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# hw6 - Massachusetts Institute of Technology Department of...

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Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.976 High Speed Communication Circuits and Systems Spring 2003 Homework #6: Phase-Locked Loop Circuits c Copyright 2003 by Michael H. Perrott Reading: PLL Design Assistant Manual (found at http://www-mtl.mit.edu/research/perrottgroup/tools.html). Chapter 15 of Thomas H. Lee’s book. 1. This problem focuses on a simplified method of representing a phase-locked loop circuit with a given noise profile for system level simulations. We will focus on deriving the appropriate noise parameters to achieve a given level on noise performance, and then investigate simulation using CppSim. In all cases, assume that K v = 20 MHz/V, K 1 = -95 (dBc/Hz), K 2 = -60 (dBc), f p = 100 kHz, f s = 90 kHz, and that the carrier frequency f o = 200 MHz. S Φ out (f) K 1 dBc/Hz -20 dBc/Hz/dec K 2 dBc out(t) = cos ( 2 π ( f o +K v vin( τ ) ) d τ ) vin out t 1 + s/(2 π f p ) v ph 2 v spur = Asin(2 π f s t) s/(2 π f p ) 0 f s f p f offset Figure 1: Simplified frequency source simulation implementation with given phase noise and spurious noise. (a) Draw the block of the system shown in Figure 1 in which all blocks are cast as transfer functions (i.e., the VCO is an integrator block). (b) Based on your drawing in part (a), compute the variance of the phase noise source, v 2 ph , to achieve the specified phase noise profile at low frequencies, K 1 . 1

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(c) Compute the amplitude of the spurious noise source, v spur ( t ), to achieve the spec- ified spurious noise at frequency f s , K 2 . (d) Simulate the system in CppSim to verify your calculations using a Gaussian noise source (noise module), a sine wave source (signal source, gain modules), a summer (add2 module), an appropriate filter (must create), and a VCO (vco module). Use a simulation sampling frequency of 2 GHz, and simulate over 1,000,000 sample points. To plot the phase noise, use the Matlab script comp psd.m located in /mit/6.976/CppSim/MatlabCode (be sure to change the value of K v in the script to match the value assumed here).
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