end{eqnarray}$$

where $G\left(s\right)$ is the transfert function of the direct gain and $H\left(s\right)$ is the transfert function of the feedback gain. At the frequency cut-off $f_{n}$ of the open loop transfert function :

$$\begin{eqnarray} \Vert A\left(j\omega_{n}\right) \Vert^{2}&=&1,\\ \frac{d\varphi\left(\omega_{n}\right)}{d\omega_{n}}&=&0, \end{eqnarray}$$

and then

$$\begin{eqnarray} \tau_2&=&\frac{-\tan \left(\varphi \left(\omega _{n}\right)\rig... ...{n}^{2}\tau _{1}^{2}}}{\sqrt{1+\omega _{n}^{2}\tau _{2}^{2}}}.\\ \end{eqnarray}$$

Calling Sequence

[tau1,tau,tau2] = calcul_3eme_ordre(fn,phi,kv,icp,N)

Parameters

• fn : real. natural frequency of the open-loop transfert function [Hz]
• phi : real. phase margin at the cut-off frequency [rad]
• kv : real. local sensitivity of the Voltage Controlled Oscillator [Hz/V]
• icp : real. maximum charge pump output current [A]
• N : integer. feedback divider value
• tau1 : real. zero of the transfert function of the loop filter (s)
• tau : real. first pole of the transfert function of the loop filter (s)
• tau2 : real. second pole of the transfert function of the loop filter (s)

File content

• MODNUMSCI/macros/pll/calcul_3eme_ordre.sci [view code]

See Also

• calcul_4eme_ordre - return the zeros and the pole of a fourth order digital PLL type 2 (Scilab Function)

Authors

A. Layec

Bibliography

[1] U. Rhode, Digital PLL Frequency Synthesizers.Prentice Hall, 1983.