Using Transmission Lines III – class 7

1. Using Transmission Lines III – class 7 Purpose – Consider finite transition time edges and GTL. Acknowledgements: Intel Bus Boot Camp: Michael Leddige

2. Agenda • Source Matched transmission of signals with finite slew rate • Real Edges • Open and short transmission line analysis for source matched finite slew rates • GTL • Analyzing GTL on a transmission line • Transmission line impedances • DC measurements • High Frequency measurements Using Transmission Lines

3. Introduction to Advanced Transmission Line Analysis • Propagation of pulses with non-zero rise/fall times • Introduction to GTL current mode analysis Now the effect of rise time will be discussed with the use of ramp functions to add more realism to our analysis. Finally, we will wrap up this class with an example from Intel’s main processor bus and signaling technology. Using Transmission Lines

4. Ramp into Source MatchedT- line • Ramp function is step function with finite rise time as shown in the graph. • The amplitude is 0 before time t0 • At time t0 , it rises with straight-line with slope • At time t1 , it reaches final amplitude VA • Thus, the rise time (TR) is equal to t1 - t0 . • The edge rate (or slew rate) is • VA /(t1 - t0 ) T = T0l Using Transmission Lines

5. T = T0l Ramp into Source MatchedT- line Using Transmission Lines

6. Ramp Function • Ramp function is step function with finite rise time as shown in the graph. • The amplitude is 0 before time t0 • At time t0 , it rises with straight-line with slope • At time t1 , it reaches final amplitude VA • Thus, the rise time (TR) is equal to t1 - t0 . • The edge rate (or slew rate) is • VA /(t1 - t0 ) Using Transmission Lines

7. Ramp Cases • When dealing with ramps in transmission line networks, there are three general cases: • Long line (T >> TR) • Short line (T << TR) • Intermediate (T ~ TR) Using Transmission Lines

8. Real Edges Assignment: Find sajf for a Gaussian and capacitive edge Using Transmission Lines

9. Next step Replace the step function response with one modified with a finite rise time The voltage settles before the reflected wave is encountered. Short Circuit Case Current Voltage Using Transmission Lines

10. I T 1 I R A I 2 0.75I A Current (A) 0.5I A T 0.25I R A T R T T T T 0 2 3 4 Time (ns) V 1 V A V 2 0.75V A Voltage (V) T R 0.5V A 0.25V A T T T T T 0 2 3 4 Time (ns) R Open Circuit with Finite Slew Rate Current Voltage Using Transmission Lines

11. Consider the Short Circuit Case • Voltage and current waveforms are shown for the step function as a refresher • Below that the ramp case is shown • Both the voltages and currents waveforms are shown with the rise time effect • For example I2 doubles at the load end • in step case, instantaneously • in the ramp case, it takesTR Using Transmission Lines

12. R S T Z , 0 0 V V 1 2 Ramp into Source MatchedShortT-line • Very interesting case • Interaction between rising edge and reflections • Reflections arrive before the applied voltage reaches target amplitude • Again, let us consider the short circuit case • Let TR = 4T • The voltage at the source (V1) end is plotted • showing comparison between ramp and step • The result is a waveform with three distinct slopes • The peak value is 0.25VA • Solved with simple geometry and algebra I I 1 2 L, T Short V S Using Transmission Lines

13. Ramp into a Source Matched,Intermediate Length T-Line • For the intermediate length transmission line, let the TR = 2T • The reflected voltage arrives at the source end the instant the input voltage has reached target peak • The voltage at the source (V1) end is plotted for two cases • comparison between ramp and step • Short circuit case • Negative reflected voltage arrives and reduces the amplitude until zero • The result is a sharp peak of value 0.5VA • Open circuit case • Positive reflected voltage arrives and increases the amplitude to VA • The result is a continuous, linear line Short Circuit Case Open Circuit Case Using Transmission Lines

14. Gunning Transistor Logic (GTL) V Chip (IC) Chip (IC) • Voltage source is outside of chip • Reduces power pins and chip power dissipation • “Open Drain” circuit • Related to earlier open collector switching • Can connect multiple device to same. • Performs a “wire-or” function • Can be used for “multi-drop bus” Using Transmission Lines

15. Basics of GTL signaling – current mode transitions Low to High High to Low Steady state low Steady state high Vtt Vtt Rtt Rtt Zo Zo R(n) R(n) Switch opens Switch closes Vtt Vtt Rtt Rtt Zo Zo R(n) R(n) Using Transmission Lines

16. V(b) V(a) Basics of current mode transitions - Example 1.6 1.5 V 1.4 V(a) 70 ohms 50 ohms 1.2 V(b) 12 Ohms 1.0 0.8 Volts 0.6 0.4 0.2 0.0 0 2 4 6 8 10 12 Using Transmission Lines Time, ns

17. Vtt Vtt V(A) Rtt Rtt Zs V(B) Zo R(n) GTL, GTL+ BUS LOW to HIGH TRANSITION END AGENT DRIVING - First reflection IL = Low steady state current VL = Low steady state voltage Vdelta = The initial voltage step launched onto the line Vinitial = Initial voltage at the driver T = The transmission coefficient at the stub Notice termination was added at the source Why? Using Transmission Lines

18. Vtt Vtt V(A) Rtt Rtt Zs V(B) Zo GTL, GTL+ BUS HIGH to LOW TRANSITION END AGENT DRIVING - First reflection R(n) IL = Low steady state current VL = Low steady state voltage Vdelta = Initial voltage launched onto the line Vinitial = Initial voltage at the driver T = The transmission coefficient at the stub Using Transmission Lines

19. Transmission Line Modeling Assumptions • All physical transmission have non-TEM characteristic at some sufficiently high frequency. • Transmission line theory is only accurate for TEM and Quasi-TEM channels • Transmission line assumption breaks down at certain physical junctions • Transmission line to load • Transmission line to transmission line • Transmission line to connector. • Assignment • Electrically what is a connector (or package)? • Electrically what is a via? I.e. via modeling • PWB through vias • Package blind and buried vias Using Transmission Lines

20. Driving point impedance – freq. domain • Telegraphers formula • Driving point impedance • MathCAD and investigation R, L, C, G per unit length Zin Rdie Cdie Using Transmission Lines

21. Driving Point Impedance Example Using Transmission Lines

22. OhmMeter I*r=ERROR Measure V UNK I Measurement – DC (low frequency) 2 Wire Method Calibration Method Z=(V_measure-V_short)/I OhmMeter Measure V 4 Wire or Kelvin measurement eliminates error UNK I Using Transmission Lines

23. High Frequency Measurement • At high frequencies 4 wires are impractical. • The 2 wire reduces to a transmission line • The Vshort calibration migrates to calibration with sweep of frequencies for selection of impedance loads. • Because of the nature of transmission lines illustrated in earlier slides • Vector Network Analyzers (VNAs) used this basic method but utilized s-parameters • More later on s parameters. Using Transmission Lines

24. Assignment • Find driving point impedance vs. frequency of a short and open line • (a) Derive the equation • (b) given L=10inch, Er=4, L=11 nH/in, C=4.4 pF/in, R=0.2 Ohm/in, G=10^(-14) Mho/in, plot the driving point impedance vs freq for short & open line. (Mathcad or Matlab) • (c) Use Pspice to do the simulation and validate the result in (b) Using Transmission Lines