With the advent of Internet of Things (IoT) it has become clear that radio-frequency (RF) designers have to be aware of power constraints, e.g., in the design of simplistic ultra-low power receivers often used as wake-up radios (WuRs). The objective of this work, one of the first systematic studies of power bounds for RF-systems, is to provide an overview and intuitive feel for how power consumption and sensitivity relates for low-power receivers. This was done by setting up basic circuit schematics for different radio receiver architectures to find analytical expressions for their output signal-to-noise ratio including power consumption, bandwidth, sensitivity, and carrier frequency. The analytical expressions and optimizations of the circuits give us relations between dc-energy-per-bit and receiver sensitivity, which can be compared to recent published low-power receivers. The parameter set used in the analysis is meant to reflect typical values for an integrated 90 nm complementary metal-oxide-semiconductor fabrication processes, and typical small sized RF lumped components.