1. © H. Heck 2008Section 2.31 Module 2:Transmission Lines Topic 3: Reflections OGI ECE564 Howard Heck

2. Reflections ECE 564 © H. Heck 2008 Section 2.32 Where Are We? 1.Introduction 2.Transmission Line Basics 1.Transmission Line Theory 2.Basic I/O Circuits 3.Reflections 4.Parasitic Discontinuities 5.Modeling, Simulation, & Spice 6.Measurement: Basic Equipment 7.Measurement: Time Domain Reflectometry 3.Analysis Tools 4.Metrics & Methodology 5.Advanced Transmission Lines 6.Multi-Gb/s Signaling 7.Special Topics

3. Reflections ECE 564 © H. Heck 2008 Section 2.33 Contents Reflections at Discontinuities Reflection and Transmission Coefficients Examples  Open Circuit  Short Circuit  Matched Load Summary References

4. Reflections ECE 564 © H. Heck 2008 Section 2.34 Reflections At Discontinuities Define the reflection coefficients: [2.4.1a] [2.4.1b] V i V r V t I t I i -I r Z 01 Z 02 I z Important: Be sure to define a direction for positive current flow & then use it.

5. Reflections ECE 564 © H. Heck 2008 Section 2.35 Reflection Coefficient Derivation Apply KCL at z : [2.4.3] Use Ohm’s law: [2.4.4] Combine [2.4.3] & [2.4.4]: [2.4.5] Combine [2.4.2] & [2.4.5]: [2.4.6] [2.4.7] Apply Ohm’s law to [2.4.7] [2.4.8] [2.4.2] Apply KVL at z :

6. Reflections ECE 564 © H. Heck 2008 Section 2.36 Transmission Coefficient Define transmission coefficients: [2.4.9a] [2.4.9b] Divide [2.4.2] by V i : [2.4.10] [2.4.11]

7. Reflections ECE 564 © H. Heck 2008 Section 2.37 Example: Open Circuit R S = Z 0 Z 0 2V V i = V V t = 2V V r = V I i = I I t = 0 -I r = I

8. Reflections ECE 564 © H. Heck 2008 Section 2.38 I I 2I z l Wave Propagation: Open Circuit l z V V l I I 2I z l I I zz V V 2V l t0t0 t 0 < t 1 <  d  l  d  l < t 2 z V l V R S = Z 0 Z 0 2V

9. Reflections ECE 564 © H. Heck 2008 Section 2.39 Waveforms: Open Circuit 0  d  d I 2I 0 z = 0 z = lz z = l V 2V 0  d  d 0 R S = Z 0 Z 0 2V

10. Reflections ECE 564 © H. Heck 2008 Section 2.310 Example: Short Circuit R S = Z 0 Z 0 2V V i = V V r = -V V t = 0 I i = I -I r = -I I t = 2I

11. Reflections ECE 564 © H. Heck 2008 Section 2.311 V z V 2V l Wave Propagation: Short Circuit t0t0 t 0 < t 1 <  d  l  d  l < t 2 z V l V l I I 2I z l I I z l I I zz V l V R S = Z 0 Z 0 2V

12. Reflections ECE 564 © H. Heck 2008 Section 2.312 Waveforms: Short Circuit 0  d  d I 2I 0 z = 0 z = l V 2V 0  d  d 0 z = 0 z = l R S = Z 0 Z 0 2V

13. Reflections ECE 564 © H. Heck 2008 Section 2.313 Special Case: Matched Circuit R S = Z 0 2V R TT = Z 0 Z 0 V i = V V r = 0 V t = V I i = I -I r = 0 I t = I

14. Reflections ECE 564 © H. Heck 2008 Section 2.314 V z V 2V l Wave Propagation: Matched Circuit t0t0 t 0 < t 1 <  d  l  d < t 2  l z V l V l I I 2I z l I I z l I I zz V l V

15. Reflections ECE 564 © H. Heck 2008 Section 2.315 dd 0  V 2V 0 Waveforms: Matched Circuit 0  d  d I 2I 0 z = 0 z = lz z = l

16. Reflections ECE 564 © H. Heck 2008 Section 2.316 Summary Reflected voltage and current waves are generated when the incident waves encounter a discontinuity in the transmission line. The magnitude of the reflection is determined by the impedances of the lines and by the amplitude of the incident signal. Special cases:  Open circuits fully reflect the voltage signal.  Short circuits reflect the incident signal with equal magnitude but opposite sign.  Matched circuits do not generate reflections.

17. Reflections ECE 564 © H. Heck 2008 Section 2.317 References S. Hall, G. Hall, and J. McCall, High Speed Digital System Design, John Wiley & Sons, Inc. (Wiley Interscience), 2000, 1 st edition. W. Dally and J. Poulton, Digital Systems Engineering, Cambridge University Press, 1998. R. Poon, Computer Circuits Electrical Design, Prentice Hall, 1 st edition, 1995. Ramo, Whinnery, and Van Duzer, Fields and Waves in Communication Electronics, 1985. H.B.Bakoglu, Circuits, Interconnections, and Packaging for VLSI, Addison Wesley, 1990. K.M. True, “Reflections: Computations and Waveforms,” National Semiconductor Application Note AN-807, March 1993. “Transmission Line Effects in PCB Applications,” Motorola Application Note AN1051, 1990. W.R. Blood, MECL System Design Handbook, Motorola, Inc., 1988.