Module 2: Transmission Lines Topic 3: Reflections

1. Module 2: Transmission LinesTopic 3: Reflections OGI ECE564 Howard Heck Section 2.3

2. Where Are We? • Introduction • Transmission Line Basics • Transmission Line Theory • Basic I/O Circuits • Reflections • Parasitic Discontinuities • Modeling, Simulation, & Spice • Measurement: Basic Equipment • Measurement: Time Domain Reflectometry • Analysis Tools • Metrics & Methodology • Advanced Transmission Lines • Multi-Gb/s Signaling • Special Topics Section 2.3

3. Contents • Reflections at Discontinuities • Reflection and Transmission Coefficients • Examples • Open Circuit • Short Circuit • Matched Load • Summary • References Section 2.3

4. Reflections At Discontinuities V i V t V r I i I t -I r [2.4.1a] [2.4.1b] • Define the reflection coefficients: z Z Z 01 02 I Important: Be sure to define a direction for positive current flow & then use it. Section 2.3

5. Reflection Coefficient Derivation • Apply KVL at z: [2.4.2] • 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] Section 2.3

6. Transmission Coefficient • Define transmission coefficients: [2.4.9a] [2.4.9b] • Divide [2.4.2] by Vi: [2.4.10] [2.4.11] Section 2.3

7. Example: Open Circuit Vt = 2V Vi = V R = Z S 0 Vr = V Z 0 It = 0 2V Ii = I -Ir = I Section 2.3

8. Wave Propagation: Open Circuit R = Z S 0 V I 2I Z 0 2V V I z z l l V I V I z z l l V I 2V 2I V I z z l l t0 t0 < t1 < tdl tdl< t2 Section 2.3

9. Waveforms: Open Circuit R = Z S 0 = 0 z = 0 z Z 0 = = z l z l 2V 2V 2I V I 0 0 t 2t t 2t 0 0 d d d d Section 2.3

10. Example: Short Circuit Vi = V Vt = 0 Vr = -V R = Z S 0 Z 0 2V Ii = I It = 2I -Ir = -I Section 2.3

11. Wave Propagation: Short Circuit V I 2I R = Z S 0 V I Z 0 2V z z l l V I V I z z l l V I 2V 2I V I z z l l t0 t0 < t1 < tdl tdl< t2 Section 2.3

12. Waveforms: Short Circuit = 0 z = 0 z R = Z S 0 = = z l z l 2V 2I Z 0 2V V I 0 0 t 2t t 2t 0 0 d d d d Section 2.3

13. Special Case: Matched Circuit Vi = V Vt = V Vr = 0 R = Z R = Z S 0 TT 0 Z 0 2V Ii = I It = I -Ir = 0 Section 2.3

14. Wave Propagation: Matched Circuit V I 2I V I z z l l V I V I z z l l V I 2V 2I V I z z l l t0 t0 < t1 < tdl td < t2l Section 2.3

15. Waveforms: Matched Circuit = 0 = 0 z z = = z l z l 2V 2I V I 0 0 t 2t t 2t 0 0 d d d d Section 2.3

16. 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. Section 2.3

17. References • S. Hall, G. Hall, and J. McCall, High Speed Digital System Design, John Wiley & Sons, Inc. (Wiley Interscience), 2000, 1st edition. • W. Dally and J. Poulton, Digital Systems Engineering, Cambridge University Press, 1998. • R. Poon, Computer Circuits Electrical Design, Prentice Hall, 1st 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. Section 2.3