TABLE OF CONTENTS Two oscillators can be connected in such a way that a signal from one oscillator is injected into the second oscillator and a signal from the second oscillator is injected into the first. The result is that the two oscillators become locked in frequency, typically oscillating in quadrature. Very often, quadrature signals are required; for example, mixers in an image reject configuration require quadrature oscillator signals. Other techniques to generate quadrature signals, including polyphase filters and ring oscillators, are discussed in Section 8.9.
The most common technique is the parallel connection shown in Figure 8.24, where each oscillator is made up of a tank circuit and cross-coupled feedback circuit. In addition, each oscillator output is connected to the other oscillator with transistors in parallel to the cross-coupled transistors. Thus, oscillator 1 has feedback transistors M 1 and M 2 and coupling from oscillator 2 via transistors M 5 and M 6. Typically, feedback and coupling transistors are made the same size. Furthermore, because of symmetry, the oscillation amplitudes of the two oscillators should be the same.
To understand why the two oscillators oscillate in quadrature, first note that the two oscillators can be modeled as gain stages, as shown in Figure 8.25. Each stage has a gain and a phase, as shown in Figure 8.17. We note that, as for any...
