Filter and multiplexer

A filter comprising:

• an input terminal;
• an output terminal;
• a ground terminal;
• a first capacitor and a second capacitor that are connected in series between the input terminal and the output terminal;
• a capacitive element that is connected in parallel to the first capacitor and the second capacitor between the input terminal and the output terminal;
• a resistive element that is connected in parallel to the first capacitor and the second capacitor and that is connected in series with, or connected in parallel with, the capacitive element, between the input terminal and the output terminal;
• and
• an inductor that has a first end and a second end, the first end being coupled to a node that is provided between the first capacitor and the second capacitor and that is coupled to the capacitive element through the first capacitor and the second capacitor, the second end being coupled to the ground terminal,
• wherein the resistive element is connected to the ground terminal only through a first path and a second path, the first path being formed by the first capacitor and the inductor and the second path being formed by the second capacitor and the inductor, so that the resistive element is not connected to the ground terminal through any path other than the first path and the second path.

A filter comprising:

• an input terminal;
• an output terminal;
• a ground terminal;
• a first capacitor and a second capacitor that are connected in series between the input terminal and the output terminal;
• a capacitive element that is connected in parallel to the first capacitor and the second capacitor between the input terminal and the output terminal;
• a resistive element that is connected in parallel to the first capacitor and the second capacitor and that is connected in series with, or connected in parallel with, the capacitive element, between the input terminal and the output terminal;
• and
• an inductor that has a first end and a second end, the first end being coupled to a node that is provided between the first capacitor and the second capacitor and that is coupled to the capacitive element through the first capacitor and the second capacitor, the second end being coupled to the ground terminal,
• wherein a combined Q factor of the capacitive element and the resistive element is equal to or less than 0.6 times a Q factor of the first capacitor and is equal to or less than 0.6 times a Q factor of the second capacitor.