Phase Locked Loops

This book is devoted to a detailed and comprehensive study of phase locked loops aimed at preparing the reader to design them and to understand their applications. It is written at a level corresponding to a final year electronics undergraduate or a postgraduate student. Linear and semidigital phase locked loops are studied in nine chapters. Most of this book is concerned with analogue PLLs, but there are chapters on semidigital PLLs and on applications. The mathematical tools and background required are described at the end of the book. Important symbols A Amplifier gain Mixer gain (V -1) A Filter bandwidth (Hz) Bi Low pass filter bandwidth (Hz) BL Unilateral equivalent noise bandwidth (Hz) Bn D(s) Polynomial of variable s Peak amplitude of signal voltage (V) Ee Peak amplitude of reference signal voltage (V) Er Carrier frequency (Hz) Ie Intermediate frequency (Hz) Ii Intermediate frequency (Hz) IIF Local oscillator frequency (Hz) it Reference frequency (Hz) Ir F(s) Transfer function of loop filter G Amplifier voltage gain k FM modulator sensitivity (rad s -1 V -1) m K Motor coefficient (rad s -1) Back-electromotive force coefficient (V s rad -1) K1 Reverse back -electromotive force coefficient (rad V -1 S -1) Ke PC conversion gain (V rad s -1) Kd Motor torque coefficient (N m A -1) KM 1 1 VCO conversion gain (rads- V- ) Ko Conversion gain of PLL (S-2) Kv m Modulation factor m Integer n Integer n Loop order N ,N Integers representing division 1 2 1