Why do we need electrostatics?

1. Why do we need electrostatics? Understanding Resistance, Capacitance and Inductance

2. EEE 161 Understanding resistance

3. Resistance of Interconnect • Resistance • Bulk resistivity • Length • Cross-section area Example: Wire bond: l=0.2cm, dia=1mil, rho=2.5

4. Bulk resistivity • http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

5. EEE 161 Understanding capacitance

6. The Physical Basis of Capacitance • Between any two conductors separated by insulaterthere is some capacitance! • Def: Amount of charge on each conductor divided by the voltage between them

8. Simple definition • Capacitance is a measure of how much current we can get through a pair of conductors when the voltage between them changes.

9. Example – Time Domain

10. Go back to the previous slide and check whether Z=1/jwc makes sense?

12. Estimating capacity • How many electric field lines connect two conductors • The closer the spacing, the greater the area of overlap, the more field lines connect the conductors, the larger the capacity to store charge. • The capacitance depends on geometry and material properties

13. Capacitance of a sphere • Permittivity of free space • r radius of the inner sphere • rb radius of the outer sphere

14. An isolated sphere • When rb>>r • An isolated conductor has capacitance with respect to ground. • Rule of thumb: 1inch diameter sphere has a 2pF capacitance

15. Parallel-plate capacitor • Permittivity of free space • A- area of plates • h – separation of plates

16. 1pF capacitance

17. Dielectric Constant of Materials • http://en.wikipedia.org/wiki/Relative_permittivity

18. Power and Ground Planes and Decoupling Capacitance • To reduce rail collapse we need a lot of decoupling capacitance. • Capacitance C will prevent the rail droop for a time t.

22. Capacitance per unit length • Coax • Wire over plane • Parallel wires

23. PCB Interconnects capacitance • Microstrip • Stripline

24. EEE 161 Understanding Inductance

25. There are circular rings of magnetic-field around all currents

26. Right Hand Rule Number of magnetic field lines unit is Weber http://en.wikipedia.org/wiki/File:Manoderecha.svg

27. What affects the # of magnetic field lines? • Current. (double I -> double # lines) • Length of wire ( l increases -> #lines increases) • Cross section of the wire (CS increases -> # lines decreases) • Other currents in the vicinity (can increase or decrease # of lines) • Metal that the wire is made of if ferromagnetic

28. Inductance is # of H lines around the conductor per amp of current through it • L=N/I • Unit Henry • Inductance is related to the geometry of conductors, and magnetic material properties

30. Types of Inductances • Self-Inductance • Mutual Inductance • Loop inductance • Partial Inductance • Total Inductance / Net Inductance / Effective inductance

31. Self-Field Line Rings and Mutual-Field Line Rings

32. Self Inductance • Self-Field line rings – magnetic field rings due to current in the wire • Number of field-line rings around a wire per amp of current in its own wire

33. Mutual Inductance • Mutual-Field line rings- magnetic field rings around a wire due to a current from another wire. • Number of field-line rings around one wire, per Amp of current in another wire.

34. Practice

35. Induced Voltage • When the number of magnetic field lines changes around one wire, the voltage is induced across the wire.

36. The polarity of induced voltage • Induced voltage drives a current that opposes the change in # of field lines.

37. Partial Inductance • We can’t have a partial current • Currents always flow in loops • However, sometimes we don’t know how the rest of the loop looks like so: • We define inductance of a small part of the loop as partial inductance • Two types of partial inductance • Partial self-inductance • Partial mutual-inductance

38. Partial Self-Inductance of a Rod • 30-gauge wire, 1mm long -> 25nH/inch or 1nH/mm The more spread out the current distribution, the lower the partial self-inductance.

39. Estimate the inductance of a via-hole through a substrate 64mils thick.

41. Partial Mutual Inductance between two round wires • In general partial mutual inductance between two wires is much smaller than partial self-inductance of either wire.

42. Rule of thumb for partial inductance • If the spacing between two conductors is farther apart than their length: • For example two 20mil via holes spaced 20 mils apart have no coupling between them

43. Effective, total or Net Inductance • The total number of field lines around just this section per amp of current in the loop • It included the contribution of field line rings from all the current segments in the loop

44. Ground Bounce - Voltage between two points in the return path due to a changing current

45. Ground Bounce • To decrease ground-bounce: • Decrease the partial self-inductance of the return path (short lengths and wider interconnects) • Increase the mutual inductance of the two legs (by brining them closer together)

46. Example: Calculate Ground Bounce • Two wire bonds of a chip are 1 mil in diameter and 100 mils long. • One carries power current and the other carries ground current (the same I but opposite direction), ΔI=100mA that switches in 1nsec. • Find the following: • Partial self-inductance of each wire • Mutual inductance if the wires are more than 100 mils apart • Mutual inductance if the wires are 5 mils apart • Total inductance in both cases (when 100 mils and 5 mils apart) • Ground bounce voltage in both cases

48. Example: What if the wires carry current in the same direction? Total inductance is??

50. Placement for decoupling capacitor pads between Vss and Vcc planes • Conventional placement • Optimized for lowest voltage-collapse noise