Talk:Circuit Idea/Demystifying gyrator circuits

Yesterday, I conducted one of the most interesting exercises with my students. We managed to reveal the secrets of gyrators circuits (in particular, of the simulated inductor). Here are some extracts from the record on my solid state recorder. Please, join the discussion. Circuit-fantasist (talk) 15:16, 16 April 2010 (UTC)



The problem: How to convert a capacitor into an inductor


Inductors are inconvenient: they are bulky, heavy and expensive; they cannot be miniaturized. So, it would be extremely useful if we manage to replace them by capacitors. The question is "How do we convert a capacitor into an inductor?" We begin looking for an idea how to convert the capacitor into an inductor. Krasimir: "We have to compare the properties of the two elements, to see what capacitor and inductor are. Well, it seems we can't simulate all the inductor's properties; we will manage to simulate only particular properties.

What are the basic properties of these time-dependant elements? Krasimir: "They are frequency dependent elements. You are right. But for our purposes (intuitive understanding) it is more convenient to investigate how they behave through time. Frequency dependent reactance (impedance), averaged and rms quantities are more abstract; they hide the circuit operation. Instantaneous voltages and currents are more real. At given moment (if we "snap" the circuit operation), we have a pair of two quantities: current flowing through the capacitor and voltage drop across it. The real things that we see at given moment are only the instantaneous voltage and current; and they are real, actual. Impedance is some derivative, more abstract quantity, based on the primary voltage and current quantity. Impedance is not a ratio of the instantaneous voltage and current quantity since they are phase shifted. That is why complex numbers are used to analyze AC circuits.



How do capacitor and inductor in RC/RL circuit behave through time?




What is the main property of the two elements? First at all, they can accumulate, store energy. But we will not simulate this property in these circuits; storing is not our aim now. If you want, we may try to create such circuits but I am not sure if it is possible... Let's continue looking for another property... Krasimir: "The one element creates voltage when we try to pass a current through it while the other does the opposite..." So, we talk about the behavior of the two elements through time. We begin investigating how the voltages across them and the currents through them change through time.

What do we investigate - the particular elements or composed RC and RL circuits? If we get the particular elements, we can drive them by a voltage source or by a current source. Well, let's connect a voltage source to a capacitor. What will happens? It is quite incorrect connection, isn't it? How does the voltage change through time? If the voltage source is a power enough (an "ideal" voltage source), it will force the capacitor to take the voltage. And what about the current? It should be infinite in the beginning and then to decrease gradually... But there is some confusing in these "ideal" things... So, let's make them more real; for example, we may assume the input voltage source is real and it has some internal resistance or we may just connect a resistor R in series with the capacitor C. In other words, let's build and investigate a classic RC and RL circuit and investigate the particular element in this circuit. Then, let's apply the input voltage across the whole RC (RL) circuit and imagine what happens with the capacitor and the inductor. What is the voltage across the capacitor and the inductor? What is the current flowing through them? Let's present the voltages across the two elements constituting the circuits by bars and the currents by loops. There are two voltage drops in every circuit (across the accumulating element and across the resistor) and they are complementary; of course, the current flowing through the two elements is the same. Thinking in this way, we probably may find the solution...

How does the inductor behaves when the input voltage increases sharply? It produces an equal opposing voltage at the first moment. So, the input voltage source tries to change the current but the inductor impedes this attempt by subtracting an equal voltage from the input voltage. As a result, no current flows in the beginning; then, it begins increasing gradually. The current and the voltage drop across the resistor increase (exponentially) while the voltage across the inductor decreases. The inductor opposes the input voltage at the beginning and does not oppose it at the end (it is just a piece of wire then). There is no voltage across the inductor at the end; there is only (maximum) current according to Ohm's law. This action resembles the "bootstrapping" circuit trick. Well, let's we (Krasimir and I) illustrate this clever trick by a "lever" analogy - I raise my pointer from the one end; at the same time, Krasimir raises the other end.

The capacitor has a "reverse" behavior. In the beginning, the voltage across the capacitor is zero and it does not impede the input voltage source to produce current. As a result, the current is maximum at the beginning and then it begins decreasing. So, if we compare the two circuits, we see that in the RC and RL circuits the processes are reversed. Let's superimpose the voltages across an inductor and a capacitor and write the expressions showing how these voltages change through time (see the top of the picture on the right)... 

How do capacitor and resistor of RC circuit behave through time?


So far we have been comparing an RC with an RL circuit. Maybe, we have to pay attention to the particular RC circuit and to compare the voltage drops across the particular elements C and R. If we draw them (on the bottom of the figure above), we will see that the two curves are vertical mirrored; the voltage drop across the resistor is the complement of the voltage across the capacitor and v.v. At every moment, the sum of the instanteneous voltages is constant and it is equivalent to the input voltage; the two curves are complement. What else do we see looking at the picture? Krasimir: "The voltage drop across the resistor represents the current through the capacitor...and the voltage across the dual inductor..." Here is the clever idea - the resistor in each of these circuits (RC/RL) behaves as the dual element (L/C) from the other circuit (RL/RC). Let's repeat: the resistor of an RC circuit behaves as the inductor of an RL circuit. Then, what is the idea? It is so simple and powerful:

As the resistor of an RC circuit behaves as the inductor of an RL circuit then let's use this resistor as a virtual inductor.



Trying to simulate directly an inductor by a resistor


This is our inductor, the resistor... Krasimir: "We have to use also the voltage across the capacitor to create a current flowing through the virtual inductor..." Yes, you are right. To simulate an inductor, we have to make a two-terminal element have the same current and the same voltage as the ones of the resistor. Figuratively speaking, we can compose the inductor's behavior by its ingredients - the instantaneous voltage and current. As I can see, your idea is to get the resistor from an RC circuit and to use it as a virtual inductor. But how to realize this clever idea? Let's begin thinking...

What do we want? We have some external circuit; let's draw it in a blue color. It contains some input source (sinusoidal, square, etc.) with some internal resistance. And we want to supply an inductor by this input source. But, for some reasons, we do not have an inductor or it is inconvenient. So, we want to connect a simulated (virtual) inductor at this place; we want to connect here our element that has the same behavior. But how to connect it? It is a two-terminal element. Can we place it directly at this place? Will it has an inductor behavior? Obviously, we can't because we (the input circuit) will destroj the RC circuit operation... What do we do then?

Simulating an inductor by "copying" the resistor's voltage


Maybe, we have not to place the "resistive inductor" directly to this place but to "copy" its behavior. This is the next powerful idea:

Since we can't connect the virtual element directly into the circuit, we may "copy" it by another element.

How do we "copy" quantities in this world? Of course, by active followers (the most elementary negative feedback systems). Let's realize this idea. The problem was to "copy" a capacitor with the purpose to create an inductor. So, the voltage across the resistor has to be copied; it has to be the voltage across our inductor. We have to connect a follower (an amplifier with gain = +1). But let's first do it simpler. Imagine we do not know what a follower is and we have to make it ourselves. For this purpose, we place a varying voltage source and adjust its voltage equal to the input one; thus a voltage equal to VR appears on the right. This source acts as a "following" voltage source that changes its voltage in the same manner as the voltage VR changes through time. But VR = IC.R.

Actually we have created the voltage across our virtual inductor - the voltage of the following voltage source will behave in the same manner as the voltage across an actual inductor. 122 min







































Wikipedia discussions
(a copy from the Wikipedia talk page about gyrator circuits)

Discussion about energy storage in Gyrator circuit
I would like to discuss thoroughly the basic idea, the operation and the properties of this odd circuit. I suggest using the Elliot's example as a base.

The basic idea
We may consider this circuit as consisting of two parts (branches) - an input part (the RC circuit) and an output part (the op-amp and the resistor RL). We may think of the input part as of a "modeling", "shaping" part that drives the power output part. Building a CR differentiator. The current flowing through a capacitor is proportional to the derivative of the voltage applied across it; so, a capacitor acts as a simple differentiator with voltage input and current output. But we need a voltage output; for this purpose, we connect in series a resistor acting as a current-to-voltage converter and get the voltage across the resistor as an output. Building an L differentiator. Dually, the voltage across an inductor is proportional to the derivative of the current flowing through it; so, an inductor acts as a simple differentiator with current input and voltage output. In this way, the voltage across the resistor R of the input CR circuit behaves as the voltage across the inductor; so, we may use this voltage to simulate an inductor. For this purpose, we buffer the weak "shaping" input part by an op-amp follower and apply this voltage back to the input. To limit the maximum current through the "inductor" (the op-amp), we connect a low resistor (RL); it represents the inductor's internal resistance... Circuit dreamer (talk) 19:04, 3 April 2010 (UTC)

The operation
In the classical voltage supplied RL circuit (voltage source --> resistor --> inductor), the inductor opposes to the input voltage variations by producing a contrary voltage that substracts from the input one (figuratively speaking, when the input source "moves" the left end of the resistor, the inductor "moves" the right end in the same direction). In our circuit, the op-amp does the same by "moving" the right end of the resistor RL. This "bootstrapping" increases many times the resistance RL when the input voltage changes; the combination of the resistor RL and the op-amp acts as a time-dependent dynamic resistor. Let's consider the typical moments of the transition process.

Imagine the input voltage (the voltage at the left side of the resistor RL) changes suddenly from zero to VH. The capacitor transfers immediately this change and the voltage drop across R becomes VH as well. The op-amp follower "copies" this voltage drop and applies the same voltage at the right side of the resistor RL. As a result, no currents flows through the resistor and the circuit shows infinite large input resistance (impedance). In the course of time, the capacitor charges, the current passing through it decreases and the voltage drop across the resistor R decreases as well. The op-amp follower "lowers" continously the right end of RL and finally reaches the ground. At the end of the transition, the current is maximum - IMAX = VH/RL. Circuit dreamer (talk) 21:14, 3 April 2010 (UTC)

The output part dominates over the input one
Well, let's continue... The two parts (branches) of the circuit are connected in parallel. The output part (RL + op-amp) is the very "inductor" and it has to dominate over the input part (the input part has only "shaping" properties and it has not to disturb the "inductor"). In addition, the capacitor has to have as much as possible small capacitance (dimensions). So, the resistor R has very high resistance. In the Elliot's example, C = 100 nF and R = 100 kΩ whlie RL is only 100 Ω. The obtained "inductance" is as many as 1 H.

Does the circuit store energy?
Lets' make a final conclusion. The capacitor is the only element that can store energy in this circuit. But it has very, very small capacitance and the resistor R has extremely high resistance; so, the stored energy is negligible. I give a chance to the formal thinking Wikipedians to calculate and compare the energy stored in the capacitor C = 100 nF through a resistor R = 100 kΩ with the energy stored in the equivalent real inductor with inductance 1 H through a resistance R = 100 Ω. So, the final conclusioh is:

'The simulated inductor has the same behavior through time as the real inductor but it does not have the same accumulating properties. The simulated inductor does not store energy.' Circuit dreamer (talk) 22:47, 3 April 2010 (UTC)

The small energy accumulated in the capacitor is even undesired in this "inductive" circuit as it behaves in the opposite ("capacitive") manner - when the input voltage decreases, the capacitor passes a reverse current through the input source. If we want to eliminate completely this influence, we may connect another op-amp follower before the RC circuit. Circuit dreamer (talk) 10:47, 4 April 2010 (UTC)


 * The circuit has no need of storing energy - it is an active circuit - it just uses the capacitor as a impedance reference. The energy comes from the power supply of the op-amp or whatever other active element is used. --Ozhiker (talk) 00:01, 4 April 2010 (UTC)


 * The capacitor is not part of the gyrator; it is a termination placed on port 2. An ideal gyrator neither stores energy nor requires a power-supply - though this isn't obvious from the article. --catslash (talk) 01:42, 4 April 2010 (UTC)


 * As I have stated above and several times earlier it is incorrect to say that a gyrator circuit that has a reactance does not store energy.  This does not imply that you would use it to replace an inductor in a power switching circuit, like a switching regulator, etc.  That would be impractical.   Most people reading this article would assume this and anyway it is mentioned near the end of the article.  So the article does not need to be further adumbrated upon to the extent that is now present in other articles.  Zen-in (talk) 04:49, 5 April 2010 (UTC)


 * I think most of you are confusing the inductor example with the strict definition of a gyrator. A gyrator is an impedance transformer; it converts the i–v characteristics at one port to different i–v characteristics at a different port. It is true that in the inductor example, the capacitor "stores" energy. However, if you replaced a DC source at the input of the inductor circuit by a ground short, the energy that would be dissipated across RL would be different than the energy stored in the capacitor. Thus, some of the energy would come from the amplifier's power supply (which is not shown in the diagram). In fact, in that particular example, all of the energy dissipated across RL would come from the power supply; the capacitor's energy would be dissipated across R. So it really sounds like the page should reflect that:
 * A gyrator is an impedance transformer; it need not store any energy. It just needs to translate one i–v relationship to another. In the case of generating a purely resistive impedance, there would be no storage elements to find anywhere near the circuit.
 * The particular inductor example given, which is an active design, the i–v characteristics of a capacitor are being transformed into the i–v characteristics of an inductor. Hence, in the process of impedance transformation, some energy is being stored in the capacitor. However, this "storage" has nothing to do with the gyrator action.
 * It would be incorrect to say that a transformer dissipated energy just because a generator attached to the primary side of the transformer faces a real load when a resistor is placed on the secondary side of the transformer. Hence, it is also inappropriate to say that a gyrator IN GENERAL must store energy. Having said that, the EXAMPLE CIRCUIT itself does have storage elements, but that's tangential to the topc of gyration. &mdash;TedPavlic (talk/contrib/@) 17:35, 5 April 2010 (UTC)

Grounding
The circuit happens to be drawn connected to ground. There is no such restriction as far as I'm aware; why couldn't we float the gyrator? Oli Filth(talk&#124;contribs) 17:21, 7 April 2010 (UTC)


 * Of course, we may float the circuit but together with the power supply. See for example, how I have floated a VINIC in the story about negative resistance (BTW, I created it a year ago after Zen-in mutilated the Wikipedia page about negative resistance). Circuit dreamer (talk) 17:50, 7 April 2010 (UTC)


 * At the risk of starting a discussion about the circuit itself, why does the power supply matter? We could just as well connect R to any other voltage, and the analysis for Zin would be the same.  Oli Filth(talk&#124;contribs) 17:52, 7 April 2010 (UTC)


 * I hope you will see the same powerful idea (modifying an initial 2-terminal real element to obtain a new artificial element) behind negative impedance converters.


 * I'm not sure if your clever "shifting" trick will allow us to connect the simulated inductor in series (between) two other circuit components. I need time to think about it. Circuit dreamer (talk) 18:00, 7 April 2010 (UTC)

RL considerations
"There are contradictory requirements to the value of RL. From one side, it has to have some acceptable resistance to limit the maximum current through the simulated inductor (the op-amp output) and to obtain large inductance. From the other side, it has to have as much as possible low resistance to obtain high Q factor. Note if RL = 0, the circuit will stop working at all: the op-amp output voltage will be zero, the op-amp will keep (almost) zero voltage across the capacitor and no current will flow through it."


 * Won't the Q factor be constant? It's going to be (from Inductor):
 * $$Q = \frac{\omega R_L R C}{R_L} = \omega R C$$
 * Oli Filth(talk&#124;contribs) 22:05, 7 April 2010 (UTC)


 * I'm not familiar enough with Q factor topic and I need time to realize it. But really it is very important to clarify the role of RL as someone may try to make an "ideal inductor" (RL = 0). The results will be unfortunate - zero inductance (as the expression L = RLRC says) and what is more important, the circuit will not operate at all (here I suppose an ideal op-amp). Circuit dreamer (talk) 06:06, 8 April 2010 (UTC)

Demystifying gyrator circuits
I start this discussion here to demystify, once and for all, the basic idea, implementation and operation of these exotic circuits. I will use the text below as a base (I wrote it two days ago):

"Gyrator circuits imitate real elements by dynamic voltage sources with swapped instantaneous values of the voltage and the current (the voltage across the new virtual element is proportional to the current flowing through the initial real element and the current flowing through the virtual element is proportional to the voltage across the real element). These voltage sources (gyrator's outputs) are connected in opposite direction to the exciting input sources as they mimic voltage drops (in contrast, negative impedance converters with voltage inversion produce voltages). So gyrators are not only positive impedance inverters; they can "invert" in this manner any elements (linear, non-linear, time-dependent, sources, etc.) connected as a load..." Circuit dreamer (talk) 18:20, 11 April 2010 (UTC)

Impedance is a misleading concept here
The lede says "the gyrator is a positive impedance inverter" and this is true, especially in the case of a simulated inductor that converts a capacitive reactance into an inductive reactance (a capacitor into an inductor). But the problem is that impedance "impedes" the understanding gyrator circuits. What is the problem?

The problem is that impedance Z = V/I is defined as a ratio of the rms ("effective") values of the voltage and the current (see hyperphysics). Being some kind of averaged quantity, impedance hides the concepts behind all these odd circuits - gyrators, multipliers, negative impedance converters, etc. Impedance viewpoint does not allow us to realize what all these circuits actually do. As an example, you may see the result of this misleading "impedance approach" in the area of negative impedance if you browse these archived talk. Then I (Circuit-fantasist) wasted plenty of time to show how simple the idea behind negative impedance is but I didn't manage. Now I realize why. The reason of this failure to understand one another was simple - I was thinking in terms of instantaneous values while my opponents were thinking in terms of averaged (rms) values.

The article says what a gyrator does (inverts an impedance) but it does not say how it does this magic. But the idea behind this mystic circuit is extremely simple; we will grasp it immediately if only we forget the misleading concept impedance and begin thinking in terms of instantaneous voltage and current quantities! This is the remedy - to imagine what the particular voltage and current are at each moment, to think "instantaneously":)

What is actually a gyrator?
To understand what the particular gyrator is, it is extremely useful to understand what all related exotic circuits are. Multipliers, gyrators and negative impedance converters are used to create virtual elements that are accordingly multiplied, inverse (dual) and negative copies of actual elements. These virtual elements only mimic the original elements; they have not the same nature as the initial elements since they are implemented as dynamic voltage sources. Actual capacitors and inductors create voltage drops: a capacitor impedes the input voltage source by subtracting a voltage drop VC from the input voltage; an inductor impedes the input voltage source by creating a back emf VL and subtracting it from the input voltage. So, to simulate these behaviors, the "multiplied" and inverse virtual elements (voltage sources) are connected in opposite direction to the exciting input source to subtract a voltage drop while negative impedance converters (VNIC) are connected in the same direction to the input source to add a voltage.

What does a gyrator actually do?
A gyrator does only a simple donkeywork: it continuously "observes" the instantaneous values of the voltage across and the current through the original element (model, sample, pattern, load here...) and makes its own instantaneous output voltage proportional to the initial current and its current proportional to the initial voltage. Thus, the combination of the gyrator and the connected actual load acts as a dual 2-terminal virtual element. Shortly, a gyrator is a dynamic voltage source with swapped initial voltage and current.

You can guess that a multiplier does the same but without inversion - e.g., it makes its own output voltage equal to the initial voltage and its current proportional to the initial current. For example, a capacitance multiplier emulates an actual capacitor with an opposing dynamic voltage source (see AN-29, page 11, fig. 19 and try to guess how this clever circuit operates). Finally, you will probably realize that a negative impedance converter with voltage inversion (VNIC) is a dynamic voltage source emulating a negative resistor by adding a voltage that is equal to the voltage drop across the initial element (see this Chua's material and try to see the clever idea behind this circuit). But let's return to the gyrator.

Imagine how simple it is! The gyrator does not "know" what it converts; it is not "interested" in what an initial element is connected. The only thing that a gyrator can do is to observe the input (load's) voltage and current to produce an output (simulated) current and voltage.

Following this simple procedure, a gyrator can "invert" not only classical impedance elements (capacitors and inductors); it can invert elements of all kinds including non-linear ones. For example, a gyrator can convert a diode or a varistor (voltage-stable elements) into a transistor or a baretter (current-stable elements) and v.v. I suppose a gyrator can invert a negative impedance (negative capacitor into a negative inductance) and this extremely odd combination will have some fancy name (e.g., "injectoplactor":) It turns out a gyrator can convert almost everything. If even we put some wikipedian (e.g., Zen-in/Circuit dreamer) at the place of the load (this is only a joke!), the gyrator will convert the poor wikipedian into his/her inversion (Circuit dreamer/Zen-in). It is wonderful, isn't it?

How does a gyrator do this magic?


The circuit works by inverting and multiplying the effect of the capacitor in an RC differentiating circuit where the voltage across the resistor behaves through time in the same manner as the voltage across an inductor. The idea of the circuit is revealed in the figure on the right by an equivalent balanced bridge circuit. It consists of two legs connected in parallel: the left leg is the "shaping" RC circuit; the right leg is the virtual inductor VL with its internal resistance RL.

In balanced bridge circuits the voltages across the opposite elements are equal. Here, the varying voltage source Vs (the op-amp follower) balances the bridge by "copying" the voltage drop across the resistor R that is proportional to the current flowing through the capacitor. As a result, the voltage drop across the resistor RL is equal to the voltage across the capacitor; so, the current flowing through RL is proportional to the voltage across the capacitor. The desired effect is an impedance of the form of an ideal inductor L with a series resistance RL.




 * I'm not sure what you're hoping to achieve with all this text that you keep adding to talk pages? Oli Filth(talk&#124;contribs) 08:04, 12 April 2010 (UTC)


 * Incidentally, impedance is not defined in terms of RMS values; it is defined as the complex ratio between the voltage phasor and current phasor. Oli Filth(talk&#124;contribs)


 * Actually, I think I understand what you may be trying to say. Essentially: "a gyrator inverts all I-V relationships.  In the case of an LTI component (resistor, capacitor, inductor), the effect of this is to invert the impedance.  Therefore, the article should explain the gyrator in terms of I-V relationships, not impedances (which are a specific case)."  Is that what you mean?  Oli Filth(talk&#124;contribs) 07:10, 13 April 2010 (UTC)


 * Yes! Yes! Yes! This is exactly what I want to say! Impedance is not a suitable concept here as it is a some kind of "derivative" quantity based on the particular voltage and current quantities; impedance is a more general, global quantity that "combines" the two particular quantities into one. In the case of linear elements, it works fine, but it can't represent the circuit operation in the case of non-linear loads. But, what is worse, impedance can't explain what a gyrator does even in the case of these linear loads since it is not something real; it is some "fiction". Only the instantaneous voltages and currents are real quantities in this (and in any) circuit; at each moment, there are only a pair of voltage drop across and a current through the load and a corresponding pair of voltage across and a current through the simulating virtual element. The gyrator does not know what it actually converts - impedance or "no impedance"; it acts as a functional converter that measures "blindly" the instant input voltage and current and converts them immediately into output current and voltage. Thus, if the input element (load) has an impedance, the output virtual element will have an impedance as well and v.v. If we want to see impedance here, we will see; if we do not want, we can think in terms of special voltage and current quantities. Circuit dreamer (talk) 12:11, 13 April 2010 (UTC)


 * In that case, I'm inclined to agree with you. Let's wait to see what Zen-in's thoughts are (or anybody else's).  However, even if we're all in agreement, we must follow the presentation of available references.  What do they have to say?  Oli Filth(talk&#124;contribs) 12:32, 13 April 2010 (UTC)


 * A few days ago, I managed to grasp "how a gyrator does this magic" and started the section above. I found a powerful viewpoint at these multiplying, gyrator and NIC circuits and prepared informative pictures revealing the clever trick. This morning, in the beginning of the lecture, I posed the problem to my students. I drew the circuit on the whiteboard and asked them to reveal the basic idea behind it (I have been using this didactic approach since 80's). One of them (the best student) immediately began thinking and proposing ideas; as a result, I didn't manage to take a cup of coffee during the break:) I hope some of them will see the brilliant idea till the next week when we will investigate these circuits in the laboratory by Microlab. Circuit dreamer (talk) 12:56, 13 April 2010 (UTC)


 * Impedance implies LTI, which in turn implies the load has a defined transfer function. A diode (for instance) doesn't have a defined transfer function, and hence doesn't have a meaningful impedance (at least far as I understand it; it certainly can't be expressed in terms of a ratio of phasors).  However, the gyrator still inverts its I-V characteristic.  So I think Circuit-Dreamer's point stands.

...However, what I am saying is that Circuit-Dreamer does have a valid point. Oli Filth(talk&#124;contribs) 22:36, 13 April 2010 (UTC)


 * There is no transfer function of a diode; all there is are transfer functions of linearised (i.e. approximated) small-signal models, which only hold over small regions of operation around the bias point. Whilst this may be what Spice uses to perform AC analysis, this is not what I'm referring to (and presumably, not what C-D is referring to).  The small-signal approximation is a consequence of the large-signal behaviour, which is what (IMHO) is the crux here.


 * I'm not suggesting that we change an awful lot, merely that we start in terms of I-V relationships, rather than impedances (if sources permit us). I may attempt this tomorrow.  Oli Filth(talk&#124;contribs) 23:07, 13 April 2010 (UTC)

Latest additions
I've reverted these latest additions because: Oli Filth(talk&#124;contribs) 22:59, 19 April 2010 (UTC)
 * As has been mentioned previously, this is your own bespoke analysis. If you can find a reference that supports the idea that this is a bridge topology, then perhaps we'll revisit.
 * There have been multiple objections in the past to the hand-drawn diagrams.
 * This isn't really a positive-feedback topology.


 * Thank you for the elucidations. Definitely, talk pages become more interesting than the main pages and I am apprehensive that our readers will begin reading talks instead articles:) Well, let's discuss the section about circuit operation that you have reverted.


 * Bridge viewpoint. Of course, we may consider the circuit without seeing any bridge idea behind it; we may see only the "trees" (the particular C, R, RL, op-amp, power supply) without seeing the "forest" (the bridge topology). But the bridge configuration is something familiar to nearly everyone; it is a concept helping understanding. We, human beings, understand new things (systems) by discerning old well-known patterns (subsystems, components, ideas, tricks, etc.) inside them..., by making associations based on what is familiar... Balanced bridge is another powerful concept whose amazing feature is the equality (horizontal symmetry) of the voltage drops. I realized it as far back as 1968 when I, 14-year-old boy, made a simple servo system by two potentiometers, a polarized relay with neutral position, split supply and a motor with reduction gear...




 * Wikipedia says "...bridge circuit is a type of electrical circuit in which two circuit branches (usually in parallel with each other) are "bridged" by a third branch connected between the first two branches at some intermediate point along them. .." Look at the picture now: R and C constitute the left branch; Vs and RL constitute the right branch. The two branches are connected in parallel and they are "bridged" by the op-amp differential input. The bridge is balanced since the op-amp follower keeps Vs = VR... plain, clear and simple... Tell me now, should we look for "a reference that supports the idea that this is a bridge topology"? BTW, an INIC (drawn in such a symmetrical form), is another example of balanced bridge circuit where the op-amp changes the supply voltage to balance the bridge.


 * Diagram. It is a "snapshot" of the circuit operation where the instantaneous voltages across the elements and the currents flowing through them are shown by proportional voltage bars and current loops. This presentation allows readers to grasp the idea (equal voltages across the opposite elements) only by a glance at the picture. It is a colorful just because our world is colorful. Is your monitor black & white? Do you watch black & white TV? Then, why do you make readers look at this colorful world through black glasses? And what is the problem with this kind of hand-written diagrams in a Forrest Mims style? If you do not like it, feel free to redraw the pictures by an editor.


 * Positive feedback. There is no feedback in this circuit only if it is driven by a perfect voltage source (with zero internal resistance). Normally, in the case of a real voltage source (with some internal resistance), there is a positive feedback with a closed-loop gain 0 < A.β = 1.β < 1. So, this feedback is "under control" (the Armstrong's regenerative receiver idea). In comparison, in Schmitt triggers, the positive feedback is out of control as A.β >> 1. This is the "trick" here - to "bridle" the positive feedback by using a unity-gain amplifier. Another trick to make the positive feedback stay under control is to "neutralize" it by a negative feedback; an INIC operating in a linear mode is based on this powerful idea. In INIC operating in a bistable mode, the positive feedback dominates and it is out of control.


 * Circuit dreamer (talk, contribs, email) 22:59, 20 April 2010 (UTC)