ECE 352 Electronics II - Course Overview

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Active Filters

• Based on use of amplifiers to achieve
  filter function
• Frequently use op amps so filter may have
  some gain as well.
• Alternative to LRC-based filters
• Benefits
• Provide improved characteristics (gain and
  filtering)
• Smaller size and weight
• Monolithic integration in IC
• Implement without inductors
• Lower cost
• More reliable
• Less power dissipation
• Price
• Added complexity
• More design effort

Vo(s)
Vi (s)
Transfer Function
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Filter Types

• Four major filter types
• Low pass (blocks high frequencies)
• High pass (blocks low frequencies)
• Bandpass (blocks high and low
  frequencies except in narrow band)
• Bandstop (blocks frequencies in a
  narrow band)

Low Pass
High Pass
Bandpass
Bandstop
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Filter Specifications

• Specifications - four parameters needed
• Example low pass filter Amin, Amax, Passband,
  Stopband
• Parameters specify the basic characteristics
  of filter, e.g. low pass filtering
• Specify limitations to its ability to
  filter, e.g. nonuniform transmission in
  passband, incomplete blocking of frequencies
  in stopband

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Filter Transfer Function

• Any filter transfer function T(s) can be
  written as a ratio of two polynomials in
  s
• Where M lt N and N is called the order
  of the filter function
• Higher N means better filter performance
• Higher N also means more complex circuit
  implementation
• Filter transfer function T(s) can be
  rewritten as
• where zs are zeros and ps are poles
  of T(s)
• where poles and zeroes can be real or
  complex
• Form of transfer function is similar to
  low frequency function FL(s) seen previously
  for amplifiers where A(s) AMFL(s)FH(s)

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First Order Filter Functions
First order filter functions are of the
general form
Low Pass
a1 0
High Pass
a0 0
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First Order Filter Functions
First order filter functions are of the
form
General
a1 ? 0, a2 ? 0
All Pass
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Example of First Order Filter - Passive

• Low Pass Filter

0 dB
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Op Amp Characteristics

• Consider only ideal op amps in our study
  of active filters.

Note Since the open-loop gain A is
infinite, there needs to be
virtually no voltage difference
between the two inputs to get a
finite output. Ex. For A 100,000 and
Vout 1 V, then v v- Vout / A
1V/100,000 0.00001 V So for our analysis
of op amps in active filters, we will
frequently make the approximation that v
v- 0 or simply v v- .
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Example of First Order Filter - Active

• Low Pass Filter

I1 Io
I_ 0
Io
V_ 0
Gain
Filter function
20 log (R2/R1)
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Second-Order Filter Functions
j?
Second order filter functions are of the
form which we can rewrite as where
?o and Q determine the poles There
are seven second order filter types Low
pass, high pass, bandpass, notch, Low-pass
notch, High-pass notch and All-pass
s-plane
x
?o
?
x
This looks like the expression for the new
poles that we had for a feedback
amplifier with two poles.
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Second-Order Filter Functions
Low Pass
a1 0, a2 0
High Pass
a0 0, a1 0
Bandpass
a0 0, a2 0
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Second-Order Filter Functions
Notch
a1 0, ao ?o2
Low Pass Notch
a1 0, ao gt ?o2
High Pass Notch
a1 0, ao lt ?o2
All-Pass
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Passive Second Order Filter Functions

• Second order filter functions can be
  implemented with simple RLC circuits
• General form is that of a voltage divider
  with a transfer function given by
• Seven types of second order filters
• High pass
• Low pass
• Bandpass
• Notch at ?o
• General notch
• Low pass notch
• High pass notch

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Example - Passive Second Order Filter Function

• Low pass filter

T(dB)
Q
0 dB
General form of transfer function
?
?0
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Example - Passive Second Order Filter Function

• Bandpass filter

T(dB)
0 dB
General form of transfer function
-3 dB
?
?0
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Low Pass Butterworth Filter Design
T(dB)
0 dB
Q(dB)
Vo
NOTE 40 dB/dec
Vi
?
?0
Given the filter specification (?0), we
can determine the R and C. One
specification, two parameters R and C
Pick a convenient value, say C 5 nF.
Calculate R from C and ?o.
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