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Integrators are key building blocks in many analog signal processing circuits and systems. The DC gain of conventional opamp-RC or Gm- C integrators is severely limited by the gain of operational transconductance amplifier (OTA) used to implement them. Process scaling reduces transistor output resistance, which further exacerbates this issue. We propose applying ring oscillator integrators (ROIs) in the design of high order analog filters. ROIs implemented with simple CMOS inverters achieve infinite DC gain at low supply voltages independent of transistor non-idealities and imperfections such as finite output impedance. Consequently, ROIs scale more effectively into newer processes. A prototype fourth order filter designed using the ROIs was fabricated in 90 nm CMOS and occupies an area of 0.29 mm2. Operating with a 0.55 V supply, the filter consumes 2.9 mW power and achieves bandwidth of 7 MHz, SNR of 61.4 dB, SFDR of 67.6 dB and THD of 60.1 dB. The measured IM3 obtained by feeding two tones at 1 MHz and 2 MHz is 63.4 dB.