Core design - Design of Transformers
Net iron area of the leg or limb or core Ai. For a given area Ai, different types of core section that are used in practice are circular, rectangular and square.
Core design
Net iron area of the leg or limb or core Ai
For a given area Ai, different types of core section that are used in practice are circular, rectangular and square.
It is clear that the rectangular
core calls for more length of copper for the same number of turns as compared
to circular core. Therefore circular core is preferable to rectangular or
square core.
Very high
values of mechanical forces under short circuit conditions tries to deform the
shape of the square or rectangular coil (the mechanical forces try to
deform to a circular shape) and hence damage the coil and insulation.
Since this is not so in case of circular coils, circular coils are preferable
to square or rectangular coils.
Leg or limb section details: -
The different
types of leg sections used are rectangular, square and stepped.
a = width
of the stamping or leg
b = gross
thickness of the assembled core or width of the transformer
Ai = net
iron area of the leg or limb or core
= a xKi b for a core type
transformer
Ki = iron factor
or stacking factor
2a = width
of the central leg
b = width
of the transformer
Ai = 2a x Kib for a shell type
transformer
(a) Square core (with a square coil)
a = width of the
leg
a = width of the
transformer
Ai =
Kia2 for a core transformer
2a = width of the
central leg
2a = width of the
transformer
Ai =
Ki (2a)2 for a shell type transformer
(b) Square core (with a circular coil)
a = width of
the stamping or leg
= d Sin45
or d Cos45
= 0.71d
where d is the diameter of the circumscribing circle
Ai =
Kia2 = Ki(0.71d)2
= 0.9 x
0.5d2 for 10% insulation or Ki = 0.9
= 0.45d2
Area of the
circumscribing circle Ac = πd2/4 = 0.785d2
It is clear that
Ai is only 57.3% of Ac. Rest of the area 42.7% of Ac is not being utilized
usefully. In order to utilize the area usefully, more number of steps is
used. This leads to 2 stepped, 3 stepped etc core.
Cruciform or 2-stepped core:
a = width of the largest
stamping
b = width of the
smallest stamping
Gross area of the
core Ag = ab + 2b(a-b)/2 = 2ab-b2
Since a=d
Cosθ and b=d Sinθ
It is clear
that addition of one step to a square core, enhances the utilization of more
space of the circumscribing circle area.
Three stepped core:
Width of
the largest stamping a = 0.9d
Width of
the middle stamping b = 0.7d
Width of
the smallest stamping c = 0.42d
Ai =0.6d2
Four stepped core:
Note : As the number of steps increases, the diameter of the
circumscribing circle reduces. Though the cost of the core increases,
cost of copper and size of the coil or transformer reduces.
Yoke section details:
The purpose
of the yoke is to connect the legs providing a least reluctance path. In order
to limit the iron loss in the yoke, operating flux density is reduced by
increasing the yoke area. Generally yoke area is made 20% more than the
leg area..
Note:
1. Whenever the yoke
area is different from the leg area, yoke can considered to be of
rectangular type for convenience.
The different types
of yoke sections used are square, rectangular and stepped.
Window area and core proportion
If Hw = height of the
window, Ww =
width of the window, then Aw = HwWw
In order to limit
the leakage reactance of the transformer, Hw is made more than Ww. In practice Hw / Ww lies between 2.5 and 3.5.
