An accurate and robust adaptive notch filter-based phase-locked loop

Abstract

The use of an adaptive notch filter (ANF) is one of the most popular methods to block harmonics in a phase-locked loop (PLL). Existing ANFs suffer from drawbacks such as a low harmonic rejection capability, complex structure or instability. To improve the performance of ANF-based PLLs, an enhanced ANF (EANF) is proposed in this paper. Its structure, filtering characteristics and frequency-adaptive method are analyzed. Multiple EANFs can be easily cascaded and achieve adaptation through a common frequency feedback loop (FFL). A small signal model is provided, and its control parameters are tuned through the symmetrical optimum method. The harmonic rejection capability and stability of the proposed method are confirmed through simulation and experimental results.

Appendix

See (Fig. 

Fig. 21

Derivation process of an EANF, The derivation process of the EANF is shown in Fig. 21a through Fig. 21f. This process consists of six steps.

21).

The transfer functions corresponding to Fig. 21a through Fig. 21f can be obtained as follows:

$$G_{a} (s) = \frac{\omega }{s}$$

(17)

$$G_{b} (s) = \frac{{{\kern 1pt} {\kern 1pt} G_{a} (s)}}{{{\kern 1pt} 1 + {\kern 1pt} G_{a} (s){\kern 1pt} {\kern 1pt} G_{a} (s)}} = \frac{s\omega }{{s^{2} + \omega^{2} }}$$

(18)

$$G_{c} (s) = {\kern 1pt} {\kern 1pt} \zeta G_{b} (s) = \frac{\zeta \omega s}{{s^{2} + \omega^{2} }}$$

(19)

$$G_{d} (s) = \frac{{{\kern 1pt} {\kern 1pt} G_{c} (s)}}{{{\kern 1pt} 1 + {\kern 1pt} {\kern 1pt} G_{c} (s)}} = \frac{\zeta \omega s}{{s^{2} + \zeta \omega s + \omega^{2} }}$$

(20)

$${\kern 1pt} G_{e} (s) = 1 - {\kern 1pt} {\kern 1pt} G_{d} (s) = \frac{{s^{2} + \omega^{2} }}{{s^{2} + \zeta \omega s + \omega^{2} }}$$

(21)

$$G_{{EANF_{n} }} (s) = G_{f} (s) = \frac{{s^{2} + (n\omega )^{2} }}{{s^{2} + \zeta n\omega s + (n\omega )^{2} }}(f)$$

(22)