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# Guide about transformers and how to design them Use your ← → (arrow) keys to browse

### 4. EXAMINING AN UNKNOWN TRANSFORMER:

First you need to make an eye inspection. Check out its size, its core type, look up in what part of the equipment it was in previously, to get an idea of its type. Also check out the wires. Their thickness will give you a good guess as to which is the primary, and the secondary. Low voltage, high current winding’s typically use thicker wires, and vice versa.

Next, find a safer voltage range to work with, when examining the transformer. Use a known step down transformer, for which you know the output voltage. In our example, we will use a 10V transformer. We will hook it up to the HIGH VOLTAGE SIDE of the unknown transformer. Remember what I said, about finding out the high voltage/low voltage out. The less thick wire is the high voltage side. Okay, so after hooking it up, we measure the secondary on the unknown transformer.

Lets say we measure around 1V. This means the transformer stepped down the voltage a 10 times. From this you can determining the winding ratio. This Is a measure as to how many windings there are in the secondary, in respect to the primary. in this case we have a 1:10 ratio. This means that if you apply 220V on the primary, you will get 22V on the secondary. Next, if you want to use this as an audio transformer for a tube amp, you need to determine the reflected impedance of the load onto the primary of the transformer. It is equal to the square of the turn ratio multiplied by the load. Lets say we have an 8 ohm speaker. Then the impedance will be 10 ^ 2 x 8= 800ohm. The primary side of the transformer will see a load of 800ohm, where the secondary will see a load of 8ohms.

This is one of the uses of transformers, to match the impedance of mismatched circuits. A high impedance tube amp, will not efficiently supply the load current, without such a transformer. This is proven by the Thevenin Maximum Current Transfer theorem, which states that for most efficient utilization of the power of an external source, with finite resistance, the load must have equal resistance as the source, as viewed from its output terminals.

### 5. DESIGNING YOUR OWN TRANSFORMER:

Okay guys, here goes the real deal. Every engineer has once found himself in a situation where they need a custom designed transformer. Every engineer has a different tactics in designing one. This is what I have trusted over the years, so far without remorse.

1. Your design starts with finding out how much power you need out of the secondary of your transformer. This is given by the formula P2=I2.V2. In our example we will assume it to be 50W.
2. After knowing the secondary power rating, we need to find out the primary power rating, based on the expected efficiency of the transformer. Typically low power transformers are more inefficient, and for transformers up to 10W, an efficiency of 80% can be assumed. From 10W up to around 50W, the efficiency can be assumed anywhere from 80% up to 90%, and above 50W, the efficiency stays at around 90% (except for highly efficient toroidal cores, which we will not be covering today).
3. Next, turn the efficiency percentage into ratio. Just divide it by a hundred. The power required from the primary is given by the formula P1= P2 / Eff (where Eff is the efficiency ratio). For a 50W transformer and a 0.9 assumed ratio, a primary power rating can be assumed to be 55W ( P1 = 50 / 0.9 ) The leftover 5W will be dissipated as heat losses.
4. Next, you need to find the needed cross section area of the core, required for the power rating you need. This is given by the very simple formula S= √P1. In our example the core area needs to be S = √55 = 7.41cm^2. Always leave a little extra, for the core, the effective cross section is always lower, than what you measure, due to air gaps when stacking the lamination’s and the overall imperfections of the core. So for our example lets use a core with a cross section of 8cm^2.
5. Now, lets use what we have got this far, and calculate the number of turns for the core. By now, you should know what voltage your transformer will be working with, both the primary and the secondary. Lets assume the primary voltage to be V1=220V, and the secondary V2=25V. The formulas that give the number of turns you need are as it follows W1 = 40 x V1 / S and W2 = 44 x V2 / S. This gives us 1100 turns for the primary of our example and 138 turns for the secondary.
6. Almost there, now you just need to calculate the wire gauge for the winding’s. I’m European, so I will be working with mm as wire size, and not AWG. The formula is very simple d = 0.02x√I(mA), where the current is in mA. Now you need to calculate the current, which your winding’s will be handling.
7. For the primary it is I= 55W / 220V= 0.25A, or 250mA. For the secondary, the current is I = 50 / 25 = 2A or 2000mA. Now you can add those numbers in the formula and we get d = 0.02 x √250 = 0.32mm for the primary and d=0.02 x √2000=0.89mm.
8. Its always good to round up to the higher possible size. For instance, a standardized wire size for the primary will be 0.4mm, and for the secondary 1mm

By following these steps you will be able to design your own custom transformer. Hope this tutorial would have been a great use.