active filter design techniques

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    Active Filter Design Techniques - 2

    Fundamentals of Low-Pass Filters Low-Pass Filter Design High-Pass Filter Design Band-Pass Filter Design Band-Rejection Filter Design All-Pass Filter Design Practical Design Hints Design Tools

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    Fundamentals of Low-Pass Filters

    A filter is a device that passes electric signals at certain frequencies orfrequency ranges while preventing the passage of others . Webster.

    Passive Filter Active Filter

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    Passive Filter Active Filter

    Equivalent Filters

    Typical for filters > 1MHz.

    For freq < 1MHz, L isphysically large.

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    Gyrator Positive Impedance Inverter

    http://upload.wikimedia.org/wikipedia/commons/6/69/Gyrator.svg
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    Low-Pass Filter Design

    Normalized Frequency:

    Transfer Function:

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    Cascading of Passive Low-pass Filter Stages

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    Cascading of Passive Low-pass Filter Stages

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    Passive RC Low-Pass FilterResponses

    Gain Phase

    Roll-off Slope for 1 st Order:

    20dB/decade 6dB/octave

    Phase Shift for 1 st Order:

    0 @ low freq -90 @ high freq

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    Non Ideal Filter ResponseCharacteristics

    Gain Phase

    Passband Stopband

    1.5 Octaves

    Gradual transition fromPassband to Stopband

    Uneven gainin the pass

    band

    Nonlinearphase slope

    leading todistortion

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    Optimization of Filter Design

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    Optimization of Filter Design

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    Butterworth Filter Response

    Optimized for maximum flatness in the passband

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    Tschebyscheff Filter

    Optimized to sharpen the transition from passband to stopband

    Passband Stopband

    Steep TransitionSlopes

    Ripple in thePassband

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    Filters Optimized to Sharpen the Transition fromPassband to Stopband

    Ripple in

    Passband

    Ripple inStopband

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    Elliptic (Cauer) FilterOptimized for steepest transition from passband to stopband for a

    given filter order.Has ripple in both passband and stopband, however.

    Ripple inPassband

    Ripple inStopband

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    Infinite Impulse Response (IIR)Filter Design Template Filter in Software

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    Bessel Filter

    Optimized for linear phase response up to f c

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    Group delay is a measure of the transit time of asignal versus frequency.

    Group delay is a useful measure of phasedistortion, and is calculated by differentiating the

    phase response versus frequency.

    Group Delay

    Gain and

    Group Delayof a Bessel

    FilterConstant GroupDelay and Linear

    Phase in TransitionRegion

    http://en.wikipedia.org/wiki/Phase_responsehttp://en.wikipedia.org/wiki/Phase_response
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    Another way to say this is that group delay is ameasure of the slope of the transmission phaseresponse .

    The linear portion of the phase response isconverted to a constant value (representing theaverage signal-transit time) and deviations fromlinear phase are transformed into deviations fromconstant group delay.

    The variations in group delay cause signaldistortion, just as deviations from linear phase causedistortion.

    Group Delay

    http://en.wikipedia.org/wiki/Phase_responsehttp://en.wikipedia.org/wiki/Phase_responsehttp://en.wikipedia.org/wiki/Phase_responsehttp://en.wikipedia.org/wiki/Phase_responsehttp://en.wikipedia.org/wiki/Phase_responsehttp://en.wikipedia.org/wiki/Phase_response
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    Gain, Phase and Group Delays across Filter Types

    PhaseResponse

    Group delayGain

    Response

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    Quality or Q Factor

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    Filter Coefficient Design Tables

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    Low-Pass Filter Design

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    Cascading of Filter Stages to Achieve Higher Order Filters

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    First Order Filter Implementation

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    First Order Filter Implementation

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    First Order Filter Implementation

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    Second Order Filter Implementation

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    Second Order Filter ImplementationSallen and Key Topology for 2 nd Order Lowpass Filter

    Sallen and Key Topology for 2 nd Order Lowpass Filter

    (Unity Gain)

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    Second Order Filter ImplementationSallen and Key Topology for 2 nd Order Lowpass Filter

    Unity Gain

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    Sallen and Key Topology for 2 nd Order Lowpass Filter

    Unity Gain

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    Second Order Filter ImplementationMultiple Feedback Topology for 2 nd Order Lowpass Filter

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    Second Order Filter ImplementationMultiple Feedback Topology for 2 nd Order Lowpass Filter

    Sallen and Key

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    Second Order Filter ImplementationMultiple Feedback Topology for 2 nd Order Lowpass Filter

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    Second Order Filter ImplementationMultiple Feedback Topology for 2 nd Order Lowpass Filter

    where

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    Cascading of Filter Stages to Achieve Higher Order Filters

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    High-Pass Filter Design

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    High-pass Low-pass

    Noninverting

    Inverting

    First Order High- and Low-pass Filter Topologies

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    High-passLow-pass

    Noninverting

    First Order High- and Low-pass Filter Topologies

    Low-pass High-passExchange Rs with Cs

    1/

    S 1/S

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    High-passLow-passNoninverting

    First Order High- and Low-pass Filter Topologies

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    High-pass

    Noninverting

    First Order High- and Low-pass Filter Topologies

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    High-pass Low-pass

    Second Order High- and Low-pass Filter Topologies

    Sallen and Key

    Multiple Feedback

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    Low-pass to Band-pass Filter Design

    S

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    Low-pass to Band-pass Filter Design

    S

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    Low-pass to Band-pass Filter Design

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    Low-pass to Band-pass Filter Design

    Wide-band Filters

    Narrow-band Filters

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    High-pass Low-pass

    Sallen and Key Second Order Topologies

    Band-pass

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    Sallen and Key Band-pass Filter

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    High-pass Low-pass

    Multiple Feedback Second Order Topologies

    Band-pass

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    Multiple Feedback Band-pass Filter

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    Active Filter Design Techniques

    Fundamentals of Low-Pass Filters Low-Pass Filter Design High-Pass Filter Design Band-Pass Filter Design Band-Rejection Filter Design All-Pass Filter Design Practical Design Hints Design Tools

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    Band-Pass Filter Design

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    Band-Rejection Filter Design

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    All-Pass Filter Design

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    Practical Design Hints

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