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    Lic Ti-135-136

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    Barath Kumar
    The document discusses second-order low-pass filters, specifically the Sallen-Key and Multiple Feedback (MFB) topologies. It provides details on the Sallen-Key topology, including its general configuration, unity-gain configuration, advantages, and limitations. Equations for the transfer function and determining resistor and capacitor values for a unity-gain Sallen-Key filter are also presented. The MFB topology is noted to be used for high-Q filters but is more dependent on op-amp parameters.

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    Lic Ti-135-136

    Uploaded by

    Barath Kumar
    28 views2 pages
    The document discusses second-order low-pass filters, specifically the Sallen-Key and Multiple Feedback (MFB) topologies. It provides details on the Sallen-Key topology, including its general configuration, unity-gain configuration, advantages, and limitations. Equations for the transfer function and determining resistor and capacitor values for a unity-gain Sallen-Key filter are also presented. The MFB topology is noted to be used for high-Q filters but is more dependent on op-amp parameters.

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    The document discusses second-order low-pass filters, specifically the Sallen-Key and Multiple Feedback (MFB) topologies. It provides details on the Sallen-Key topology, including its general configuration, unity-gain configuration, advantages, and limitations. Equations for the transfer function and determining resistor and capacitor values for a unity-gain Sallen-Key filter are also presented. The MFB topology is noted to be used for high-Q filters but is more dependent on op-amp parameters.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    28 views2 pages

    Lic Ti-135-136

    Uploaded by

    Barath Kumar
    The document discusses second-order low-pass filters, specifically the Sallen-Key and Multiple Feedback (MFB) topologies. It provides details on the Sallen-Key topology, including its general configuration, unity-gain configuration, advantages, and limitations. Equations for the transfer function and determining resistor and capacitor values for a unity-gain Sallen-Key filter are also presented. The MFB topology is noted to be used for high-Q filters but is more dependent on op-amp parameters.

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    www.ti.

    com Butterworth Low-Pass Filters

    4.6.3. Second-Order Low-Pass Filter


    There are two topologies for a second-order low-pass filter - the Sallen-Key and the Multiple Feedback
    (MFB) topologies.

    4.6.3.1. Sallen-Key Topology


    The general Sallen-Key topology in Figure 4.12 allows for separate gain setting via A0= 1+R4/R3.
    However, the unity-gain topology in Figure 4.13 is usually applied in filter designs with high gain
    accuracy, unity gain, and low Qs (Q < 3).

    Fig 4.12 General Sallen-Key Low-Pass Filter

    Fig 4.13 Unity-Gain Sallen-Key Low-Pass Filter

    Active Filter 135


    Butterworth Low-Pass Filters www.ti.com

    This configuration shows the least dependence of filter performance on the performance of the op amp
    because the op amp is configured as an amplifier, as opposed to an integrator, which minimizes the
    gain-bandwidth requirements of the op amp. Another advantage of this configuration is that the ratio of
    the largest resistor value to the smallest resistor value, and the ratio of the largest capacitor value to
    the smallest capacitor value (component spread) are low, which is beneficial for manufacturability.
    While the Sallen-Key filter is widely used, a serious drawback is that the filter is not easily tuned, due
    to interaction of the component values on F0 and Q. Another limitation is the relatively low maximum Q
    value obtainable.
    The transfer function of circuit shown in figure 4.12 yields:

    Ao
    A( s)  (4.11)
    1  wc C1 ( R1  R2 )  (1  A0 ) R1C 2 s  wc2 R1 R2 C1C 2 s 2
    For the unity-gain circuit in Figure 4.12 (Ao=1), the transfer function simplifies to:
    1
    A( s ) 
    1  wc C1 ( R1  R2 ) s  wc2 R1 R2 C1C 2 s 2 (4.12)
    The coefficient comparison between this transfer function yields:
    Ao  1
    a1  wc C1 ( R1  R2 )
    b1  wc2 R1 R2 C1C 2 (4.13)
    Given C1 and C2, the resistor values for R1 and R2 are calculated through:

    a1C 2  a12 C 22  4b1C1C 2


    R1, 2 
    4f c C1C 2 (4.14)
    Table 4.1 Second order filter coefficients for Butterworth and Chebyshev filters

    SECOND-ORDER BUTTERWORTH 3- dB CHEBYSHEV

    a1 1.4142 1.065

    b1 1 1.9305

    Q 0.71 1.3

    R4/R3 0.568 0.234

    4.6.3.2. Multiple Feedback Topology


    The MFB topology is commonly used in filters that have high Qs and require a high gain. Therefore,
    the dependence of the transfer function on the op amp parameters is greater than in the Sallen-Key
    realization. It is difficult to generate high Q, high frequency sections due to the limitations of the open-
    loop gain of the op amp. The peaking due to Q causes amplitude, A0
    𝐴0 = 𝐻 𝑄 (4.15)
    Where H is the gain of the circuit. The multiple feedback filter inverts the phase of the signal. This is
    equivalent to adding the resulting 180° phase shift to the phase shift of the filter itself.

    136 Active Filter

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