Step by step DCM Flyback Design calculation - Part 1

 I have been trying to design the flyback convertor for very long time. Each time I came across different different material and got confused like anything and drop. So this time, I have decided to take only one material and follow it completely start to end, and then proceed with further materials and designs.

I came across Infineon technologies material for designing DCM flyback convertor.

I started with understanding the  formulas and step by step procedure.

Flyback convertor generally we go if power needed is around 100W

Below is the basic specifications needed to start designing flyback convertor.

1. Input voltage range
2. Output Voltage
3. Output current/ Load current
4. Output Ripple voltage
5. Efficiency

I think it is better to make one flow diagram to represent all the steps than by writing all the steps.

I thought of making formulas also as a flow diagram. But  I looks messy. So I will mention them as step by step as below.

Step 1: Calculating maximum input Power

The maximum input power will be calculated by using required Output power and efficiency of the convertor.

`P_{i n_{max}}=\frac{P_{out}}{ η }`

                                                       

From the input power, The input capacitor value can be calculated on basics of 2uF per Watt of input power.

Step 2: Calculating VDC minimum and maximum

The VDC minimum voltage shall be calculated by using AC voltage minimum, line frequency and input capacitor. 

  

Here dcharge =tc/T, where tc is the time capacitor charge after rectification and T is the time period of half sine wave.

The VDC maximum shall be calculated by multiplying VAC maximum with 1.414 which is similar to calculation of RMS voltage.

Step 3: Calculating Mosfet maximum drain to source Voltage

The maximum drain to source voltage of the mosfet is the summation of VDC maximum, reflected Voltage VR caused by leakage inductance of transformer and voltage spike caused during mosfet turn off time.

`V_{DS_{max}}=V_{DC_{max}}+V_{R}+V_{Sp ike}`

Here the reflected voltage can in between 60V - 100V for 85V-265V ac systems.

The voltage spike can be taken approximately as 30% of VDCmax.

Step 4: Calculating Maximum Duty cycle

The maximum duty cycle of the convertor can be calculated from reflected voltage and VDC minimum voltage.

`D_{max}=\frac{V_{R}}{V_{R}+V_{DC_{min}}}`

Step 5: Calculating Primary inductance and Primary Peak Current

Here starts the calculation of flyback transformer parameters. First and foremost , We find out the Primary peak current and maximum primary inductance value.

The primary peak current calculated using novel way of dividing the input power with minimum VDC voltage. 

`I_{P}=\frac{2 \times P_{i n_{max}}}{V_{DC_{min}}\times D_{max}}`

The inductance value is also calculated by using general inductor formula where inductance equals to voltage divided by current and then multiplied with Time.

`L_{Pri_{max}}=\frac{V_{DC_{min}}\times D_{max}}{I_{P}\times F_{sw}}`

Step 6: Choosing Right Transformer

The selection of flyback transformer is the combination of core geometry, core size and core material.

I am thinking of writing separate article for transformer selection alone.

i. Core Geometry--> EE core, RM core, PQ core

ii. Core Size--> EE19, RM8 PQ20,...

iii. Core Material-->3C96, TP4 3F3

Finally bobbin selection

Step 7: Determining minimum number of turns

Once primary inductance and primary peak current calculated, the another important parameters number of turns required needs to be calculated.

i. Primary Turns:

The primary turns shall be calculated using primary inductance, primary peak current, magnetic density of the core and area of the core.

`N_{P}=\frac{L_{Pri}\times I_{P}}{B_{max}\times A_{e}}`

Here the magnetic saturation Bsat= 400mT, so the maximum magnetic density shall be taken as 300mT.

ii. Secondary turns

To calculate secondary turns, turns ratio shall be calculated

`n=\frac{N_{P}}{N_{s}}`

where n can also be calculated using reflected voltage as below.

`n=\frac{V_{R}}{V_{out}+V_{D}}`

iii. Auxillary Turns

To supply the voltage to the PWM convertor IC, We will use auxillary winding. The number of turns in auxillary winding can be calculated as below.

`N_{aux}=\frac{V_{aux} + V_{D_{aux}}}{V_{out}+V_{D}}`

Step 8: Determining Wire Size

To calculate wire size, RMS current of primary secondary shall be calculated

To calculate secondary side RMS current, Secondary side Peak current shall be calcualted

`I_{sec_{pk}}=I_{P}\times\frac{N_{P}}{N_{S}}`

from the calculated secondary peak current, the secondary RMS current can be calculated.

Step 9: Designing Snubber circuits 

Now time for designing snubber circuit. The Rclamp of the snubber circuit calculated as below.

 `R_{Clamp}=\frac{4\times V_{R}^{2}}{L_{leak} \times I_{P}^{2} \times F_{sw}}`

Value of Cclamp shall be 100pF to 4.7nF.

Step 10: Output Diode selection

The Output side diode plays a major role in flyback convertor by blocking voltage duirng mosfet turn on time. The reverse voltage of the diode calculated as below.  

`V_{RV_{diode}}=V_{out}+\frac{N_{s}}{N_{p}}`

The maximum reverse breakdown voltage of the diode shall be 30% higher than VRV diode voltage.

and forward current of the diode shall be 50% more than secondary RMS current.

Step 11: Output capacitor calculation

The output capacitor plays the major role of filtering the output voltage. For output capacitor, the minimum capacitance, rms current and maximum ESR value are calculated as follows.

i. Capacitance

To calculate the output capacitance, the ripple voltage value should be considered.

`C_{out_{min}}=\frac{I_{out_{max}}\times N_{cp}}{F_{sw}\times V_{out_{ripple}}}`

ii. Capacitor RMS current

The capacitor RMS current can be calculates as simple as Pythagoras theorem

iii. ESR Value

The ESR value can be calculated by divided ripple voltage by secondary peak current.

`ESR_{max}=\frac{\triangle V_{out}}{I_{sec_{pk}}}`

Step 12: Other Design Consideration

i. Input Diode bridge Rectifier voltage and current

  The input rectifier diode RMS current and maximum reverse voltage can be calculated as below.

`I_{ac_{rms}}=\frac{P_{ i n_{max}}}{PF \times V_{ac_{min}}}`

VRV>VACmax×1.414

Here, PF- Power factor, which is roughly considered as 0.5.

ii. Current Sense Resistor

The Current sense resistor is used as feedback which is connected in series with switching mosfet.

`R_{Sense}=\frac{V_{ csth}}{ I_{P_{max}}}`

iii. Feedback loop Compensation

The convertor output is feedback to the PWM convertor for voltage regulation through TL491 programmable diode and PC843 optocoupler.

The resistor and capacitor value for loop compensation can be calculated as below.

Rcomp-->1K ohm - 20Kohm

Ccomp-->100nF - 470nF

iv. Vcc Capacitor

The Value of Vcc Capacitor which used for start up time should be selected around 22uF - 47uF.

So I am planning to create the one excel sheet with all the above formulas for the flyback convertor design.

Here is the link for Infineon material for reference

https://www.mouser.com/pdfdocs/2-8.pdf?srsltid=AfmBOopUQPqsA2N0GAh0l1aKxjBNbBZNAp2t5rHDDjuO-LxjQ3fzlNCo