Reason for small-valued feedback resistors in low noise Op AmpOP-AMP Positive/Negative Feedback togetherop...

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Reason for small-valued feedback resistors in low noise Op Amp


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$begingroup$


I am wondering why the feedback resistor values specified in the datasheet of the AD797 are so small. My understanding is that the low feedback resistances keep the noise small, but isn't it also not ideal to have large currents flowing through the feedback network? My understanding was that feedback resistors should be >1k.



Here is a link to the datasheet: https://www.analog.com/media/en/technical-documentation/data-sheets/ad797.pdf



And a picture of an example application:
enter image description here



26.1 ohms seems like far too small a value for feedback resistors.










share|improve this question









$endgroup$

















    1












    $begingroup$


    I am wondering why the feedback resistor values specified in the datasheet of the AD797 are so small. My understanding is that the low feedback resistances keep the noise small, but isn't it also not ideal to have large currents flowing through the feedback network? My understanding was that feedback resistors should be >1k.



    Here is a link to the datasheet: https://www.analog.com/media/en/technical-documentation/data-sheets/ad797.pdf



    And a picture of an example application:
    enter image description here



    26.1 ohms seems like far too small a value for feedback resistors.










    share|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      I am wondering why the feedback resistor values specified in the datasheet of the AD797 are so small. My understanding is that the low feedback resistances keep the noise small, but isn't it also not ideal to have large currents flowing through the feedback network? My understanding was that feedback resistors should be >1k.



      Here is a link to the datasheet: https://www.analog.com/media/en/technical-documentation/data-sheets/ad797.pdf



      And a picture of an example application:
      enter image description here



      26.1 ohms seems like far too small a value for feedback resistors.










      share|improve this question









      $endgroup$




      I am wondering why the feedback resistor values specified in the datasheet of the AD797 are so small. My understanding is that the low feedback resistances keep the noise small, but isn't it also not ideal to have large currents flowing through the feedback network? My understanding was that feedback resistors should be >1k.



      Here is a link to the datasheet: https://www.analog.com/media/en/technical-documentation/data-sheets/ad797.pdf



      And a picture of an example application:
      enter image description here



      26.1 ohms seems like far too small a value for feedback resistors.







      op-amp feedback






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 3 hours ago









      SaundersSaunders

      515




      515






















          5 Answers
          5






          active

          oldest

          votes


















          3












          $begingroup$

          This op-amp boasts input noise of 0.9nV/rt.Hz, which is roughly equal to the Johnson noise of a 50 Ω resistor over the human audio bandwidth. If you aren't putting resistors smaller than that around it, you're wasting some of this op-amp's performance, and probably should be buying something cheaper.






          share|improve this answer









          $endgroup$





















            0












            $begingroup$

            A graph in the datasheet of the opamp shows it clipping with an output voltage swing of only plus and minus 2V into the 26.1 ohm resistors which might not be enough.






            share|improve this answer









            $endgroup$













            • $begingroup$
              But the graph has it rated down to about 20 ohms, with a weak output as you indicated. Up to the designer to keep the load over 50 ohms if possible. At 200 ohm loads you get full output swing.
              $endgroup$
              – Sparky256
              2 hours ago






            • 1




              $begingroup$
              Thank you for making an intelligent comment. In the future, please use the comment section when you want to make an intelligent comment. I believe you have enough reputation to do so. We try to reserve the Answer section for answers to the question.
              $endgroup$
              – mkeith
              2 hours ago



















            0












            $begingroup$

            If you refer to figure 34, the total noise (assumed to be the white noise region for both en and in) is approximately 8x better at 10 ohms source resistance compared to 1K.



            enter image description here



            Remember that it’s not only the noise voltage and the Johnson-Nyquist noise from the feedback resistors but the input noise current multiplied by the resistance seen looking out from the inverting input.



            The transistors at the input are run at very high currents so the voltage noise is quite low, but there is a cost in current noise.



            They all add in quadrature, of course, since they are typically uncorrelated.



            The resistors as shown are tolerable for smallish output swings and if you don’t care too much about accuracy of gain.






            share|improve this answer









            $endgroup$





















              0












              $begingroup$

              Datasheet states that with +/- 5 volt supplies minimum load is 30 ohms. At +/-15 volts minimum load is 200 ohms. Output resistance is 3 milliohms. GBW at G = 10 is 8MHZ. This is a awesome op-amp. It is not the fastest or has the lowest noise for audio purest, but for a GP op-amp is it much better than just 'ok'.



              Due to a fast slew rate the board layout needs to be as good as if this was an RF amp IC. 100nF bypass capacitors right at the supply pins, or within 1/4" or 7mm. Close by should be 4.7uF MLCC caps, plus within a few inches 100uF aluminum caps for wide band filtering, and a stable supply when driving 50 ohm or even 600 ohm loads.



              The resistors shown in the schematic are the lowest safe value possible, and still maintain somewhat normal operation. The idea here is to get the resistor noise levels to a minimum. Many op-amps could not tolerate such low resistor values, but that resistance range is on the datasheet. It is implied on the datasheet that at such low resistance levels supply voltage should be +/- 5 volts.






              share|improve this answer











              $endgroup$













              • $begingroup$
                I am still confused. Are these anwsers trying to say that the feedback resistors factor into the load resistance of the op amp? If that were the case why not use large valued resistors
                $endgroup$
                – Saunders
                2 hours ago






              • 2




                $begingroup$
                But why are the resistors small?
                $endgroup$
                – Scott Seidman
                2 hours ago










              • $begingroup$
                @ScottSeidman To keep the noise level extra low, though it loads the op-amp at its minimal limits.
                $endgroup$
                – Sparky256
                26 mins ago



















              0












              $begingroup$

              With honor to Walt Jung (of ADI, et al), low values of resistors can cause detectable THERMAL distortion. Drive the opamp with 20Hz and 2,000Hz; use a spectrum analyzer, and you'll see the 2,000Hz output with some 20Hz sidebands.



              Which means what? Use physically larger resistors. Or experiment with resistors having different resistive element structures? The very thin metal-file-spiral-trimmed has a very fast timeconstant for heating/cooling, as heat is dumped into the ceramic/clay core.





              share









              $endgroup$













                Your Answer





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                5 Answers
                5






                active

                oldest

                votes








                5 Answers
                5






                active

                oldest

                votes









                active

                oldest

                votes






                active

                oldest

                votes









                3












                $begingroup$

                This op-amp boasts input noise of 0.9nV/rt.Hz, which is roughly equal to the Johnson noise of a 50 Ω resistor over the human audio bandwidth. If you aren't putting resistors smaller than that around it, you're wasting some of this op-amp's performance, and probably should be buying something cheaper.






                share|improve this answer









                $endgroup$


















                  3












                  $begingroup$

                  This op-amp boasts input noise of 0.9nV/rt.Hz, which is roughly equal to the Johnson noise of a 50 Ω resistor over the human audio bandwidth. If you aren't putting resistors smaller than that around it, you're wasting some of this op-amp's performance, and probably should be buying something cheaper.






                  share|improve this answer









                  $endgroup$
















                    3












                    3








                    3





                    $begingroup$

                    This op-amp boasts input noise of 0.9nV/rt.Hz, which is roughly equal to the Johnson noise of a 50 Ω resistor over the human audio bandwidth. If you aren't putting resistors smaller than that around it, you're wasting some of this op-amp's performance, and probably should be buying something cheaper.






                    share|improve this answer









                    $endgroup$



                    This op-amp boasts input noise of 0.9nV/rt.Hz, which is roughly equal to the Johnson noise of a 50 Ω resistor over the human audio bandwidth. If you aren't putting resistors smaller than that around it, you're wasting some of this op-amp's performance, and probably should be buying something cheaper.







                    share|improve this answer












                    share|improve this answer



                    share|improve this answer










                    answered 1 hour ago









                    Warren YoungWarren Young

                    3,3571628




                    3,3571628

























                        0












                        $begingroup$

                        A graph in the datasheet of the opamp shows it clipping with an output voltage swing of only plus and minus 2V into the 26.1 ohm resistors which might not be enough.






                        share|improve this answer









                        $endgroup$













                        • $begingroup$
                          But the graph has it rated down to about 20 ohms, with a weak output as you indicated. Up to the designer to keep the load over 50 ohms if possible. At 200 ohm loads you get full output swing.
                          $endgroup$
                          – Sparky256
                          2 hours ago






                        • 1




                          $begingroup$
                          Thank you for making an intelligent comment. In the future, please use the comment section when you want to make an intelligent comment. I believe you have enough reputation to do so. We try to reserve the Answer section for answers to the question.
                          $endgroup$
                          – mkeith
                          2 hours ago
















                        0












                        $begingroup$

                        A graph in the datasheet of the opamp shows it clipping with an output voltage swing of only plus and minus 2V into the 26.1 ohm resistors which might not be enough.






                        share|improve this answer









                        $endgroup$













                        • $begingroup$
                          But the graph has it rated down to about 20 ohms, with a weak output as you indicated. Up to the designer to keep the load over 50 ohms if possible. At 200 ohm loads you get full output swing.
                          $endgroup$
                          – Sparky256
                          2 hours ago






                        • 1




                          $begingroup$
                          Thank you for making an intelligent comment. In the future, please use the comment section when you want to make an intelligent comment. I believe you have enough reputation to do so. We try to reserve the Answer section for answers to the question.
                          $endgroup$
                          – mkeith
                          2 hours ago














                        0












                        0








                        0





                        $begingroup$

                        A graph in the datasheet of the opamp shows it clipping with an output voltage swing of only plus and minus 2V into the 26.1 ohm resistors which might not be enough.






                        share|improve this answer









                        $endgroup$



                        A graph in the datasheet of the opamp shows it clipping with an output voltage swing of only plus and minus 2V into the 26.1 ohm resistors which might not be enough.







                        share|improve this answer












                        share|improve this answer



                        share|improve this answer










                        answered 3 hours ago









                        AudioguruAudioguru

                        42413




                        42413












                        • $begingroup$
                          But the graph has it rated down to about 20 ohms, with a weak output as you indicated. Up to the designer to keep the load over 50 ohms if possible. At 200 ohm loads you get full output swing.
                          $endgroup$
                          – Sparky256
                          2 hours ago






                        • 1




                          $begingroup$
                          Thank you for making an intelligent comment. In the future, please use the comment section when you want to make an intelligent comment. I believe you have enough reputation to do so. We try to reserve the Answer section for answers to the question.
                          $endgroup$
                          – mkeith
                          2 hours ago


















                        • $begingroup$
                          But the graph has it rated down to about 20 ohms, with a weak output as you indicated. Up to the designer to keep the load over 50 ohms if possible. At 200 ohm loads you get full output swing.
                          $endgroup$
                          – Sparky256
                          2 hours ago






                        • 1




                          $begingroup$
                          Thank you for making an intelligent comment. In the future, please use the comment section when you want to make an intelligent comment. I believe you have enough reputation to do so. We try to reserve the Answer section for answers to the question.
                          $endgroup$
                          – mkeith
                          2 hours ago
















                        $begingroup$
                        But the graph has it rated down to about 20 ohms, with a weak output as you indicated. Up to the designer to keep the load over 50 ohms if possible. At 200 ohm loads you get full output swing.
                        $endgroup$
                        – Sparky256
                        2 hours ago




                        $begingroup$
                        But the graph has it rated down to about 20 ohms, with a weak output as you indicated. Up to the designer to keep the load over 50 ohms if possible. At 200 ohm loads you get full output swing.
                        $endgroup$
                        – Sparky256
                        2 hours ago




                        1




                        1




                        $begingroup$
                        Thank you for making an intelligent comment. In the future, please use the comment section when you want to make an intelligent comment. I believe you have enough reputation to do so. We try to reserve the Answer section for answers to the question.
                        $endgroup$
                        – mkeith
                        2 hours ago




                        $begingroup$
                        Thank you for making an intelligent comment. In the future, please use the comment section when you want to make an intelligent comment. I believe you have enough reputation to do so. We try to reserve the Answer section for answers to the question.
                        $endgroup$
                        – mkeith
                        2 hours ago











                        0












                        $begingroup$

                        If you refer to figure 34, the total noise (assumed to be the white noise region for both en and in) is approximately 8x better at 10 ohms source resistance compared to 1K.



                        enter image description here



                        Remember that it’s not only the noise voltage and the Johnson-Nyquist noise from the feedback resistors but the input noise current multiplied by the resistance seen looking out from the inverting input.



                        The transistors at the input are run at very high currents so the voltage noise is quite low, but there is a cost in current noise.



                        They all add in quadrature, of course, since they are typically uncorrelated.



                        The resistors as shown are tolerable for smallish output swings and if you don’t care too much about accuracy of gain.






                        share|improve this answer









                        $endgroup$


















                          0












                          $begingroup$

                          If you refer to figure 34, the total noise (assumed to be the white noise region for both en and in) is approximately 8x better at 10 ohms source resistance compared to 1K.



                          enter image description here



                          Remember that it’s not only the noise voltage and the Johnson-Nyquist noise from the feedback resistors but the input noise current multiplied by the resistance seen looking out from the inverting input.



                          The transistors at the input are run at very high currents so the voltage noise is quite low, but there is a cost in current noise.



                          They all add in quadrature, of course, since they are typically uncorrelated.



                          The resistors as shown are tolerable for smallish output swings and if you don’t care too much about accuracy of gain.






                          share|improve this answer









                          $endgroup$
















                            0












                            0








                            0





                            $begingroup$

                            If you refer to figure 34, the total noise (assumed to be the white noise region for both en and in) is approximately 8x better at 10 ohms source resistance compared to 1K.



                            enter image description here



                            Remember that it’s not only the noise voltage and the Johnson-Nyquist noise from the feedback resistors but the input noise current multiplied by the resistance seen looking out from the inverting input.



                            The transistors at the input are run at very high currents so the voltage noise is quite low, but there is a cost in current noise.



                            They all add in quadrature, of course, since they are typically uncorrelated.



                            The resistors as shown are tolerable for smallish output swings and if you don’t care too much about accuracy of gain.






                            share|improve this answer









                            $endgroup$



                            If you refer to figure 34, the total noise (assumed to be the white noise region for both en and in) is approximately 8x better at 10 ohms source resistance compared to 1K.



                            enter image description here



                            Remember that it’s not only the noise voltage and the Johnson-Nyquist noise from the feedback resistors but the input noise current multiplied by the resistance seen looking out from the inverting input.



                            The transistors at the input are run at very high currents so the voltage noise is quite low, but there is a cost in current noise.



                            They all add in quadrature, of course, since they are typically uncorrelated.



                            The resistors as shown are tolerable for smallish output swings and if you don’t care too much about accuracy of gain.







                            share|improve this answer












                            share|improve this answer



                            share|improve this answer










                            answered 2 hours ago









                            Spehro PefhanySpehro Pefhany

                            208k5159421




                            208k5159421























                                0












                                $begingroup$

                                Datasheet states that with +/- 5 volt supplies minimum load is 30 ohms. At +/-15 volts minimum load is 200 ohms. Output resistance is 3 milliohms. GBW at G = 10 is 8MHZ. This is a awesome op-amp. It is not the fastest or has the lowest noise for audio purest, but for a GP op-amp is it much better than just 'ok'.



                                Due to a fast slew rate the board layout needs to be as good as if this was an RF amp IC. 100nF bypass capacitors right at the supply pins, or within 1/4" or 7mm. Close by should be 4.7uF MLCC caps, plus within a few inches 100uF aluminum caps for wide band filtering, and a stable supply when driving 50 ohm or even 600 ohm loads.



                                The resistors shown in the schematic are the lowest safe value possible, and still maintain somewhat normal operation. The idea here is to get the resistor noise levels to a minimum. Many op-amps could not tolerate such low resistor values, but that resistance range is on the datasheet. It is implied on the datasheet that at such low resistance levels supply voltage should be +/- 5 volts.






                                share|improve this answer











                                $endgroup$













                                • $begingroup$
                                  I am still confused. Are these anwsers trying to say that the feedback resistors factor into the load resistance of the op amp? If that were the case why not use large valued resistors
                                  $endgroup$
                                  – Saunders
                                  2 hours ago






                                • 2




                                  $begingroup$
                                  But why are the resistors small?
                                  $endgroup$
                                  – Scott Seidman
                                  2 hours ago










                                • $begingroup$
                                  @ScottSeidman To keep the noise level extra low, though it loads the op-amp at its minimal limits.
                                  $endgroup$
                                  – Sparky256
                                  26 mins ago
















                                0












                                $begingroup$

                                Datasheet states that with +/- 5 volt supplies minimum load is 30 ohms. At +/-15 volts minimum load is 200 ohms. Output resistance is 3 milliohms. GBW at G = 10 is 8MHZ. This is a awesome op-amp. It is not the fastest or has the lowest noise for audio purest, but for a GP op-amp is it much better than just 'ok'.



                                Due to a fast slew rate the board layout needs to be as good as if this was an RF amp IC. 100nF bypass capacitors right at the supply pins, or within 1/4" or 7mm. Close by should be 4.7uF MLCC caps, plus within a few inches 100uF aluminum caps for wide band filtering, and a stable supply when driving 50 ohm or even 600 ohm loads.



                                The resistors shown in the schematic are the lowest safe value possible, and still maintain somewhat normal operation. The idea here is to get the resistor noise levels to a minimum. Many op-amps could not tolerate such low resistor values, but that resistance range is on the datasheet. It is implied on the datasheet that at such low resistance levels supply voltage should be +/- 5 volts.






                                share|improve this answer











                                $endgroup$













                                • $begingroup$
                                  I am still confused. Are these anwsers trying to say that the feedback resistors factor into the load resistance of the op amp? If that were the case why not use large valued resistors
                                  $endgroup$
                                  – Saunders
                                  2 hours ago






                                • 2




                                  $begingroup$
                                  But why are the resistors small?
                                  $endgroup$
                                  – Scott Seidman
                                  2 hours ago










                                • $begingroup$
                                  @ScottSeidman To keep the noise level extra low, though it loads the op-amp at its minimal limits.
                                  $endgroup$
                                  – Sparky256
                                  26 mins ago














                                0












                                0








                                0





                                $begingroup$

                                Datasheet states that with +/- 5 volt supplies minimum load is 30 ohms. At +/-15 volts minimum load is 200 ohms. Output resistance is 3 milliohms. GBW at G = 10 is 8MHZ. This is a awesome op-amp. It is not the fastest or has the lowest noise for audio purest, but for a GP op-amp is it much better than just 'ok'.



                                Due to a fast slew rate the board layout needs to be as good as if this was an RF amp IC. 100nF bypass capacitors right at the supply pins, or within 1/4" or 7mm. Close by should be 4.7uF MLCC caps, plus within a few inches 100uF aluminum caps for wide band filtering, and a stable supply when driving 50 ohm or even 600 ohm loads.



                                The resistors shown in the schematic are the lowest safe value possible, and still maintain somewhat normal operation. The idea here is to get the resistor noise levels to a minimum. Many op-amps could not tolerate such low resistor values, but that resistance range is on the datasheet. It is implied on the datasheet that at such low resistance levels supply voltage should be +/- 5 volts.






                                share|improve this answer











                                $endgroup$



                                Datasheet states that with +/- 5 volt supplies minimum load is 30 ohms. At +/-15 volts minimum load is 200 ohms. Output resistance is 3 milliohms. GBW at G = 10 is 8MHZ. This is a awesome op-amp. It is not the fastest or has the lowest noise for audio purest, but for a GP op-amp is it much better than just 'ok'.



                                Due to a fast slew rate the board layout needs to be as good as if this was an RF amp IC. 100nF bypass capacitors right at the supply pins, or within 1/4" or 7mm. Close by should be 4.7uF MLCC caps, plus within a few inches 100uF aluminum caps for wide band filtering, and a stable supply when driving 50 ohm or even 600 ohm loads.



                                The resistors shown in the schematic are the lowest safe value possible, and still maintain somewhat normal operation. The idea here is to get the resistor noise levels to a minimum. Many op-amps could not tolerate such low resistor values, but that resistance range is on the datasheet. It is implied on the datasheet that at such low resistance levels supply voltage should be +/- 5 volts.







                                share|improve this answer














                                share|improve this answer



                                share|improve this answer








                                edited 27 mins ago

























                                answered 3 hours ago









                                Sparky256Sparky256

                                11.8k21636




                                11.8k21636












                                • $begingroup$
                                  I am still confused. Are these anwsers trying to say that the feedback resistors factor into the load resistance of the op amp? If that were the case why not use large valued resistors
                                  $endgroup$
                                  – Saunders
                                  2 hours ago






                                • 2




                                  $begingroup$
                                  But why are the resistors small?
                                  $endgroup$
                                  – Scott Seidman
                                  2 hours ago










                                • $begingroup$
                                  @ScottSeidman To keep the noise level extra low, though it loads the op-amp at its minimal limits.
                                  $endgroup$
                                  – Sparky256
                                  26 mins ago


















                                • $begingroup$
                                  I am still confused. Are these anwsers trying to say that the feedback resistors factor into the load resistance of the op amp? If that were the case why not use large valued resistors
                                  $endgroup$
                                  – Saunders
                                  2 hours ago






                                • 2




                                  $begingroup$
                                  But why are the resistors small?
                                  $endgroup$
                                  – Scott Seidman
                                  2 hours ago










                                • $begingroup$
                                  @ScottSeidman To keep the noise level extra low, though it loads the op-amp at its minimal limits.
                                  $endgroup$
                                  – Sparky256
                                  26 mins ago
















                                $begingroup$
                                I am still confused. Are these anwsers trying to say that the feedback resistors factor into the load resistance of the op amp? If that were the case why not use large valued resistors
                                $endgroup$
                                – Saunders
                                2 hours ago




                                $begingroup$
                                I am still confused. Are these anwsers trying to say that the feedback resistors factor into the load resistance of the op amp? If that were the case why not use large valued resistors
                                $endgroup$
                                – Saunders
                                2 hours ago




                                2




                                2




                                $begingroup$
                                But why are the resistors small?
                                $endgroup$
                                – Scott Seidman
                                2 hours ago




                                $begingroup$
                                But why are the resistors small?
                                $endgroup$
                                – Scott Seidman
                                2 hours ago












                                $begingroup$
                                @ScottSeidman To keep the noise level extra low, though it loads the op-amp at its minimal limits.
                                $endgroup$
                                – Sparky256
                                26 mins ago




                                $begingroup$
                                @ScottSeidman To keep the noise level extra low, though it loads the op-amp at its minimal limits.
                                $endgroup$
                                – Sparky256
                                26 mins ago











                                0












                                $begingroup$

                                With honor to Walt Jung (of ADI, et al), low values of resistors can cause detectable THERMAL distortion. Drive the opamp with 20Hz and 2,000Hz; use a spectrum analyzer, and you'll see the 2,000Hz output with some 20Hz sidebands.



                                Which means what? Use physically larger resistors. Or experiment with resistors having different resistive element structures? The very thin metal-file-spiral-trimmed has a very fast timeconstant for heating/cooling, as heat is dumped into the ceramic/clay core.





                                share









                                $endgroup$


















                                  0












                                  $begingroup$

                                  With honor to Walt Jung (of ADI, et al), low values of resistors can cause detectable THERMAL distortion. Drive the opamp with 20Hz and 2,000Hz; use a spectrum analyzer, and you'll see the 2,000Hz output with some 20Hz sidebands.



                                  Which means what? Use physically larger resistors. Or experiment with resistors having different resistive element structures? The very thin metal-file-spiral-trimmed has a very fast timeconstant for heating/cooling, as heat is dumped into the ceramic/clay core.





                                  share









                                  $endgroup$
















                                    0












                                    0








                                    0





                                    $begingroup$

                                    With honor to Walt Jung (of ADI, et al), low values of resistors can cause detectable THERMAL distortion. Drive the opamp with 20Hz and 2,000Hz; use a spectrum analyzer, and you'll see the 2,000Hz output with some 20Hz sidebands.



                                    Which means what? Use physically larger resistors. Or experiment with resistors having different resistive element structures? The very thin metal-file-spiral-trimmed has a very fast timeconstant for heating/cooling, as heat is dumped into the ceramic/clay core.





                                    share









                                    $endgroup$



                                    With honor to Walt Jung (of ADI, et al), low values of resistors can cause detectable THERMAL distortion. Drive the opamp with 20Hz and 2,000Hz; use a spectrum analyzer, and you'll see the 2,000Hz output with some 20Hz sidebands.



                                    Which means what? Use physically larger resistors. Or experiment with resistors having different resistive element structures? The very thin metal-file-spiral-trimmed has a very fast timeconstant for heating/cooling, as heat is dumped into the ceramic/clay core.






                                    share











                                    share


                                    share










                                    answered 9 mins ago









                                    analogsystemsrfanalogsystemsrf

                                    14.7k2718




                                    14.7k2718






























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