How I Revealed the Secret of Parallel Negative Feedback Circuits

I wrote this circuit story in 2001 when I began creating with a great ehthusuasm the site of circuit-fantasia.com (How do we understand, present and invent electronic circuits). Then I wasted a few months of my life to create an animated version of this story – a kind of a fairy “story tale”:-) As naive now seeming to me then I did it all to impress a remarkable person - Thom  Hayes, who had written in his Student Manual for the Art of Electronics ingenious guesses about the virtual ground phenomenon...

In traditional electronic courses, analog circuits are unnaturally divided into passive and active ones. First, we are persuaded how imperfect passive circuits are. Then we are given finished active versions, analogous to passive ones, and it is proved formally they are almost ideal. But nobody shows us what we really need to comprehend active circuit operation; the relation between passive and active versions and how passive circuits have been converted into active ones i.e., circuit evolution. For a long time, I had been feeling intuitively that such a relation existed and so I began looking for it. For that purpose I started with the circuit of the ideal ammeter, so simple but so unintelligible. 

STEP 1: Removing a disturbance by an antidisturbance. 

How many times I have asked myself the question, "What does the op-amp really do in the circuit of the ideal ammeter"? Eventually I realized that the op-amp compensates the power losses in the circuit, injecting exactly as much energy as it loses in the imperfect ammeter. In real life we behave in the same manner: when a harmful disturbance stands in our way we remove it by an equally useful “antidisturbance". So the general idea was removing a disturbance by an antidisturbance, which, in this particular circuit, was manifested as removing a voltage by an antivoltage. 

I was proud because I already knew how to convert an imperfect current meter (meter movement) with an arbitrary internal resistance into an ideal ammeter with zero resistance. In series with the “bare” movement, I connected a small adjustable supplementary battery (i.e., a properly supplied op-amp), which copied the harmful voltage drop across the current meter adding it to the internal voltage (electromotive force) of the basic input source. The op-amp did that by “keeping a sharp eye” on the potential at the upper side of the ammeter and pulling this potential to the corresponding side so that it always stayed zero. Thus the op-amp was keeping up the “mystical” virtual ground.

I felt almost like a magician as I was already able to convert any given resistance into zero resistance. Practically, I could make “ideal” diodes and transistors (without forward voltage drop), “bottomless" capacitors, etc. By the way, much later it occurred to me to make the supplemental source “overact”, by adding several times larger than needed voltage to the basic source (just as in real life sometimes one goes too far in his/her help). Then I felt really elated because I was not only able to zero the ordinary "positive" resistance, but also to convert it to negative resistance. In such a way I figured out what the op-amp did and how it did it in the abstract circuit of the negative impedance converter (NIC) and in the famous Howland current source, which I failed to find in any book. But now let us come back again to more ordinary circuits with parallel negative feedback.

STEP 2: Measuring a disturbance by an antidisturbance.

I began to see the idea of removing a disturbance by an “antidisturbance” in many other circuits (current-to-voltage converter, integrator, logarithmator, etc.). There the op-amp performed exactly the same function: it compensates the power losses in the passive circuit, copying the “harmful” voltage across the corresponding passive element (resistor, capacitor, diode, etc.) and adding the copy to the voltage of the input source.

I was faced with an interesting technical contradiction. On the one hand, the voltage drop across the element was harmful for the input source, and because of that we had removed it by an “antivoltage"; on the other hand, however, this “harmful” voltage was useful for us because, just with that end in mind, we had included the respective passive element into the circuit (as you say in your book, “… the output moves away from ground; but of course it must move away from ground …”). But why on earth was the op-amp output voltage the output signal of the circuit instead of the useful (for us and for the load) voltage drop across the passive element?

Again I found out the answer to this question in many everyday situations when it was more convenient to use an indirect rather than a direct estimation of a value. Thus I managed to formulate the next principle which I called measuring a disturbance by an “antidisturbance”: the magnitude of the useful “antidisturbance” gives us an indirect idea about the magnitude of the harmful disturbance we have removed it with.

Then I realized why the output signal was taken at the op-amp output - the compensating “antivoltage” was found there, which was the exact inverted copy of the original voltage across the passive element. Therefore all the circuits based on that idea were inverting. What a wonderful trick! First, the load is connected to common ground; second, the load may have arbitrary low resistance because it consumes energy from the op-amp power supply instead of the input source!

STEP 3: A general “recipe” for converting passive circuits into active ones.

I triumphed in real earnest because I was already able to convert every passive circuit into an active one with parallel negative feedback, using one and the same “scenario”:

1. Build a passive circuit (unloaded).
2. Attach a load (passive device such as a resistor, capacitor, diode, etc.) across which a “harmful” voltage appears.
3. Compensate the “harmful” voltage by an “antivoltage”.
4. Use the “antivoltage” as an output signal.

STEP 4: A general rule for choosing a series or parallel negative feedback.

Now a problem of choice arose because I had another opportunity - to convert a passive circuit into an active one with a series negative feedback (I had mastered that long before). Then which of the alternatives should I use in each particular case? In order to answer this interesting question, first, I had to clarify the difference between those two kinds of circuits with negative feedback.

1. Parallel negative feedback circuits (PNFBC) compensate the power losses in the passive circuit by means of additional energy injection. They influence circuit operation adding exactly the same voltage as it is lost across the passive element and keeping up invariable the current flowing through the element. In other words, PNFBC copy the original voltage from the passive element onto the load, thus destroying the voltage.
2. Series negative feedback circuits (SNFBC) do not compensate the power losses in the passive circuits and do not influence circuit operation at all. They only “observe” the original voltage drop across the passive element and copy it onto the load without destroying the voltage.

I could already formulate the general rule of the negative feedback choice:

1. If the voltage drop across the passive element is harmful for us we destroy it by a parallel negative feedback thus getting an inverting circuit.
2. And vice versa, if the voltage drop is useful for us we just buffer it by a series negative feedback system thus getting a non-inverting circuit.