Electrical circuits wyklad 1b -2019

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Dr inż. Agnieszka Wardzińska

Room: 105 Polanka

agnieszka.wardzinska@put.poznan.pl

cygnus.et.put.poznan.pl/~award

Advisor hours: Tuesday: 10.00-10.45 Thursday: 10.00-10.45

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Impedance of AC components

Impedance Z compose of resistance R and

reactance X.

The inverse of impedance is admitance Y .

Admitance has real part conductance G and

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Impedance of AC components

Note:

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-A few notes about notation

Proper naming and symbolic representation of

electrical quantities are important for understanding!

AC: time domain – small letters

Symbolic domain (complex numbers domain) –

underlined uppercase letters

Resistance, reactance, conductance and susceptance are

always real numbers, so the symbols are not underlined.

Impedance Z is always a complex number (every real

number can be treated as a complex number with a zero

imaginary part), so Z letter (not underlined) can be used

interchangeably with Z as unmistakable.

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Linearity

Linear transformation must satisfy two

conditions

:

homogenity

If r(t) is a response on x(t),

then Ar(t) is a response on Ax(t)

addtivity

then Ar(t) is a response on Ax(t)

If r₁(t) is a response on x₁(t), and r₂(t) is a response on x₂(t), then a sum (r₁(t)+ r₂(t)) is a response on sum (x₁(t)+x₂(t))

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Linear circuits

All transformations in a circuit (voltage and currend

dependencies) are linear transformations

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Ohms Law

For the DC

For the AC

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AC capacitor circuits

Real capacitor model

.

Quality factor (Q factor)

. . .

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AC inductor circuits

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AC inductor circuits

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AC inductor circuits

Real inductor

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AC inductor circuits

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AC inductor circuits

Real inductor

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Circuit Elements

Ideal

Independent Voltage Source

DC circuit

E – electromotive force, source voltage, voltage of the source… [V]

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Circuit Elements

Ideal

independent current source

DC circuit

J – current from the source,

source current… [A]

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Circuit Elements –

dependent

sources

Ideal dependent

voltage source

The voltage defined by the

source depends on the

voltage or current

Ideal dependent

current source

voltage or current

determined in this or other

circuit

The current defined by the

source depends on the

voltage or current

determined in this or other

circuit

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The real voltage sources

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The real current sources

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Ideal Wires

we will assume that an ideal wire has zero total

resistance, no capacitance, and no inductance.

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Kirchhoff’s Circuit Laws

Kirchhoff’s circuit laws were first described in 1845 by

Gustav Kirchhoff. They consist from two equalities for

the lumped element model of electrical circuits. They

describe the current and voltage behaviour in the

circuit.

Lumped parameter model (lumped

element) – it’c electrical parameters can be treated as reduced to a finite point of space.

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Kirchhoff’s First Law - Kirchhoff’s

Current Law (KCL)

The algebraic sum of currents in a network of conductors meeting at a node is zero.

It can be described by the equation:

The currents flowing into the node (I1, I6) we describe as positive, the currents flowing out the node (I2, I3, I4, I5) we describe as negative.

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Kirchhoff’s Second Law

-Kirchhoff’s Voltage Law (KVL)

The algebraic sum of the potential rises and drops

around a closed loop or path is zero.

where U_i describes both the potential drops at the elements and the

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Series Connection

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Series Connection

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Series Connection

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Series Connection

Voltage drops add to total voltage.

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Series Connection

Ohm’s Law

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Series Connection

Ohm’s Law

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Series Connection

/

Ohm’s Law

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Series Connection

/

Ohm’s Law

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Series Connection

/

Ohm’s Law

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Series Connection

/

Ohm’s Law

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Parallel Connection

All components are conected between the same two sets of electrically

common points.

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Parallel Connection

All components are conected between the same two sets of electrically

common points.

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Parallel Connection

Currents add to total current.

u

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Parallel Connection

Currents add to total current.

u

Currents add to total current.

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Parallel Connection

u

Ohm’s Law

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Parallel Connection

u

Ohm’s Law

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Parallel Connection

u

Ohm’s Law

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Parallel Connection

u

Ohm’s Law

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Parallel Connection

u

Ohm’s Law

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Series-Parallel Connection

Z1 – series – Z2 Z3 – series – Z4 Z1+Z2 parallel to Z3+Z4 parallel to Z5