In this circuit what is that transformer's rating. I am making this circuit So I need help on this topic.
To protect from future edits and to provide a more readable and properly cropped copy, here is the circuit you are asking about:
Your question is what are the specs for Tr1. However, that's the wrong question.
Look at the overall purpose of the circuit. It would be better to copy its function than its detailed implementation. This circuit is a rather convoluted way to generate regulated 5 V from a battery of nominal 3.7 V. There are easier and simpler ways, and they will have better performance.
First, look at this circuit and try to understand at least its basic operation. T1 pulses, which drives Tr1. The positive peaks of these pulses pass thru VD1 to make the output voltage. VD2 provides course regulation by interfering with the oscillations when the output voltage gets too high. L1, C4, and C5 are additional passive filters to reduce the ripple on the output.
So again, all this does is take the battery voltage as input, and produce a somewhat regulated 5 V on the output. Otherwise this is not a great circuit. My guess is that it was designed to use particular cheap parts in high volume and to be well suited to the production capability of a particular factory. Some of the parts may also have been chosen because they were already used in volume on other products.
However, none of these benefits pertain to you who just wants to build one on his own. You are only left with the convoluted, overly-complex, and inefficient design, calling for parts with unknown specs.
What you really want is a plain and simple boost converter. There are many chips out there that do most of this for you. Particularly at these low voltages, look at the offerings from Microchip. You can get parts that contain the switch and control circuitry, maybe even with a synchronous rectifier. You add the inductor and output caps, the input cap, and a few extra parts. The result will have much better output regulation, lower ripple, and higher efficiency that the circuit you show.
This appears to be intended to be a "battery bank" or 5V "USB"powered by a single LiIon cell and outputting 5V.
BUT you call it a solar battery charger. Why? (It's not).
A key question is "Why build this?". There are many many many such devices already available and their cost in most cases will be below what you can build one for.
IF you wish to build these to sell commercially then this is probably not the best circuit and, again, Chinese ones will cost far less than you can make them for. IF you need one of these and do not have access to them then building may be an option. BUT access to components may be an issue and you need to understand the circuit.
SO: What is your application?
What is your specification?
One or few or many?
In this circuit what is that transformer's rating.
The 2N5551 transistor data sheet here is rated at 160V and 600 mA.
The IRFZ44 MOSFET datasheet here is rated at 55V & 51A.
Assume that the "designer" intends the circuit to be able to handle at least 10's of amps in the primary. With a 3.7V nominal battery (LiIon presumably) at say 20A the mean power could be in the order of V x I x dc. With say 3V in after voltage drops and 5V out duty cycle would be around <= 3/(3+5) = say 33% to start. So power = V x I x dc = 3 x 20 x 0.33 = 20 Watts.
With the above assumptions the transformer will be rated to handle this power level at the design frequency.