1. Oct 13, 2005CS477: Analog and Digital Communications1 PLL and Noise in Analog Systems Analog and Digital Communications Autumn 2005-2006

2. Oct 13, 2005CS477: Analog and Digital Communications2 FM Detection: Phase Lock Loops Basic Task of PLL: Lock the instantaneous angle of a VCO with the instantaneous angle of an external signal. i.e., lock (or track) the phase and frequency. VCO LPF

3. Oct 13, 2005CS477: Analog and Digital Communications3 Phase Lock Loops Used in Modulators and demodulators Synchronizers Frequency synthesizers Multiplexers Locks or synchronizes the external angle with the output angle of VCO A negative feedback system based on phase comparison

4. Oct 13, 2005CS477: Analog and Digital Communications4 PLL: Phase Comparator LPF

5. Oct 13, 2005CS477: Analog and Digital Communications5 Linearized PLL Models Integrator Assumptions: 1. Incoming frequency is approximately the same as the VCO free running frequency 2. Phase error is small such that: Consider phases as the signals for further analysis

6. Oct 13, 2005CS477: Analog and Digital Communications6 Linearized PLL Models

7. Oct 13, 2005CS477: Analog and Digital Communications7 FM Detection using Linear PLL Model First order PLL requires loop gain to be greater than the frequency deviation Thus second order PLLs are used in practice. (for FM input) If is a lowpass filter, i.e., Then is a first-order lowpass filter

8. Oct 13, 2005CS477: Analog and Digital Communications8 Non-linearities in FM We need a BPF; what are the requirements? (Non-linear channel) FM transmission is robust against channel variations! (Carson’s rule) With this BPF, output is: Unlike AM, FM can combat amplitude non-linearities!

9. Oct 13, 2005CS477: Analog and Digital Communications9 Noise White Noise Filtered/Colored Noise LPF

10. Oct 13, 2005CS477: Analog and Digital Communications10 Noise Equivalent Bandwidth Average power in filtered noise: (Noise equivalent bandwidth)