Download Filters

Lesson 24:
Introduction to Filters
1
Learning Objectives
•
•
•
Become familiar with the frequency response of high-pass and low-pass
filters. Learn to calculate the cutoff frequency and describe the phase
response.
Be able to calculate the cutoff frequencies and sketch the frequency
response of a pass-band or stop-band filter.
Develop skills in interpreting and establishing the frequency response of
any filter.
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Filters Introduction
• Filters are used extensively in communications applications to
either select a particular frequency of interest or to ignore
(reject) frequencies that may be interfering with your
equipment.
• As the image of the antennas on the ship shows there are many
opportunities for interference to occur during the transmitting
and receiving of signals.
• This is where the filter comes in…
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Filters
• Some Types:
• Passive filters are those filters composed of series or parallel combinations of
R, L, and C elements.
• Low-Pass
• High-Pass
• Band-Pass
• Band-Stop
• Active filters are filters that employ active devices such as transistors and
operational amplifiers in combination with R, L, and C elements.
• Some terms:
•
•
Stop Band – are the frequencies that are
rejected.
Pass Band – are the frequencies which are
accepted into the system.
Stop Band
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Pass Band
Filters
• Any frequency in the pass band will ‘pass’ through to the next
stage of the circuit with at least 70.7% of the maximum output
voltage.
• Recall the use of the 0.707 level to define the bandwidth of a
series or parallel resonant circuit (both with the general shape
of the pass-band filter).
Stop Band
Pass Band
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Low-Pass Filter
• Again, as the name would indicate, a low-pass filter (LPF) will
allow signals of some lower desired frequency to ‘pass’ into
the circuit, but at the same time it rejects frequencies above the
cutoff frequency.
• The cutoff frequency is that point at which higher frequencies
are rejected.
Av is the normalized value of the ratio of Vo / Vi. The maximum value of Av is
1 and the cutoff frequency is defined at the 0.707 level.
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Low-Pass Filter
•
At very high frequencies the reactance (Xc) of the capacitor is very small
(and thus acts like a short) and can be it can be shown that Vo = 0V in this
case.
X C f  HighH z 
•
At very low frequencies the reactance (Xc) of the capacitor is very large
(thus acts like an open) and it can be shown that Vo = Vi in this case.
X C f 0 H z
•
1
 0
2 fC
1

 
2 fC
To summarize, the magnitude of the ratio of Vo to Vi can be found by:
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High-Pass Filter
• A high-pass filter (HPF) allows signals of some higher desired
frequency to ‘pass’ into the circuit, but at the same time it
rejects frequencies below the cutoff frequency.
• The cutoff frequency is that point at which lower frequencies
are rejected.
RC High-Pass Filter
Av is the normalized value of the ratio of Vo / Vi. The maximum value of Av is
1 and the cutoff frequency is defined at the 0.707 level.
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High-Pass Filter
•
At very high frequencies the reactance (Xc) of the capacitor is very small
(and thus acts like a short) and can be it can be shown that Vo = Vi in this
case.
X C f  HighH z
•
1

 0
2 fC
At very low frequencies the reactance (Xc) of the capacitor is very large
(thus acts like an open) and it can be shown that Vo = 0 in this case.
X C f 0 H z 
•
1
 
2 fC
To summarize, the magnitude of the ratio of Vo to Vi can be found by:
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Basic Low and High Pass
Filter Design
• For both a low pass and high pass filter response we can find
the inflection point called the cutoff frequency which is
simply:
1
fc 
2 *
• Where τ is the time constant we discussed in RC and RL
circuits:
  R *C
• Therefore, to find the cutoff frequency:
1
fc 
2 * RC
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Band-Pass Filter
• As the name would indicate, a band-pass filter (BPF) will
allow signals of a desired frequency to ‘pass’ into the circuit,
but at the same time it rejects all other unwanted frequencies.
• The last lesson showed us that a series resonant circuit has a
frequency response characteristic similar to the one appearing
in the figure below.
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Band-Stop Filter
• The band-stop filter will reject signals of some specified
bandwidth (i.e. frequency range) from entering the circuit.
• ALL other frequencies (not within the specified bandwidth)
are accepted.
• Also known as a notch filter because it ‘notches out’ (rejects) a
specific frequency.
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Radio Spectrum
• The primary frequencies used in the Navy are:
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Example Problem 1
Design an RC Low Pass Filter for the HF band (3-30MHz) using
a resistor value of 5Ω. Draw the circuit and label the frequency
response curve.
From the problem statement we know that our cutoff frequency (fc) is 30MHz and the
R=5 Ω.
1
,   R *C
fc 
2 *
1
2 * R * C
1
1
C

 1.06nF
2 * R * f c 2 *5 *30 MHz
fc 
R  5
C  1.06nF
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30MHz
QUESTIONS?
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