The winding voltage and current of the transformer are three times/six times the supply frequency. Kindly suggest me the proper core material and also other design consideration for the transformer. Also, suggest me the books.
Something doesn't fit: either the voltage is three/six time the input voltage and the current is a third/sixth - or the other way round. This is how a transformer is working.
But important additional data is completely missing: frequency and power.
Please specify - otherwise nobody will be able to give useful answers.
I could not understand your question yet replying. For any transformer working flux density should remain in linear region of B-H curve, below Knee point, not saturate. The basic equation for induced voltage in primary or secondary, is Ep/s= 4.44 f Qmax.Np/s. (f the frequency, Qmax the maximum flux and Np/s the primary or secondary turns). Hence (Ep/s)/f should be constant with given number of turns for the Qmax below knee point for the slected material for core, to obtain waveform without distortion. Thus if frequency increased six times voltage must increased six times to keep Qmax same for the core material used and the turns. The core material used in modern transformer are CRGO grad M2H,N3H,M4 etc. Secondary load current(depending on conductor diameter) flux are balance by primary intake(load) such Qmax remain below knee point. It would be more clear by referring my paper," Laboratory method to generate inrush current patern......".
1. You cannot compare voltage which is measured in Volt to the Frequency which is measure in Hz.
2. It seams that you need a high frequency core transformer (150 Hz to 300 Hz). If this is the case, try low loss and thin electrical steel like amorphous sheet or so.