Flux lines in an air coil are very leaky (hard to control), so use magnetic core to control it

• high permeability material allows control of where flux flows

• if the primary flux flows to secondary flux, can get transformer voltage conversion

S is magnetic reluctance

• if you have a core with high permeability (μr = 1000), then only the reluctance of the gap really matters (since μ0 = 4pi*10^-7

B can be defined as Bmax, saturation flux density

• energy is stored in volume of air gap (B = Area * Length of Air Gap)

• if you need a tranformer that stores a certain amount of energy, then u can set B = Bmax and then solve for volume of air gap

Focusing on L = N^2/S, we see that as S increases, we need greater N to get the desired amount of inductance

Power Loss Mechanisms:

1. Hysteresis in magnetic material (energy in graph is energy lost per switch)

2. Eddy Currents (since the core itself is conductive)

Datasheets provide core power loss, in Watts, as a function of frequency

Ferrite has lowest core loss, but has lower Bsat and worse under high temperature conditions (but we don’t need high so let’s use Ferrite)

Skin Effect: When in AC, the current ends up flowing around the skin of the conductor, not the whole area

• So if we plot it for copper, we see that, for a given frequency, you shouldn’t use a wire with a greater diameter than the skin depth (e.g. at 100kHz, don’t use conductor with >0.42mm dia)

Proximity loss: conductors flowing next to each other will repel or attract

• reduces area used to conduct, so impedance increases

• so stacking lots of coils next to each other will increase impedance

Fringing loss: fringing magnetic fields leaking from the core will hit the primary coils and start generating eddy currents, which will increase heat! (and thus also impedance)

Rule of thumb: Keep windings >3 airgap distances from the airgap

Designing a Transformer for a Flyback Converter:

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Notes:

• E = 0.5*Ipk*L^2

Questions:

• How to calc Ipk?

• What is current density J? Why is it 3A/mm?

• What is a reasonable packing factor to assume?

Building the transformer:

• Use Tex-E wire for secondary wire so there’s no shorts and no additional insulation needed

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Notes:

Measuring Properties:

• Primary Leakage Inductance can be calculated by shorting the secondary coils together and then powering the primary side

• Primary/Secondary resistance: AC has much higher resistance than DC (cuz losses above)

• Using RMS current, switchin freqneyc and resistance, can find winding loss (W)