Differential Impedance …finally made simple

1 Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignDifferential simpleEric Bogatin PresidentBogatin Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignOverview What s Impedance Differential Impedance : a simple perspective Coupled Transmission line formalism Measuring Differential Impedance Emulating effects of a split in return path Calculating Differential Impedance Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignFirst Order Model of a Transmission Line(Loss Less Model) x(unbalanced transmission line)C=CL xL=LL xcapacitanceinductance (loop)The circuit analysis result:Z0=LLCL =1 LLCLTDLC totaltotal=CLCLCLCLCLCL Eric Bogatin 2000 Slide for Signal Integrity and Interconnect design .

2 Be the signal courtesy ICE Eric Bogatin 2000 Slide for Signal Integrity and Interconnect Design0th Order Model of Transmission LineCCCCCCCCC xCL= Capacitance per length [pF/in]C=CL x Q=CV,every t= xvI= Q t=vCL xV x=vCLVVinI, V definition of Transmission Line:What s the Impedance ? Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignInstantaneous Impedance of a Transmission LineI=vCLVZ=VI=VvCLV=1vCLZ0=1vCLFeatures of the Impedance : looks like a resistor dependant on intrinsic properties only is an intrinsic property independent of length defined as the "characteristic Impedance " = Z0 also called the surge Impedance or wave Impedance Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignCharacteristic Impedance and Capacitance per LengthWhat happens to the capacitance per length?

3 The characteristic Impedance ?What happens to the capacitance per length? The characteristic Impedance ?h = 5 milsw = 10 mils50 Ohm PCB cross sectionincrease hincrease wZCL01~ Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignWhat Does it Mean to Have a 50 Ohm Line? What will Ohm-meter read?For the first second? After 3 seconds? After 10 sec?Verrrry longgggg 50 Ohm coax Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignAn important Distinction THEimpedance of the transmission line (may be time dependent) Theinstantaneousimpedance of the transmission line The Characteristicimpedance of the transmission lineJust referring to.

4 The Impedance may be a bit ambiguous Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignReturn Path in T LinesCurrent into signal lineWhere is the return path? For DC currents:For RF currents? When does current come out return path?TD = 1 sec Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignCurrent Flow in the Transmission LinesignalWhat happens initially if the end is open?, shorted?, terminated?To control Impedance , manage the return path as carefully as the signal pathCLCLCLCLCLCLIt s a propagating wave.

5 Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignThe Growing Importance of Differential Pair UseEarly Applications for Differential PairsMECL I1962 MECL II1966 MECL III1968 MECL 10k1979 MECL 10kH1981 ANSI/TIA/EIA-644-1995 is the generic physical layer standard for LVDS. It was approved in November of 1995, and first published in March of 1996. Example: high speed serial transmission TI Gbps LVDS TRX IEEE1394 IEEE488 Gigabit Ethernet Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignWhat s a Differential Pair Transmission Line?

6 ??? Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignWhat s a Differential Pair Transmission Line?Answer: ..any two, coupled transmission lines (with their return paths).12 What s Differential Impedance ?What s Differential Impedance ?A special case: a symmetric pair Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignDifferentially Driving a Differential PairV = 0 1vV = 1v 0vDifference signalWhat is the difference signal?1212 Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignThe Difference SignalV = 0 1vV = 1v 0vDifference voltage = 2v : -1v +1vDifference signalWhat is the Impedance the difference signal sees?

7 What is the Impedance the difference signal sees?12-1+1 Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignDifferential ImpedanceDifferential Impedance : the Impedance the difference signal sees()())(220smallZIVI diffVdiffZoneone == Differential Impedance decreases as coupling increases+1v-1vxIoneItwoHow will the capacitance matrix elements be affected by spacing?C12C22C11 Eric Bogatin 2000 Slide for Signal Integrity and Interconnect design +1v+1vSCapacitance Matrix Elements01234012345678910111213141516171 81920 Edge to Edge Separation (mils)Capacitance per Length (pF/in)C11C21C12C22C11 What happens to the Differential Impedance as S gets smaller?

8 Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignHow to Terminate the Difference Signal?V = 0 1vV = 1v 0vDifference signal()())(220smallZIVI diffVdiffZoneone ==Terminate with a resistor to match Impedance of the difference signalIf there is no coupling, and each line is 50 , what resistor terminates the Differential pair? Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignFormalism:Mode Pattern for Identical TracesHyperlynx simulation+1v-1v+1v+1vMode: odd, or 1, or aMode: even, or 2, or bCorresponds to Differential drivenCorresponds to common drivenxIoddxIevenWhat is Ioddcompared to Ieven?

9 How do they vary with spacing? Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignOdd and Even Mode ImpedanceHyperlynx simulation+1v-1v+1v+1vMode: odd, or 1, or aMode: even, or 2, or bOdd mode current increases as traces are brought togetherOdd mode Impedance decreasesxIoddxIevenEven mode current decreases as traces are brought togetherEven mode Impedance increasesoddoddIVZ=evenevenIVZ= Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignDifferential Impedance and Odd Mode Impedance ()()oddoneoneZxIVIdiffVdiffZ22= ==V = 0 1vV = 1v 0vDifference signal Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignThe Characteristic Impedance MatrixV1V2xxI1I2 Define a Characteristic Impedance MatrixHow is Z12influenced by coupling?

10 Is Z12large or small? 2121111 IZIZV+=1212222 IZIZV+=Characteristic Impedance Matrix [ohms]:1 21 simulation Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignDefinition of Odd and Even Mode Impedance V1V2xxI1I2 Define:()2121 VVVodd =()2121 VVVeven+=(Special case: symmetric)01==evenVoddoddIVZ01==oddVeven evenIVZWhat is the voltage when Veven= 0? When Vodd= 0? Eric Bogatin 2000 Slide for Signal Integrity and Interconnect DesignOdd and Even Mode Impedance2121111 IZIZV+=1212222 IZIZV+=()()112112121 IZZVVVodd = =21II =Odd Mode:Even Mode.