Synchronous measurement of even and odd order intermodulation distortion at the resonant frequency of a superconducting resonator

Abstract

A method has been developed that uses three input tones to measure both even and odd order intermodulation distortions (IMDs) inside the pass band of resonant devices. With this technique the surface current density of both the driving signal and the IMD tones can be quantified. Synchronous, or same frequency, measurement of both even and odd order distortions permits quantitative comparison of the respective nonlinearity currents measured within the same time scale. As an example of this technique, a superconducting resonator is used to generate even and odd order IMDs at the same frequency, resulting in physical conclusions, which are pertinent to current research in high temperature superconductors. While varying the level of only one tone, the expected slope of the IMD current versus the driving signal current for both orders is unity, but that is only observed at high temperature when the superconductor becomes very lossy. An observed smaller slope at lower temperatures gives support to the linear-nonlinear interaction model. Also, a sharp increase in the third order IMD relative to the second order IMD near T(C) gives support to a substantial nonlinear Meissner effect.

Relaxation of Microwave Nonlinearity in a Cuprate Superconducting Resonator

“…Measuring IMD instead of harmonics presents some unique opportunities, but reflects the same physics. Both the 2nd and the 3rd order nonlinearities are at nearly the same frequency as well as inside the resonance band of the structure, aligning the current distribution at the nonlinear frequency components with that of the quasi-TEM resonant mode [3]. Practically synchronous IMD also eliminates issues brought up by other authors including ambiguity from different time scales of the nonlinearity orders [14]- [15] and different skin depth dispersion for each order [14].…”

Microwave nonlinearity and photoresponse of superconducting resonators with columnar defect micro-channels

“…raster probe introduces non-resonant tones which generate IMD only at the probe's location and allows for the measurement of the current at the IMD frequency 19 .…”

“…Electromagnetic field simulation, in this work using HFSS (Ansys, Inc., Canonsburg, PA, USA), is at the heart of converting the detected IMD power into the surface current density that generates the IMD, and is described in Reference [19]. Briefly, field simulation at resonance provides a current density profile K(ℓ) along the transmission line, such as shown in (colour on-line) The Three-tone IMD measurement involves three loop probes.…”

“…ℓ is a linear coordinate along the resonant line. The dissipated power, which is easily computed from the loaded Q, and coupling coefficients 19 , versus measured output power is converted into a function K(P out ), where P out is measured with the spectrum analyser at the resonance peak. The surface current density that produces the measured IMD power is then determined by inserting the IMD output P IMD, instead of the carrier output P out , into the function K(P IMD ).…”

“…Sheet resistance with resolution better than 100 m was measured using near-field microwave microscopy 14 , 15 . Also, near field microwave microscopy using magnetic loop probes 16,17 or a high resolution magnetic write-head 18 and scanning three-tone excitation 19 have been used to map harmonic generation and IMD, respectively, which increase as the nonlinearity scaling current density J NL decreases, a behavior understood to occur around microscopic material defects.…”