The effect of mismatch and disturbances on the quadrature relation of a cross-coupled relaxation oscillator

A 5.8-GHz quadrature cross-coupled oscillator

“…The cross-coupled relaxation oscillator [3-51 is the cross connection of two first-order relaxation oscillators in a feedback structure. First-order oscillators exhibit a large tuning range a.nd can operate at very high frequencies; the cross-coupling enhances the frequencylphase stability and accuracy with respect to an individual oscillator due to the feedback [5].…”

“…If a soft-limiter is added at the output of the integrator, its output is 90" out of phase with the Schmitt-trigger output and can be used to trigger another first order oscillator, resulting in a cross-coupled relaxation oscillator with feedback structure, represented in Fig.2 [5]. It was shown in [5] that the cross-coupled oscillator has two outputs with exactly the same frequency, with an accurate quadrature relation and that the soft-limiter gain imposes a tradeoff it should be high to minimize phase error, and low to maximize the attainable frequency. Since we are aiming at a 5.8GHz oscillator in a 35 GHz process, where only NPN bipolar transistors have this high fT, the circuit should be as simple as possible.…”

On Phase Noise in Quadrature Cross-Coupled Oscillators

“…It means that the oscillators are working at a frequency where the effective Q of each oscillator is lower than that for ω 0 . Strong coupling ensures good quadrature outputs, which allows one to have good image suppression in a complete receiver [2,5]. Stronger coupling simultaneously improves the quadrature relationship and phase noise performance in RC oscillators.…”

“…In [1] and [2] a theoretical study of the quadrature RC oscillator was presented. Cross-coupling increases significantly the precision of oscillation frequency, and guarantees that the two outputs are in exact quadrature.…”

A 5-GHz combined oscillator/mixer

“…It consists of two relaxation oscillators that determine the switching instants of each other's Schmitt-triggers, thus causing the output signals to be in quadrature. A detailed description of the oscillator behaviour is available in [3,5].…”