Models and modeling are an important of part engineering. Whether related to IC physics, passive components, discrete devices, PCB traces, signal integrity, thermal and mechanical issues, or system-level dynamics, models help us understand what we've got and likely problems we'll encounter.
The first time I met the model concept, it was an intellectual eye-opener to me. The professor drew a simple capacitor symbol, and proceeded to make clear that this was a greatly simplified version of reality. He skillfully added dc resistance, stray inductance, and stray capacitance, and told us this was a more accurate model, but only up to a certain frequency band.
Finally, he layered on even more internal, external, and stray elements to show us what the capacitor looked like at even-higher frequencies. If we did any thorough analysis, using Spice or similar tools, we'd need to pick the appropriate model and values for its elements.
Modeling recently came to me again in another guise. Our new washing machine's fast-acting solenoid valves incited severe water hammer. It is annoying and can cause cracks in the pipe joints due to the repeated shock and vibration. Luckily, it's a common problem with several available solutions.
One approach is to add a piece of pipe from 12 to 18 inches long, as a stub near the hammer source, to act as an air chamber. The rushing water compresses the air, which then acts as a cushion, somewhat like a bypass capacitor. However, while this passive solution is reliable mechanically, the capacitor literally has leakage, as the air cushion eventually dissolves into the water and renders the chamber useless, so you have to periodically drain the pipes and reestablish the air column.
A better solution is a semi-active arrestor, a pipe about 5 inches long and which has a piston inside (http://www.siouxchief.com/B_Product_Detail.cfm?GroupID=350200). As the water suddenly flows, the piston compresses the air and cushions dampens the hammering, but the air and water are isolated. This eliminates the problem of the passive unit, but the piston seal will wear out after 50,000 cycles (10 years typical).
Unlike many analogies, which are illustrative but technically inaccurate, water and electricity analysis had many similar elements and equations. When I have explain volts and current to young students, it's clear that voltage and current are fairly abstract to them. But when I describe volts as similar to water pressure, amps to water flow, narrow pipes to resistors, valves to switches, and chambers to capacitors, it all makes sense. Even better, it's a legitimate model and analog between the two worlds.
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