Microsoft PowerPoint - lesson-chapter 2a-EC.pptx

[Virtual Presenter] Prof. Piergiorgio Sonato Department of Industrial Engineering University of Padova ELECTRIC CIRCUITS Information Engineering Chapter 2a Electric Network fundamentals and permament regimes.

[Audio] 2 Index Chapter 2a Chapter 2a: Electric Networks fundamentals and permanent regimes – 2.1 Electric Network model – 2.2 Electric Bipoles 2.2.1 Ideal Voltage source 2.2.2 Ideal Current source.

[Audio] 3 2.1 Electric Network model: applicability and limits - 1 A system in which we observe "quasi-stationary" electromagnetic phenomena can be represented by an Electric Network/Circuit Quasi stationary regimes are defined as: – The electromagnetic radiation is neglected The dynamic of the current and voltage variation is "slow", not close to the light speed – The dimension of the network representing the electromagnetic phenomena is "limited" or "small" in such a way that the propagation of the field parameters is "instantaneous" A physical phenomena is usually described through the introduction of scalar and vector fields It can be described by introducing a network if: – It is possible to define integral physical parameters of the scalar and vector fields – And if in the region where the phenomena has to be described we can assume an infinite speed of propagation of the physical parameters.

[Audio] 4 2.1 Electric Network model: applicability and limits - 2 The "quasi stationary regimes" that we are considering are: – Permanent – DC regime (this chapter) – Sinusoidal – Periodic – Variable non-periodic - Transient In our course we address only 2-D networks, no 3-D networks will be analyzed.

[Audio] 5 terminal n-pole 2.1 Electric Network model: definitions which no forces are acting on the electrical charges Potential 1) The connections bewteen n-poles are "ideal electrical conductors" in 2) Outside the connections the space is electrically insulated 3) Outside the n-poles the electric field is conservative: only Electric 4) No electrical charges accumulation is allowed outside the n-poles The network is based on "boxes" from which "n-terminals" connect different boxes, they are called: – n-poles Fundamental conditions:.

[Audio] 6 2.1 Electric Network model: n-poles Quadrupole or Double bipole Tripole n-pole Bipole The electrical charge conservation is prescribed for each n-pole: – Therefore the sum of the overall currents entering and exiting from the npole must be equal to 0 In general we can introduce:.

[Audio] 7 Branch: electrical connection between two nodes 2.1 Electric Network model: first topological elements Mesh or Loop: any closed path that can be identified in the network Node: point in which at least 3 terminals are connected.

[Audio] 8 2.2 Electric Bipoles - 1 – Resistor – Inductor – Capacitor – Sources: Current source Voltage source – …. Main bipoles in the electrical networks:.

[Audio] 9 B A + i(t) vAB(t) AB = ( ) ( ( ) ) 2.2 Electric Bipoles: characteristic equation AB = ( ) ( ) ( t ) g v i t f i t t v The bipole characteristic equation or bipole external characteristic: – is the mathematic function correlation current and voltage Based on the type of mathematical equation we can firstly distinguish: – Linear bipoles: characterized by linear differential equations – Non-linear bipoles: characterized by non-linear differential equations.

[Audio] 10 The choice of the convention is totally arbitrary and does not depend on the nature of the bipole A B A B + + I VAB I VAB 2.2 Electric Bipoles: VAB-I conventions enter into the bipole terminal marked positively the bipole terminal marked positively – Load convention: The current direction is assumed to – Source convention: The current is assumed to exit from Fundamental conventions:.

[Audio] 11 ∆ = ∆ ∆ t t AB ∆ ∆ = ∆ → ∆ → ∆ → Q AB = ∆ ( ) ( ) ( ) lim lim lim 0 0 0 p t t L t Q Q L t i t v AB 2.2 Electric Bipoles: power conventions – Pabs > 0  dissipated power (to heat or mechanical or …) – Pabs < 0  produced power (from non-elect. energy to electric energy) – Psup > 0  produced power (from non-elect. energy to electric energy) – Psup < 0  dissipated power (to heat or mechanical or …) If we consider a bipole in which we assume one of the two VAB-I convention, for example the load convention – The product VAB . I (that coincides with the voltage potential difference for the assumption in the electric network): ∆LAB is the work done by the electric field forces to move the el. current from A to B Bipole with load convention: the product VAB . I  Absorbed Power in Watt Bipole with source convention: the product VAB . I  Supplied power in Watt.

[Audio] 12 τ 0 ( ) ( ) ( ) ≥ =  ∞ − I I I τ v t i t dt w I=0; VAB≠0 I=0, VAB=0 VAB 2.2 Electric Bipoles: categories VAB VAB Inert bipole: Passive bipole: – VAB .I always same sign independently from the convention The absorbed energy from a passive bipole having load convention: Active bipole Linear bipole Non-linear bipole.

[Audio] 13 I I VAB Load Convention Source Convention VAB A B A B + + I VAB I VAB 2.2 Electric Bipoles: category and convention The characteristic equation of a bipole changes if different conventions are adopted.

[Audio] 14 I1 I2 I4 I5 1 2 3 4 5 I I3 I + 1 A B i � ��� 1 2 3 + + + 1' 2' A B V1 V2 V3 + 5 4 3 2 1  = = − + − + = n iI I I I I I I 2.2 Electric Bipoles: series and parallel ��� � ���� � ����� � ���� � �� � �� � �� � � �� – they are connected in such a way that the same current I flows – They are connected in such a way that the same voltage VAB is applied Series connected bipoles: Parallel connected bipoles:.

[Audio] 15 2.2 Electric Bipoles: Permanent regime First two bipoles in Permanent – DC regime: – Ideal voltage source – Ideal current source Networks in which the sources generate constant current and constant voltage "from infinite time" and "for an infinite time" Therefore the networks in permanent regime are time independent In this regime the three bipoles that will be considered are: – Ideal Voltage Source – Ideal Current Source – Resistor.

[Audio] 16 I B A + VAB E E I A B + I VAB = E 2.2.1 Electric Bipoles: Ideal Voltage Source convention is: The Ideal Voltage Source is a bipole that converts non-electric energy into electrical energy The characteristic equation adopting the source – Where VAB= constant , independently from the current flowing through it – The Ideal Voltage Source fixes the voltage at the terminal of the branch in which it is connected – Theoretical infinite power generated – It is also: VBA = - E Specific case if VAB = 0 – Is called short circuit bipole.

[Audio] 17 I + Eeq=VAB + A B I 2.2.1 Electric Bipoles: IdV Source series & parallel – From the definition of the bipole parallel connection: it is possible only if all the Ideal Voltage Sources in parallel connected have the same voltage + + + + Series connected Ideal Voltage Sources: Parallel connected Ideal Voltage Sources: A B ...... 4 3 2 1 + + − + = E E E E VAB E1 E2 E3 E4 +.

[Audio] 18 I J VAB I Irev VAB B + A J + 2.2.2 Electric Bipoles: Ideal Current Source The Ideal Current Source is a bipole that converts non-electric energy into electrical energy The characteristic equation is: I = J – Where I = constant , independently from the voltage applied at the terminals – The Ideal Current Source fixes the current in the branch in which it is connected – Theoretical infinite power generated – If we reverse the I current convention: Irev = -J Specific case if I = 0 – Is called open circuit bipole A B.

[Audio] 19 I J3 J2 J1 A B + Jeq=I + A B 2.2.2 Electric Bipoles: IdC Source series & parallel ..... 3 2 1 + − + = J J J I – From the definition of the bipole series connection: it is possible only if all the Ideal Current Sources in series connected have the same current – VAB it is the same for all the Ideal Current Sources – On obtain an equivalent Ideal Current Source: Series connected Ideal Current Sources: Parallel connected Ideal Current Sources:.

[Audio] 20 A B Eg + + + + + Ee int + - - - int = − r r g e E E Ee r iE r g E 2.2 Electric Bipoles: appendix on electrical sources - 1 – This is able to separate the two types of electrical charges – Inside the source an electrostatic force is established to compensate the specific electrical force – Outside the source we observe only the electrostatic force in agreement with the conditions for which the network model can be adopted for the electromagnetism Electric sources convert into electrical energy other types of energy Frequently in the electrical sources we have rotational forces that separates the electrical charges at the source terminals If we indicate the specific electrical force inside the source as:.

[Audio] 21 A B Eg l + + + + + + - - - Ee int Ee ext r r g i E E B A e B A e l l r , ˆ A A ≡  ⋅ = B e B   ⋅ = ⋅ = , , ˆ ˆ int 0 B g AB td E e A e AB td E td E v ext l l l r l r 2.2 Electric Bipoles: appendix on electrical sources - 2 l l l l r l r l r 0 int int , , , ˆ ˆ ˆ AB A B g AB v td E td E td E e    = ⋅ = ⋅ − = ⋅ = – The voltage inside the source is 0 – Outside the source the voltage correspond to the difference of potential Inside the source the E.M.F can be evaluated as: When the equilibrium is achieved: And on obtain also:.

[Audio] 22 2.2 Electric Bipoles: appendix on electrical sources - 3 – Thermoelectric Sources Thermocouples – Piezoelectric sources Mechanical measurements Small actuators (valves) – Electrochemical sources Piles Electric accumulators – Photovoltaics sources – Electromechanical sources Types of electrical sources:.