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Cascading ideal transformers

Discussion in 'Electronic Design' started by Ben, Oct 31, 2006.

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  1. Ben

    Ben Guest

    Hiya,

    This is for a college exercise (non-electronic engineering module), but
    the module is about designing a program to calculate the best ordering
    of transformers to give the maximum input current, not about how to
    actually calculate the maximum input current, and we haven't really been
    told how to calculate this, hence why I am asking:

    If I have 3 ideal transformers, I know the turns ratio and their maximum
    input and output currents.

    I can work out the following, Iout(max) = Iin(max)/n, where n is the
    turns ratio.

    Say I am given three transformers, with the following data

    T1: Turns ratio =2, Iin(max) = 2.7, Iout(max) = 2.1
    T2: TR = 1.5, Iin = 0.2 Iout = 0.3
    T3: TR = 1.2 Iin = 0.3, Iout = 1.6

    How would I calculate the maximum input current that could be applied to
    the whole cascade bearing in mind that I don't have input values.


    I tried several ideas such as taking the Iin(max) of T1, working out the
    Iout by using 2.7/2 = 1.35A, then trying to find a transformer that
    would accept that Iout, but obviously, this doesn't work as none of the
    other transformers will accept 1.35A without blowing out.

    One idea I am toying with is working backwards, taking a transformer,
    using its max Iout, working out the Iin at that output current, and
    finding a transformer that outputs that current or higher, then working
    out the Iin of that, and so on...

    Any help/pointers would be appreciated.

    Thanks,

    Ben
     
  2. Tom Bruhns

    Tom Bruhns Guest

    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
     
  3. Genome

    Genome Guest

    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
     
  4. Genome

    Genome Guest

    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
     
  5. neon

    neon

    1,325
    0
    Oct 21, 2006
    they [transformes]do not know or care how you connect them. that is just not true try put primary 120 v into a bell transformer. you will do that only once.
     
  6. robb

    robb Guest

    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
     
  7. futrtrubl

    futrtrubl Guest

    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
     
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