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Lecture 4 Active Filter (Part I). Introduction of passive and active filter Categories of filter Low pass, high pass, band-pass, band stop (notch) Butterworth/chebyshev/Bessel response Poles and multiple stages Transfer Function Bode Plot. Book references.

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Lecture 4 Active Filter (Part I)


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lecture 4 active filter part i
Lecture 4 Active Filter (Part I)
  • Introduction of passive and active filter
  • Categories of filter
    • Low pass, high pass, band-pass, band stop (notch)
  • Butterworth/chebyshev/Bessel response
  • Poles and multiple stages
  • Transfer Function
  • Bode Plot

EE3110 Active Filter (Part 1)

book references
Book references
  • Microelectronic Circuits Analysis and Design, By Muhammad H. Rashid (PWS Publishing Company)
  • Microelectronic Circuit Design, By Richard C. Jaeger and Travis N. Blalock (Mc Graw Hill)
  • Introduction to Filter Theory, By David E. Johnson (Prentice Hall)

EE3110 Active Filter (Part 1)

passive filters
Passive Filters
  • made up of passive components - resistors, capacitors and inductors
  • no amplifying elements (- transistors, op-amps, etc)
  • no signal gain
  • 1st order - design is simple (just use standard equations to find resonant frequency of the circuit)
  • 2nd order - complex equations
  • require no power supplies
  • not restricted by the bandwidth limitations of the op-amps
  • can be used at very high frequencies
  • can handle larger current or voltage levels than active devices
  • buffer amplifiers might be required

EE3110 Active Filter (Part 1)

passive elements inductor big problem
Passive elements : Inductor BIG PROBLEM!
  • high accuracy (1% or 2%), small physical size, or large inductance values are required ??
  • standard values of inductors are not very closely spaced
  • difficult to find an off-the-shelf inductor within 10 percent of any arbitrary value
  • adjustable inductors are used
  • tuning such inductors to the required values is time-consuming and expensive for larger quantities of filters
  • inductors are often prohibitively expensive

EE3110 Active Filter (Part 1)

active filter
Active Filter
  • no inductors
  • made up of op-amps, resistors and capacitors
  • provides virtually any arbitrary gain
  • generally easier to design
  • high input impedance prevents excessive loading of the driving source
  • low output impedance prevents the filter from being affected by the load
  • at high frequencies is limited by the gain-bandwidth of the op-amps
  • easy to adjust over a wide frequency range without altering the desired response

EE3110 Active Filter (Part 1)

categories of filters

High-pass response

Low-pass response

Categories of Filters

Low Pass Filters:

pass all frequencies from dc up to the upper cutoff frequency.

High Pass Filters:

pass all frequencies that are above its lower cutoff frequency

EE3110 Active Filter (Part 1)

categories of filters7

Band Pass Response

Band Stop Response

Categories of Filters

Band Pass Filters:

pass only the frequencies that fall between its values of the lower and upper cutoff frequencies.

Band Stop (Notch) Filters:

eliminate all signals within the stop band while passing all frequencies outside this band.

EE3110 Active Filter (Part 1)

filter response characteristics
Filter Response Characteristics

EE3110 Active Filter (Part 1)

bessel characteristic
Bessel Characteristic
  • Flat response in the passband.
  • Role-off rate less than 20dB/decade/pole.
  • Phase response is linear.
  • Used for filtering pulse waveforms without distorting the shape of the waveform.

EE3110 Active Filter (Part 1)

butterworth characteristic
Butterworth Characteristic
  • Very flat amplitude, Av(dB) , response in the passband.
  • Role-off rate is 20dB/decade/pole.
  • Phase response is not linear.
  • Used when all frequencies in the passband must have the same gain.
  • Often referred to as a maximally flat response.

EE3110 Active Filter (Part 1)

chebyshev characteristic
Chebyshev Characteristic
  • Overshoot or ripples in the passband.
  • Role-off rate greater than 20dB/decade/pole.
  • Phase response is not linear - worse than Butterworth.
  • Used when a rapid roll-off is required.

EE3110 Active Filter (Part 1)

slide12
Pole
  • A pole is nothing more than an RC circuit –
  • n-pole filter  contains n-RC circuit.

EE3110 Active Filter (Part 1)

single pole low high pass filter
Single-Pole Low/High-Pass Filter

High Pass Filter

Low Pass Filter

EE3110 Active Filter (Part 1)

two pole sallen key filters
Two-Pole (Sallen-Key) Filters

High Pass Filter

Low Pass Filter

EE3110 Active Filter (Part 1)

three pole low pass filter
Three-Pole Low-Pass Filter

EE3110 Active Filter (Part 1)

two stage band pass filter
Two-Stage Band-Pass Filter

BW = f2 – f1

Q = f0 / BW

EE3110 Active Filter (Part 1)

multiple feedback band pass filter
Multiple-Feedback Band-Pass Filter

EE3110 Active Filter (Part 1)

band stop notch filter
Band-Stop (Notch) Filter

The notch filter is designed to block all frequencies that fall within its bandwidth. The circuit is made up of a high pass filter, a low-pass filter and a summing amplifier. The summing amplifier will have an output that is equal to the sum of the filter output voltages.

Frequency response

Block diagram

EE3110 Active Filter (Part 1)

notch filter
Notch filter

EE3110 Active Filter (Part 1)

transfer function h j
Transfer function H(j)

EE3110 Active Filter (Part 1)

passive single pole low pass filter
Passive single pole low pass filter

or

where

where

EE3110 Active Filter (Part 1)

slide23

  0 Vo = Vi max. value

 ∞ Vo = 0  min. value

Vo = ??

EE3110 Active Filter (Part 1)

decibel db

By Definition:

Decibel (dB)

(1) Power Gain in dB :

(2) Voltage Gain in dB: (P=V2/R)

EE3110 Active Filter (Part 1)

cascaded system
Cascaded System

EE3110 Active Filter (Part 1)

bode plot single pole
Bode Plot (single pole)

Single pole low-pass filter

For >>o

EE3110 Active Filter (Part 1)

slide27

For octave apart,

For decade apart,

EE3110 Active Filter (Part 1)

bode plot two pole
Bode plot (Two-pole)

EE3110 Active Filter (Part 1)