How do I get the name or number of device?

In many cases when I am designing a circuit, I use transistors, ICs, etc, by using calculations. But when I go to the market I have to ask the product by its name which I don't know. How do I get the name of device,I am looking for? Is there any simple way? Or I have to memorize hundreds of datasheets?

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Determining the exact part numbers is part of doing electrical design. After a while, you will get to know some parts, particularly general purpose ones. For example when I need a "jellybean" transistor, I generally use a MMBT4401 for NPN and MMBT4403 for PNP. These are widely available, cheap, with reasonable specs, and I know enough about them to know when to pick a part more carefully.

When you do have to search for a new part, doing a parametric search on a good website is the best way. I like Mouser for this. They have the best parameteric search in the business, at least last time I checked. Their prices also seem to be generally better than other distributors, so if Mouser has a suitable part I'm usually done. Next I go to DigiKey because their web site is pretty good too (used to be the best until Mouser fixed theirs), and they have a wider selection.

There will always be parts you don't know and have to look up. Over time you'll get used to some, but you can never hope to know more than a tiny fraction of what is out there. This is normal and you shouldn't feel bad about that.

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A not uncommon approach is to start by seeing what parts others have used for tasks with similar requirements. This can be especially true if you are buying support components for one main device that has a manufacturer's reference design.

With time, you build up some personal or organizational knowledge of preferred parts; there's a lot of advantage to designing with something you are already using elsewhere, if it's a decent fit. Of course keeping an eye on alternatives that enter the market can also be wise. In an industrial setting people will be knocking on your door trying to interest you in their offerings.

The more you know about the application and the type of device in question, the better position you are in to tackle one of the parametric selection charts or search forms on a manufacturer or vendor's website. This process can be helped both by reading up on the meaning of the various properties, and seeing where possible candidate devices / devices used by others fall on those selection charts.

Finally remember that non-technical considerations such as acquisition difficulties (lead time, security of source, pricing) can be as important as technical ones. A "perfect" device isn't much good if you can't actually get them when you need them.

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You look through the available parts and pick one that satisfies your requirements and is not too expensive.

Some distributors (e.g. Farnell) have nice search functions that allow to specify various properties of the desired part.

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I don't get this. How can you make calculations for components if you haven't selected a part yet? There's no such thing as a generic transistor with a generic $H_{FE}$. If you can use a specific value for $H_{FE}$ it's because you have a specific transistor.
OK, so there are thousands of them around, and it's not easy to know how to pick one. With growing experience you'll notice that certain parts keep popping up. The 1N4148 is a good example if you need a signal diode, for a rectifier the 1N400x is often used. For transistors there are more personal preferences. Olin mentions the MMBT4401, I would use a BC847.
Select a few parts on distributors' sites like DigiKey. Most distributors will allow you to filter parts based on their main parameters. Make sure you have the model in your favorite simulator's and EDA's libraries.

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