Active filter with series inductor and resistor - do these exist? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Second order active filter design using differentiatorActive and Passive FilterActive Notch Filter SimulationTwin T active notch filterFrequency characteristic of active high pass filterSallen-Key active bandpass first order filterLoudspeaker crossover network using Sallen key filters (MATLAB transfer functions)Choosing resistor and capacitor for active filterActive inductor CircuitPurpose of a resistor in active filter circuit

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Active filter with series inductor and resistor - do these exist?



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Second order active filter design using differentiatorActive and Passive FilterActive Notch Filter SimulationTwin T active notch filterFrequency characteristic of active high pass filterSallen-Key active bandpass first order filterLoudspeaker crossover network using Sallen key filters (MATLAB transfer functions)Choosing resistor and capacitor for active filterActive inductor CircuitPurpose of a resistor in active filter circuit



.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;








5












$begingroup$


I have seen (online) and in books basic active filters (involving an op-amp) with a series R C branch at the input side. This series R C branch at the input side would make the circuit a high-pass filter. Series RC configuration at the input is quite commonly seen online. However, there appear to be no circuit diagrams seen online involving series R and L (resistor and inductor in series) for the input branch, as shown below in the drawing. enter image description here



There is likely some reasons for no diagrams like this seen online - anywhere. I don't know those reasons, and definitely interested to know why. Anyone know why op-amp configurations with series RL inputs are not seen? Thanks in advance for any comments!










share|improve this question









New contributor




Kenny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$







  • 2




    $begingroup$
    This is a really excellent question. I remember when I was a student, I always wondered where inductors went when we got into the topic of amplifiers and transistors.
    $endgroup$
    – KingDuken
    Apr 14 at 16:34

















5












$begingroup$


I have seen (online) and in books basic active filters (involving an op-amp) with a series R C branch at the input side. This series R C branch at the input side would make the circuit a high-pass filter. Series RC configuration at the input is quite commonly seen online. However, there appear to be no circuit diagrams seen online involving series R and L (resistor and inductor in series) for the input branch, as shown below in the drawing. enter image description here



There is likely some reasons for no diagrams like this seen online - anywhere. I don't know those reasons, and definitely interested to know why. Anyone know why op-amp configurations with series RL inputs are not seen? Thanks in advance for any comments!










share|improve this question









New contributor




Kenny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$







  • 2




    $begingroup$
    This is a really excellent question. I remember when I was a student, I always wondered where inductors went when we got into the topic of amplifiers and transistors.
    $endgroup$
    – KingDuken
    Apr 14 at 16:34













5












5








5


1



$begingroup$


I have seen (online) and in books basic active filters (involving an op-amp) with a series R C branch at the input side. This series R C branch at the input side would make the circuit a high-pass filter. Series RC configuration at the input is quite commonly seen online. However, there appear to be no circuit diagrams seen online involving series R and L (resistor and inductor in series) for the input branch, as shown below in the drawing. enter image description here



There is likely some reasons for no diagrams like this seen online - anywhere. I don't know those reasons, and definitely interested to know why. Anyone know why op-amp configurations with series RL inputs are not seen? Thanks in advance for any comments!










share|improve this question









New contributor




Kenny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I have seen (online) and in books basic active filters (involving an op-amp) with a series R C branch at the input side. This series R C branch at the input side would make the circuit a high-pass filter. Series RC configuration at the input is quite commonly seen online. However, there appear to be no circuit diagrams seen online involving series R and L (resistor and inductor in series) for the input branch, as shown below in the drawing. enter image description here



There is likely some reasons for no diagrams like this seen online - anywhere. I don't know those reasons, and definitely interested to know why. Anyone know why op-amp configurations with series RL inputs are not seen? Thanks in advance for any comments!







active-filter






share|improve this question









New contributor




Kenny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




Kenny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited Apr 14 at 21:00







Kenny













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asked Apr 14 at 2:41









KennyKenny

263




263




New contributor




Kenny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor





Kenny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Kenny is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







  • 2




    $begingroup$
    This is a really excellent question. I remember when I was a student, I always wondered where inductors went when we got into the topic of amplifiers and transistors.
    $endgroup$
    – KingDuken
    Apr 14 at 16:34












  • 2




    $begingroup$
    This is a really excellent question. I remember when I was a student, I always wondered where inductors went when we got into the topic of amplifiers and transistors.
    $endgroup$
    – KingDuken
    Apr 14 at 16:34







2




2




$begingroup$
This is a really excellent question. I remember when I was a student, I always wondered where inductors went when we got into the topic of amplifiers and transistors.
$endgroup$
– KingDuken
Apr 14 at 16:34




$begingroup$
This is a really excellent question. I remember when I was a student, I always wondered where inductors went when we got into the topic of amplifiers and transistors.
$endgroup$
– KingDuken
Apr 14 at 16:34










3 Answers
3






active

oldest

votes


















12












$begingroup$

Inductors are generally more expensive, more bulky and less ideal than capacitors so you'll usually see a strong preference for capacitors over inductors. Only very tiny values can be put into an IC, whereas useful values of capacitors can be integrated.



However, series inductance is frequently used where conductors enter a shielded enclosure or signals enter a PCB. Sometimes as inductors, sometimes as ferrite beads (which are inductive over a range of frequencies) and sometimes as common-mode chokes.






share|improve this answer











$endgroup$








  • 1




    $begingroup$
    Thanks very much for your help Spehro! Really appreciated that a lot. I attempted to add +1 to your reply, but getting a popup message that says users with less than some number of reputation points can't do the +1 (or something like that!). Thanks again!
    $endgroup$
    – Kenny
    Apr 14 at 2:46







  • 3




    $begingroup$
    You won't be able to upvote comments until you get more reputation, but you can accept answers or not. It's recommended to wait some time before accepting a given answer because a better answer may come along.
    $endgroup$
    – Spehro Pefhany
    Apr 14 at 3:06


















6












$begingroup$

To add to Sphero Pefhany's reasons, the circuit as shown has a gain at DC, which may cause issues with the following circuitry because of any DC offset voltage in the amplifier.



Also, if the power supply is disconnected at the instant while current is flowing through the inductor, the induced (possibly large) voltage spike may damage other components. Adding protection diodes etc in a simple way would most likely make the response of the circuit nonlinear.



Circuits using capacitors are immune from issues like the above.



Note that using active circuit elements like op amps, it is possible to create a "virtual inductor," as in this example circuit. Such virtual inductors can have a wider range of values and be closer to ideal components than real inductors, are unaffected by stray magnetic fields, and do not have the same issues with high back EMFs. Unless the "non-ideal" and/or non-linear behaviour of a real inductor is essential for a circuit to function correctly, it is not necessary to use an inductor at all.






share|improve this answer









$endgroup$




















    5












    $begingroup$

    The primary reasons for not using inductors in filters is that it is bulky. It takes up considerable amount of space as compared to resistors and capacitor if fabrication is done. Cost is also a factor. There is also a fundamental reason for not using inductors. For an inductor, impedance goes up with frequency. It behaves as a short circuit at low frequencies, and an open circuit at high frequencies which may be pose a problem for the user. So, operating frequency has to be selected properly for proper operation.



    Other reasons includes inductors are known to show parasitic effect i.e if current is passed through inductors, magnetic field is generated which may change the impedance of other components and as a result the net impedance of circuit is changed. So, cutoff frequency also changes. Also, inductors used in circuits do not possess much of an inductance. So, if they are to be used in filters, cutoff frequency do not change a lot. So, presence of inductors in filter do not make much of a difference.



    Inductors are severely nonideal as compared to resistors and capacitors and this nonlinearity may pose problem when deriving the transfer function of the filter. Lastly, inductors generate electromagnetic interference(EMI) than resitor and capacitor and also they are more susceptible to EMI.



    I could find a parallel R-L connection in a filter which is a 1st order active HPF and also an inductor in feedback present in a 2nd order active cascade HPF.



    enter image description here



    enter image description here



    References




    1. https://www.cs.cmu.edu/~tdear/ee/filters.pdf (pictures)

    2. http://www.swarthmore.edu/NatSci/echeeve1/Ref/FilterBkgrnd/Filters.html

    3. http://alignment.hep.brandeis.edu/Lab/Filter/Filter.html

    4. https://www.allaboutcircuits.com/technical-articles/inductor-out-op-amp-in-an-introduction-to-second-order-active-filters/





    share|improve this answer









    $endgroup$













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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      12












      $begingroup$

      Inductors are generally more expensive, more bulky and less ideal than capacitors so you'll usually see a strong preference for capacitors over inductors. Only very tiny values can be put into an IC, whereas useful values of capacitors can be integrated.



      However, series inductance is frequently used where conductors enter a shielded enclosure or signals enter a PCB. Sometimes as inductors, sometimes as ferrite beads (which are inductive over a range of frequencies) and sometimes as common-mode chokes.






      share|improve this answer











      $endgroup$








      • 1




        $begingroup$
        Thanks very much for your help Spehro! Really appreciated that a lot. I attempted to add +1 to your reply, but getting a popup message that says users with less than some number of reputation points can't do the +1 (or something like that!). Thanks again!
        $endgroup$
        – Kenny
        Apr 14 at 2:46







      • 3




        $begingroup$
        You won't be able to upvote comments until you get more reputation, but you can accept answers or not. It's recommended to wait some time before accepting a given answer because a better answer may come along.
        $endgroup$
        – Spehro Pefhany
        Apr 14 at 3:06















      12












      $begingroup$

      Inductors are generally more expensive, more bulky and less ideal than capacitors so you'll usually see a strong preference for capacitors over inductors. Only very tiny values can be put into an IC, whereas useful values of capacitors can be integrated.



      However, series inductance is frequently used where conductors enter a shielded enclosure or signals enter a PCB. Sometimes as inductors, sometimes as ferrite beads (which are inductive over a range of frequencies) and sometimes as common-mode chokes.






      share|improve this answer











      $endgroup$








      • 1




        $begingroup$
        Thanks very much for your help Spehro! Really appreciated that a lot. I attempted to add +1 to your reply, but getting a popup message that says users with less than some number of reputation points can't do the +1 (or something like that!). Thanks again!
        $endgroup$
        – Kenny
        Apr 14 at 2:46







      • 3




        $begingroup$
        You won't be able to upvote comments until you get more reputation, but you can accept answers or not. It's recommended to wait some time before accepting a given answer because a better answer may come along.
        $endgroup$
        – Spehro Pefhany
        Apr 14 at 3:06













      12












      12








      12





      $begingroup$

      Inductors are generally more expensive, more bulky and less ideal than capacitors so you'll usually see a strong preference for capacitors over inductors. Only very tiny values can be put into an IC, whereas useful values of capacitors can be integrated.



      However, series inductance is frequently used where conductors enter a shielded enclosure or signals enter a PCB. Sometimes as inductors, sometimes as ferrite beads (which are inductive over a range of frequencies) and sometimes as common-mode chokes.






      share|improve this answer











      $endgroup$



      Inductors are generally more expensive, more bulky and less ideal than capacitors so you'll usually see a strong preference for capacitors over inductors. Only very tiny values can be put into an IC, whereas useful values of capacitors can be integrated.



      However, series inductance is frequently used where conductors enter a shielded enclosure or signals enter a PCB. Sometimes as inductors, sometimes as ferrite beads (which are inductive over a range of frequencies) and sometimes as common-mode chokes.







      share|improve this answer














      share|improve this answer



      share|improve this answer








      edited Apr 14 at 16:43

























      answered Apr 14 at 2:45









      Spehro PefhanySpehro Pefhany

      214k5164436




      214k5164436







      • 1




        $begingroup$
        Thanks very much for your help Spehro! Really appreciated that a lot. I attempted to add +1 to your reply, but getting a popup message that says users with less than some number of reputation points can't do the +1 (or something like that!). Thanks again!
        $endgroup$
        – Kenny
        Apr 14 at 2:46







      • 3




        $begingroup$
        You won't be able to upvote comments until you get more reputation, but you can accept answers or not. It's recommended to wait some time before accepting a given answer because a better answer may come along.
        $endgroup$
        – Spehro Pefhany
        Apr 14 at 3:06












      • 1




        $begingroup$
        Thanks very much for your help Spehro! Really appreciated that a lot. I attempted to add +1 to your reply, but getting a popup message that says users with less than some number of reputation points can't do the +1 (or something like that!). Thanks again!
        $endgroup$
        – Kenny
        Apr 14 at 2:46







      • 3




        $begingroup$
        You won't be able to upvote comments until you get more reputation, but you can accept answers or not. It's recommended to wait some time before accepting a given answer because a better answer may come along.
        $endgroup$
        – Spehro Pefhany
        Apr 14 at 3:06







      1




      1




      $begingroup$
      Thanks very much for your help Spehro! Really appreciated that a lot. I attempted to add +1 to your reply, but getting a popup message that says users with less than some number of reputation points can't do the +1 (or something like that!). Thanks again!
      $endgroup$
      – Kenny
      Apr 14 at 2:46





      $begingroup$
      Thanks very much for your help Spehro! Really appreciated that a lot. I attempted to add +1 to your reply, but getting a popup message that says users with less than some number of reputation points can't do the +1 (or something like that!). Thanks again!
      $endgroup$
      – Kenny
      Apr 14 at 2:46





      3




      3




      $begingroup$
      You won't be able to upvote comments until you get more reputation, but you can accept answers or not. It's recommended to wait some time before accepting a given answer because a better answer may come along.
      $endgroup$
      – Spehro Pefhany
      Apr 14 at 3:06




      $begingroup$
      You won't be able to upvote comments until you get more reputation, but you can accept answers or not. It's recommended to wait some time before accepting a given answer because a better answer may come along.
      $endgroup$
      – Spehro Pefhany
      Apr 14 at 3:06













      6












      $begingroup$

      To add to Sphero Pefhany's reasons, the circuit as shown has a gain at DC, which may cause issues with the following circuitry because of any DC offset voltage in the amplifier.



      Also, if the power supply is disconnected at the instant while current is flowing through the inductor, the induced (possibly large) voltage spike may damage other components. Adding protection diodes etc in a simple way would most likely make the response of the circuit nonlinear.



      Circuits using capacitors are immune from issues like the above.



      Note that using active circuit elements like op amps, it is possible to create a "virtual inductor," as in this example circuit. Such virtual inductors can have a wider range of values and be closer to ideal components than real inductors, are unaffected by stray magnetic fields, and do not have the same issues with high back EMFs. Unless the "non-ideal" and/or non-linear behaviour of a real inductor is essential for a circuit to function correctly, it is not necessary to use an inductor at all.






      share|improve this answer









      $endgroup$

















        6












        $begingroup$

        To add to Sphero Pefhany's reasons, the circuit as shown has a gain at DC, which may cause issues with the following circuitry because of any DC offset voltage in the amplifier.



        Also, if the power supply is disconnected at the instant while current is flowing through the inductor, the induced (possibly large) voltage spike may damage other components. Adding protection diodes etc in a simple way would most likely make the response of the circuit nonlinear.



        Circuits using capacitors are immune from issues like the above.



        Note that using active circuit elements like op amps, it is possible to create a "virtual inductor," as in this example circuit. Such virtual inductors can have a wider range of values and be closer to ideal components than real inductors, are unaffected by stray magnetic fields, and do not have the same issues with high back EMFs. Unless the "non-ideal" and/or non-linear behaviour of a real inductor is essential for a circuit to function correctly, it is not necessary to use an inductor at all.






        share|improve this answer









        $endgroup$















          6












          6








          6





          $begingroup$

          To add to Sphero Pefhany's reasons, the circuit as shown has a gain at DC, which may cause issues with the following circuitry because of any DC offset voltage in the amplifier.



          Also, if the power supply is disconnected at the instant while current is flowing through the inductor, the induced (possibly large) voltage spike may damage other components. Adding protection diodes etc in a simple way would most likely make the response of the circuit nonlinear.



          Circuits using capacitors are immune from issues like the above.



          Note that using active circuit elements like op amps, it is possible to create a "virtual inductor," as in this example circuit. Such virtual inductors can have a wider range of values and be closer to ideal components than real inductors, are unaffected by stray magnetic fields, and do not have the same issues with high back EMFs. Unless the "non-ideal" and/or non-linear behaviour of a real inductor is essential for a circuit to function correctly, it is not necessary to use an inductor at all.






          share|improve this answer









          $endgroup$



          To add to Sphero Pefhany's reasons, the circuit as shown has a gain at DC, which may cause issues with the following circuitry because of any DC offset voltage in the amplifier.



          Also, if the power supply is disconnected at the instant while current is flowing through the inductor, the induced (possibly large) voltage spike may damage other components. Adding protection diodes etc in a simple way would most likely make the response of the circuit nonlinear.



          Circuits using capacitors are immune from issues like the above.



          Note that using active circuit elements like op amps, it is possible to create a "virtual inductor," as in this example circuit. Such virtual inductors can have a wider range of values and be closer to ideal components than real inductors, are unaffected by stray magnetic fields, and do not have the same issues with high back EMFs. Unless the "non-ideal" and/or non-linear behaviour of a real inductor is essential for a circuit to function correctly, it is not necessary to use an inductor at all.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered Apr 14 at 9:01









          alephzeroalephzero

          952411




          952411





















              5












              $begingroup$

              The primary reasons for not using inductors in filters is that it is bulky. It takes up considerable amount of space as compared to resistors and capacitor if fabrication is done. Cost is also a factor. There is also a fundamental reason for not using inductors. For an inductor, impedance goes up with frequency. It behaves as a short circuit at low frequencies, and an open circuit at high frequencies which may be pose a problem for the user. So, operating frequency has to be selected properly for proper operation.



              Other reasons includes inductors are known to show parasitic effect i.e if current is passed through inductors, magnetic field is generated which may change the impedance of other components and as a result the net impedance of circuit is changed. So, cutoff frequency also changes. Also, inductors used in circuits do not possess much of an inductance. So, if they are to be used in filters, cutoff frequency do not change a lot. So, presence of inductors in filter do not make much of a difference.



              Inductors are severely nonideal as compared to resistors and capacitors and this nonlinearity may pose problem when deriving the transfer function of the filter. Lastly, inductors generate electromagnetic interference(EMI) than resitor and capacitor and also they are more susceptible to EMI.



              I could find a parallel R-L connection in a filter which is a 1st order active HPF and also an inductor in feedback present in a 2nd order active cascade HPF.



              enter image description here



              enter image description here



              References




              1. https://www.cs.cmu.edu/~tdear/ee/filters.pdf (pictures)

              2. http://www.swarthmore.edu/NatSci/echeeve1/Ref/FilterBkgrnd/Filters.html

              3. http://alignment.hep.brandeis.edu/Lab/Filter/Filter.html

              4. https://www.allaboutcircuits.com/technical-articles/inductor-out-op-amp-in-an-introduction-to-second-order-active-filters/





              share|improve this answer









              $endgroup$

















                5












                $begingroup$

                The primary reasons for not using inductors in filters is that it is bulky. It takes up considerable amount of space as compared to resistors and capacitor if fabrication is done. Cost is also a factor. There is also a fundamental reason for not using inductors. For an inductor, impedance goes up with frequency. It behaves as a short circuit at low frequencies, and an open circuit at high frequencies which may be pose a problem for the user. So, operating frequency has to be selected properly for proper operation.



                Other reasons includes inductors are known to show parasitic effect i.e if current is passed through inductors, magnetic field is generated which may change the impedance of other components and as a result the net impedance of circuit is changed. So, cutoff frequency also changes. Also, inductors used in circuits do not possess much of an inductance. So, if they are to be used in filters, cutoff frequency do not change a lot. So, presence of inductors in filter do not make much of a difference.



                Inductors are severely nonideal as compared to resistors and capacitors and this nonlinearity may pose problem when deriving the transfer function of the filter. Lastly, inductors generate electromagnetic interference(EMI) than resitor and capacitor and also they are more susceptible to EMI.



                I could find a parallel R-L connection in a filter which is a 1st order active HPF and also an inductor in feedback present in a 2nd order active cascade HPF.



                enter image description here



                enter image description here



                References




                1. https://www.cs.cmu.edu/~tdear/ee/filters.pdf (pictures)

                2. http://www.swarthmore.edu/NatSci/echeeve1/Ref/FilterBkgrnd/Filters.html

                3. http://alignment.hep.brandeis.edu/Lab/Filter/Filter.html

                4. https://www.allaboutcircuits.com/technical-articles/inductor-out-op-amp-in-an-introduction-to-second-order-active-filters/





                share|improve this answer









                $endgroup$















                  5












                  5








                  5





                  $begingroup$

                  The primary reasons for not using inductors in filters is that it is bulky. It takes up considerable amount of space as compared to resistors and capacitor if fabrication is done. Cost is also a factor. There is also a fundamental reason for not using inductors. For an inductor, impedance goes up with frequency. It behaves as a short circuit at low frequencies, and an open circuit at high frequencies which may be pose a problem for the user. So, operating frequency has to be selected properly for proper operation.



                  Other reasons includes inductors are known to show parasitic effect i.e if current is passed through inductors, magnetic field is generated which may change the impedance of other components and as a result the net impedance of circuit is changed. So, cutoff frequency also changes. Also, inductors used in circuits do not possess much of an inductance. So, if they are to be used in filters, cutoff frequency do not change a lot. So, presence of inductors in filter do not make much of a difference.



                  Inductors are severely nonideal as compared to resistors and capacitors and this nonlinearity may pose problem when deriving the transfer function of the filter. Lastly, inductors generate electromagnetic interference(EMI) than resitor and capacitor and also they are more susceptible to EMI.



                  I could find a parallel R-L connection in a filter which is a 1st order active HPF and also an inductor in feedback present in a 2nd order active cascade HPF.



                  enter image description here



                  enter image description here



                  References




                  1. https://www.cs.cmu.edu/~tdear/ee/filters.pdf (pictures)

                  2. http://www.swarthmore.edu/NatSci/echeeve1/Ref/FilterBkgrnd/Filters.html

                  3. http://alignment.hep.brandeis.edu/Lab/Filter/Filter.html

                  4. https://www.allaboutcircuits.com/technical-articles/inductor-out-op-amp-in-an-introduction-to-second-order-active-filters/





                  share|improve this answer









                  $endgroup$



                  The primary reasons for not using inductors in filters is that it is bulky. It takes up considerable amount of space as compared to resistors and capacitor if fabrication is done. Cost is also a factor. There is also a fundamental reason for not using inductors. For an inductor, impedance goes up with frequency. It behaves as a short circuit at low frequencies, and an open circuit at high frequencies which may be pose a problem for the user. So, operating frequency has to be selected properly for proper operation.



                  Other reasons includes inductors are known to show parasitic effect i.e if current is passed through inductors, magnetic field is generated which may change the impedance of other components and as a result the net impedance of circuit is changed. So, cutoff frequency also changes. Also, inductors used in circuits do not possess much of an inductance. So, if they are to be used in filters, cutoff frequency do not change a lot. So, presence of inductors in filter do not make much of a difference.



                  Inductors are severely nonideal as compared to resistors and capacitors and this nonlinearity may pose problem when deriving the transfer function of the filter. Lastly, inductors generate electromagnetic interference(EMI) than resitor and capacitor and also they are more susceptible to EMI.



                  I could find a parallel R-L connection in a filter which is a 1st order active HPF and also an inductor in feedback present in a 2nd order active cascade HPF.



                  enter image description here



                  enter image description here



                  References




                  1. https://www.cs.cmu.edu/~tdear/ee/filters.pdf (pictures)

                  2. http://www.swarthmore.edu/NatSci/echeeve1/Ref/FilterBkgrnd/Filters.html

                  3. http://alignment.hep.brandeis.edu/Lab/Filter/Filter.html

                  4. https://www.allaboutcircuits.com/technical-articles/inductor-out-op-amp-in-an-introduction-to-second-order-active-filters/






                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered Apr 14 at 14:10









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