What is happening in ADSL modem(In bridge mode)?

I have a ADSL input and I need ethernet output.

Then you need an ADSL modem.

I would like to substitute it with a circuit or a PCB module.

The ADSL modem is actually a rather complex telephony device that has a microcontroller and firmware. It has to negotiate the line parameters before the connection is established (aka training). You can only replace this functionality with another ADSL modem.

I would like to know what is happening in the modem when it functions as Bridge mode.

The unit that you're calling an "ADSL modem" probably has both modem and router functionality contained within it.
By "router" I do not mean "wireless". (What people commonly refer to as a "router" is really a "wireless router" which has router, wireless access point and Ethernet switch functionality.)
By router functionality I am referring to services that include NAT, DHCP, DNS and firewall.

Bridge mode is for disabling the router functionality within the unit so that you can use just the ADSL modem functionality. You are by-passing or going over the router functionality. You still have to properly configure the modem to connect to your ISP with the proper ATM VPI/VCI settings. You would also still need to attach a router to protect your LAN.

See ADSL modem+router in bridge mode tutorial.

Networking is a complex topic. And the terminology often isn't intelligent.

What you have are devices with multiple functions.. routing is a function, modem is a function, PPP is a function.

A network bridge and a network switch are functionally the same thing. Some say a bridge often has 2 ports and the network mediums differ, whereas a switch tends to have multiple ports and the network mediums are the same. The logic of what it does is the same though. So if you look up switching, that's the function.

But also, they can get the name of router, or switch, even when they technically might not really need to do any routing or switching. For example, aside from juniper and cisco, who sell routers that do a lot of routing, the items sold as routers by others, are technically routers, but only just about. They have 2 interfaces and on one of the interfaces is a network switch.

I recommend the book 'computer networking first step' by wendell odom. He has some ugly analogies but you can skip the analogies and he has some good stuff.

A switch is receiving "packets" and redirecting them.

But you could then probably simplify the device a lot if e.g. it has only one computer connected to it then there's more functionality there than it needs.

Many of these devices, particularly older ones, you could typically telnet to them and get a console up, 'cos they not only run linux. So a Router might have a whole routing table in there but really since it only has 2 interfaces it could probably get pretty far (i'm not sure how far but perhaps pretty far), by simply saying if a packet comes in one side then send it out the other side. (unless it's destined for local). It perhaps doesn't technically need a whole routing table to do that. Maybe similar for "bridging" mode. If going from scratch from an electronics background you might be able to make it simpler particularly if it only has one computer connected to it.

Also, I suggest you look into a PCI DSL modem.. That is a bridging dsl modem. As an electronics person, that may interest you. And when they say bridging that also means it isn't doing any PPP(logging in), so the PPP is then done on the computer from windows. As is it when a modem is put in bridge mode.. or it can be done by a downstream device.. e.g. by a "router" plugged into the modem where the router supports ppp.