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

2 Using Transmission Lines 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

3 Using Transmission Lines Introduction to Advanced Transmission Line Analysis  Propagation of pulses with non-zero rise/fall times  Introduction to GTL current mode 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.

4 Using Transmission Lines Ramp into Source Matched T- line  Ramp function is step function with finite rise time as shown in the graph. The amplitude is 0 before time t 0 At time t 0, it rises with straight-line with slope At time t 1, it reaches final amplitude V A Thus, the rise time (T R ) is equal to t 1 - t 0. The edge rate (or slew rate) is V A /(t 1 - t 0 ) T = T 0 l

5 Using Transmission Lines Ramp into Source Matched T- line T = T 0 l

6 Using Transmission Lines Ramp Function  Ramp function is step function with finite rise time as shown in the graph. The amplitude is 0 before time t 0 At time t 0, it rises with straight-line with slope At time t 1, it reaches final amplitude V A Thus, the rise time (T R ) is equal to t 1 - t 0. The edge rate (or slew rate) is V A /(t 1 - t 0 )

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

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

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

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

11 Using Transmission Lines 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 I 2 doubles at the load end in step case, instantaneously in the ramp case, it takesT R

12 Using Transmission Lines Ramp into Source Matched Short T-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 T R = 4T The voltage at the source (V 1 ) end is plotted showing comparison between ramp and step The result is a waveform with three distinct slopes The peak value is 0.25V A  Solved with simple geometry and algebra Z 0,  0 V 1 V 2 L, T I 2 I 1 V S Short R S

13 Using Transmission Lines Ramp into a Source Matched, Intermediate Length T-Line  For the intermediate length transmission line, let the T R = 2T The reflected voltage arrives at the source end the instant the input voltage has reached target peak  The voltage at the source (V 1 ) 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 0.5V A  Open circuit case Positive reflected voltage arrives and increases the amplitude to V A The result is a continuous, linear line Short Circuit Case Open Circuit Case

14 Using Transmission Lines Gunning Transistor Logic (GTL) Chip (IC) V  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”

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

16 Using Transmission Lines Time, ns Volts V(b) V(a) 50 ohms 1.5 V 12 Ohms 70 ohms V(a) V(b) Basics of current mode transitions - Example

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

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

19 Using Transmission Lines 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

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

21 Using Transmission Lines Driving Point Impedance Example

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

23 Using Transmission Lines 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.

24 Using Transmission Lines 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)