VIEWS: 6 PAGES: 24 POSTED ON: 10/21/2011 Public Domain
Using Transmission Lines III – class 7 Purpose – Consider finite transition time edges and GTL. Acknowledgements: Intel Bus Boot Camp: Michael Leddige Agenda 2 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 Ramp into Source Matched T- line 4 Ramp function is step function with finite rise time as shown in the graph. RS I1 I2 Z0 ,T0 The amplitude is 0 before time t0 VS V1 l V2 At time t0 , it rises with straight-line with slope At time t1 , it reaches final T = T0l amplitude VA Thus, the rise time (TR) is equal to t1 - t0 . The edge rate (or slew rate) VA is VA /(t1 - t0 ) t0 t1 Using Transmission Lines 5 Ramp into Source Matched T- line RS I1 I2 Z0 ,T0 l VS V1 V2 T = T0 l VA t0 t1 Using Transmission Lines Ramp Function 6 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 Set up time array 12 t max 9 ps 10 sec t min 0 ns t max 1.5 ns imax 1000 i 0 imax t t min i ns 10 sec i imax Specify Rise Time Spec amplitude Spec Waveshape Spec Slew Adj Fctr r .5 ns A 1 n 3 sajf .849 Define Wave signal vs. time array sajf n t i 1 e r a A i b A a i i Assignment: Find 1 0.9 sajf for a Gaussian 0.8 0.7 Amplitude and capacitive edge 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 time in nanoseconds Neat tr ick to find rise time t hreshold .1 A t hreshold .9 A define 10 and 90% thresholds 1 2 riset ime i_thresholds hist ( t hreshold a) riset ime t t 0.5 i_thresholds 1 i_thresholds 0 i_thresholds 0 ns Using Transmission Lines Short Circuit Case 9 I1 IA I2 Current (A) 0.75IA 0.5I A 0.25IA Current 0 T 2T 3T 4T Time (ns) V1 VA V2 Voltage (V) 0.75VA 0.5VA Voltage 0.25VA Next step 0 T 2T 3T 4T Time (ns) Replace the step function response with one modified with a finite rise time The voltage settles before the reflected wave is encountered. Using Transmission Lines 10 Open Circuit with Finite Slew Rate I TR 1 I A I 2 Current (A) 0.75I A 0.5I A TR Current 0.25I A T R 0 T 2T 3T 4T Time (ns) V1 V A Voltage (V) V2 0.75V A TR Voltage 0.5V A 0.25V A 0 TR T 2T 3T 4 T Time (ns) Using Transmission Lines Consider the Short Circuit Case 11 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 Ramp into Source Matched Short T-line RS I1 I2 Very interesting case Z0 , T0 Interaction between rising VS V1 L, T V2 Short edge and reflections Reflections arrive before the applied voltage reaches target amplitude TR Again, let us consider the short circuit case 0.5VA VRamp Let TR = 4T Voltage (V) 0.375VA VStep The voltage at the source 0.25VA (V1) end is plotted showing comparison between 0.125VA ramp and step The result is a waveform with three distinct slopes Time (ns) 0 2T 4T 6T 8T The peak value is 0.25VA Solved with simple geometry and algebra Using Transmission Lines 13 Ramp into a Source Matched, Intermediate Length T-Line For the intermediate length Short Circuit Case transmission line, let the TR = 2T TR The reflected voltage arrives at 0.5VA the source end the instant the VRamp Voltage (V) 0.375VA VStep input voltage has reached target 0.25VA peak The voltage at the source (V1) 0.125VA end is plotted for two cases Time (ns) 0 T 2T 3T 4T comparison between ramp and step Short circuit case Open Circuit Case Negative reflected voltage arrives TR and reduces the amplitude until VA zero Voltage (V) 0.75VA The result is a sharp peak of value 0.5VA VRamp 0.5VA VStep 0.25VA Open circuit case Positive reflected voltage arrives 0 T 2T 3T 4T Time (ns) and increases the amplitude to VA The result is a continuous, linear line 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 Basics of GTL signaling – current mode transitions 15 Low to High High to Low Steady state low Steady state high Vtt R(n) Vtt VL Vtt Rtt R(n) Rtt Zo Rtt Zo R(n) Vtt R(n) V Vtt IL Rtt R(n) Switch opens Switch closes Vtt Rtt Zo Vtt Rtt Zo V Vstep 1 VL V Vtt Vstep 1 Rtt Zo Rtt Rtt Zo Rtt Zo Zo R(n) Zo R(n) Vstep I L Zo Vstep Vtt Zo R (n) Using Transmission Lines 16 Basics of current mode transitions - Example VV ( a ) _ rise VL Vstep VL I L Zo 70 50 VV (b ) _ rise 18 .29 mA 50 1 0.219 1.29V (0.219) (18.29mA 50) 1.13V 70 50 1.6 1.5 V 1.4 V(a) 70 ohms 1.2 50 ohms V(b) 1.5 1.0 12 Ohms IL 18.29mA V(b) 70 12 Volts 0.8 V(a) 50 VV ( a ) _ fall 1.5 1.5 0.29 50 12 0.6 0.4 50 70 50 VV (b ) _ fall 1.5 1.5 1 0.088V 50 12 70 50 0.2 1.5 12 VL 0.219V 70 12 0.0 0 2 4 6 8 10 12 Time, ns Using Transmission Lines 17 GTL, GTL+ BUS LOW to HIGH TRANSITION END AGENT DRIVING - First reflection Vtt IL 1 Vtt Vtt Rtt R (n) 2 Rtt V(A) Rtt Vtt R (n) Zs VL 1 Zo V(B) Rtt R (n) R(n) 2 I L Zo Rtt Vdelta I L Zo || Rtt IL = Low steady state current Zo Rtt VL = Low steady state voltage Zo || Zs Zo Vdelta = The initial voltage step launched onto the line @ stub Vinitial = Initial voltage at the driver Zo || Zs Zo T = The transmission coefficient at the stub T 1 @ stub Notice termination was Vinitial Vdelta VL added at the source V ( A) 2 T Vdelta VL Why? Rtt Zo V ( B ) T Vdelta 1 VL Rtt Zo Using Transmission Lines 18 GTL, GTL+ BUS HIGH to LOW TRANSITION END AGENT DRIVING - First reflection Vtt R(n) Vtt Vtt VL 1 Rtt V(A) Zs Rtt Rtt R(n) 2 Zo V(B) Rtt || Zo Vdelta Vtt R(n) Rtt || Zo R(n) Zo || Zs Zo @ stub IL = Low steady state current Zo || Zs Zo VL = Low steady state voltage Vdelta = Initial voltage launched onto the line T 1 @ stub Vinitial = Initial voltage at the driver Vinitial Vtt Vdelta T = The transmission coefficient at the stub V ( A) Vtt 2 T Vdelta Rtt Zo V ( B) Vtt T Vdelta 1 Rtt Zo 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 Driving point impedance – freq. domain 20 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 Physical Constants 12 9 9 6 7 mho 7 henry ps 10 sec ns 10 sec nH 10 henry h 10 henry 5.96710 o 4.0 10 r 1 o r r 4.3 m m Propagation Constant Speed of light Vc 3 108 m a b Function for parallel circuit: Cap function ZC( Cx f) sec 1 par( a b ) Tp d 1 r ( f) 2 f Tp d Tp d 2.107 ns ab j 2 f Cx Vc ft Input Impedance of a Transmission Line Set up Frequency Range For Plotting Zl cos l j Zo sin l ( fmax fmin) nf Zin Zl Zo l Zo nl 100 nf 0 nl 1 fmin 1MHz fmax 1GHz freq fmin Zo cos l j Zl sin l nf nl 14 mho Linear Lossy Transmission Line Parameters L 11 nH C 4.4 pF R .2 G 10 Characteristic Impedance in in in in L j 2 f R Z0( f) Load Impedance Cdie 1pF Rdie 40ohm Z1( f) par( ZC( Cdie f) Rdie) C j 2 f G Expand and impedances to define driving point Impecnace 1 1 Z1( f) cos 2 er len i Z0( f) sin 2 er len f 2 f 2 Zin( er len f) Z0( f) Vc Vc 1 1 80 f Z0( f) cos 2 er 2 len i Z1( f) sin 2 f er 2 len Vc Vc 60 Zin r 10in freq nf 40 20 2 10 4 10 6 10 8 10 1 10 8 8 8 8 9 0 freq nf Using Transmission Lines 22 Measurement – DC (low frequency) 2 Wire Method Calibration Method Ohm Meter I*r=ERROR Z=(V_measure-V_short)/I Measure V I UNK Ohm Meter Measure 4 Wire or Kelvin V measurement I UNK eliminates error 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