Elec and Comp Tech 62B Circuits and Systems

1
Elec and Comp Tech 62BCircuits and Systems

• Chapter 9
• Active Filters

2
Overview

• Basic filter responses
• Filter response characteristics
• Active low-pass filters
• Active high-pass filters
• Active band-pass filters
• Active band-stop filters
• Filter response measurements

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Basic Filter Responses

• A low-pass filter passes frequencies up to
  certain frequency, then attenuates frequencies
  above that frequency.

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Basic Filter Responses

• The cutoff or critical frequency, fc, defines the
  end of the passband, and is where the output has
  dropped 3 dB
• 70.7 of the voltage
• 50 of the power
• Also called the half power or 3 dB down point
• Since the filter response is from DC to fc the
  bandwidth (BW) fc.
• The attenuation slope is determined by the number
  of poles, or bypass circuits

5
Roll-off Rate

• A single pole (bypass circuit), such as a RC
  filter, rolls off at a -20 dB/decade (same as a
  -6 db/octave) rate

• 2 poles produce a -40 db/decade, 3 poles produce
  -60 db/decade, and so on.

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Transition Region

• The transition region is the span of frequencies
  in between the passband and the constant-slope
  roll-off
• Cascading multiple passive filter networks
  produces a large and gradual transition region,
  an undesirable filter characteristic.
• Active filters allow for multiple poles with a
  smaller transition region

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High-Pass Filters

• A high-pass filter attenuates frequencies below
  fc and passes frequencies above fc.

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Band-Pass Filters

• A band-pass filter has two critical frequencies,
  fc1 and fc2
• BW fc2fc1
• The center frequency fo fc1fc2

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Band-Stop Filters

• A band-pass filter has two critical frequencies,
  fc1 and fc2
• BW fc2fc1
• The center frequency fo fc1fc2

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Filter Response Characteristics

• In active filters, tailoring the feedback to
  alter the transition region defines the response
  characteristic.
• The most common are Butterworth, Chebyshev, and
  Bessel

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Filter Response
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Damping Factor

• The damping factor of an active filter circuit
  determines the response characteristic.
• The correct damping factor for the desired
  response depends on the number of poles
• For a 2nd-order (2 poles)Butterworth filter,
  thedamping factor is 1.414
• DF2R1/R2

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Sallen-Key Low-Pass Filter

• A basic building-block for 2nd-order filters is
  the Sallen-Key filter.

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Sallen-Key Parameters

• For simplicity, make CACB and RARB. Then,
  fc1/2pRC

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Sallen-Key Parameters

• For Butterworth damping factor of 1.414,
  R1/R2.586, so if R21k?, R1586 ?

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3rd 4th-Order Low-Pass Filter

• All R and C filter values are equal
• R1 through R4 damping values are taken from
  tables (pg. 478)