1 / 30

ECE 124a/256c Transmission Lines as Interconnect

ECE 124a/256c Transmission Lines as Interconnect. Forrest Brewer Displays from Bakoglu, Addison-Wesley. Interconnection. Circuit rise/fall times approach or exceed speed of light delay through interconnect Can no longer model wires as C or RC circuits Wire Inductance plays a substantial part

dadelaide
Download Presentation

ECE 124a/256c Transmission Lines as Interconnect

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ECE 124a/256cTransmission Lines as Interconnect Forrest Brewer Displays from Bakoglu, Addison-Wesley

  2. Interconnection • Circuit rise/fall times approach or exceed speed of light delay through interconnect • Can no longer model wires as C or RC circuits • Wire Inductance plays a substantial part • Speed of light: 1ft/nS = 300um/pS

  3. Fundamentals • L dI/dt = V is significant to other effects • Inductance: limit on the rate of change of the current • E.g. Larger driver will not cause larger current to flow initially R L G C

  4. v V +I -I dx Lossless Tranmission R=G=0 • Step of V volts propagating with velocity v • Initially no current flows – after step passes, current of +I • After Step Voltage V exists between the wires

  5. Lossless Tranmission R=G=0 • Maxwell’s equation: • B is field, dS is the normal vector to the surface • F is the flux • For closed surface Flux and current are proportional

  6. Lossless Tranmission R=G=0 • For Transmission Line I and F are defined per unit length • At front of wave: • Faraday’s Law: V = dF/dt = IL dx/dt = ILv • Voltage in line is across a capacitance Q=CV • I must be: • Combining, we get: • Also:

  7. Units • The previous derivation assumed e = m = 1 • In MKS units: • c is the speed of light = 29.972cm/nS • For typical IC materials mr = 1 • So:

  8. Typical Lines • We can characterize a lossless line by its Capacitance per unit length and its dielectric constant.

  9. Circuit Models

  10. Circuit Models II • Driver End • TM modeled by resistor of value Z • Input voltage is function of driver and line impedance: • Inside Line • Drive modeled by Step of 2Vi with source resistance Z • Remaining TM as above (resistor) • Load End • Drive modeled by Step of 2Vi with source resistance Z • Voltage on load of impedance ZL:

  11. Discontinuity in the line (Impedance) • Abrupt interface of 2 TM-lines • Incident wave: Vi = Ii Z1 Reflected Wave: Vr = IrZ1 • Transmitted Wave: Vt = ItZ2 • Conservation of charge: Ii = Ir + It • Voltages across interface: Vi + Vr = Vt • We have:

  12. Reflection/Transmission Coefficients • The Coefficient of Reflection G = Vr/Vi • Vi incident from Z1 into Z2 has a reflection amplitude Gvi • Similarly, the Transmitted Amplitude = 1+G

  13. Inductive and Capacitive Discontinuities

  14. Typical Package Pins

  15. Discontinuity Amplitude • The Amplitude of discontinuity • Strength of discontinuity • Rise/Fall time of Impinging Wave • To first order Magnitude is: • Inductive: Capacitive:

  16. Critical Length (TM-analysis?) • TM-line effects significant if: tr < 2.5 tf • Flight time tf = d/v

  17. Un-terminated Line Rs = 10Z

  18. Un-terminated Line Rs = Z

  19. Un-terminated Line Rs = 0.1Z

  20. Unterminated Line (finite rise time) • Rise Time Never Zero • For • Rs>Zo, tr>tf • Exponential Rise • Rs<Z0, • “Ringing” • Settling time can be much longer than tf.

  21. Line Termination (None)

  22. A B V VA V VB tF Line Termination (End) Z G = 0 R = Z V

  23. Line Termination: (Source)

  24. Piece-Wise Modeling • Create a circuit model for short section of line • Length < rise-time/3 at local propagation velocity • E.G. 50mm for 25pS on chip, 150nm wide, 350nm tall • Assume sea of dielectric and perfect ground plane (this time) • C = 2.4pF/cm = 240fF/mm = 12fF/50mm • L = 3.9/c2C = 1.81nH/cm = 0.181nH/mm = 9.1pH/50mm • R = r L/(W H) = 0.005cm*2.67mWcm/(0.000015cm*0.000035cm) = 25W/50mm 25W 9.1p 12f 200mm:

  25. Lossy Transmission • Attenuation of Signal • Resistive Loss, Skin-Effect Loss, Dielectric Loss • For uniform line with constant R, L, C, G per length:

  26. Conductor Loss (Resistance)

  27. Conductor Loss (step input) • Initial step declines exponentially as Rl /2Z • Closely approximates RC dominated line when Rl >> 2Z • Beyond this point, line is diffusive • For large resistance, we cannot ignore the backward distrbitued reflection

  28. Conductor Loss (Skin Effect) • An ideal conductor would exclude any electric or magnetic field change – most have finite resistance • The depth of the field penetration is mediated by the frequency of the wave – at higher frequencies, less of the conductor is available for conducting the current • For resistivity r (Wcm), frequency f (Hz) the depth is: • A conductor thickness t > 2d will not have significantly lower loss • For Al at 1GHz skin depth is 2.8mm

  29. Skin Effect in stripline (circuit board) • Resistive attenuation: • At high frequencies:

  30. Dielectric Loss • Material Loss tangent: • Attenuation:

More Related