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Q&A Design rules for opamp bootstrapping

Here is the bootstrapping technique for opamps, as exposed in the Art of Electronics:. This technique is supposed to increase considerably the input impedance of the opamp for an AC input source (...

2 answers  ·  posted 4y ago by coquelicot‭  ·  edited 1y ago by Lorenzo Donati‭

#8: Post edited by user avatar Lorenzo Donati‭ · 2023-08-11T12:03:33Z (over 1 year ago)
Corrected use of "non-standard" (hence unclear) abbreviation for operational amplifier.
  • Design rules for oamp bootstrap
  • Design rules for opamp bootstrapping
#7: Post edited by user avatar Lorenzo Donati‭ · 2023-08-11T12:00:18Z (over 1 year ago)
Retagged. Corrected use of "non-standard" (hence unclear) abbreviation for operational amplifier.
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • **Edit**: Here is a simulation done with LT spice. I've more or less given random values, following nothing but some intuitive guess:
  • Simulation with bootstrap:
  • ![bootstrap2](https://electrical.codidact.com/uploads/X8HF9d62zhy2hwsMo4aZUwsM)
  • Result (current through the sine generator):![bootstrap3](https://electrical.codidact.com/uploads/W5cHDUP6pwmdrKfxZqWZjPgB)
  • Result of the same simulation but without cap C1:
  • ![bootstrap4](https://electrical.codidact.com/uploads/f8FPxLBYWm1JP28VtM5z7mWs)
  • **Edit 2:**
  • Perhaps the schematic will make more sense if we pass the input signal through a capacitor, as is usually the case.
  • Here is the schematic for the simulation:
  • ![bootstrap5](https://electrical.codidact.com/uploads/5wd6pDu7VcMVkwHmY6tojtr9)
  • And here are the results: the first trace is the current through cap C2, and the second trace is the current at the in+ of the oamp:
  • ![bootstrap6](https://electrical.codidact.com/uploads/UgL1fcxKWsRj5ZuDvxrN9j4F)
  • So, we see that the amplitude of the current through C2 is about 2nA, and the amplitude of the AC current at in+ is 6nA, more than I_C2.
  • Without cap C1, the current through the sine generator (and hence through C2) is the same as previously
  • Here is the bootstrapping technique for opamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the opamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current opamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp opamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • **Edit**: Here is a simulation done with LT spice. I've more or less given random values, following nothing but some intuitive guess:
  • Simulation with bootstrap:
  • ![bootstrap2](https://electrical.codidact.com/uploads/X8HF9d62zhy2hwsMo4aZUwsM)
  • Result (current through the sine generator):![bootstrap3](https://electrical.codidact.com/uploads/W5cHDUP6pwmdrKfxZqWZjPgB)
  • Result of the same simulation but without cap C1:
  • ![bootstrap4](https://electrical.codidact.com/uploads/f8FPxLBYWm1JP28VtM5z7mWs)
  • **Edit 2:**
  • Perhaps the schematic will make more sense if we pass the input signal through a capacitor, as is usually the case.
  • Here is the schematic for the simulation:
  • ![bootstrap5](https://electrical.codidact.com/uploads/5wd6pDu7VcMVkwHmY6tojtr9)
  • And here are the results: the first trace is the current through cap C2, and the second trace is the current at the in+ of the opamp:
  • ![bootstrap6](https://electrical.codidact.com/uploads/UgL1fcxKWsRj5ZuDvxrN9j4F)
  • So, we see that the amplitude of the current through C2 is about 2nA, and the amplitude of the AC current at in+ is 6nA, more than I_C2.
  • Without cap C1, the current through the sine generator (and hence through C2) is the same as previously
#6: Post edited by user avatar coquelicot‭ · 2020-09-14T14:28:00Z (about 4 years ago)
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • **Edit**: Here is a simulation done with LT spice. I've more or less given random values, following nothing but some intuitive guess:
  • Simulation with bootstrap:
  • ![bootstrap2](https://electrical.codidact.com/uploads/X8HF9d62zhy2hwsMo4aZUwsM)
  • Result (current through the sine generator):![bootstrap3](https://electrical.codidact.com/uploads/W5cHDUP6pwmdrKfxZqWZjPgB)
  • Result of the same simulation but without cap C1:
  • ![bootstrap4](https://electrical.codidact.com/uploads/f8FPxLBYWm1JP28VtM5z7mWs)
  • **Edit 2:**
  • Perhaps the schematic will make more sense if we pass the input signal through a capacitor, as is usually the case.
  • Here is the schematic for the simulation:
  • ![bootstrap5](https://electrical.codidact.com/uploads/5wd6pDu7VcMVkwHmY6tojtr9)
  • And here are the results: the first trace is the current through cap C2, and the second trace is the current at the in+ of the oamp:
  • ![bootstrap6](https://electrical.codidact.com/uploads/UgL1fcxKWsRj5ZuDvxrN9j4F)
  • So, we see that the amplitude of the current through C2 is about 2nA, and the amplitude of the AC current at in+ is 6nA, more than I_C2.
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • **Edit**: Here is a simulation done with LT spice. I've more or less given random values, following nothing but some intuitive guess:
  • Simulation with bootstrap:
  • ![bootstrap2](https://electrical.codidact.com/uploads/X8HF9d62zhy2hwsMo4aZUwsM)
  • Result (current through the sine generator):![bootstrap3](https://electrical.codidact.com/uploads/W5cHDUP6pwmdrKfxZqWZjPgB)
  • Result of the same simulation but without cap C1:
  • ![bootstrap4](https://electrical.codidact.com/uploads/f8FPxLBYWm1JP28VtM5z7mWs)
  • **Edit 2:**
  • Perhaps the schematic will make more sense if we pass the input signal through a capacitor, as is usually the case.
  • Here is the schematic for the simulation:
  • ![bootstrap5](https://electrical.codidact.com/uploads/5wd6pDu7VcMVkwHmY6tojtr9)
  • And here are the results: the first trace is the current through cap C2, and the second trace is the current at the in+ of the oamp:
  • ![bootstrap6](https://electrical.codidact.com/uploads/UgL1fcxKWsRj5ZuDvxrN9j4F)
  • So, we see that the amplitude of the current through C2 is about 2nA, and the amplitude of the AC current at in+ is 6nA, more than I_C2.
  • Without cap C1, the current through the sine generator (and hence through C2) is the same as previously
#5: Post edited by user avatar coquelicot‭ · 2020-09-14T14:25:23Z (about 4 years ago)
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • **Edit**: Here is a simulation done with LT spice. I've more or less given random values, following nothing but some intuitive guess:
  • Simulation with bootstrap:
  • ![bootstrap2](https://electrical.codidact.com/uploads/X8HF9d62zhy2hwsMo4aZUwsM)
  • Result (current through the sine generator):![bootstrap3](https://electrical.codidact.com/uploads/W5cHDUP6pwmdrKfxZqWZjPgB)
  • Result of the same simulation but without cap C1:
  • ![bootstrap4](https://electrical.codidact.com/uploads/f8FPxLBYWm1JP28VtM5z7mWs)
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • **Edit**: Here is a simulation done with LT spice. I've more or less given random values, following nothing but some intuitive guess:
  • Simulation with bootstrap:
  • ![bootstrap2](https://electrical.codidact.com/uploads/X8HF9d62zhy2hwsMo4aZUwsM)
  • Result (current through the sine generator):![bootstrap3](https://electrical.codidact.com/uploads/W5cHDUP6pwmdrKfxZqWZjPgB)
  • Result of the same simulation but without cap C1:
  • ![bootstrap4](https://electrical.codidact.com/uploads/f8FPxLBYWm1JP28VtM5z7mWs)
  • **Edit 2:**
  • Perhaps the schematic will make more sense if we pass the input signal through a capacitor, as is usually the case.
  • Here is the schematic for the simulation:
  • ![bootstrap5](https://electrical.codidact.com/uploads/5wd6pDu7VcMVkwHmY6tojtr9)
  • And here are the results: the first trace is the current through cap C2, and the second trace is the current at the in+ of the oamp:
  • ![bootstrap6](https://electrical.codidact.com/uploads/UgL1fcxKWsRj5ZuDvxrN9j4F)
  • So, we see that the amplitude of the current through C2 is about 2nA, and the amplitude of the AC current at in+ is 6nA, more than I_C2.
#4: Post edited by user avatar coquelicot‭ · 2020-09-14T13:40:27Z (about 4 years ago)
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • **Edit**: Here is a simulation done with LT spice. I've more or less given random values, following nothing but some intuitive guess:
  • Simulation with bootstrap:
  • ![bootstrap2](https://electrical.codidact.com/uploads/X8HF9d62zhy2hwsMo4aZUwsM)
  • Result:![bootstrap3](https://electrical.codidact.com/uploads/W5cHDUP6pwmdrKfxZqWZjPgB)
  • Result of the same simulation but without cap C1:
  • ![bootstrap4](https://electrical.codidact.com/uploads/f8FPxLBYWm1JP28VtM5z7mWs)
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • **Edit**: Here is a simulation done with LT spice. I've more or less given random values, following nothing but some intuitive guess:
  • Simulation with bootstrap:
  • ![bootstrap2](https://electrical.codidact.com/uploads/X8HF9d62zhy2hwsMo4aZUwsM)
  • Result (current through the sine generator):![bootstrap3](https://electrical.codidact.com/uploads/W5cHDUP6pwmdrKfxZqWZjPgB)
  • Result of the same simulation but without cap C1:
  • ![bootstrap4](https://electrical.codidact.com/uploads/f8FPxLBYWm1JP28VtM5z7mWs)
#3: Post edited by user avatar coquelicot‭ · 2020-09-14T13:38:35Z (about 4 years ago)
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • **Edit**: Here is a simulation done with LT spice. I've more or less given random values, following nothing but some intuitive guess:
  • Simulation with bootstrap:
  • ![bootstrap2](https://electrical.codidact.com/uploads/X8HF9d62zhy2hwsMo4aZUwsM)
  • Result:![bootstrap3](https://electrical.codidact.com/uploads/W5cHDUP6pwmdrKfxZqWZjPgB)
  • Result of the same simulation but without cap C1:
  • ![bootstrap4](https://electrical.codidact.com/uploads/f8FPxLBYWm1JP28VtM5z7mWs)
#2: Post edited by user avatar coquelicot‭ · 2020-09-14T11:07:33Z (about 4 years ago)
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
  • Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).
  • This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
  • The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps.
  • I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).
  • Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.
  • Now, to make my question precise:
  • Assume
  • 1. I have an AC sinusoidal source of known frequency w;
  • 2. I want the output signal (voltage) be at least n percents of the input signal (e.g. 99%);
  • 3. I want the RMS input current be equal to at most I_max.
  • **Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?
#1: Initial revision by user avatar coquelicot‭ · 2020-09-14T11:04:33Z (about 4 years ago)
Design rules for oamp bootstrap
Here is the bootstrapping technique for oamps, as exposed in the Art of Electronics:![bootstrap](https://electrical.codidact.com/uploads/DhdJbRm5BarYY8HTxfzxkQvG).

This technique is supposed to increase considerably the input impedance of the oamp for an AC input source (usually passed through a cap).
The Art of Electronics considers it somewhat outdated, as it is now possible to use extremely low bias input current oamps. 

I disagree with him: I see no reason to buy a somewhat expensive femtoamp oamp when you can obtain the same result with a more banal one (as long as we deal with AC sources).

Actually I do have an application where I use the self capacitance of a rotating half cylinder to measure the ambient electric field, which is perfectly tailored to bootstrapping.

Now, to make my question precise:

Assume 

1. I have an AC sinusoidal source of known frequency w;

2. I want the output signal (voltage) be n percents of the input signal (e.g. 99%);

3. I want the RMS input current be equal to at most I_max. 

**Question**: how should I choose the values of the two resistors and of the capacitor in the schematic above?