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Jun 25 2014

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The Universal Secondary Winding

toroid-schem

So here comes the riddle:   I want a universal secondary winding.

An “All for One and One for All” winding …

Is it at all possible to achieve such universal secondary winding, capable of delivering ANY possible voltage within a range of “useable” voltages ?

Not possible ?  Well, not quite…. We can try to approach this design goal with fairly good overall results.

Imagine, that you have a toroid that comes with a field strength that generates 1V of output voltage per each 10 turns of wire.

You have prepared a toroidal transformer with the following independent windings, each with the count of turns as shown:

a).   1 turn
b).   3 turns
c).   9 turns
d).  27 turns
e).  81 turns
f).  243 turns
g).   ………..
My question to you is as follows:

Please list all the possible voltages, that you can conceive, as a result of the creative connection of any or parts or all of the windings as above.

Have Fun !!

I will return to you shortly on this.

Regards.

Ziggy.

P.S.

…. and Oh!, By the way … try to guess what is the correct count of turns for the winding  g).  is.

P.S. (2).

OK, so obviously, each winding can be connected with a different winding in series. …. but the “series” connection can take place in any of the two following ways:

01 = 1

02 = 3 – 1

03 = 3

04 = 3 + 1

05 = 9 – 3 – 1  ……………………….. = 9 – ( 3 + 1 )

06 = 9 – 3

07 = 9 – 3 + 1

08 = 9 – 1

09 = 9

10 = 9 + 1

11 = 9 + 3 – 1

12 = 9 + 3

13 = 9 + 3 + 1

14 = 27 – 9 – 3 – 1 …………………….. = 27 – ( 9 + 3 + 1 )

15 = 27 – 9 – 3

16 = 27 – 9 – 3 + 1

17 = 27 – 9 – 1

18 = 27 – 9

19 = 27 – 9 + 1

20 = 27 – 9 + 3 -1

21 = 27 – 9 + 3

22 = 27 – 9 + 3 + 1

23 = 27 – 3 – 1

24 = 27 – 3

25 = 27 – 3 + 1

26 = 27 – 1

27 = 27

28 = 27 + 1

29 = 27 + 3 – 1

30 = 27 + 3

31 = 27 + 3 + 1

32 = 27 + 9 – 3 – 1

33 = 27 + 9 – 3

34 = 27 + 9 – 3 + 1

35 = 27 + 9 – 1

36 = 27 + 9

37 = 27 + 9 + 1

38 = 27 + 9 + 3 – 1

39 = 27 + 9 + 3

40 = 27 + 9 + 3 + 1

41 = 81 -27 – 9 – 3 – 1 ……………………………… = 81 – ( 27 + 9 + 3 + 1)

81 = 81

121 = 81 + 40

122 = 243 – 81 – 40

242 = 242 -1

243 = 243

 

 

 

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