Cascading ideal transformers

Ben,

You were on the right track with your first attempt. You just need to realize that what you connect that transformer to may limit the input current to a value less than the input winding of the first transformer is rated for. You just need to make sure, in practice, that you observe the lowest of the maximum ratings, reflected through the turns ratios.

Remember that a transformer can be turned around either way; the transformer itself doesn't know the difference between "in" and "out" sides. So if the "out" side has a higher rating and the turns ratio is in the right direction, just turn the transformer around the other way. (It _appears_ from what you've written that the "out" side always has more turns than the "in" side, and therefore you'd always want to connect the "out" of one to the "in" of the next in the chain; see the next paragraph for more on that. But I'd be inclined to ask the instructor if the turns ratio given was always the ratio from "in" to "out" or not: it's very unusual for an "out" side with more turns than the "in" side to be rated for higher current, like T2 and T3 are! If I assumed they were "reasonable" transformers, I'd say the turns ratio for them was in-turns/out-turns instead of the other way around. I'm thinking it would be poetic justice if there is a particular hell waiting for professors/instructors that don't present problems that align at all well with what you will find in the practicing engineering world.)

Also, notice that if the rating of the low-current side is less than the the rating of the high-current side divided by the turns ratio, that low-current-side limit reflected through the turns ratio becomes the new effective high-current-side limit. That limit, for example, applies to T3 in your case. (Similarly, for the others, you can generate effective maximum currents for the low current sides based on the primary side limit divided by the turns ratio.) It may be useful to recast the ratings in those terms first, before trying to select which transformer to put in which position.

Did that help? What answer do you get?

Cheers, Tom

I would order them with all their primaries in parallel.........

I suppose I would short circuit their secondaries.

Then we can all go down the pub!!!!!

DNA

Bugger!!!!!!!!!!

Tom was right. I'd order them with all their secondaries in parallel and then short circuit their primaries. Assuming......

Too late. I drank the first round. Mine's a Ruddles. We can play kick the lecturer later, unless he's got a small willy and then we have to practice smooching.

DNA

a *programming* assignment to calculate...

sounds like a pseudo-practical problem designed to make the *programming* assignment more interesting and possibly more difficult by either distracting one from the real problem, that is, how to get a program to do all the work of calculating, comparing results and generate a solution, or giving partial problem requirements forcing one to research what extra info is needed to write an algorithm

so the problem could have been stated in other ways e.g. i have three flight Destinations {D1, D2, D3} select a route through all three cities with highest passenger throughput factor where flying through D1 has on board carry limit factors of 2.7 and 2.1 etc....

i think the solution here is to implement your "on paper ideas/recipe/algorithm" for solving the stated problem and let program do all the comparing, organizing until an optimal sequence/combination is found

are you required to use particular lang ?

sounds like two different recipe/algorithms

For this I would brute force it. Test all possible combinations of transformer cascades and pick the best. Asuming you're using an OO language the following pseudo code might work T1 = {TR=2,Iin = 2.7,Iout=2.1} T2 = {TR=1.5,Iin = 0.2,Iout=0.3} T3 = {TR=1.2,Iin = 0.3,Iout=1.6}

and asuming the transformers can be reversed... T4 = {TR=1/T1.TR,Iin = T1.Iout,Iout=T1.Iin} T5 = {TR=1/T2.TR,Iin = T2.Iout,Iout=T2.Iin} T6 = {TR=1/T3.TR,Iin = T3.Iout,Iout=T3.Iin}

set up the cascades, {T1,T2,T3},{T1,T2,T4}.....

Then starting from the end take your Iout of the last transformer and multiply it by its TR. Get the min of that, that transformer's Iin and the Iout of the previous transformer in the chain to find the limiting value for that step. Times by TR of the 2nd transformer, repeat the min as above for the relevent transformers, times by the TR of the 1st transformer in the cascade and get the min of that and the first transformers Iin and now you have the max Iin for that cascade. Iterate through the cascades and select the one with the highest Iin and return it.

Edward