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The design of a photonic frequency discriminator with enhanced linearity is proposed and analyzed. The discriminator consists of a Mach-Zehnder Interferometer and two ring resonators which linearize the magnitude and phase response, respectively. The discriminator is flexible as it can be switched between linear-intensity and linear-field regimes. The linearity of the discriminator is demonstrated by simulating the third-order intermodulation distortion (IMD3) and corresponding third-order output intercept point (OIP3). Simulation results show that the linearity of the phase response plays a critical role in suppressing IMD3 and resonance-enhanced IMD3 suppression by the double-ring structure is observed. Corresponding OIP3 even exceeds that of a perfect linear intensity discriminator.