# How to Derive QR Flyback Secondary Current

The key to deriving the current levels of every switching converter knows the type of waveforms. For flyback converter, the primary and secondary current waveforms are in triangular shape. Another important aspect is to know the operation of a QR flyback. The complete operation of a QR flyback is here.

The current wave shape is could be summarized as:

The secondary current will stay zero during Ton and it will start from the peak and linearly decrease to zero after Ton expiration. The secondary current is can be difficult to derive when the quasi-resonant flyback operates in DCM. However, much easier to derive when operating at transition mode or at the boundary. Read the QR flyback operation modes here.

## Transition Mode QR Flyback – DC Current

In transition or boundary mode, the current in the secondary winding will reach zero exactly when the next switching cycle happen. See below figure.

Doing integration,

Substitute Ton = D.T

Then getting rid of Toff by substituting Toff = T- Ton

Getting rid of Ton again by substituting Ton = D.T

Getting rid of Ton again by substituting Ton = D.T

The DC current of the secondary winding is equal to the DC level of the load. So, the derived equation above will give the peak current Ipeak instead.

Where;

Idc – this is the DC current of the secondary winding which is also equal to the load current DC level

Ipeak – This is the peak level of the current as shown on the figure above

Duty – this is the duty cycle of QR flyback operating in the boundary. Read Quasi-resonant flyback Duty Cycle Derivation.

## Transition Mode Quasi-resonant Flyback – RMS Current

Doing the usual integration,

Further simplification

Then doing substitution

Where;

Irms – rms current

Ipeak – peak current as derived above

Duty – duty cycle. If you want to know how the duty cycle derived, read Quasi-resonant flyback Duty Cycle Derivation.

## DCM Quasi-resonant Flyback – DC Current

DCM mode is more complicated than TM or boundary mode as there is an added Td of dead time at the end of each switching cycle. See below waveform.

Doing integration,

Sub Toff = T-Ton-Td

Expressing Ipeak

Substitute T = 1/Fsw will give the Ipeak.

Substitute T = 1/Fsw will give the Ipeak.

Further simplification will yield

Where;

Ipeak – peak secondary current

Idc – DC level of the secondary winding current. This is also equal to the DC level of the load current.

D – duty cycle. See the “Quasi-resonant flyback Duty Cycle Derivation”.

Fsw – Switching frequency

## DCM QR Flyback – RMS Current

Doing integration,

Simplification

Further simplification

Then yield the Irms equation

Where;

Irms – rms value of the current

Ipeak – peak level of the current

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