#SMPS TRANSFORMER DESIGN PLUS#

This is the equation you can find online in many places. Often what is of importance in determining the turns for a given input voltage, time period (reciprocal of the frequency), core area, and a desired operating flux density. This equation relates the applied volt-secвЂ™s to the turns, core area, and flux density in that core. Now the voltage above is a MAX or peak voltage because the flux density is a MAX or peak valueвЂ¦ since this is a sinusoidal voltage letвЂ™s make the voltage be in rmsвЂ¦ Substituting back into our transformer equation:

#SMPS TRANSFORMER DESIGN PLUS#

Now, we donвЂ™t need this as a function of time so letвЂ™s drop the cosine part this only acts to bring the value between plus and minus the MAX over time. LetвЂ™s assume the flux density is of the form: Since the voltage is sinusoidal, so is the current and so is the flux in the core. LetвЂ™s start with a sinusoidal input as in used with our UL Class 2 recognized power transformers. In the above transformer design equation, the derivative of the flux density with respect to time is an equation that is a function of time that represents the slope of that flux density versus timeвЂ¦ this will become important soon. This is the equation we will work with for the different transformers already introduced. The flux density is simply this flux per unit area, so we can re-write the above equation as: Written as an equation (ignoring the sign) it is: This law states that an induced voltage across some coil is directly proportional to the turns of that coil and the negative time rate of change in flux through the surface enclosed by the loop. LetвЂ™s start with FaradayвЂ™s law of inductionвЂ¦ We will then show how the transformer design equation can easily be manipulated so as to be applied to inductors. We will derive these 3 factors after we do the transformer equation itself first. This equation can be found online in many places but what IвЂ™ve yet to see anywhere in the derivation of this voltage factor for these different types of applied voltage input waveforms. The transformer design equation only differs between the 3 due to what is known as a вЂњvoltage factorвЂќ. It is these 3 types of transformers that I will derive this equation for.

It is also useful for higher frequency switching transformers such as push-pull transformers or flyback transformers. The usual voltage forms are sinusoids as seen in lower frequency silicon steel type transformers such as UL Class 2 recognized power transformers.

This transformer equation is applicable for inputs that are of most any voltage. This transformer equation is known as the вЂњtransformer design equationвЂќ. When it comes to transformer design, there is an equation most of us are familiar with.

Smps transformer design