FWIW if you tape the filter to the back then the fan doesn't get dirty as quickly. [Every now and then you should clean the accumulated dust off a fan.]
BTW you need not cover the entire area of the fan with filter material. So, for instance, if your fan's breaker is shutting the motor down b/c of the load of the filter, you can slide the filter up to cover less of the fan with the filter, reducing the load on the fan motor. While not all air passing through the fan will be filtered, over time most air will eventually pass through the filter and the room will be cleared of particulates.
Similarly, it is not necessary that the filter be the same shape or size as the fan, since with each pass at least part of the airstream is cleaned. Eventually all the air in a room will pass through the filter area.
BTW you need not cover the entire area of the fan with filter material. So, for instance, if your fan's breaker is shutting the motor down b/c of the load of the filter, you can slide the filter up to cover less of the fan with the filter, reducing the load on the fan motor. While not all air passing through the fan will be filtered, over time most air will eventually pass through the filter and the room will be cleared of particulates.
Similarly, it is not necessary that the filter be the same shape or size as the fan, since with each pass at least part of the airstream is cleaned. Eventually all the air in a room will pass through the filter area.