Transformer with Square-Wave Voltage and Bipolar Flux
Transformer with square – wave voltage and bipolar flux:
Fig: Winding voltage and core flux waveforms for a H-bridge type SMPS supply
- SMPS topologies that utilize an H-bridge converter to get high frequency ac voltage from the dc input. The primary side of the SMPS transformer is connected to the H-bridge output and the secondary side voltage is rectified and filtered to get regulated dc output voltage of desired magnitude.
- The transformer windings carry bi-direction current and the flux linking the windings is also bipolar. The input dc bus voltage is unregulated and often varies over a large range.
- The duty ratio ‘D’ of the switches is controlled within 0 < D < 0.5 to regulate the output voltage
- . The mean of the rectified secondary side voltage, under steady state and after accounting for voltage drops in the rectifier diode and filter inductor, equals the desired load voltage and can be assumed fixed to the output voltage ‘Vo’.
- Under dynamic condition, which arises due to sudden change in load or supply voltage, the mean (dc) output voltage on the secondary side may be significantly higher than its steady state magnitude.
- For calculation of peak flux in the core, the worst-case condition will correspond to maximum duty ratio (D=0.5) and maximum magnitude of input voltage. The worst-case current through the windings will correspond to maximum duty ratio (D=0.5) and peak magnitude of output (load) current. Now the transformer may be designed as per the design steps given below:
Determination of primary to secondary turns ratio (NP/ NS):
knowing that the operating range over which the input dc voltage may vary is the basic idea of determining it. Let the input voltage vary from Vmin to Vmax. With minimum input voltage ‘Vmin’ and duty ratio ‘D’ = 0.5, the magnitude of square-shaped secondary side voltage should equal (Vo VR), where VR is the estimated voltage drop in the transformer winding, output rectifier and filter circuit under maximum load condition. The transformer turns ratio can thus be estimated to NP/ NS = Vmin /(Vo VR).
Determination of peak magnitude of flux in the transformer core:
The maximum flux in the core will correspond to a square wave voltage of magnitude Vmax across the primary winding. The frequency of voltage waveform ‘f’(=1/T) is same as the frequency at which the converter switches are turned on and is fixed beforehand. Now by simple integration of the square wave voltage waveform, the peak flux ‘φm’’ is related to the input voltage as, Vmax = 4.0 f φm NP= 4.0 f Bm Ac NP