Alternating Circuits Report PPT Lecture 16

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A network is in resonance (or resonant) when
the voltage and current at the network input
terminals are in phase.

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The resonant frequency is

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For the parallel RLC
circuit, the quality factor at
resonance is
Q0 = 2π f0RC = ω0RC

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The damping factor defined as ζ=1/2Qo
Now the quadratic factor can be written in several
equivalent ways:

8. ω1: the lower half-power
frequency
ω2: the upper half-power
frequency.
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The (half-power) bandwidth is defined as the difference of
these two half-power frequencies:
B ≡ ω2 − ω1

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11. Scaling allows us to design practical circuits at
realistic frequencies.
The following simple but unrealistic circuit will
serve to illustrate the method:
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Km=2000

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Kf=5×10−6

14.  A Bode diagram or Bode plot is a useful tool
for visualizing transfer functions and
frequency responses.
 A Bode plot shows either magnitude or phase
on a logarithmic scale for frequency ω.
 Magnitude is shown on a decibel (dB) scale
defined as:
HdB = 20 log10 |H( jω)|
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The two asymptotes intersect at ω = a, the
frequency of the zero.
This frequency is also described as the corner,
break, 3 dB, or half-power frequency.

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H(s)=20+0.2s=20(1+s/100)

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24. The transfer function is H(s)=1/(1+sRC) and the
corner frequency is ω=1/RC.
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25. The transfer function is H(s)=sRC/(1+sRC) and
the corner frequency is ω=1/RC.
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The bandwidth is R/L and the center
frequency is ω0 = 1/√LC

27. The following circuit is an active lowpass filter
with a corner frequency of 1/R2C and a gain of
1+Rf / R1.
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28.  Filters can be designed to achieve various attenuation, step-
response, and ripple goals
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• Butterworth and
Chebyshev are famous
classes of filters with
well-designed
characteristics, and can
be built using the
Sallen-Key amplifier
shown.