Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.976 High Speed Communication Circuits and Systems Spring 2003 Homework #1: Sparameters, transformers, ISI, and eye diagrams c Copyright 2003 by Michael H. Perrott Reading: Chapters 46 of Thomas H. Lee's book, CppSim manual, Hspice toolbox manual. 1. Consider the high speed trace and it's associated twoport model shown in Figure 1. In the model, the transmission line corresponds to the RF connector and PCB trace (both assumed to be ideal), C1 is the capacitance of the package pin to the package substrate and adjoining pins, L1 is the bondwire inductance, C2 is the onchip pad capacitance, and RL is the onchip termination resistor. For all calculations to follow, it assumed that the source driving impedance is precisely matched to the transmission line characteristic impedance, Ro .
High Speed Trace (RF Connector to Chip Die)
package Connector Adjoining pins Controlled Impedance PCB trace die Driving Source TwoPort Model
OnChip
Delay = x Characteristic Impedance = Ro Ro
Ei1 L1 C1 C2
Ei2 Er2 Vin Er1 Ideal Transmission Line RL Vout Figure 1: Example high speed trace and associated 2port model. Calculate S11 and S21 for each of the following cases: (a) Ro = 50 Ohms, x = 0 ps, C1 = 0.0 pF, L1 = 0 nH, C2 = 0 pF, RL = 55 Ohms (b) Ro = 50 Ohms, x = 0 ps, C1 = 0.0 pF, L1 = 0 nH, C2 = 1 pF, RL = 55 Ohms (c) Ro = 50 Ohms, x = 100 ps, C1 = 0.0 pF, L1 = 0 nH, C2 = 1 pF, RL = 55 Ohms 1 (d) Ro = Zo , x = delay, C1 = C1 , L1 = L1 , C2 = C2 , RL = ZL (e) Using CppSim on Athena, verify part(c) by simulating the impulse response of the system using the hw1 1e i (C1 = 0.0 pF)and hw1 1e ii (C1 =1.0 pF) cells within the CppExamples Cadence library and its associated test.par files in the UNIX directory /CppSim/SimRuns/CppExamples. Based on the simulation results, plot the magnitude and phase of S11 (f ) and S21 (f ) for both cases. 2. The following problem is taken from problem 2 of Chapter 4 from Thomas Lee's book. Suppose we wish to deliver 1 Watt of power into a 50 Ohm load at 1 GHz, but are constrained to using a power amplifier that has a peaktopeak sinusoidal voltage of only 3 V due to transistor breakdown issues. Design the following matching newworks to allow that 1 W to be delivered. Use lowpass versions in all cases, and assume that all reactive elements are ideal. (a) Lmatch (b) match (Q = 10) (c) Tmatch (Q = 10) (d) Tapped capacitor (Q = 10) (e) If the maximum allowable onchip capacitance is 200 pF and the maximum al lowable onchip inductance is 20 nH, are any of your designs amenable to a fully integrated implementation? If so, which one(s)? 3. Simulate the transformer networks computed in Problem 2 in Hspice on Athena. Be sure to use Cadence for design entry as specified in the documents handed out in class. Assume that the source driving impedance is a resistor that matches the nominal input impedance of the transformer at 1 GHz. Adjust the input source voltage such that 3 V peaktopeak exist at the inputs of the transformer networks. Based on the Hspice results, compute and plot S21 of each transformer network (from transformer input to output) across the frequency range of 900 MHz to 1.1 GHz. Com mment on the differences between the performance of each transformer. (Note: you should reference the input as the signal source rather than the input to the transformer  why?) 4. Now consider the high speed trace and it's associated twoport model shown in Fig ure 2, which is similar to that examined in Problem 1. In this case, we will relate the transmission line parameters to physical PCB characteristics, simulate the system, and observe eye diagrams of high speed data being sent across the trace. For all parts of this problem, assume that C1 and L1 are zero unless otherwise noted. (a) Assuming that the PCB trace is a 0.5 ounce Microstrip whose dielectric has r = 4.4 and a height of 10 mils, use the webbased tool at http://www.emclab.umr.edu/pcbtlc to perform the following calculations (note: you must use Internet Explorer). 2 High Speed Trace (RF Connector to Chip Die)
package Connector Adjoining pins Controlled Impedance PCB trace die Driving Source TwoPort Model
OnChip
Delay = 100 ps Characteristic Impedance = 50 100 Ei1 L1 C1 1 pF
Ei2 Er2 Vin Er1 Ideal Transmission Line 55 Vout Figure 2: Example high speed trace and associated 2port model. i. Determine the required width of the PCB trace to achieve 50 Ohms charac teristic impedance. ii. Calculate how long the trace must be to match the assumed propogation delay of 100 ps. (b) Using CppSim on Athena, simulate the step response of the system using the hw1 4b cell within the CppExamples Cadence library and its associated test.par file in the UNIX directory /CppSim/SimRuns/CppExamples. i. Label the cause of the first 5 steps in the overall step response. ii. Why does the cap cause its respective reflection to go negative? (c) Using CppSim on Athena, simulate the response of the system to an input data se quence using the hw1 4c cell within the CppExamples Cadence library and its as sociated test.par file in the UNIX directory /CppSim/SimRuns/CppExamples. i. Plot the eye diagram (spanning two data periods) corresponding to Vout for a data rate of 1 Gb/s. Mark the ideal sampling point assuming a harddecision detector is used, and comment on the quality of the eye. ii. Plot the eye diagram (spanning two data periods) corresponding to Vout for a data rate of 10 Gb/s. Mark the ideal sampling point assuming a harddecision detector is used, and comment on the quality of the eye. (d) Create a new module to support the load having C1 and L1 with nonzero values. Note that the symbol is already provided as trline load2 in the Cadence library CppModules as well as a template of the module function in modules.par under the same name. So, for this part of the homework, simply turn in the appropriate code for module trline load2 in modules.par. 3 ...
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 Spring '03
 MICHAELPERROTT
 Electrical Engineering, Inductor, Transmission line, high speed trace

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