Forward Transformer and Inductor Calculation

Calculate the transformer AP value and select the transformer core bobbin

: area product, (cm⁴)

: input power (W)

: window utilization factor (0.2 recommended for transformers, 0.3 for toroidal inductors)

: waveform factor: sine wave: , square wave:

: operating frequency (Hz)

: maximum operating flux density (T). 0.2~0.3T recommended for ferrite; 1.0 for iron powder cores

: current density (A/cm²). Selected according to temperature rise; 200~400A/cm² recommended.

: unit conversion factor (when and are converted from m² to cm², , but since J uses A/cm² etc., the final factor simplifies to )

For this case, the calculation is as follows:

Input power (W):

Window utilization factor:

Waveform factor:

Operating frequency (Hz):

Maximum operating flux density (T):

Current density (A/cm²):

AP value calculation:

Actually selected core: PQ3225, with core parameters:
The AP value of this core: , greater than the required 1.28.

Calculate the primary/secondary turns ratio and the primary/secondary winding currents

Determine the Input/Output Parameters

Input PFC voltage parameter:

Output voltage:

Output current:

Output power:

Preset efficiency:

Input power:

Switching frequency:

Period:

Preset maximum duty cycle:

Reference output diode forward voltage drop:

Turns ratio calculation:

Rounded turns ratio:

Define the ripple factor:

Ripple factor value:

Primary-side average current: 1.9A

Primary peak current:

Primary RMS current:

Secondary peak current:

FIG.01 · CLICK TO ENLARGE

Secondary RMS current:

Calculate the transformer primary and secondary turns

Selected core model: PQ3225

Ae value of the selected core:

Maximum flux density of the core:

Minimum primary turns:

Minimum secondary turns: 1.5

Rounded secondary turns:

Primary turns calculated from the rounded secondary turns:

Actually chosen primary turns:

Summary of actual primary/secondary turns and turns ratio:

Verify the B value:

Calculate the transformer inductance

Transformer core material: PC40
AL value without gap (unit: nH/turns²):

For a forward transformer, the larger the inductance the better, as it reduces the magnetizing current; therefore no air gap is needed.

Calculate the transformer inductance

Transformer magnetizing current I_mag_max = Vdc_bus*Ton/Lm=400*0.3*0.013/9.46= 0.16A <<

Calculate the transformer wire diameter

Selected current density: , forced-air cooling

Primary RMS current obtained above:

Required wire cross-section:

Selected single-strand diameter:

Calculate the primary strand count: (minimum strands)

Selected current density: , forced-air cooling

Secondary RMS current obtained above:

Required cross-section:

Select the copper foil width:

Copper foil thickness:

Therefore: the primary uses single-strand 0.5mm copper wire, and the secondary uses 10mm-wide, 0.35mm-thick copper foil

Calculate the Transformer Losses

Mean turn length: MLT=0.065

Single wire:

Total cross-section:

Total length:

DC resistance:

AC/DC resistance ratio:

Primary copper loss:

Secondary winding copper loss:

Cross-section:

Total length:

DC resistance:

AC/DC resistance ratio:

Secondary copper loss:

Total transformer copper loss:

Calculate the transformer core loss Pcore= K*fsa*Bb*Ve

fs is the frequency, B is the flux density change, Ve is the effective core volume

fs in kHz, Bac in mT, Ve in cm3, Pcore in mW

K, a, b are constants: K=1~3×10⁻⁶, a=1~1.5, b=2~3 For the PC40 core, typical values are K=2.4×10⁻⁶, a=1.22, β=2.55

For this case, B=218mT, core volume, switching frequency

Therefore: total transformer loss = 0.9+4.7=5.6W

Calculate the output energy-storage inductance and wire diameter

Calculate the minimum duty cycle

The output energy-storage inductor of the forward circuit is calculated from the inductor voltage formula U=L*di/dt and volt-second balance (the voltage-time products across the inductor are equal when the main switch is on and off); we compute using the main-switch-off interval,

U=Vout, di=ripple factor*Iout=0.2*Iout, dt=T_off=(1-D)/f,

L >= Vout*(1-D)/(f*0.2*Iout)=5.5*0.7/(75*0.2*40)=0.0064 mH=6.4uH; 8uH is used in practice

Selected current density: , forced-air cooling

Output inductor RMS current:

Required wire cross-section:

Selected single-strand diameter: , cross-section 1.13mm2. Since the DC component of the energy-storage inductor far exceeds the AC component, high-frequency skin effect can be ignored and a large-diameter copper wire can be chosen.

Calculate the strand count: (minimum strands). Since the turns are few and it is air-cooled, 4 parallel wires are sufficient in practice

Calculate the inductor AP value; select the inductor material, size, wire diameter and turns

Actual energy-storage inductance:

The energy-storage inductor of a forward circuit carries a large DC current component, which equals the output current. Therefore a high-saturation iron powder core or similar toroid must be chosen with Bmax above 1.0T. Here we select a Sendust (Fe-Si-Al) toroid whose saturation flux density Bmax reaches 1.6T

Inductor RMS current:

Inductor peak current:

Bmax is the peak flux density:

Ku is the window factor:

J is the current density; 400-600A/cm2 for forced-air cooling (air-cooled)

AP value:

Selected toroid parameters: T28*14*12MM (OD*ID*H), Sendust

Verify the AP, greater than the required 0.53

Calculate the required minimum turns: dB<=0.25T, from Uout = N*dB*Ae/Toff,

N>=Uout*Toff/(dB*Ae)=5*(1-0.3)/(75000*0.25*0.000084)=2.22. This turn count is very small; to balance the core copper and iron losses it can be taken as large as possible, so we take N=7

DC Resistance

DC resistance loss=40*40*0.0011=1.7W Calculate the inductor core loss Pcore= K*fsa*Bb*Ve dB=5*0.7/(0.000084*75000*7)=0.08T For Sendust (black toroid), typical values are K=4.5×10⁻⁶, a=1.6, β=2.7

For this case, B=80mT, core volume, switching frequency

Total energy-storage inductor loss P_loss_se_ind=1.7+2.9=4.6W