Active Filters: concepts

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Active Filters concepts

• All input signals are composed of sinusoidal
  components of various frequencies, amplitudes and
  phases.
• If we are interested in a certain range of
  frequencies, we can design filters to eliminate
  frequency components outside the range
• Filters are usually categorized into four types
  low-pass filter, high-pass filter, band-pass
  filter and band-reject filter.
• Low-pass filter passes components with
  frequencies from DC up to its cutoff frequency
  and rejects components above the cutoff
  frequency.
• Low-pass filter composed of OpAmp are called
  active filter (as opposed to lumped passive
  filter with resistor, capacitor and inductor)
• Active filters are desired to have the following
  characteristics
• Contain few components
• Insensitive to component variation
• Not-too-hard-to-meet specifications on OpAmp
• Easy reconfiguration to support different
  requirements (like cutoff freq)
• Require a small spread of component values

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Applications of Analog Filters

• Analog filters can be found in almost every
  electronic circuit.
• Audio systems use them for pre-amplification,
  equalization, and tone control.
• In communication systems, filters are used for
  tuning in specific frequencies and eliminating
  others (for example, to filter out noise).
• Digital signal processing systems use filters to
  prevent the aliasing of out-of-band noise and
  interference.

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Butterworth low-pass filter

• Many low-pass filter are designed to have a
  Butterworth transfer function with magnitude
  response as follows

Graphs from Prentice Hall
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Low-pass filter Sallen-Key Circuits

• Active low-pass Butterworth filter can be
  implemented by cascading modified Sallen-Key
  circuits.
• The Sallen-Key circuit itself is a 2nd order
  filter. To obtain an nth order filter, n/2 SK
  circuits should be cascaded
• During design, capacitance
• can be selected first and then
• resistor values.
• As K increase from 0 to 3,
• the transfer function displays
• more and more peaking.
• It turns out that if Kgt3, then
• the circuit is not stable.
• Empirical values have been
• found for filters of different
• orders

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Comparison of gain versus frequency for the
stages of the fourth-order Butterworth low-pass
filter.
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Butterworth high-pass filter

• By a change, the lowpass Butterworth transfer
  function can be transformed to a high-pass
  function.

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Butterworth high-pass filter Sallen-Key

• By a change, the lowpass Butterworth transfer
  function can be transformed to a high-pass
  function.
• With real OpAmp, the Sallen-Key is not truly a
  high-pass filter, because the gain of the OpAmp
  eventually falls off. However, the frequencies at
  which the OpAmp gain is fairly high, the circuit
  behaves as a high-pass filter.
• Since the high-pass Sallen
• Key circuit is equivalent the
• same as the low-pass one,
• the empirical values for K
• would be still valid in this
• case also.

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Band-pass filter Sallen-Key Circuits

• If we need to design a band-pass filter in which
  the lower cutoff frequency is much less than the
  upper cutoff frequency, we can cascade a low-pass
  filter with a high-pass filter.
• The below band-pass filter uses the first stage
  as a low-pass filter which passes frequency less
  than 10KHz and the second stage as a high-pass
  filter that passes only frequency above 100Hz.
  Thus, frequency components in-between is passed
  to the output.

Graphs from Prentice Hall
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Figure 11.11 Bode plots of gain magnitude for
the active filter of Example 11.2.
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Band-pass filter Delyiannis-Friend

• If the bandwidth is small compared to the center
  frequency of a band-pass filter,
  Delyiannis-Friend circuit performs better.

Graphs from Prentice Hall
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A summary