690 likes | 709 Views
Explore the fundamental concepts of resistance, capacitance, and inductance in EEE 161. Learn about factors impacting resistance of interconnects, the physical basis and estimation of capacitance, and different types of inductances such as self and mutual inductance. Dive into topics like capacitance per unit length, ground planes, and decoupling capacitance, and understand the intricacies of magnetic field lines affecting inductance. Discover practical applications like induced voltage and methods to minimize ground bounce in electrical circuits.
E N D
Why do we need electrostatics? Understanding Resistance, Capacitance and Inductance
EEE 161 Understanding resistance
Resistance of Interconnect • Resistance • Bulk resistivity • Length • Cross-section area Example: Wire bond: l=0.2cm, dia=1mil, rho=2.5
Bulk resistivity • http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity
EEE 161 Understanding capacitance
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
Simple definition • Capacitance is a measure of how much current we can get through a pair of conductors when the voltage between them changes.
Go back to the previous slide and check whether Z=1/jwc makes sense?
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
Capacitance of a sphere • Permittivity of free space • r radius of the inner sphere • rb radius of the outer sphere
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
Parallel-plate capacitor • Permittivity of free space • A- area of plates • h – separation of plates
Dielectric Constant of Materials • http://en.wikipedia.org/wiki/Relative_permittivity
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.
Capacitance per unit length • Coax • Wire over plane • Parallel wires
PCB Interconnects capacitance • Microstrip • Stripline
EEE 161 Understanding Inductance
There are circular rings of magnetic-field around all currents
Right Hand Rule Number of magnetic field lines unit is Weber http://en.wikipedia.org/wiki/File:Manoderecha.svg
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
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
Types of Inductances • Self-Inductance • Mutual Inductance • Loop inductance • Partial Inductance • Total Inductance / Net Inductance / Effective inductance
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
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.
Induced Voltage • When the number of magnetic field lines changes around one wire, the voltage is induced across the wire.
The polarity of induced voltage • Induced voltage drives a current that opposes the change in # of field lines.
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
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.
Estimate the inductance of a via-hole through a substrate 64mils thick.
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.
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
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
Ground Bounce - Voltage between two points in the return path due to a changing current
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)
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
Example: What if the wires carry current in the same direction? Total inductance is??
Placement for decoupling capacitor pads between Vss and Vcc planes • Conventional placement • Optimized for lowest voltage-collapse noise