A DIY Bluetooth Tranciever

I am working on a school project to build a simple mobile robot that would be either autonomous or RC driven, depending on the selected setting. Now, for that I need some form of wireless communication between the robot and a PC. For that purpose I have selected a bluetooth module cheap from e-Bay for like $6. However, it is all neat and blue and SMD but for my project all of the parts need to be custom built. After looking through the internet for a while, I could not find a single schematic of such a device and I really need one. Now, is it possible to build one that will have the same quality and does it comprise of parts that are generally available?

I cannot imagine that your teacher is expecting you to “custom build” things like the Bluetooth device. One reason you may be having problems finding schematics for such devices is that they are actually very complex inside. If you do get a data sheet for the device you are using (or just about any Bluetooth device you can purchase), you might get a block diagram that probably includes a microcontroller at its heart. Some of the cheaper ones that I use have their own ARM processor in them, as well as the necessary 2,4GHz transmitter and Low Noise Amplifier and receiver - those things are very difficult to design and build.
In the extreme situation, you would still need to buy transistors, resistors, capacitors, inductors etc. that you simply cannot build yourself - especially as a student!
I suspect that your teacher is meaning that you are to buy and build the mechanical parts of the robot yourself rather than going out an buying a pre-built robot. Further, I would think that the object is to see how you go about designing such a device, thinking about what it should do and what parts are needed to make it do that.
I build my own devices (mainly for amateur radio) but these are made from a PCB that I have designed but some other factory has made for me, from ICs, connectors and other components that I have bought. I do tend to wind my own coils around toroids, do my own circuit design and construction so I think of these as “custom built”.
Susan

Of course a teacher can't expect us to build it entirely from scratch. What I meant was by "custom built" is that we have to make our own PCB, and can't use an Arduino shield or a kit. Even for the Arduino itself, we are allowed to use the Arduino bootloader, but have to redesign the PCB. So I only wanted to know about a general list of components that are on the chip, so I can build one myself.

You cant build a bluetooth radio yourself, as Bluetooth operates at 2.4 Ghz and building the RF components for such a radio needs specialised hardware which you wont have. The best you can hope for is buy an existing bluetooth radio module and mount it on your PCB.

You can get Bluetooth chips:

http://www.digikey.com/product-detail/en/BC41B143A06-IXB-E4/BC41B143A06-IXB-E4CT-ND/1219155

Gonna have to reflow solder that BGA though, and carefully design your antenna traces and connections (RF trace design isn’t easy).