©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

©F.M. Rietti

Electro Dynamics

Fundamentals

LM-18 Computer Science SSI Embedded Systems I

2

©F.M. Rietti

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

R

VI


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• Intuitive Understanding


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• Simple DC Circuits


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• AC Circuits (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


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• Inductorsis 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.


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• 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

dt

tdiLtv

ftfIdt

tdi 2cos2 ftfLItv 2cos2

titv

fLZ

2


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• Capacitorsis 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.


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• 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.

0

0

1tVdI

CC

tQtV

t

t


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• Capacitors (cont)RC circuitLet 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:V0 – R*I(t) –Vc(t) = 0


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• Capacitors (cont)RC Circuit Charging

• Details onRC Circuits ChargingRC Circuits DischargingRC Circuits Var Sign IN

• Capacitor Impedance for Sinusoidal Signal IN is

fCZ

2

1


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• 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


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• 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 signalsLink for further


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• 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 circuit


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• 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


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• 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, femin <> femout

• Remember: no variable current -> no variable magnetic flux -> no induction -> no fem out Transformers doesn’t work in DC circuits

Documents

©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