 # Quasi Resonant Flyback Primary Current Derivation

In order to derive the primary current of a Quasi resonant flyback, it is important to know the waveform of the current. Quasi resonant flyback primary current is rectangular in shape. It will rise linearly when the flyback switch is ON while drop immediately to zero once the switch is turned OFF. Below figure do more the explanations.

Quasi Resonant Flyback Primary Current Derivation – DC

In power electronics, in order to derive the current equations, most of the times you will need to integrate. So, the primary DC current of a quasi resonant flyback is can be derived by integration as below.

The limit of the integration is from zero to Ton. Ton is the time the current is present referring to above current waveform.

By substituting D.T to Ton on the first equation above, the equation will become

The DC current is can be estimated as below equation

Equating both Idc equations will give the estimated peak current.

Where;

• Idc – this is the DC value of the Quasi resonant flyback primary current waveform
• D or Duty – is the actual duty cycle of operation. However, for easier analysis, the duty cycle derived at the boundary or transition will be used. Read the article Quasi Resonant Flyback Duty Cycle Derivation.
• Ipeak – this is the peak of the waveform and derived above
• Pin or Pin_total – this is the total estimated DC power on the primary
• Vin – this is the applied voltage on the flyback primary winding
• Ton – is the time the current waveform rising from zero to peak level
• T – this is the switching period

## Quasi Resonant Flyback Primary Current Derivation – RMS

The rms current will be derived by the same waveform and timings. However, the integration is different.

By performing integration

Then substitute Ton = Duty.T will give

Where;

• Ipeak – this is the peak of the waveform and already derived above
• Duty – is the actual duty cycle of operation. However, for easier analysis, the duty cycle derived at the boundary or transition will be used. Read the article Quasi Resonant Flyback Duty Cycle Derivation.

In dealing with the DC and RMS value of switching converters not only with Quasi-resonant flyback, will involve integration. However, do not extend anymore effort to know the mathematical background to all of these. All the equations above are verified in the actual design and simulation and they are giving accurate results. Use them in your design!

If you want a step by step guide on how to design a quasi resonant flyback, read Quasi Resonant Flyback Step by Step Design Guide.

You can also make use of the design templates: