Magnetostatics Recall Magnetostatics Current in an inductor BioSavarts

Magnetostatics

Recall: Magnetostatics • • • Current in an inductor Bio-Savart’s Law Right-hand rule Not conservative Magnetic Flux Density Magnetic Field Induction machines Transformers? Magnets Inductance. . Emf

Magnetic Force on a Current Element

Magnetic Force on a Current Loop

Ampère’s Law

Internal Magnetic Field of Long Conductor For r < a Cont.

External Magnetic Field of Long Conductor For r > a

Magnetic Field of Toroid Applying Ampere’s law over contour C: Ampere’s law states that the line integral of H around a closed contour C is equal to the current traversing the surface bounded by the contour. The magnetic field outside the toroid is zero. Why?

Recall: Inductance • • • Types? Where did you hear about inductance? What is it? Units Any other info?

Coils of wire Stores electromagnetic field Oppose the change in current Electromagnetic waves Mutual inductance Units Henry Using transformers to do something to voltage Motors or generators Step up or step down Isolation

There are circular rings of magneticfield 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-Field Line Rings and Mutual-Field Line Rings

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.

Practice

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

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, 1 mm long -> 25 n. H/inch or 1 n. H/mm The more spread out the current distribution, the lower the partial self-inductance.

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

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

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

What will happen here?

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 groundbounce: – Decrease the partial selfinductance of the return path (short lengths and wider interconnects) – Increase the mutual inductance of the two legs (by brining them closer together)