1 Electrical Engineering BA (B), Analog Electronics, Lecture 2 ET065G 6 Credits ET064G 7.5 Credits Muhammad Amir Yousaf.

Muhammad Amir Yousaf

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Electrical Engineering BA (B), Analog Electronics,

Lecture 2

ET065G 6 CreditsET064G 7.5 Credits


Frequency Response of R,L,C

How varying frequency affects the opposition offered by R,L and C

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Impedance Diagram

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Impedance Diagram

The resistance appears on the positive real axis, the inductive reactance on the positive imaginary axis, and the capacitive reactance on the negative imaginary axis.

Circuits combining different types of elements will have total impedances that extend from 90° to -90°

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AC Circuit Analysis

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Complex Numbers

• A complex number represents a point in a two-dimensional plane located with reference to two distinct axes.

• This point can also determine a radius vector drawn from the origin to the point.

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Complex Numbers

Rectangular and Polar forms

Rectangular Form

Polar Form

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Conversion between Forms

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MATHEMATICAL OPERATIONSWITH COMPLEX NUMBERS

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Complex Conjugate

simply changing the sign of the imaginary part

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Reciprocal

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Addition Subtraction

Addition or subtraction cannot be performed in polar form unless thecomplex numbers have the same angle u or unless they differ only bymultiples of 180°.

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Multiplication Division

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Phasors• The radius vector, having a constant magnitude (length) with one end

fixed at the origin, is called a phasor when applied to electric circuits.

It should be pointed out that in phasor notation, the sine wave is always the reference, and thefrequency is not represented.

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Phasors

Phasor algebra for sinusoidal quantities is applicable only for waveforms having the same frequency.

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R,L,C in series

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Voltage Divide Rule

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Frequency response of series R-C circuit

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Bode Diagram

• It is a technique for sketching the frequency response of systems (i.e. filter, amplifiers etc) on dB scale . It provides an excellent way to compare decibel levels at different frequencies.

• Absolute decibel value and phase of the transfer function is plotted against a logarithmic frequency axis.

fHangle

fHdB

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Decibel, dB decibel, dB is very useful measure to compare two levels

of power.

It is used for expressing amplification (and attenuation)InVOutV

VAVdBA

InVOutV

InV

OutV

RInV

ROutV

InPOutP

PdBA

R

VIVP

InPOutP

PAPdBA

log20log20

log20

2

log102

2

log10log10

2

log10log10

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Bode Plot for a RC Circuit

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This gives an idealized bode plot.

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Note that as the frequency of interest approaches fc , the dB gain becomes less negative and approaches the final normalized value of 0 dB.

The resulting plot is a straight line intersectingthe 0 dB line at fc . It increases to the right at a rate of 6 dB per octave or 20 dB per decade.

At higher frequencies:

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The phase response can also be sketched using straight-line asymptotes by considering a few critical points in the frequency spectrum.

An asymptote at theta = 90 for f << fc/10, an asymptote at theta = 0 for f >> 10fc and an asymptote from fc/10 to

10fc that passes through theta = 45 at f= fc.

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Bode diagram for multiple stage filter

According to logarithmic laws

dBA

dBA

dBA

dBtotA

AAAtotA

321

321

321 AangleAangleAangletotAangle

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Bode diagram for multiple stage filter

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Bode diagram for multiple stage circuit

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Bode diagram

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Bode diagram

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Exercise

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Exercise

Draw a detailed asymptotic bode-diagram for a system’s gain. Both the amplitude and phase should be clearly visualized.

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Exercise

Derive to get Bode plot format equation for the system shown in the figure

fHangle

fHdB

Z1

Z2

Gain = -Z2/Z132

Thank You


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References

• Introductory Circuit Analysis By Boylestad


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1 Electrical Engineering BA (B), Analog Electronics, Lecture 2 ET065G 6 Credits ET064G 7.5 Credits Muhammad Amir Yousaf.

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