Question about time capsule backup with time machine

Is there a limit to the size of the usb drive I can use when attached to the time capsule?

No, but I would stay at 4 TB or less.

Can I use a 1 or 2 tb thumb drive attached to the time capsule to do wireless backup with time machine?

Yes

Keep in mind that the drive must be formatted in Mac OS Extended (Journaled) to work with Time Machine.

Now, a few possible downsides:

The USB port on the Time Capsule is an old and slow USB 2.0 design that runs at only about half of normal USB 2.0 speeds due to the limitations of the processing in the Time Capsule, so backups are going to be.......s---l--o--w.

Most newer USB drives are going to be USB 3.0 designs. While this is supposed to be compatible with USB 2.0, this is not always the case.

Finally, the USB port on the Time Capsule is underpowered compared to a USB port on a computer. You may need to use a powered USB hub with the Time Capsule.....even if the USB drive has its own power supply.

Is there a limit to the size of the usb drive I can use when attached to the time capsule?

Not in capacity terms but maybe in power consumption.. large sticks can use a well over the USB 2 port power quota.. 500ma or a bit more on the Gen5 TC.

Yes, you can use large thumb drives but they tend to be poor if you subject them to multiple rewrites as a typical backup will do.

A better option is a 2.5 spinning drive.. it will actually use less power and last much longer.

Even better is 3.5" Desktop drive as they have separate power supply.. faster and more reliable.

My thinking is that if I use a usb stick it most likely won’t need an external power supply with the time capsule due to low power needs

Possibly, but in general a USB stick may require more power.....not less.....than a spinning drive. If you have not yet purchased the drive, go with the recommendations from LaPastenague......a desktop type of drive with a separate power supply. That being said, I've had good luck with a WD Passport 1 TB drive that is powered only by the USB port on the AirPort. But, I also don't use the drive for any critical storage.

I do have a windows server that’s always on with 8 tb of storage. do you know of a way to make time machine backup to a windows server?

Even if you could set up a separate partition and the backup partition of the drive could be formatted in Mac OS Extended (Journaled).....Windows will still "see" the drive as a FAT32 volume. That won't work for Time Machine.