You may have an old Apple Time Capsule lying around, which you may not be using because it has a failing hard drive. These were expensive at the time Apple first introduced them and for many people, a failed power supply or hard drive might have forced them to stop using the device. If you are not familiar with the Time Capsule, it is a backup arrangement for everything on your Mac. Apple coined the name Time Capsule for the hardware and Time Machine for the software. Windows users will not have seen anything like it, and you can read about Time Capsule on Apple’s official link.
You can bring your dead Time Capsule back to life using the low-cost credit card sized single board computer Raspberry Pi (RBPi). Even if you do not have a Time Capsule to modify, you can simply add a Solid State Drive to your RBPi, house the two in a suitable box and make a Pi Capsule for using on your Mac with the Time Machine software. For information, Linux users may backup to the Pi Capsule using any one of the 21 backup software programs listed here.
Backing up over the wireless may be slow, depending on the Wi-Fi speed. However, you can get much faster speeds using the Pi Capsule over wired Ethernet. Of course, the first time you start a backup, the process will take a long time, so try not to interrupt it. Future backups will be faster because they will be only incremental.
You will need a power supply suitable to power up both your RBPi and the Time Capsule (in case the power supply in the Time Capsule has given up the ghost). Connect the SSD hard drive using a SATA to mini-USB cable via a powered USB hub. It is essential to connect only the wireless mouse and the powered USB hub to the RBPi. Anything else you want to connect to the RBPi, such as the keyboard, SSD, wireless card, etc., goes through the powered USB hub.
For the RBPi, you will need an 8GB SD card with the latest “Wheezy” Linux operating system on it. For instructions on how to load Linux on the SD card, see instructions here. Connect a display through the HDMI. When booted the first time, you will be taken to “Raspi-config” automatically, allowing proper setting for the keyboard connected to the RBPi. Now connect the Hard Drive or the SSD to the RBPi using a SATA to mini-USB cable via the USB hub. For getting the RBPi working with the Time Machine on a Mac, follow the guide here.
Pi Capsule has some extended features over the Apple Time Capsule. For one, it can plug into your TV or any other display. Apart from using it only as backup device, the Pi Capsule is actually a full-fledged computer, which you can simultaneously use for web surfing or emailing. If you are not using an Apple Time Capsule and if you have the ability to make cases, build one to house both the hard drive and the RBPi, taking care to leave openings for the RBPi connectors.