CH. 12
Filters and Tuned Amplifiers
•Filter Transmission
•Filter Types
•Transfer function
•1st Order filter functions
•2nd order Filter functions
•Biquadratic active filter
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Filters
Gain Function
Attenuation Function
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Ideal transmission characteristics of the four
major filter types
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Filter Specification; Low Pass
To approximate
Brick wall response
High-order filters
are required
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Filter Specification; Band Pass
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Filter Transfer Function
Poles (natural modes) and Zeros
real or complex conjugate pairs
For Stability, All poles must lie in
the left hand side of the s plane
Example: Pole–zero pattern for the low-pass filter . This is a fifth-order filter (N = 5).
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Filter Transfer Function
N=6 Band Pass
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Transmission characteristics of a 5th order low-pass filter
having all transmission zeros at infinity; All Pole Filter
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First Order Filters
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Continued
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Second-Order Filter Functions
Q> 1
Q= 1
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2
Peak in the response
Butterworth, maximally
flat
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Single-Amplifier Biquadratic
Active Filters
• Require only one opamp per biquad (second
order)
• Sensitive to tolerances in the values of
capacitors and resistors than the multiple-opamp.
• Limited to pole Q factor less than 10
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Example1;
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Example 2;
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2.5
Frequency response of the H.P.F. shown in example 2
2
1.5
Vo
LM741
Ideal
1
0.5
0
1
10
2
10
3
10
4
10
5
10
6
10
7
10
Frequncy in Hz, Log-Scale
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Synthesis of the Feedback Loop
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The feedback loop gain
The characteristic eq.
The poles of closed loop circuit
Ideally, A = ∞ and the poles
The filter poles are identical to the zeros of the RC network t(s)
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Two bridge-T Networks that have complex zeros
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An active-filter feedback loop generated using
the bridge T-network
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Injecting the Input Signal
The signal can be injected at any
Point connected to ground
without affecting the poles
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Generation of Equivalent Feedback
Loops
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Generation of Equivalent Feedback
Loops Cont.
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Feedback loop
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