These multiplication effects are unsurprising to hobbyists who studied electronics from the basics using a textbook.
Amplifier circuits multiply impedances. For instance in a common emitter amplifier stage around a BJT (bipolar junction transistor), the input impedance is much larger than what is implied by the emitter resistor. In effect, the transistor multiplies the apparent resistance of that component. If a capacitor is put in parallel with the emitter resistor, that capacitor looks smaller: from the base current's point of view, the capacitor is filling up very rapidly (which is due to the collector current) making it look shallower. The feedback capacitance in the stage is multiplied though (e.g. capacitor connected from collector to base, or such a naturally present parasitic capacitance). This is called the Miller effect.
Though this op-amp circuit creates a virtual larger capacitor, it's not useful as a general capacitor. You can't use this to make a 10,000 uF cap to use as a power supply filter; it doesn't actually have backing energy storage to deliver the transient current on demand. Now, yes, if that op-amp itself has a huge power reservoir behind it, then maybe this small capacitor can be made to work like a huge one in this manner. But it will be the op-amp circuit and its supply doing the actual work. This is essentially a voltage regulator.
In a voltage regulator circuit you have an amplifier with some capacitors upstream of it. The amplifier amplifies a fixed DC reference voltage to the desired voltage level. It holds that level very stiff: much more stiffly than those upstream capacitors would be able to on their own, so effectively it multiplies them.
Another thing you can't do is use it as a coupling capacitor, which is very useful role, allowing an AC signal to pass between two domains that are biased to different voltage levels.
In the circuit, one end of the capacitor is grounded, so ...
It fascinates me how many utterly critical foundational technologies have become specialist niches (while only ever growing more foundational and critical) over the past century. 8I
The last circuit, in steady state, behaves exactly as R2, but when the signal changes, the current through the capacitor is the derivative of the signal, reducing the amount by which the circuit is just R2.
I speculate it acts like an inductor because that would be a logically silly thing for it to do but I'm not doing the math at 1am on my phone.
I came up with a nice schematic layout whereby we have the gyrators in a column on the right and then the mixer resistors which plug them into the fixed equalizer to the right, making it easier to follow.
Similarly, this capacitance multiplier is more likely to be seen on a chip than outside one. Capacitance inside an IC takes up a lot of chip area, while transistors are small.
Capacitance multipliers are how wah-wah pedals work.
The classic Vox / Dunlop/ Cry Baby wah-wah pedal used by Hendrix, Gilmour, Clapton, Harrison, and so many others, is built from a resonant LC filter.
How do you change the resonant frequency of an LC filter with a pedal mechanism? The pedal turns a pot, and that controls a capacitance multiplier circuit.
"I keep coming back to this topic for two reasons. First, I think these components are usually explained poorly, making them a major stumbling block for folks trying to learn the craft. Second, op-amps have gotten really good, inexpensive, and small, so I think they should be used more."
No offense, but these are words typically spoken by someone who has never taken any electrical engineering courses or read any of Walter Jungs books, after having some electronics background.
"gotten really good"? Really, like in the 1970s?? (the 741, still widely used today was released in 1968). I recall in the 1980s in the electronics that were once completely discrete, they were _everywhere_ and still are today.
Eh there are also decades worth of audio electronics designs which use the 741 and the decision of which actual part to use is often an aesthetic one. (i.e., assuming all other parameters are compatible then just use your ears). There are always new (hobbyist) designs being drafted around specific parts that are otherwise obsolete simply due to the musical character of certain parts
I've done a few EE courses across two countries on the path to masters. The opamps were used at most for small signal processing in those. No more creative uses like frequency/capacitance multipliers. Comparing notes with friends in other unis, it wasn't that different there. You'd have to go into degrees much more focused on electonics to go to that level.
These multiplication effects are unsurprising to hobbyists who studied electronics from the basics using a textbook.
Amplifier circuits multiply impedances. For instance in a common emitter amplifier stage around a BJT (bipolar junction transistor), the input impedance is much larger than what is implied by the emitter resistor. In effect, the transistor multiplies the apparent resistance of that component. If a capacitor is put in parallel with the emitter resistor, that capacitor looks smaller: from the base current's point of view, the capacitor is filling up very rapidly (which is due to the collector current) making it look shallower. The feedback capacitance in the stage is multiplied though (e.g. capacitor connected from collector to base, or such a naturally present parasitic capacitance). This is called the Miller effect.
Though this op-amp circuit creates a virtual larger capacitor, it's not useful as a general capacitor. You can't use this to make a 10,000 uF cap to use as a power supply filter; it doesn't actually have backing energy storage to deliver the transient current on demand. Now, yes, if that op-amp itself has a huge power reservoir behind it, then maybe this small capacitor can be made to work like a huge one in this manner. But it will be the op-amp circuit and its supply doing the actual work. This is essentially a voltage regulator.
In a voltage regulator circuit you have an amplifier with some capacitors upstream of it. The amplifier amplifies a fixed DC reference voltage to the desired voltage level. It holds that level very stiff: much more stiffly than those upstream capacitors would be able to on their own, so effectively it multiplies them.
Another thing you can't do is use it as a coupling capacitor, which is very useful role, allowing an AC signal to pass between two domains that are biased to different voltage levels. In the circuit, one end of the capacitor is grounded, so ...
Analog electronics is a topic that was widely covered in mid-century textbooks, but it's definitely become more of a specialist niche today.
It fascinates me how many utterly critical foundational technologies have become specialist niches (while only ever growing more foundational and critical) over the past century. 8I
I have always found the term "capacitance multiplier" misleading. I see it as a voltage regulator with a filtered input.
I know that capacitance multipliers are commonly used in audio circuits like specific Equalizer circuits, mainly to allow to use smaller capacitors.
The last circuit, in steady state, behaves exactly as R2, but when the signal changes, the current through the capacitor is the derivative of the signal, reducing the amount by which the circuit is just R2.
I speculate it acts like an inductor because that would be a logically silly thing for it to do but I'm not doing the math at 1am on my phone.
I've always admired lcamtuf.
Yep. That topology is called a gyrator. Often used in IC's where it is hard to make an inductor.
I spotted a fixed equalizer in the middle of a guitar power amp schematic (Randall G3 series), so I banged it up in LTSpice for a simulation:
https://www.ssguitar.com/index.php?topic=5751.msg45172
I came up with a nice schematic layout whereby we have the gyrators in a column on the right and then the mixer resistors which plug them into the fixed equalizer to the right, making it easier to follow.
https://en.wikipedia.org/wiki/Gyrator#Simulated_inductor
Similarly, this capacitance multiplier is more likely to be seen on a chip than outside one. Capacitance inside an IC takes up a lot of chip area, while transistors are small.
Capacitance multipliers are how wah-wah pedals work.
The classic Vox / Dunlop/ Cry Baby wah-wah pedal used by Hendrix, Gilmour, Clapton, Harrison, and so many others, is built from a resonant LC filter.
How do you change the resonant frequency of an LC filter with a pedal mechanism? The pedal turns a pot, and that controls a capacitance multiplier circuit.
Simple and elegant.
Is it possible to create an audio-grade capacitance multiplier in CMOS?
Wait until he hears about negative Miller capacitance.
Yeah we can do really weird things with op amps, negative resistance and capacitance comes to mind.
"I keep coming back to this topic for two reasons. First, I think these components are usually explained poorly, making them a major stumbling block for folks trying to learn the craft. Second, op-amps have gotten really good, inexpensive, and small, so I think they should be used more."
No offense, but these are words typically spoken by someone who has never taken any electrical engineering courses or read any of Walter Jungs books, after having some electronics background.
"gotten really good"? Really, like in the 1970s?? (the 741, still widely used today was released in 1968). I recall in the 1980s in the electronics that were once completely discrete, they were _everywhere_ and still are today.
to be fair, the 741 is not a particularly good op-amp nowadays. It's used mainly through sheer inertia.
Everybody uses the 741's pin-outs, but nobody should be using the actual 741 for new designs. And that's been true for many decades.
Eh there are also decades worth of audio electronics designs which use the 741 and the decision of which actual part to use is often an aesthetic one. (i.e., assuming all other parameters are compatible then just use your ears). There are always new (hobbyist) designs being drafted around specific parts that are otherwise obsolete simply due to the musical character of certain parts
I think you're doing a https://xkcd.com/2501/
I've done a few EE courses across two countries on the path to masters. The opamps were used at most for small signal processing in those. No more creative uses like frequency/capacitance multipliers. Comparing notes with friends in other unis, it wasn't that different there. You'd have to go into degrees much more focused on electonics to go to that level.