©F.M. Rietti Electro Dynamics Fundamentals

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 2 Electro Dynamics (cont) Ohm Law (DC) –Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship currentconductorproportionalpotential differenceresistance

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 3 Electro Dynamics (cont) Intuitive Understanding

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 4 Electro Dynamics (cont) Simple DC Circuits

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 5 Electro Dynamics (cont) AC Circuits (follow this web link)follow this web link –Consider V(t) was Vo sin(2πft+φ) then I(t) = V(t)/R –In AC circuits we have two other base components: Inductors Capacitors

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 6 Electro Dynamics (cont) Inductors is a passive two-terminal electrical component which resists changes in electric current passing through it. It consists of a conductor such as a wire, usually wound into a coil. When a current flows through it, energy is stored temporarily in a magnetic field in the coil. When the current flowing through an inductor changes, the time- varying magnetic field induces a voltage in the conductor, according to Faraday’s law of electromagnetic induction, According to Lenz's law the direction of induced e.m.f is always such that it opposes the change in current that created it. As a result, inductors always oppose a change in current.passivetwo-terminalelectrical componentelectric currentcoilenergymagnetic fieldvoltageFaraday’s law of electromagnetic induction

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 7 Electro Dynamics (cont) Inductors (cont) The relationship between the time-varying voltage v(t) across an inductor with inductance L and the time-varying current i(t) passing through it is described by the differential equation: L mean inductance If i(t)=I sin(2πft) then When frequency increase Z (impedance), that is equivalent to R, increase, then an inductors is a barrier for high frequency

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 8 Electro Dynamics (cont) Capacitors is a passive two-terminal electrical component used to store electrical energy temporarily in an electric field. The forms of capacitors contain two electrical conductors separated by a dielectric. When there is a potential difference across the conductors (e.g., when a capacitor is attached across a battery), an electric field develops across the dielectric, causing positive charge +Q to collect on one plate and negative charge −Q to collect on the other plate. If a battery has been attached to a capacitor for a sufficient amount of time, no current can flow through the capacitor. However, if a time- varying voltage is applied across the leads of the capacitor, a displacement current can flow.passivetwo-terminalelectrical componentenergyelectric fieldelectrical conductorsdielectricpotential differenceelectric fieldchargedisplacement current

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 9 Electro Dynamics (cont) Capacitors (cont) capacitor is characterized by a single constant value, its capacitance. Capacitance is defined as the ratio of the electric charge Q on each conductor to the potential difference V between them. This is the integral form of the capacitor equation.capacitance

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 10 Electro Dynamics (cont) Capacitors (cont) RC circuit Let us assume above, that the capacitor, C is fully “discharged” and the switch (S) is fully open. These are the initial conditions of the circuit, then t = 0, i = 0 and q = 0. When the switch is closed the time begins at t = 0 and current begins to flow into the capacitor via the resistor. Since the initial voltage across the capacitor is zero, ( Vc = 0 ) the capacitor appears to be a short circuit to the external circuit and the maximum current flows through the circuit restricted only by the resistor R. Then by using Kirchoff’s voltage law (KVL), the voltage drops around the circuit are given as: V 0 – R*I(t) –Vc(t) = 0

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 11 Electro Dynamics (cont) Capacitors (cont) RC Circuit Charging Details on RC Circuits Charging RC Circuits Discharging RC Circuits Var Sign IN RC Circuits Charging RC Circuits Discharging RC Circuits Var Sign IN Capacitor Impedance for Sinusoidal Signal IN is

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 12 Electro Dynamics (cont) Capacitors (cont) Two wires separated by a dielectric are a capacitor then: –Cables when transports signals are both capacitors & resistors –From two track on a PCB there is an hidden capacitor

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 13 Electro Dynamics (cont) Conclusions –Increasing frequency: Inductors Impedance go to high values Capacitors Impedance go to 0 –Combining Inductors & Capacitors is possible do a passive filter for complex signals Link for further Link for further

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 14 Electro Dynamics (cont) Faraday Neumann Lenz Law –The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux enclosed by the circuitmagnetic flux

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 15 Electro Dynamics (cont) Viceversa a current in a coil, produced by a fem, generate a magnetic field Fixed current generate a fixed magnetic field, variable current generate a variable magnetic field Only variable magnetic field induce in a coil or single wire a fem (variable them selves) Induced fem depend from number of turns, more turns -> more fem

©F.M. Rietti LM-18 Computer Science SSI Embedded Systems I 16 Electro Dynamics (cont) Transformers –Two closed circuits connected by a magnetic flux –Variable current in first circuit, induce a magnetic flux, this flux induce a fem in second circuit –Fem depend from turns, if turns are differents for two circuits, fem in <> fem out Remember: no variable current -> no variable magnetic flux -> no induction -> no fem out Transformers doesn’t work in DC circuits