Complex bandpass filter having a transfer function with two poles

A system comprising:

• a first Rauch filter circuit that includes a first amplifier, the first Rauch filter circuit configured to receive a first component of a complex signal and provide a filtered version of the first component of the complex signal;
• and
• a second Rauch filter circuit that includes a second amplifier, the second Rauch filter circuit configured to receive a second component of the complex signal and provide a filtered version of the second component of the complex signal,
• wherein the first Rauch filter circuit comprises a first capacitor branch coupled to the first amplifier,
• wherein the second Rauch filter circuit comprises a second capacitor branch coupled to the second amplifier,
• wherein a portion of the first Rauch filter circuit before the first capacitor branch is coupled to a portion of the second Rauch filter circuit before the second capacitor branch, and
• wherein a portion of the first Rauch filter circuit after the first capacitor branch and before the first amplifier is coupled to a portion of the second Rauch filter circuit after the second capacitor branch and before the second amplifier, and
• wherein an output of the first Rauch filter circuit is coupled to the portion of the second Rauch filter circuit after the second capacitor branch and before the second amplifier, and an output of the second Rauch filter circuit is coupled to the portion of the first Rauch filter circuit after the first capacitor branch and before the first amplifier.

A method comprising:

• receiving, by a first signal path that includes a first capacitor branch and a first amplifier, a first component of a complex signal;
• receiving, by a second signal path that includes a second capacitor branch and a second amplifier, a second component of the complex signal;
• providing cross-coupling of a portion of the first signal path before the first amplifier to a portion of the second signal path before the second amplifier;
• providing, by the first signal path after the first amplifier, a filtered version of the first component of the complex signal to the second signal path before the second amplifier;
• and
• providing, by the second signal path after the second amplifier, a filtered version of the second component of the complex signal to the first signal path before the first amplifier,
• wherein providing cross-coupling of the portion of the first signal path before the first amplifier to the portion of the second signal path before the second amplifier comprises:
• providing cross-coupling of the first signal path before the first capacitor branch to the second signal path before the second capacitor branch, and
• providing cross-coupling of the first signal path after the first capacitor branch and before the first amplifier to the second signal path after the second capacitor branch and before the second amplifier.