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Chapter
26
Filters
Topics Covered in Chapter 26
26-1: Examples of Filtering
26-2: Direct Current Combined with Alternating Current
26-3: Transformer Coupling
26-4: Capacitive Coupling
26-5: Bypass Capacitors
26-6: Filter Circuits
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
Topics Covered in Chapter 26
 26-7: Low-Pass Filters
 26-8: High-Pass Filters
 26-9: Analyzing Filter Circuits
 26-10: Decibels and Frequency Response Curves
 26-11: Resonant Filters
 26-12: Interference Filters
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© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
26-1: Examples of Filtering
 Electronic circuits often have currents of different
frequencies corresponding to voltages of different
frequencies because a source produces current with
the same frequency as the applied voltage.
Examples:
 The ac signal input to an audio circuit can have high
and low audio frequencies.
 An rf circuit can have a wide range of radio frequencies
in its input.
26-1: Examples of Filtering
Filter examples (continued):
 The audio detector in a radio has both radio frequencies
and audio frequencies in the output.
 The rectifier in a power supply produces dc output with
an ac ripple superimposed on the average dc level.
 In such applications where the current has different
frequency components, it is usually necessary either
to favor or to reject one frequency or a band of
frequencies.
26-2: Direct Current Combined
with Alternating Current
 Current that varies in amplitude but does not reverse in polarity is
considered pulsating or fluctuating direct current.
 Fig. 26-2 illustrates how a circuit can have pulsating direct current or
voltage.
 The steady dc voltage of the battery VB is in series with the ac voltage
VA.
 Since the two series generators add, the voltage across RL is the sum,
as shown in (b).
Fig. 26-2
26-3: Transformer Coupling
 A transformer produces induced secondary voltage just for variations in
primary current.
 With pulsating direct current in the primary, the secondary has a
voltage only for ac variations.
 The steady dc component in the primary has no effect in the
secondary.
Fig. 26-5
26-4: Capacitive Coupling
 Capacitive coupling is probably the most common
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type of coupling in amplifier circuits.
The coupling connects the output of one circuit to the
input of the next.
The requirements are to include all frequencies in the
desired signal, while rejecting undesired components.
Usually, the dc component must be blocked from the
input to the ac amplifiers.
The purpose is to maintain a specific dc level for the
amplifier operation.
26-4: Capacitive Coupling
 Fig. 26-6 illustrates that the RC coupling blocks the dc component.
 With fluctuating dc voltage applied, only the ac component produces
charge and discharge for the output voltage across R.
Fig. 26-6
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26-5: Bypass Capacitors
 A bypass is a path around a component.
 In circuits, the bypass is a parallel or shunt path.
 Capacitors are often used in parallel with resistance to
bypass the ac component of a pulsating dc voltage.
 The result is steady dc voltage across the RC parallel
combination.
26-5: Bypass Capacitors
Fig. 26-7 illustrates that the low reactance of bypass capacitor C1
short-circuits R1 for an ac component of fluctuating dc input voltage.
Fig. 26-7:
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26-6: Filter Circuits
 In terms of their function, filters can be classified as
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either low-pass or high-pass.
A low-pass filter allows the lower frequency
components of the applied voltage to develop output
voltage across the load resistance.
A high-pass filter allows the higher frequency
components of the applied voltage to develop voltage
across the output load resistance.
The most common type filters using L and C are the L,
T, and π.
The ability of a filter to reduce the amplitude of
undesired frequencies is called attenuation.
26-7: Low-Pass Filters
 With an applied input voltage having different
frequency components, the low-pass filter action
results in maximum low-frequency voltage across RL,
while most of the high-frequency voltage is developed
across the series choke or resistance.
26-7: Low-Pass Filters
Fig. 26-9:
Using the series resistance R in Fig. 26-9 (f)
instead of a choke provides a more economical
π filter in less space.
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26-7: Low-Pass Filters
 Fig. 26-10 illustrates the response of a low-pass filter with cutoff at 15
kHz.
 The filter passes the audio signal but attenuates radio frequencies.
Fig. 26-10:
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26-8: High-Pass Filters
 The high-pass filter passes to the load all frequencies
higher than the cutoff frequency fc, whereas lower
frequencies cannot develop appreciable voltage
across the load.
26-8: High-Pass Filters
Fig. 26-11:
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26-9: Analyzing Filter Circuits
 Any low-pass or high-pass filter can be thought of as a
frequency-dependent voltage divider, since the
amount of output voltage is a function of frequency.
 Special formulas can be used to calculate the output
voltage for any frequency of the applied voltage.
 There is a mathematical approach in analyzing the
operation of the most basic low-pass and high-pass
circuits.
26-9: Analyzing Filter Circuits
 Filter types
 RC and RL low-pass – pass low frequencies and
attenuate high frequencies.
 RC and RL high-pass – pass high frequencies and
attenuate low frequencies.
 RC band-pass – a filter designed to pass only a specific
band of frequencies from its input to its output.
 RC band-stop – a filter designed to block or severely
attenuate only a specific band of frequencies.
26-10: Decibels and Frequency
Response Curves
 In analyzing filters, the decibel (dB) unit is often used
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to describe the amount of attenuation offered by the
filter.
In basic terms, the decibel is a logarithmic expression
that compares two power levels.
Expressed mathematically,
NdB = 10log (Pout/Pin)
If the ratio Pout/Pin is greater than one, the NdB value is
positive, indicating and increase in power.
If the ratio Pout/Pin is less than one, the NdB value is
negative, indicating a loss and referred to as an
attenuation.
26-10: Decibels and Frequency
Response Curves
 Fig. 26-22 shows a log-log graph paper.
 Notice that each octave corresponds to
a 2-to-1 range of values and each
decade corresponds to a 10-to-1 range
of values.
Fig. 26-22:
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26-10: Decibels and Frequency
Response Curves
 Figure 26-23 illustrates an RC low-pass filter frequency
response curve.
 The RC circuit is shown in (a) and the response curve is shown in
(b). (Next slide)
Fig. 26-23 (a)
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26-10: Decibels and Frequency
Response Curves
Fig. 26-23 (b)
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26-11: Resonant Filters
 Tuned circuits provide a convenient method of filtering
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a band of radio frequencies because relatively small
values of L and C are necessary for resonance.
A tuned circuit provides filtering action by means of its
maximum response at the resonant frequency.
The width of the band of frequencies affected by
resonance depends on the Q of the tuned circuit; a
higher Q provides a narrower bandwidth.
Resonant filters are often called band-stop or bandpass filters.
The band-stop filter is also referred to as a wavetrap.
26-11: Resonant Filters
 A series resonant circuit has maximum current and minimum
impedance at the resonant frequency.
 Connected is series with RL, as in Fig. 26-24 (a), the series-tuned LC
circuit allows frequencies at and near resonance to produce maximum
output across RL.
 This is band-pass filtering.
Fig. 26-24
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26-11: Resonant Filters
 A parallel resonant circuit has maximum impedance at the resonant
frequency.
 Connected in series with RL, as in Fig. 26-25 (a), the parallel-tuned LC
circuit provides maximum impedance in series with RL at and near the
resonant frequency.
 This is a band-stop filter for the bandwidth of the tuned circuit.
Fig. 26-25
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26-12: Interference Filters
 Voltage or current not at the desired frequency
represents interference.
 Usually, such interference can be eliminated by a filter.
 Some typical applications are
 Low-pass filter to eliminate rf interference from the 60-
Hz power-line input to a receiver
 High-pass filter to eliminate rf interference from the
signal picked up by a television receiving antenna
 Resonant filter to eliminate an interfering radio
frequency from the desired rf signal