Ceramic filter with differential conductivity

A system comprising:

• a printed circuit board having a top surface and including input and output pads;
• and
• a filter including:
• a block of dielectric material with a top surface including a patterned region, a bottom surface, and side surfaces,
• a through-hole extending through the block from the top surface to the bottom surface, and
• a wall extending from the top surface, the wall having an inner surface, an outer surface, and a roof, the wall including a first post formed between two spaced-apart slots extending from the inner surface to the outer surface, and a second post formed between two other spaced-apart slots extending from the inner surface to the outer surface, wherein
• the bottom surface, side surfaces, outer surface and roof have a first coating of silver and glass frit,
• the patterned region, through-hole and inner surface have a second coating of silver and glass frit, and
• the first and second coatings have different compositions.

A method of patterning a filter comprising:

• providing a dielectric block filter including a top surface, a bottom surface, side surfaces, a through-hole extending through the block filter from the top surface to the bottom surface, and a wall extending from the top surface, the wall having an inner surface, an outer surface, and a roof;
• masking the top surface, through-hole, and inner surface of the wall;
• depositing a first coating including glass frit and silver on the side surfaces, outer surface and roof;
• masking side surfaces, outer surface and roof;
• depositing a second coating including glass frit and silver on the top surface, through-hole, and inner surface of the wall;
• and
• etching the second coating deposited on the top surface such that an area entirely surrounding the through-hole includes the second coating,
• wherein the glass frit in the first coating is at least 20% greater than the glass frit in the second coating.