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Assignment – Building the SI Tool Box

Assignment – Building the SI Tool Box. Compare the parallel plate approximation to the improved microstrip and stripline formulas for the following cases:. Microstrip: W C = 6 mils, T D = 4 mils, T C = 1 mil, e r = 4. Symmetric Stripline:

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Assignment – Building the SI Tool Box

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  1. Assignment – Building the SI Tool Box Compare the parallel plate approximation to the improved microstrip and stripline formulas for the following cases: Microstrip: WC = 6 mils, TD = 4 mils, TC = 1 mil, er = 4 Symmetric Stripline: WC = 6 mils, TD1 = TD2 = 4 mils, TC = 1 mil, er = 4

  2. Transmission line equivalent circuits and relevant equations • Basic pulse launching onto transmission lines • Calculation of near and far end waveforms for classic load conditions

  3. RS RL VS VL RL VL VS = + RL RS Review: Voltage Divider Circuit • Consider the simple circuit that contains source voltage VS, source resistance RS, and resistive load RL. • The output voltage, VL is easily calculated from the source amplitude and the values of the two series resistors. Why do we care for? Next page….

  4. Solving Transmission Line Problems The next slides will establish a procedure that will allow you to solve transmission line problems without the aid of a simulator. Here are the steps that will be presented: • Determination of launch voltage & final “DC” or “t =0” voltage • Calculation of load reflection coefficient and voltage delivered to the load • Calculation of source reflection coefficient and resultant source voltage These are the steps for solving all t-line problems.

  5. TD Rs A B Vs Zo Rt 0 Vs (initial voltage) t=0, V=Vi Z0 Rt Vi Vf VS VS = = + + Z0 Rt RS RS Determining Launch Voltage Step 1 in calculating transmission line waveforms is to determine the launch voltage in the circuit. • The behavior of transmission lines makes it easy to calculate the launch & final voltages – it is simply a voltage divider!

  6. TD Rs A B Vs - Rt Zo rB Zo = Rt 0 Vs + Rt Zo (initial voltage) Vreflected = rB (Vincident) VB = Vincident + Vreflected t=0, V=Vi (signal is reflected) t=2TD, r t=TD, V=Vi + (Vi ) r (r r )(Vi ) V=Vi + (Vi) + B B A B Voltage Delivered to the Load Step 2: Determine VB in the circuit at time t = TD • The transient behavior of transmission line delays the arrival of launched voltage until time t = TD. • VB at time 0 < t < TD is at quiescent voltage (0 in this case) • Voltage wavefront will be reflected at the end of the t-line • VB = Vincident + Vreflected at time t = TD

  7. Voltage Reflected Back to the Source Rs A B Vs Zo rA rB Rt 0 Vs TD (initial voltage) t=0, V=Vi (signal is reflected) t=2TD, r t=TD, V=Vi + (Vi ) r r (r V=Vi + (Vi) + )(Vi ) B B B A

  8. - Rs Zo rA = + Rs Zo Vreflected = rA (Vincident) VA = Vlaunch + Vincident + Vreflected Voltage Reflected Back to the Source Step 3: Determine VA in the circuit at time t = 2TD • The transient behavior of transmission line delays the arrival of voltage reflected from the load until time t = 2TD. • VA at time 0 < t < 2TD is at launch voltage • Voltage wavefront will be reflected at the source • VA = Vlaunch + Vincident + Vreflected at time t = 2TD In the steady state, the solution converges to VB = VS[Rt / (Rt + Rs)]

  9. Problems • Consider the circuit shown to the right with a resistive load, assume propagation delay = T, RS= Z0 . Calculate and show the wave forms of V1(t),I1(t),V2(t), and I2(t) for (a) RL= and (b) RL= 3Z0

  10. Step-Function into T-Line: Relationships • Source matched case: RS= Z0 • V1(0)= 0.5VA, I1(0)= 0.5IA • GS = 0, V(x,) = 0.5VA(1+ GL) • Uncharged line • V2(0)= 0, I2(0)= 0 • Open circuit means RL=  • GL =  / = 1 • V1()= V2()= 0.5VA(1+1)= VA • I1()= I2 ()= 0.5IA(1-1)= 0 Solution

  11. Step-Function into T-Line with Open Ckt • At t = T, the voltage wave reaches load end and doubled wave travels back to source end • V1(T)= 0.5VA, I1(T)= 0.5VA/Z0 • V2(T) = VA, I2 (T)= 0 • At t = 2T, the doubled wave reaches the source end and is not reflected • V1(2T)= VA, I1(2T)= 0 • V2(2T) = VA, I2(2T)= 0 Solution

  12. Waveshape:Step-Function into T-Line with Open Ckt This is called “reflected wave switching” Solution

  13. Problem 1b: Relationships • Source matched case: RS= Z0 • V1(0)= 0.5VA, I1(0)= 0.5IA • GS = 0, V(x,) = 0.5VA(1+ GL) • Uncharged line • V2(0)= 0, I2(0)= 0 • RL= 3Z0 • GL = (3Z0 -Z0) / (3Z0 +Z0)= 0.5 • V1()= V2()= 0.5VA(1+0.5)= 0.75VA • I1()= I2()= 0.5IA(1-0.5)= 0.25IA Solution

  14. Problem 1b: Solution • At t = T, the voltage wave reaches load end and positive wave travels back to the source • V1(T)= 0.5VA, I1(T)= 0.5IA • V2(T) = 0.75VA , I2(T)= 0.25IA • At t = 2T, the reflected wave reaches the source end and absorbed • V1(2T)= 0.75VA , I1(2T)= 0.25IA • V2(2T) = 0.75VA , I2(2T)= 0.25IA Solution

  15. Waveshapes for Problem 1b Note that a properly terminated wave settle out at 0.5 V Solution Solution

  16. Transmission line step response • Introduction to lattice diagram analysis • Calculation of near and far end waveforms for classic load impedances • Solving multiple reflection problems Complex signal reflections at different types of transmission line “discontinuities” will be analyzed in this chapter. Lattice diagrams will be introduced as a solution tool.

  17. Zo V(load) V(source) Vs Rs TD = N ps 0 Vs Rt r r load source V(load) Time V(source) 0 a A’ N ps A b B’ 2N ps c 3N ps B d C’ 4N ps e 5N ps Lattice Diagram Analysis – Key Concepts The lattice diagram is a tool/technique to simplify the accounting of reflections and waveforms • Diagram shows the boundaries (x =0 and x=l) and the reflection coefficients (GL andGL ) • Time (in T) axis shown vertically • Slope of the line should indicate flight time of signal • Particularly important for multiple reflection problems using both microstrip and stripline mediums. • Calculate voltage amplitude for each successive reflected wave • Total voltage at any point is the sum of all the waves that have reached that point

  18. r r load source V(load) V(source) 0 Vlaunch 0 Time N ps Vlaunch V(load) V(source) Zo Vlaunch rload Vs Rs TD = N ps 0 Vs Vlaunch(1+rload) Rt Time 2N ps Vlaunch rloadrsource Vlaunch(1+rload +rload rsource) 3N ps Vlaunch r2loadrsource Vlaunch(1+rload+r2loadrsource+ r2loadr2source) 4N ps Vlaunch r2loadr2source 5N ps Lattice Diagram Analysis – Detail

  19. Transient Analysis – Over Damped

  20. Assume Zs=25 ohms Zo V(load) V(source) Zo =50ohms 2 v Zs Vs=0-2 volts TD = 250 ps 0 Vs æ ö Zo 50 = = = ç ÷ V Vs ( 2 ) 1 . 3333 initial + + Zs Zo 25 50 è ø r = 1 r = - 0 . 3333 load source V(load) Time V(source) - - Zs Zo 25 50 r = = = - 0 . 33333 0 source + + 1.33v Zs Zo 25 50 0v - ¥ - Zl Zo 50 r = = = 1 500 ps 1.33v load + ¥ + Zl Zo 50 1.33v 2.66v 1000 ps Response from lattice diagram -0.443v 3 1500 ps 2.22v -0.443v 2.5 2 Volts 1.77v 1.5 2000 ps 0.148v Source 1 0.5 Load 2500 ps 1.92 0 0.148v 0 250 500 750 1000 1250 1500 1750 2000 2250 Time, ps 2.07 Transient Analysis – Under Damped

  21. Two Segment Transmission Line Structures

  22. Assignment Previous examples are the preparation • Consider the two segment transmission line shown to the right. Assume RS= 3Z01 and Z02= 3Z01 . Use Lattice diagram and calculate reflection coefficients at the interfaces and show the wave forms of V1(t),V2(t), and V3(t). • Check results with PSPICE

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