TABLE OF CONTENTS The element values of the resonators in Figure 2-5 are symmetric with respect to the input and output. If the elements are lossless (high unloaded Q), at resonance the input impedance is purely resistive and equal to the termination resistance. If the termination resistance is 50 ohms the input resistance is 50 ohms and if the termination resistance is 1000 ohms the input resistance is 1000 ohms. Although the resonant frequency shifts with termination resistance for the three and four element resonators, at resonance the input impedance equals the termination resistance.
Earlier it was stated that one oscillator design goal was a matched cascade input and output impedance. The resonator behavior described above naturally maintains this criteria provided the cascade amplifier is matched at the input and output. If the amplifier input and output impedance are not matched, it is often possible to use the resonator as a matching device by perturbing the symmetry of a three or four element resonator. This is preferred to adding matching networks because the number of elements and the possibility of introducing additional resonances are minimized.
For example, consider resonator LC7 cascaded with an amplifier with an input resistance of 200 ohms and an output resistance of 50 ohms. The resonator is terminated in 200 ohms. The input resistance looking into the resonator would be 200 ohms if LC7 were symmetric. When C 7A is reduced to approximately 20 pF, LC7 acts as a matching network with...
