Set Up Time Capsule via Existing Router

Thanks for the additional information.

Your Plusnet Hub, as you know, is a combination Internet modem and wireless router. Your Time Capsule (TC) does not include a built-in modem, but is also a wireless router.

Let's start with the "extend and increase the wifi speed" part first. The TC cannot extend another non-Apple router using a wireless connection between them. It can; however, do so if the connection can be a wired one. Obviously, this is not always practical or desirable. So this will be your first decision to make. Is extending the Wi-Fi network of the Hub important or a "nice to have" feature.

The second part to this is speed. Regardless of how you attempt to extend the Wi-Fi network, you cannot increase its bandwidth (total speed available). Bandwidth is limited by a number of factors. Primarily, it is the capability of the wireless router and the presence of any Wi-Fi interference in the area. Both of these devices are capable of supporting the (currently latest) 802.11ac standard. To increase the "speed" we will all have to wait for the next standard and their associated equipment. Depending on ideal conditions, either device should be able to create a wireless network with a maximum data rate of between 867 to 1300 Mbps. For reference, Gigabit Ethernet would be 1000 Mbps.

Since you won't be able to extend using a wireless connection, that first decision will really be, do I really need to extend the Hub or do I really just want to use the TC for Time Machine backups and file storage? Let me know and I can help you get it set up either way.

When interconnected by wire, both routers will form the basis of what is known as a "roaming" style network. It is also another method of "extending" without the performance penalties of using a wireless connection between routers.

Now you can decide where you actually need the extended coverage and that is where you will want to place the TC. You don't mention anything about your home but I am assuming that the Hub itself is not providing sufficient wireless coverage currently ... correct? If it is, then you really don't need the extending feature and how we set up the TC will be different.

Something else to consider is the distance between the two routers. Ethernet, with using switches, can have a maximum cable run of around 100 meters. That's a pretty long cable and you may not want to snake a cable around your house to get them connected. Again, if extending is important, the other option in this case is to use what are called Powerline adapters. These devices create a pseudo Ethernet run using your existing home's electrical circuit. There convenient as they remove the need for long cables, but they are not as efficient. Just remember, with networking, there is always a compromise.

If you really don't need to extend, but still want the other features that the TC can provide, you can simply connect it with a short cable directly to the Hub and we will just configure it a bit differently for that type of setup.

Remember there is always a compromise.

Basically, you should be able to do exactly want you want here. The things to consider are:

1. If the TC will be in the same room as the Hub, you will want to disable either the Hub's wireless radios or the TC's. This will prevent any Wi-Fi interference between them.
2. If you disable the TC's radios, you can still perform Time Machine backups wirelessly from your iMac that is connected to the Hub's Wi-Fi network ... just that Apple does not support this method. FWIW. I have both of my TCs' radios disabled in my home network and both are connected by wire. I have successfully run Time Machine backups in this configuration for years without any issues with the backups.

if not I will go for the simple connect the TC to the iMac and just use the backup facility.

Not a recommend path. That's because, you would have to switch wireless networks between gaining Internet access with the Hub to running Time Machine backups with the TC. Since these backups are automatically run on a pre-defined time periods, this will become very inefficient very quickly.

Let's start with a bit more information about your current networking equipment.

1. What is the make & model of your Internet modem or gateway device that you will be connecting the new Time Capsule (TC) by Ethernet for Internet service?
2. Will you be using your iMac, running OS X Mountain Lion, to administer the TC or another device?
3. What is your overall goal for the TC? Just for Time Machine backups? File storage? ... or both?

if not I will go for the simple connect the TC to the iMac and just use the backup facility.

This sounds as if you may be thinking that the TC will behave like a USB drive that is connected directly to the iMac. It won't......since the TC is designed to operate as a "network" drive that is connected to a router.....and not a "local" drive like a USB drive that connects directly to a computer.

If the TC is still new (and eligible for return), and your primary goal is fast, reliable backups of your Mac using Time Machine, a simple USB drive connected directly to your iMac would be by far the best way to go.