Calculations for Design Parameters of Transformer Design Parameters For designing a transformer, we need: 1. Power rating 2. Voltage levels (primary and secondary) 3. Currents on both sides 4. Primary and secondary coils wire diameter/size 5. Iron Core area 6. Numbers of turns (primary and secondary We are going to design a 50 VA step down transformer of 230V to 12V. Necessary calculations along with formulae are given below in details: As we are going to design small transformer (of small power rating) so we are neglecting core and copper losses as they doesn’t matters in small transformers and seriously considered in designing power transformers (high power rating transforms).
Calculations: 1. Core Calculations: Calculate area of core (central limb) by using following formula:
Ai= area of core F= operating frequency Bm= magnetic flux Te= turns per volts (for derivation of this formula Click Here) Assumptions:
So, we know the frequency of the power system. We need magnetic flux and turns per volts. For designing a small transformer magnetic flux is averagely taken as 1 to 1.2. By putting values we will get the area of core. Current density of copper wire is taken as 2.2 A / mm2 to 2.4 A/ mm2 (approximately). So, putting values F= 50 hz Bm = 1.2 wb/m2 Te = 4 (turns per volts)
As, we are going to design a practical transformer so we must consider the core available in market. The standard Bobbins available in market practically is 1”x1”, 1.25”x1.5”, 1.5”x1.5” and so on. We took nearest core area available to our calculation. We took bobbin of 2.25 inch2 (1.5”x1.5”) or 0.00145161 meter square. We have the core area. We can calculate turns per volts using this area by following: Putting f=50 hz;
Bm = 1.2 wb/(m^2);
Ai= 0.001451 m^2,
So, Turns per volts are 2.6 Turns per volts.
Primary Winding Calculations Primary voltage = Vp = 230 V Primary current = I1= VA / Vp = 50 / 230 = 0.218
Let transformer we are going to design is 95 % efficient so, I1 = VA/ (efficiency x Vp) = 0.23A Primary Current = 0.23 Amp (approx.)
Number of Turns: Total number of turns = turns per volts x primary side voltage = 2.6 x 230 N1 = 600 turns (approximately)
we got:
Size of Conductor: As we know that
As, for copper the current density is taken as 2.3 A per mm square So, for area of copper conductor
From the standard American wire gauge table, we can choose wire of the same thickness. It can be seen that it comes out that required primary side wire is of 27 gauge which can conduct required current. (for AWG table Click here) Selection of wire can also be done by calculating primary current and by cross match the standard table of copper wire according to their current handling capabilities.
Secondary Winding Calculations Secondary voltage = Vs = 12 V
Secondary current = Is = VA/ Vs = 50 / 12 = 4.2 Amp (approx.)
From the standard copper wire, table it can be seen that wire of this thickness is of 15 gauge. So for secondary winding we need 15 gauge wire. So, Secondary Wire =15 AWG
Number of Turns:
Number of secondary turns = turns per volts x secondary volts N2 = 2.6 x 12 = 32 turns (approx.)
Weight Estimation of Windings For weight calculations, following steps will be followed: 1. Approximate length of copper wire = perimeter of bobbin x number of turns 2. Cross sectional Area of copper conductor 3. Volume = Approximate length x Cross sectional area 4. Mass = density of copper x Volume Density of copper = 8960 kg/ m3
Primary side: Perimeter of bobbin = (1.75 x 4) = 7 inch = 0.1778 m
So,
Length of one turn = 0.1778 m Total length of all turns of primary = L1
L1 = (length of one turn) x(total number of turns of primary) L1 = 0.1778 x 600 L1 = 106 m (approx.)
As, area of primary conductor = 0.1 mm2 = (0.1 x 10 ^ -6) m2 Volume of copper wire = area x length
And
density of copper = 8960 kg/ m3
So,
So we need approx. 100 grams of 27 gauge wire.
Secondary winding weight: Perimeter of bobbin = (1.75 x 4) = 7 inch = 0.1778 m
So,
Length of one turn = 0.1778 m
Total length of all turns of Secondary
= L2 = length of one turn x total number of turns of secondary
L2 = 0.1778 x 32
L2 = 6 m (approx.)
As, area of primary conductor = 1.83 mm2 = (1.83 x 10 ^ -6) m2
Volume of copper wire = area x length
So, we need approx. 100 grams of 15 gauge wire. So, from above calculations we can summarize in following table:
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At this point you have done the Calculations and you have the characteristics of transformer components. Now, for making in hard form, see few easiest steps of hardware implementation of calculations: For any Queries and further Assistance, feel free to comment below and like our facebook pagefor new updates.
