I'm trying to plug a USB-A notebook in to a USB-C travel dock. This USB-A notebook has been successfully plugged in to docks in the office - the office dock uses a chunky USB-C to A adapter that is attached to the USB-C cable, something along these lines:

I've got a small (cheap) USB-C travel dock at home and a small (very cheap) USB C to A adapter. This doesn't seem to do much of anything when the dock is plugged in to the notebook via the adapter. The dock works fine in USB-C notebooks.

Is this likely to be a problem with the dock (possibly not getting enough power from a USB-A port?) or the adapter (possibly not passing power or sufficient data bandwidth)? If the adapter, is there a certain spec that will let it work with a small dock?

Basically I'm just looking to reduce the number of cables that need plugging in and out on the occassions where this particular notebook needs to be used at home. I know I'm not getting power/charging via a USB-A port.

Alternatively, can anyone suggest the right terms to be looking for a smallish (cough, not too spendy) hub that will support both USB-A and -C notebooks?