Bright-soliton frequency combs and dressed states in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>χ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:math> microresonators

We present a theory of the frequency comb generation in high-Q ring microresonators with quadratic nonlinearity and normal dispersion demonstrate that naturally large difference repetition rates at fundamental 2nd harmonic frequencies supports family bright soliton combs providing parametric gain is moderated by tuning index-matching parameter to exceed rate significant factor. This factor equals sideband number associated high-order phase-matched sum-frequency process. The theoretical framework, i.e., dressed-resonator method, study conversion formulated including into definition resonator spectrum. Rabi splitting dressed leads four distinct down-conversion conditions (signal-idler-pump photon energy conservation laws). instability tongues sparse, Turing-pattern-like, varying are analysed details. matched exhibits optical Pockels strongly modified dispersion, which limit bandwidth also play role Turing generation. Our methodology data highlight analogy between driven multimode resonators photon-atom interaction.