1 electrical engineering ba (b), analog electronics, lecture 2 et065g 6 credits et064g 7.5 credits...
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Muhammad Amir Yousaf
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Electrical Engineering BA (B), Analog Electronics,
Lecture 2
ET065G 6 CreditsET064G 7.5 Credits
Muhammad Amir Yousaf
Frequency Response of R,L,C
How varying frequency affects the opposition offered by R,L and C
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Muhammad Amir Yousaf
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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Muhammad Amir Yousaf
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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MATHEMATICAL OPERATIONSWITH COMPLEX NUMBERS
Complex Conjugate
simply changing the sign of the imaginary part
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Muhammad Amir Yousaf
MATHEMATICAL OPERATIONSWITH COMPLEX NUMBERS
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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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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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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Muhammad Amir Yousaf
Bode Plot for a RC Circuit
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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Bode Plot for a RC Circuit
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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Muhammad Amir Yousaf
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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Muhammad Amir Yousaf
Exercise
Derive to get Bode plot format equation for the system shown in the figure
fHangle
fHdB
Z1
Z2
Gain = -Z2/Z132
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