By the mid-1990s, I had already developed my own philosophy about electronic circuits, and I decided it was time to share it with my colleagues. In the spring of 1997, I presented a series of three papers at the XXXII Scientific Conference on Communication, Electronic and Computer Systems at the Technical University of Sofia. The first of these was devoted to my heuristic course on analog circuits, in which I had implemented my circuit philosophy. There I shared my idea of using analogies for the purposes of understanding, presenting and inventing circuits. In this post, I will tell you about this venture of mine.
What are analogies?
We begin learning from the day we are born. In this way, in the early years of our childhood, we accumulate a knowledge of life for visible (mechanical, hydraulic, pneumatic, social, etc.) phenomena of our world. But this world is arranged so interesting that apparently different phenomena obey the same laws; they are analogous.
Then, why do not we use associations as educational mainstays that convey the common knowledge about visible worldly phenomena to invisible abstract electric phenomena? Thus they will look familiar, elementary and accessible. This is so because we, human beings, begin understanding new unfamiliar things when we begin discerning something familiar inside them. We just consider new complex things as composed by a few simpler well-known components. Here are some examples of applying analogies.
Real analogies
Closed loop fluid analogies
One of the earliest human representations of Ohm's elementary electric circuit is the fluid analogy (also known as "fish tank") - under the action of pressure P in a closed pipeline, a fluid current with a flow rate I meets along its path resistance R. The voltage source in this analogy is represented by a compressor that maintains a constant pressure (just like those that power pneumatic instruments).
Using a more complex fluid analogy, we can illustrate the circuit of a passive voltage summer that we use as a subtractor and comparator in op-amp circuits with negative feedback. If it is two-input, we include two pressure sources.
Their effects are summed at the common point and so the pressure on the load is the sum of the input pressures. If this is an analogy of a resistor subtractor (comparator), the positive input voltage source V1 can be thought of as a compressor that pushes air and increases the pressure in the common point. The negative input source V2 is presented as a compressor that sucks the air and creates a vacuum at the point. Figuratively speaking, the two compressors "fight" with each other and if their pressures are related as their respective air resistances (P2/P1=R2/R1) the pressure at the common point is equal to zero. This phenomenon can be figuratively called a fluid virtual ground.
Open loop fluid analogies
In addition to being a compressor that maintains a constant pressure, a voltage source can also be represented as a cylindrical vessel (on the left) with a constant water column level.
In the analogy of a voltage subtractor, the positive input voltage source V1 will represent a vessel placed at the earth's surface (zero level) and the negative source V2 a vessel lowered below the ground surface. Under some conditions, the hydraulic pressure at the common point will again be equal to zero - this can be called hydraulic virtual ground.
Mechanical Analogies
One of the most popular mechanical analogies is Archimedes' lever, which in this example is operated simultaneously from both sides. When the equality h2/h1=l2/l1 is fulfilled, a virtual mechanical mass is obtained at the common point. If we stylize this analogy, we arrive at the more abstract geometric voltage diagram.
No less famous is the weight analogy - a mechanical scale, with the help of which two weights are compared. The balance pointer points to a virtual mechanical ground when the equality P2/P1=l1/l2 is satisfied.
"Live" analogies
To show the connection between an analogy and its corresponding circuit diagram, we can "live" the analogy on the monitor screenwith the help of a computer. For this purpose, we can connect the circuit under test by means of an analog-to-digital periphery to a personal computer operating under the control of an appropriate software. An analogy of the studied circuit will be displayed on the screen, which responds adequately to changes in the circuit and thus strengthens associations with it.
"Live" analog scale
For example, in this way we can represent the operation of an op-amp circuit with negative feedback by displaying a "live" analog scale on the screen. Input and output voltages are represented by weights of proportional size on both sides of the scale.
"Live" discrete scale
Similarly, we can illustrate the operation of an analog-to-digital converter with a discrete weight, where the output value – a digital code – is presented as a sum of reference weights. The picture below shows such a demonstration in the laboratory performed using a MICROLAB system connected to an 8-bit DAC. The PC video output is connected to a multimedia projector.
A stylized image of a mechanical scale is visible on the screen. The left pan houses the analog input weight, and the right pan houses some of the 8 binary standards with weights from 1 to 128. Shown below are the reference voltage (10 V) of the on-board DAC, the input voltage (1.928 V) , the current code (49) and the DAC output voltage (1.914 V).
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