Basics of Electrical Circuits

A. L. Wicks

Mechatronics I

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A. L. Wicks

Basics of Electrical Circuits

Application of Ohms Law

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A. L. Wicks

Basics of Electrical Circuits

Mesh Current example

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A. L. Wicks

Basics of Electrical Circuits

Thevenin Examples

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A. L. Wicks

Basics of Electrical Circuits

Norton Equivalent Circuit

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A. L. Wicks

Basics of Electrical Circuits

The load resistance that absorbs the maximum power from a

two-terminal circuit is equal to the Thévenin resistance.

Maximum Power Transfer

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A. L. Wicks

Basics of Electrical Circuits

Steady-State Sinusoidal Analysis

Circuit Analysis Using Phasors and Impedances

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A. L. Wicks

Basics of Electrical Circuits

AC Power

Example

Simple model

An induction motor

Vrms=120 @60Hz R=500 ohms

L=1.5 H

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A. L. Wicks

Basics of Electrical Circuits

AC Power

LjRZ

ZZZ LR

ω+=

+=

5.1)2(500 fjZ π+=

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A. L. Wicks

Basics of Electrical Circuits

AC Power

( )θcosrmsrms IVP =

( )θcosPF =

iv θθθ −=

( )θsinrmsrmsIVQ =

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A. L. Wicks

Basics of Electrical Circuits

AC Power

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A. L. Wicks

Basics of Electrical Circuits

AC Power

rmsrmspower apparent IV=

( )2

rmsrms

22IVQP =+

RIP2

rms=

XIQ2

rms= R

VP R

2

rms=

X

VQ X

2

rms=

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A. L. Wicks

Basics of Electrical Circuits

THÉVENIN EQUIVALENT CIRCUITS

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A. L. Wicks

Basics of Electrical Circuits

THÉVENIN EQUIVALENT CIRCUITS

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A. L. Wicks

Basics of Electrical Circuits

THÉVENIN EQUIVALENT CIRCUITS

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A. L. Wicks

Basics of Electrical Circuits

THÉVENIN EQUIVALENT CIRCUITS

If the load can take on any

complex value, maximum power

transfer is attained for a load

impedance equal to the complex

conjugate of the Thévenin

impedance

If the load is required to be a

pure resistance, maximum

power transfer is attained for a

load resistance equal to the

magnitude of the Théveninimpedance.

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A. L. Wicks

Basics of Electrical Circuits

Filters

Transfer Functions

The transfer function H(f ) of the two-port filter is defined to be the ratio of the phasor output voltage to the phasor input voltage as a function of frequency:

( )in

out

V

V=fH

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A. L. Wicks

Basics of Electrical Circuits

Filters

The magnitude of the transfer function shows how the amplitude of each frequency component is affected by the filter. Similarly, the phase of the transfer function shows how the phase of each frequency component is affected by the filter.

Transfer Function Properties

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A. L. Wicks

Basics of Electrical Circuits

Filters

Low pass filter

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A. L. Wicks

Basics of Electrical Circuits

Filters

RCfB

π2

1=

( )( )Bffj

fH+

=1

1

( )( )2

1

1

BfffH

+=

( )

−=∠

Bf

ffH arctan

Low Pass filters

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A. L. Wicks

Basics of Electrical Circuits

Filters

DECIBELS

( ) ( )fHfH log20dB

=

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A. L. Wicks

Basics of Electrical Circuits

Filters

22Questions?