Design Parameters of Transformer
For Quick review and summary of Calculations, see the tables at the end of this article. (Table 1) (Table 2) For better understandings, go through the following steps for calculations. Make sure you have knowledge of Basics of Transfomer
For designing a transformer, we need:
- Power rating
- Voltage levels (primary and secondary)
- Currents on both sides
- Primary and secondary coils wire diameter/size
- Iron Core area
- 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).
1. Core Calculations:
Calculate area of core (central limb) by using following formula:
F= operating frequency
Bm= magnetic flux density
Te= turns per volts
F= 50 hz Bm = 1.2 wb/m2 Te = 4 (turns per volts)
Putting f=50 hz; Bm = 1.2 wb/(m^2); Ai= 0.001451 m^2, we got:
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)
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
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.
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:
- Approximate length of copper wire = perimeter of bobbin x number of turns
- Cross sectional Area of copper conductor
- Volume = Approximate length x Cross sectional area
- Mass = density of copper x Volume
Density of copper = 8960 kg/ m3
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 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:
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:
Here is another article for transformer core optimization using Genetic Algorithm - a heuristic method of optimization.
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