The design approach for an isolated flyback transformer for PFC is almost exactly similar to doing a design for a DCM flyback. The variation that comes into play is that for PFC Isolated flyback (hereafter “PFCIF”) the Vdc Input and Ipk current are going to vary over ½ cycle of the AC input waveform. To optimize the transformer therefore means to make an accurate computation of the winding and core losses. The method used herein is to compute the Fourier components of the voltage waveform (across the Primary) and then compute core loss for each harmonic of the waveform. This sets up nicely since the core loss curves or equations supplied by most core manufacturers are for sine wave excitation. Similarly, the Fourier components of the current waveforms for the Primary and Secondary are derived and the winding losses for each harmonic are then computed. This sets up nicely because a formulaic approach using skin and proximity effects can be used to accurately predict the loss. Suffice it to say that most traditional methods for DCM do not go into this level of detail as a 1^st order approach is often satisfactory.

 

So…… Where to begin? Well, the power to be processed is similar to DCM flyback. An engineer may have experience from a previous design or can use a suitable software design package. This will produce a result that is approximate. In the end, design equations must be written and the results there from compared to empirical data on efficiency and temperature rise. Our design is [1] phase of a [2] phase PFCIF – so, 100W Pout at 100 Khz ---our transformer design starts with the following given design parameters from the topology simulation:

 

              

 

Our 1st  goal is low cost. Another essential goal for the design is to minimize the leakage inductance since it is DCM. This is our 2nd goal.   Our 3rd goal is<1” height restriction. A 4th goal is smallest volume. These led to a 4th chosen goal—that is, to compare the results with a planar device vs a conventional wound device. Our two choices decided upon were the PQ2620 size ferrite and a std planar ferrite size. Mechanical details are (MM):

 

Core	Width	Length	Height	Core Area	Volume
PQ2620	19	27.3	20.2	1.09	5.47
PL58	20	25	11	0.75	3.2

 

                        The next comparison to be made is cost (US$):

 

Core	1K	10K	50K	100K	1M+
PQ2620	2.20	1.35	.675	.655	.62
PL58	3.80	3.20	2.50	1.80	1.50

 

The obvious conclusion from the chart above is that there is a premium to be paid for low profile height and smallest volume. The other factor that is not obvious is that the PQ core finds worldwide usage currently in existing “off-line” AC-DC power supplies. Any manufacturer in the Asian market place active in this arena has 1 or more OEM customers they are currently supplying in the 10M+ quantity. The planar cost is directly related to the number of boards or layers (lead frame or pcb) required to stack to achieve the design. Applications more amenable to planar designs usually occupy niches in telecom, “bricks”, servers, and high current/power.

 

The particulars of the PQ2620 design are as follows:

 

 

                 20 Turn Primary

 

                 Ferrite Core Gap is ~ .072cm

 

 

Checking for <Bsat:

 

                    Flux at Peak Current:

 

Actual Gap is ~ .079cm ( .031”) when accounting for fringing flux.

 

 

If specifying for core manufacturer:              

 

RMS Flux (Gauss)

 

                         Brms = 1533 Gauss

 

 

Using Core Loss Equation for Ferroxcube "3C96" mat'l at 40 degrees C temp rise:

 

   

 

Core Loss 1.18W --but this is only over 1 switching interval at Peak Vin

Accuracy requires averaging over ½ Cycle Interval or performing Fourier Analysis

 

 

SPICE Simulation yields Peak Primary & Secondary Currents at 1st four Harmonics:

 

PEAK CURRENT of first four harmonics

 

                        Corresponding RMS Flux Value:

 

Now use  Core Loss Equation above for each Harmonic and RMS Flux amplitude:

 

 

                Total Core Loss is .44W

 

Now we must assess the mechanical aspects of the design and iterate magnet wire choices with “fit” in the available bobbin window.

 

The winding length of the bobbin is .354 inches so fitting the 20 turns in a single layer

 

 

                  Which is diameter for #26 wire

 

Due to practical limitations in fitting the wire and the space taken up for the start & finish--

the part was wound with #28AWG magnet wire.

 

...and the bobbin area in square inches is:

 

..... so that the maximum build height is              

 

..and the #28 AWG primary layer has a max dia of .0127 inches. Interleaving two layers (one under the secondary and one over the secondary consumes .026 inch build allowing .115" for the secondary.

 

 

Choose 20x#30 Litz for the secondary. Wind 5 Turns

 

Calculating the DCR and Cu Losses as follows:

 

Mean turn Length (inches) is:                      

 

 

 

                           Recorded actual value 116 milli-W

 

    

 

                              Recorded actual value 4 milli-W

 

 

..and the copper loss is

 

 

    

 

 

                        Total Loss is 1.52W

 

Now on to figure temperature rise

...and the approximate core surface area is (sq cm):        

 

.. and the temperature rise is estimated to be    

 

            36C Temp Rise Convection Only

 

Nomographs from popular authors:

 

Tartar

               36C Temp Rise

 

McClyman

               40C Temp Rise

 

_____________________________________________________________________________

 

We now apply the same analysis to the planar design PL58 size core (in shortened format).

 

 

                        Center Post gap calculated is ~ .10cm (.036”)

 

 

RMS Flux (Gauss)

 

 

                  Brms is 1738 Gauss

 

 

 

 

Now use Core Loss Equation for each Harmonic and RMS Flux amplitude:

 

 

 

 

 

                    Total Core Loss is .327W

_____________________________________________________________________________

 

Now, moving on to calculate copper losses in the windings:

 

 

 

                    Primary DCR calculated & recorded = 150 milli-W

 

 

    

 

                    Primary Copper Loss is 0.415W

_____________________________________________________________________________

 

 

Secondary Turns    

 

               Secondary DCR calculated & recorded = 11.5 milli-Watt

 

 

    

 

 

            Secondary Copper Loss is 0.48W

 

 

 

                    Total Loss is 1.22W

 

As stated at the outset, we need to perform a Fourier analysis of the winding loss to verify that we chose the correct wire size for the PQ2620 core. We performed a “conventional” loss calculation for the PQ2620 and we performed a fourier loss for the planar but only for the 1^st four harmonics. In brief, we need to see the results of choosing #28AWG wire for the PQ2620 and 4oz copper for the planar design and see if there is relative agreement with winding loss.

 

The 1^st step is to compute penetration depth (cm) ---- given 100 Khz fundamental.

 

 

Dp(nn) = Penetration Depth -- in cm

 

    

 

 

A stipulated Design Goal was to minimize leakage inductance. A corollary to that goal was to minimize AC Resistance. We do that by what’s termed “sandwiching”  Secondary -- i.e. Primary will occupy 1 layer "under" -- 1 layer "over" the Secondary.

 

Pri #28AWG = .00635 inches radius, ...  .0127 dia inches thk, but assume penetration [1] side of wire, i.e proximity due to no "countervailing current flow", i.e. Flyback Inductor current flows in primary only during storage cycle and current flows in secondary only during load dump cycle.

 

Therefore, conductor thickness  = 0.32MM, .032 CM -  .000322 meters thk

 

Conductor Thickness = .032 CM |  Conductor Thickness = .013 inches (rounded off)

 

 

 

AC Resistance Formula:

 

 

 

"Effective" # Layers                          AC Resistance Ratio   

 

Conductor AC Resistance Multiplier.

 

 

Now we need to generate RMS amplitudes at all the relevant harmonics of the Primary Current Waveform and multiply each by the AC Resistance.

(DCR multiplied by each of the AC Resistance factors in the column above).

 

 

Compute fourier coefficients:

 

 

Form a partial sum of coefficients and plot at t intervals to view convergence:

 

 

Recalling the DCR value for the Primary from the above computations for PQ2620 design:

 

 

               Baseline Pri DCR = 120 milli-W

 

 

 

Primary AC Resistance for each of 1st 15 Harmonics

      Pri AC Loss @ each Harmonic   

 

 

Calculated Primary Cu Loss (including DC) is:

 

                  

 

 

 

Summary Results:

 

 

Core	Conventional Cu Loss	Core Loss	Total Loss	AC Loss	Total Loss
PQ2620	1.08	0.44	1.52	1.136	1.58
Planar PL58	-	0.33	-	.90	1.23