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Frequency combs (FC) generated by quantum cascade lasers (QCLs) are a promising tool for precision spectroscopy and gas sensing. Recently, ring QCLs have emerged as a new platform for generating FC with unique advantages over Fabry-Perot geometry. While the bandwidth of such Fabry-Perot devices is determined by the device geometry and dispersion, radio-frequency injected devices with circular geometry enable the exploitation of the full gain bandwidth in a controlled manner. Together with this platform, a predictive analytical model that shows excellent agreement with the experimental data was developed. Our results pave the way for a new approach for frequency comb generation based on fast-gain saturation.