# Transformer magnetics design

In transformer design, can someone help me understand how the no load flux is relevant to the transformer efficiency? What design parameters put constraints on the maximum core flux? Let's suppose I have a perfectly linear core material, what benefits I get by using higher flux density?

• the no load flux magnetisation (or flux density swing) doesn't change with loading. It all depends on the applied voltage, frequency and magnetising inductance i.e. $v=L \ di/dt=N \ A \ dB/dt$ (I'm sure you know what every parameter is/means). See here. constraints on the maximum core flux saturation flux density, losses, and some others that I can't think of at 11pm. Oct 2, 2023 at 21:44
• Thanks. Ok so what I can gain in terms of fabrication cost or performance from a core material that doesn't easily saturate? Oct 2, 2023 at 23:50
• @dambirambi Can use it at lower frequencies, for one. Oct 3, 2023 at 3:23
• @dambirambi you can get away with lower number of turns i.e. cheaper transformer as the copper (wire) is generally more expensive than the core. Oct 3, 2023 at 5:32

In transformer design, can someone help me understand how the no load flux is relevant to the transformer efficiency?

• Power efficiency (as I presume you mean) is irrelevant on no-load i.e. efficiency is zero
• No load flux is the only flux in the core even when the load is full-load

What design parameters put constraints on the maximum core flux?

The core permeability ($$\\mu_r\mu_0\$$), the peak magnetization current ($$\I_m\$$), the number of primary turns ($$\N\$$)and the mean length of the magnetic field around the core ($$\\ell\$$). For instance, you might be familiar with this formula: -

$$B = \mu_r\mu_0\cdot H_{peak}$$

Well, to cut a long story short, $$\H_{peak} = \dfrac{I_m\cdot N}{\ell}\$$

So, you can work out what the peak flux density is and compare it against material curves to see how saturated the core might become.

I have a perfectly linear core material, what benefits I get by using higher flux density?

• Fewer turns means less copper loss
• Fewer turns can mean avoiding issues with resonance (high frequency transformers)
• Flyback-circuit transformers usually push the the peak flux density higher to get the power throughput whereas, regular-circuit transformers try to avoid this