Resonances and signal to noise ratio of electromagnetic sensors

We illustrate the concept of the resonance for noise by considering the example of the current induced by an external electromagnetic field and the noise current in the well studied split ring resonantors in the thin wire limit, which is analytically tractable. We found that both the signal and the noise exhibit resonances at the same frequencies. However, their ratio exhibits interesting frequency dependences which also is a function of the nature of the external driving field. This previously unanticipated result suggests the signal to noise ratio does not just depend on the resonance frequency; further study is required of the fundamental physics for different structures and help improve the design of devices.

Automated summary

We demonstrate the concept of resonance in noise through the example of current induced by an external electromagnetic field and noise current in split ring resonators. Both the signal and noise show resonances at the same frequencies, but their ratio varies with frequency and external driving field. This unexpected result suggests that the signal to noise ratio is not solely determined by the resonance frequency, highlighting the need for further research to improve device design.