Talk:Circuit Idea/How to Make a Perfect RC-integrator

I would like to start this page by placing a record from the laboratory excercises with my students from group 67a. Circuit-fantasist (talk) 14:24, 21 September 2008 (UTC)

Current-to-voltage C integrator


What is the most elementary electrical integrator? Of course, this is the humble capacitor. So, if we drive a capacitor C by a constant current source I, it acts as an ideal current-to-voltage integrator with a current input IIN and a voltage output VOUT = VC. Note that the output voltage changes linearly through the time.

Building an op-amp inverting integrator - step 1 Keeping a constant current by using an ideal current source



Voltage-to-voltage RC integrator


Only, we need usually an integrator with voltage input and voltage output (voltage-to-voltage integrator). For this purpose, we can build a compound voltage integrator just connecting a voltage-to-current converter (a resistor) before the integrator:

V-to-I converter + I-to-V integrator = V-to-V integrator

Only, a problem arises here - the voltage drop VC across the capacitor C "enervates" the input voltage thus decreasing the input current. As a result, the output voltage changes exponentially through the time.

Building an op-amp inverting integrator - step 2 Keeping a constant current by depreciating the load









Active RC integrator


Remember what we do in real life when an obstacle stands in our way - we remove it by an equivalent useful "antidisturbance". Following this recipe, we may remove the "harmful" voltage VC by an "antivoltage" -VC. That means to connect an additional varying voltage source and to make its voltage equal to -VC. As a result, the "harmful" voltage VC disappears and the upper point becomes a virtual ground! The compound current source VIN,R is "fooled": it doesn't "understand" that there is a capacitor connected; it "thinks" that its output is shorted.

Building an op-amp inverting integrator - step 1 Keeping a constant current by adding an additional voltage





But where to take an output from? We have three possibilities.

First, we might use the old output; but we have already destroyed this voltage!

Second, we may use the "original" voltage as an output. It is possible but bad solution to connect the load across the capacitor for two reasons: the load has to have a differential output; the load will shunt the capacitor thus affecting the current.

Finally, we can use the "copy" voltage as an output! What a great idea! First, the load will be connected to the common ground; second, it will consume energy from the supplementary source instead from the input one!

Building an op-amp inverting integrator - go to step 3



Op-amp inverting RC integrator
Finally, we have only to replace the varying voltage source with a real one. Now the op-amp doses the voltage of the power supply thus producing a compensating voltage -VC. In other words, the combination of an op-amp and a steady battery acts as a varying voltage source.



The op-amp "observes" the potential of the virtual ground (the difference between the two voltages) and changes instantly its output voltage so that this point to stay always at zero volts. Doing that, the op-amp compensates the "harmful" voltage drop across the capacitor by copying and adding it to the voltage of the input source; doing that, the op-amp "helps" the input source.



It's time to make conclusions. What have we actually done here? How does it operate? What is the final result?

The answer is amazing: we have made a "botomless" capacitor having infinite capacitance. Looking from the side of the input source this "ideal" capacitor acts just... as a piece of wire...?!? What do you think about this speculation? Is it always right?

We are already true magicians as we can transform any imperfect component into an almost ideal one! In this lab, we have transmuted the "imperfect" capacitor into a perfect infinite one having no any voltage drop across it although a current flows continuously through it! But with the same success we can make an ideal diode, zero resistance, etc... For this purpose, we just incorporate a varying battery to the imperfect component that compensate the losses inside the component. Remember: all the op-amp inverting circuits exploit this clever trick. Circuit-fantasist (talk) 16:50, 6 May 2008 (UTC)

How to make perfect components by parallel NFB Building an op-amp inverting integrator - go to step 4

Resources
How do we build an op-amp RC integrator? shows a reliable four-step building "scenario". Building an op-amp inverting integrator is an interactive multimedia flash minitutorial that builds the circuit in four steps.

About the op-amp inverting integrator
(a copy of Wikipedia discussion) Circuit-fantasist (discuss • contribs) 11:31, 16 September 2011 (UTC)

'''The role of the op-amp in this circuit is to compensate the voltage drop across the capacitor. For this purpose, the op-amp adds so much voltage to the input voltage as it loses across the capacitor. The properly supplied op-amp acts as a compensating voltage source connected in series to the capacitor and the input voltage source.'''

This idea may be generalized for all the op-amp inverting circuits with parallel negative feedback (e.g., Inverting amplifier, Summing amplifier, Differentiator, Logarithmic output, Exponential output from this page). In all these circuits the op-amp compensates the voltage drop across the element connected between the output and the inverting input by adding the same voltage to the input voltage as it loses across this element. See also Voltage Compensation module. Circuit dreamer (talk) 18:38, 30 March 2010 (UTC)


 * Two reasons why this has been removed:
 * This is a non-standard explanation (whilst it's true, I've never seen it described like this).
 * Even if it were true, it applies to all negative-feedback topologies, so it's unnecessary to add this detail to purely the integrator and differentiator.
 * Oli Filth(talk&#124;contribs) 10:46, 31 March 2010 (UTC)


 * The page. Let's first see what happens if someone curious web reader wants to understand what an op-amp integrator is. Of course, he/she will write "op-amp integrator" in the Google window and will see this Wikipedia page at the first place from all these 100000 pages. The visitor trusts to Wikipedia, chooses Integrator from the contents and begins reading. Now answer me frankly: Will the visitor understand what this circuit does, what is the great basic idea behind it, how it operates, if there is some connection with the passive RC version, with what purpose an op-amp is added to the passive version, what the op-amp actually does in this active version, why the circuit is inverting...? Unfortunately, the visitor will not get answers to these questions from this page... For now, he/she will learn that "the integrator integrates the (inverted) signal over time", will learn the expression and will come to know that the circuit has a lot of problems... The situation with the rest of the sections is similar. In this state, the page looks like a chapter of a cookbook. But, if you please, Wikipedia is not a cookbook...


 * The sections. It is obvious that every section of this page dedicated to one of these legendary op-amp applications, has to say some words about the purpose (what it does), the basic idea behind circuit (how it is implemented), the expression, the operation (how it does what it does), the imperfections (problems) and the applications. Of course, some of these parts may be omited, depending on the specific circuits but the basic idea has to be shown in the beginning.


 * The voltage compensation idea. This idea is extremely simple and I vonder why "you've never seen it described like this". I met this powerful idea in the end of 70s (see the talk page) but I realized it only in the early 1990s. Thereafter I make my students realize and use it to build "ideal" devices (circuits): diodes, capacitors, etc. But it is not only an "electrical" idea; you may see the compensation idea everywhere around you in this world. During our life, we, human beings, continously compensate harmful quantities by useful ones; as a result we obtain zero result (virtual ground). You may see this phenomenon even here, in Wikipedia: when some vandal removes valuable text (a harmful action), we return the same text (an equivalent useful action) and the result is zero (a virtual ground).


 * The integrator. Well, let's see this idea in the op-amp integrator (see also How to Make a Perfect RC-integrator, How do we build an op-amp RC integrator? and Building an op-amp inverting integrator). What is the problem of the simple passive RC integrator? The voltage across the capacitor is the problem as it is subtracted from the input voltage; it "enervates" the input voltage source. So, this voltage is harmful and we have to compensate it. For this purpose, we connect an additional voltage source (the output of a properly supplied op-amp) in series to the capacitor and make the op-amp adjust its output voltage so that it is always equal to the voltage across the capacitor. Actually, this voltage adds to the input voltage and thus compensates the voltage across the capacitor. Let's consider the signs traveling along the circuit of four elements and beginning from the ground. If the input voltage is positive and constant, the output voltage is negative; the two voltage sources are connected in series in the same direction (-Uin+, -Uout+). You may think of this combination as of a compound voltage source (Vin + Vout) that passes a constant current through the resistor that does not depend on the voltage across the capacitor...


 * (to be continued) Circuit dreamer (talk) 20:54, 31 March 2010 (UTC)


 * The properties of all of the negative-feedback examples can be trivially derived by standard circuit analysis and the added constraint that V- = V+. At most, we should present the standard analysis, not this non-standard explanation that "the op-amp compensates for the voltage drop".  Oli Filth(talk&#124;contribs) 21:30, 31 March 2010 (UTC)


 * Well, let's now move in electronics area. I know that most people (including circuit designers as well) use ready-made circuit solutions from op-amp applications handbooks. But they frequently do not find human-friendly explanations there as producers are not interested to reveal circuit ideas; instead, they are interested to advertise their wares. Then, the reader is most likely to visit this Wikipedia page in the hope of understanding the circuit idea and he/she will be thankful to get answers to all the questions above. Circuit dreamer (talk) 15:42, 2 April 2010 (UTC)