Subject : Power Electronics
Unit : DC to DC Converters
Circuit Equations Under Continuous-Flux Operation
Fly – Back circuit waveforms under continuous magnetic flux:
Fig: Fly-back circuit waveforms under continuous magnetic flux
- Under the continuous magnetic flux conduction, ‘t_{ON}’ denotes the time for which the fly-back switch is ON during each switching cycle. ‘T’ stands for the time period of the switching cycle. The ratio ( t_{ON }/T) is known as the duty cycle (δ) of the switch.
- The primary winding current rises from I_{0 }to I_{P }in ‘δT’ time. In terms of input supply voltage (E_{DC}) and the primary winding inductance ( L_{pri}) the following relation holds :
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- Under the steady state the energy input to primary winding during each ON duration equals: 0.5E_{dc }(I_{P } I_{0}) δT
- And similarly the output energy in each cycle equals V_{0 }I_{Load }T, where V_{0 }is the output voltage magnitude and I_{Load }denotes the load current.
- Equating energy input and energy output of the converter (the converter was assumed loss-less) in each supply cycle, one gets: 0.5E_{dc }(I_{P } I_{0}) δ = V_{0 }I_{LOAD}
- The mean (dc) voltage across both primary and secondary windings must be zero under every steady state. When the switch is ON, the primary winding voltage equals input supply voltage and when the switch is OFF the reflected secondary voltage appears across the primary winding. Under the assumption of ideal switch and diode, E_{dc }δ = (N_{1 }/ N_{2}) V_{0 }(1-δ)
- Where, N_{1 }and N_{2 }are the number of turns in primary and secondary windings and (N_{1}/N_{2})V_{0 }is the reflected secondary voltage across the primary winding (dotted end of the windings at lower potential)
- During mode-2 of circuit operation. One needs to know the required ratings for the switch and the diode used in the converter. When the switch is OFF, it has to block a voltage (V_{switch}) that equals to the sum of input voltage and the reflected secondary voltage during mode-2.
- Thus, V_{switch }= E_{dc } (N_{1 }/ N_{2}) V_{0}. When the switch in ON, the diode has to block a voltage (V_{diode}) that equals to the sum of output voltage and reflected primary voltage during mode-1, i.e. V_{diode }= V_{0 } E_{dc }(N_{2 }/ N_{1}).
- Since the intended switching frequency for SMPS circuits is generally in the range of 100kHz, the switch and the diode used in the fly-back circuit must be capable of operating at high frequency. The switch and the transformer primary winding must be rated to carry a repetitive peak current equal to I_{P}.
- Similarly the secondary winding and the diode put in the secondary circuit must be rated to carry a repetitive peak current equal to the maximum expected load current. The magnetic core of the high frequency inductor-transformer must be chosen properly such that the core does not saturate even when the primary winding carries the maximum expected current.
- Also, the transformer core (made of ferrite material) must have low hysteresis loss even at high frequency operation. Since the ferrite cores have very low conductivity, the eddy current related loss in the core is generally insignificant.