Using simplified models and first-order approximations are a normal part of engineering life. Without them, we would get mired in the details and harsh reality of the components and their characteristics. We would never be able to take those critical, rough-estimate first steps; instead, the standard “paralysis by analysis” syndrome took over.
Of course, we sometimes get very comfortable tossing around equations associated with these simplifications very easily. After all, what could be simpler than a wire loop? It follows Maxwell's equations (perhaps described as Oliver Heaviside's reduction of Maxwell's twenty-plus extremely complex equations to the four classic ones we know, but that's another story, see Twenty Three Years: The Acceptance of Maxwell’s Theory and Oliver Heaviside: A first-rate oddity )
One of the first things we learn in basic EE class is the transformer-turns equations, where the ratio of the number of primary turns N1 to the number of secondary turns N2 defines the step-up/step-down voltage and impedance ratio. That simple equation makes for a good start at characterizing the transformer's behavior and what it can do for your circuit or power subsystem.
Nonetheless, it's naive to assume that all you need is N1/N2 for transformer design, or any other simple wire-loop situations. In the past few weeks, I coincidentally came across three unrelated stories which served as clear reminders that simplifications are good and necessary, but they are only starting-point approximations. You will likely need to go to more-precise models and analysis to get the fidelity you need. The items I saw were:
- Build Your Own Transformer (not sure why you would ever want to after reading this, but you might have to, for a special application),
- Analysis and Loss Mechanism of a Spiral Inductor Via the Green’s Function Model (some truly serious math here), and
- Calculating the High-Frequency Resistance of Single and Double Layer Toroidal Windings (also pretty deep stuff).
Fortunately, I could look at these from the arm's length perspective of interest only, and did not have a need to delve into them and actually understand them for a project requirement.
Still, they were sobering reminders that achieving the high levels of performance we need often requires a deep dive into the underlying physics or, alternatively, using a mostly hands-on approach of build-evaluate-redo (and then repeat until satisfied). Each approach has strengths and weaknesses, although with the quality of many of today's modeling tools and the powerful processors that execute them, the former approach is gaining more adherents: it can save time and money, reduce frustration, and allow more “what-if” analysis of changes in parameters and their associated tradeoffs.
What's your experience with “simple” passive components such as a wire loop? Have you ever wrestled with detailed models, or do you prefer using a less-analytic, more hands-on technique?