Resonator filter utilizing cascaded impedance inverters

A filter having an input terminal, an output terminal, and a common terminal, comprising:

• a first capacitive element coupled between the input terminal and a first node;
• a first inductive element coupled between the first node and the common terminal;
• a second capacitive element coupled between the first node and a second node;
• a second inductive element coupled between the second node and the common terminal;
• a third capacitive element coupled between the second node and a third node, wherein the first capacitive element, the first inductive element, the second capacitive element, the second inductive element, and the third capacitive element together provide 180 degrees of phase shift at a center frequency of the filter;
• a first quartz crystal, operably coupled between the input terminal and the output terminal, having a first resonant frequency;
• and
• a second quartz crystal, operably coupled, between the third node and the output terminal, having a second resonant frequency.

A filter having an input terminal, an output terminal, and a common terminal, comprising:

• a first capacitor connected between the input terminal and the common terminal;
• a first inductor connected between the input terminal and a first node;
• a second capacitor connected between the first node and the common terminal;
• a second inductor connected between the first node and a second node;
• a third capacitor connected between the second node and the common terminal wherein the first capacitor, the first inductor, the second capacitor, the second inductor, and the third capacitor together provide 180 degrees of phase shift at a center frequency of the filter;
• a first surface acoustic wave resonator, connected between the input terminal and the output terminal, having a first resonant frequency;
• and
• a second acoustic wave resonator, connected between the second node and the output terminal, having a second resonant frequency.