The Effect of Mismatches and Delay on the Quadrature Error of a Cross-Coupled Relaxation Oscillator

Cross-coupled relaxation oscillators can produce two highly accurate quadrature output signals (Verhoeven, 1992). We present a high-level model of these oscillators in terms of circuit parameters, from which we obtain explicit equations for duty-cycle, oscillation frequency, and quadrature error. They show the influence on the oscillator performance of component mismatches and other nonideal effects, such as delays. The results provide useful guidelines for the design of high performance oscillators. The theoretical results are confirmed by simulation and by measurements on a test chip.