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This paper proposes an optimal super-regenerative-receiver quench signal that achieves 48% narrower 3 dB bandwidth than state of the art and in addition allows independent selection of receiver gain, 3 dB bandwidth, and maximum quench frequency, facilitating design. While many previous works have focused on building block-level optimization, we present a circuit-independent, system-level optimization of the quench signal and demonstrate that key receiver performance is intricately tied to this wave shape. This work both theoretically derives how to optimize the quench signal and experimentally verifies the predicted performance improvement with a discrete-element prototype. Measured results show over 42% reduction in 3 dB bandwidth by optimally changing the quench-signal shape for a given gain and quench frequency.