How is reflecting components across a transformer intuitive? - Page 1
Forum section: electronics / beginners

author: LoveLaika
author_rank: Frequent Contributor
timestamp: June 01, 2022, 08:00:17 pm
content: I'm going through a refresher on transformers as part of my studies into power electronics, but the concepts that were presented in one example showcased different thinking than how I'm used to working with them (and it's been a really long time since I've worked with transformers), so I wanted to ask for some help and guidance on the matter.I started going over the basics of the ideal transformer; assuming a 1:N turns ratio, you can calculate the voltage/current/inductance on the secondary side (given an appropriate source and whatnot on the primary side). That was pretty straightforward. However, what tripped me up was reflecting across the transformer with multiple components at the DC-level. Realistically, a transformer can only operate with an AC source. However, with the ideal transformer, you can use DC-components. So, the relationships still hold. This is easy with one component. However, I'm a bit confused when applying it to multiple components.Take this attached example I got from a lecture. In the top circuit, what would be the equivalent circuit as seen from the secondary side? The answer is shown below, and you can see the corresponding transformer relations at each of the reflected components. Using this example as a jumping-off point, I have two questions.This may be vague, but how is this intuitive? When reflected, the components are still in the same order as they were on the primary side. How does that make sense? Without any background, I would start out writing out equations, solving for voltage across the primary, current going into the primary, etc. But with this, it would make analysis a lot simpler, as a transformer just scales up/down elements. How does one just intuitively know that this is what is seen by the secondary side (or maybe a better way to say it, why do we preserve elements in their position rather than simplify it down to an equivalent voltage/current/impedance source)?Speaking of elements, the impedance seen across the primary can be reflected across to a value seen by the secondary, but how do you derive the ones for the capacitor and the inductor as shown in the example? I'm trying to work out the capacitor as an example (just the capacitor by itself) and I'm kind of stuck.EDIT 1: Never mind about that second question. I think I managed to get it after moving variables around.EDIT 2: Doing more research about the first question and thinking about it, I think I found the concept that explains everything: Thevenin equivalency. I'm using it to roughly solve the example problem, but I'm slowly getting the idea, even if it is a bit hard to think about. Using Thevenin/Norton equivalency, I can simplify down to an equivalent voltage and impedance, and simply reflect it across the transformer. The problem I'm trying now is how to put the results back into a form similar to the primary side, so as to match up with the solution.EDIT 3: Wow..so, after the Thevenin equivalent, I think I did it. The key was to make sure that the resulting circuit be exactly the same as the primary in terms of component placement. From there, it took a bit to work out (starting with the impedance, then the current source, and then the voltage source), and I had to make sure that everything matched up with what I wrote down at the locations. Otherwise, this all fell apart, but I managed to do it. It's still a bit hand-wavey, but working out makes me feel a bit better about making such assumptions when going through theoretical problems.

author: MathWizard
author_rank: Super Contributor
timestamp: June 01, 2022, 09:05:20 pm
content: I have to learn all this stuff better too, I never tried with more than a basic circuit and resistive load.

author: LoveLaika
author_rank: Frequent Contributor
timestamp: June 01, 2022, 09:51:49 pm
content: Thanks for the reply. I'm slowly recapping Thevenin/Norton equivalency here, and it's been a great help. Working through this, I realized that I could just simplify everything to an equivalent voltage/impedance (open-circuit at the secondary side, no current), and reflect it over.The question now is how to "untangle" it in such a form that it looks like the primary side circuit.EDIT: I did it, after thinking it through. The key was to make sure that the circuit is exactly the same as the primary (in terms of component placement). From there, I had to work out the rough values of each component and seeing how it matched up with the equivalent component (starting with the impedance, and then moving on to the current source and then the voltage source).