User:Alexander Kornich/Proposed/Discrete Power Converter as mechanical model of Relaxation Oscillator
Educational value of DPC as hydro-mechanical / electrical model.
There is another useful application of DPC that makes sense to consider more in detail. We are talking about the similarities between hydraulic and electrical processes, which has long been known and used in the design (for example, when modeling processes and devices) and for educational purposes (for example, for illustrative purposes, the explanation of electrical phenomena). The electronic–hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Lodge)  is the most widely used analogy for "electron fluid" in a metal conductor. Since electric current is invisible and the processes at play inelectronics are often difficult to demonstrate, the various electronic components are represented by hydraulic equivalents. Electricity (as well as heat) was originally understood to be a kind of fluid, and the names of certain electric quantities (such as current) are derived from hydraulic equivalents. As with all analogies, it demands an intuitive and competent understanding of the baseline paradigms (electronics and hydraulics).
There is no unique paradigm for establishing this analogy. Two paradigms can be used to introduce the concept to students: • Version with pressure induced by gravity. Large tanks of water are held up high, or are filled to differing water levels, and the potential energy of the water head is the pressure source. This is reminiscent of electrical diagrams with an up arrow pointing to +V, grounded pins that otherwise are not shown connecting to anything, and so on. This has the advantage of associating electric potential with gravitational potential. • Completely enclosed version with pumps providing pressure only; no gravity. This is reminiscent of a circuit diagram with a voltage source shown and the wires actually completing a circuit. This paradigm is further discussed below. Other paradigms highlight the similarities between equations governing the flow of fluid and the flow of charge: Flow and pressure variables can be calculated in both steady and transient fluid flow situations with the use of the hydraulic ohm analogy.  Hydraulic ohms are the units of hydraulic impedance, which is defined as the ratio of pressure to volume flow rate. The pressure and volume flow variables are treated as phasors in this definition, so possess a phase as well as magnitude.
In electronic-hydraulic analogy the current represents of flow and electric potential (or voltage) represents the hydraulic head (as by formula (1) in paragraph 2) accordingly.
Since electric current is invisible and the processes at play in electronics are often difficult to demonstrate, the various electronic components are represented by hydraulic equivalents .
However in the case of DPC as subject of electronic–hydraulic analogy we can consider not only similarity of hydraulic equivalents of some electronic components (as resistor, capacitor, etc) but even clear similarity between principal of operation such hydraulic-mechanical machine (as DPC itself) and electronic device such as Astable Multivibrator (AMV) which represents class of oscillators/generators . Moreover it is becoming evident that similar principal of operation ( oscillating mode) can be explained as result of action of feedback  which has electrical nature for AMV and mechanical nature for DPC. Thus DPC can be classified as self-regulating mechanism (powered by gravity force of flowing mass –water, for example) which is operating in periodical two-stage mode and represents a hydraulic equivalent of electronic device (as circuitry of set of simple electronic components) with feedback control loop in the electrical schematic. In a sense, one can speak about a paradigm shift as “… transition from one paradigm to another …”  in the hydro-electrical analogy which corresponds the transition from equivalent terms and concepts (such as “… electric potential and gravitational potential; similarities between equations governing the flow of fluid and the flow of charge …”  to equivalents of the physical structure and principles of operation (mode) of mechanism (and electronic device accordingly) based on the action of the feedback of different physical nature, but ultimately have been realized as analogy of mode of the relaxation oscillator (electronic and hydro-mechanical). It makes sense to consider this important issue in more details by analyzing the kinematic scheme of the DPC (a) and the electrical circuit of AMV (b) on Fig. 1.
Firstly, we can define similarity AMV and DPC in the terms of classical paradigm of hydraulic analogy: 1. The potential nature source of power for AMV (as voltage of electrical power supply i.e. the difference between +V and 0V on b) of Fig.1) and for DPC (as hydraulic head i.e. the difference between High position and Low position on a) of Fig.1). 2. The equivalent of electrical current (as flow of electrical charges) which goes through electrical structure (circuitry – resistor Rc1/ transistor Q1/ground) of AMV from +V (high potential) to 0V (low potential) of power supply and hydraulic volume flow rate (as flow of water, for example) which goes through DPC machine (intake/feeding pipe/bucket/working stroke/ground) from High position to Low position. It is important to note that these “currents” caused by fields of potential nature: electrical and gravitational. 3. The equivalent of electric charges (and “capacitors” accordingly) which are accumulated alternately in the electrical capacitors (Ce1,Ce2) in the process of operation of AMV and quantity of water (volume) which is accumulated (also alternately) in the buckets (Cm1, Cm2) in the process of operation of DPC. It is important to note that these “capacitors” are “discharged” to “ground point” – zero potential in both cases. 4. The equivalent of conducting wires and resistors (like pipes and constrictions in it) for connecting parts and components in the circuitry of AMV and structure of DPC accordingly. . It is important to note that these “resistance” caused of losses of power during of operating in both devices – electrical (AMV) and hydro-mechanical (DPC). On this list the similar features (equivalence) of classical paradigm of hydraulic analogy have been completed because specific behavior of DPC (as physical principal of operation of relaxation oscillator ) can not be described and explained on this base. Secondary we have to define similarity AMV and DPC in the terms of new paradigm of hydraulic analogy: 1. Symmetrical physical structure of electronic device (AMV) and mechanical machine (DPC). We can see it clearly from similarity electrical schematic of AMV and kinematic scheme of DPC: two symmetrical combinations (left and right “shoulder”) of resistors, capacitor and transistor (for AMV); and similar two symmetrical combination of rocking levers (feeding upper pipe and working lower beam) and buckets (for DPC). 2. The equivalence of two symmetrical power amplifiers in the physical structure of AMV and DPC accordingly: transistors (Q1, Q2 for AMV) which amplify the collector current (Ic) proportionally to base current (Ib), such as Ic=k*Ib; and levers (for DPC) which amplify the gravity force (P=mg) of mass (m) of water (for example) accumulated in the bucket. The gravity force is multiplied (amplified) in accordance to law of lever depending on geometry of DPC machine (length of lever) and points of applying gravity force and mechanical load. In general case the gravity force can be amplified as F=k*P= (D/d)*P= (D/d)*mg. It is important to note that ability of DPC to amplify of gravity force is the fundamental distinct feature of innovative hydro-mechanical machine. 3. The equivalence of two symmetrical feedback crosses type in the physical structure of AMV and DPC accordingly: for AMV the connecting (wiring) of output of transistor Q1 (through capacitor Ce1) with input of transistor Q2 and conversely – the connecting (wiring) of output of transistor Q2 (through capacitor Ce2) with input of transistor Q1; for DPC the connecting (by rod or chain) the “right shoulder” of working beam (low rocking lever) with “left shoulder” of feeding pipe (top rocking lever) and conversely - the connecting (by rod or chain) the “left shoulder” of working beam (low rocking lever) with “right shoulder” of feeding pipe (top rocking lever). It is important to note that applying of two symmetrical mechanical feedback crosses type in the construction of DPC is fundamental innovation step which provides the transfer some part of mechanical power from functional “output” of mechanism (low rocking lever) to functional “input” of mechanism. This part of power is used for changing the direction (in terms of accumulating buckets) of transfer of input power (as flow of working medium – water, for example). Therefore it provides mechanical “switching effect” in DPC (as electrical switching effect in electronic circuitry of AMV, for example). Because of the alternate nature this switching effect in the time and in the space (as result of symmetrical structure of mechanism) simultaneously the mode of relaxation oscillator  can be realized in the DPC operation (at least until “a flow of input working medium” is applied). In other words we can define DPC as absolute adequate hydro-mechanical model of relaxation oscillator based on the action of mechanical feedback crosses type. This definition may be considered also as some new contribution in the paradigm  of hydraulic analogy . Any way we can see now that not only “… the various electronic components are represented by hydraulic equivalents ...” but even typical electrical oscillators may be represented by DPC “… Since electric current is invisible and the processes at play in electronics are often difficult to demonstrate. “ The possibility to demonstrate by DPC the operation of relaxation oscillator is evident cognitive value in the process of education of students.