1. SWITCH-MODE POWER SUPPLIES AND SYSTEMS
Lecture No 10
Switching transformer design rules.
Power losses analysis in switching regulators
Silesian University of Technology
Faculty of Automatic Control, Electronics
and Computer Sciences
Ryszard Siurek Ph.D., El. Eng.

2. Flyback converter transformerIT D1 I0 IC
Ipmax
UIN Zp ZS C R0 U0 B IT t BS T
energy storing during cycle I DB H
Minimum number of zP turns assuming t = tmax, DB = Bs, UIN = UINmax:
A d
Assuming required output power equal to P0
zpmin – is set for the chosen core
Certain air-gap is necessary to achieve required output power

3. Cycle II - transistor T is offID ID D1 I0
IDmax IC T ZS C R0 t t’ B U0 BS
Energy stored in the core is trans-fered to the output during cycle II H
Selecting t’ < T-t for the maximum output power Po one decides to work with the discontinuous magnetic flux flow in the whole range of load changes. To increase t’ one must also increase LS, and it is related to higher number of turns of the secondary winding zS. When t’ = T-t transformer starts to operate with continuous magnetic flux flow.
For discontinuous flux flow
For continuous flux flow

4. Flyback transformer design simplified procedure
Select maximum (nominal) output power Po
Select switching frequency – basing on specifications of available magnetic material, semiconductors etc.
Calculate tmax, current Imax and required value of Lp
Select core dimensions accordind to Hahn diagrams or using „AP” method (same as in inductor design procedure)
Calculate (find from diagrams) the air-gap
Calculate minimum number of primary turns, calculate required number of turns zP
Select operating pronciple (continuous or discontinuous flux flow)
Calculate secondary number of turns zS
Usually discontinuous flux flow is observed in flyback converters due to the following reasons :
lower number of winding turns (lower „copper” power losses)
lower level of EMC disturbances (transistor switches on with current equal to 0)
self-oscillating converter is very easy to design (low-cost solution)

5. Forward converter transformerIp Ip IS IM
UIN Zp ZS US Lp
transformer
equivalent circuit
Selection of the core - basing on diagrams (nomograms etc.) relating core dimensions to total power for certain converter topology
Calculation of minimum number of turns for the primary winding to avoid saturation in most unfavourable operating conditions
Equation identical for any
converter topology
Selection of wire cross section (diameter) taking into account primary current RMS value and calculation of number of turns for required winding inductance Lp (using Al constant for selected core) – the following condition must be performed: zp > zpmin

6. Calculation of secondary winding (windings) number of turns
Calculation of wire cross section area (copper strip, litz wire) for secondary winding resulting from secondary current RMS value ISrms=nIprms
Checking if it is enough space to place windings in the core (bobbin) window area – required isolation and winding arrangement according to safety standards must be considered
bobbin
secondary windind
magnetic core
leakage distance
(6 mm)
Safety insulation
(3 layers)
primary winding
functional insulation
(between winding layers)
3 mm

7. General notes
Core power loses are higher when frequency and flux density amplitude increase - that is why the high value of primary inductance Lp is desirable
High Lp value is related to more primary turns – more trouble with placing the winding in the bobbin and higher „copper” losses look for optimum settlemet!
Chose the magnetic core with best available performance – high saturation flux density Bs, lowest power losses, smallest dimensions
Small air-gap in transformer core may be considered (forward converter) – better utilisation of the core may be achieved by lowering magnetic remanence B
DB - without air-gap
DB - with small air -gap H
Remember that Bs value decreases with temperature – at 100oC it is lower by 20% – 25% in comparison to the value specified at 25oC

8. Switching regulator power losses analysis
1. Switching power losses (dynamic) LL L UT IL
ILmax IL I0 I0 IT ID T
UIN D C Ro t T
Ucontr t
ILmax IT
ILmin ts
QR - diode reverse charge [mC] td tf
ILmax , ID t1 t1
ILmin
overvoltage due to leakage inductance UT
-IRmax
UIN
ITrmsrds
Discharging of transistor capacitances CBCand CBE (bipolar transistors)
Eloss

9. Swith-mode power supply power losses - review
Power losses in passive components
- winding resitances (skin and proximity effects)
- capacitor series resitance (ESR) – output filer electrolytic capacitors
- magnetic core losses (hysteresis and eddy currents)
- power losses in snubbar circuits
Static power losses in semiconductors:
- related to ON- resistance of MOSFET transistor or saturation voltage drop
across bipolar transistor
- related to voltage drop across rectifier diodes (mains input rectifier)
and fast swiching output diodes
IMPORTANT!
for bipolar transistors and diodes for MOSFET trnasistors
Switching (dynamic) power losses
- related to semiconductor switching times, reverse charges
- depandant on base (gate) drive circuits

10. How to minimize power losses – general rules
Power losses in passive components
- select proper wire diameter, use copper stripes or litz wire
- select low ESR capacitors (for switching applications), as big (dimensions)
as possible, connected in parallel,
- make wide and thick copper paths on the PCB
- select modern ferrite cores with best performance at specified operating
frequency and smallest dimensions
- avoid high amplitude of flux density changes
- recover the magnetising energy – do not dissipate it
- use converter topologies with low overvoltages – decrease the influence of
leakagae inductances (eg. two-transistor „forward” topology)
Static power losses in semiconductors:
- select MOSFET trnasistors with low on-resistance
- in high power and high voltage applications use IGBT modules (simple
MOSFET drive circuits, low saturation voltage drop as for bipolar transistors)
- use Shottky diodes if possible (voltage drop below 0,5V)
- use synchronous rectification technique
After switching on the internal body diode the transistor with very low on-resistisance switches on – the voltage drop across the conducting transistor is much lower than across the diode

11. IT Zp UT CIN UIN Cs IT UT T Ds
Transistor dynamic power losses
- select fast transistors (low tr anf tf times)
- use special converter topologies with zero-current or zero-voltage switching
(eg. resonant topologies)
- design carefully snubbar circuits
Voltage UT rise without snubbar circuit IT Zp UT
CIN
Charging of the capacitor delays voltage rise across the switching transistor decreasing significantly transistor power losses
UIN Cs IT UT T t Ds
It is possible to select such value of the capacitor Cs, that the overall power loss in the transistor and snubbar circuit reaches minimum.