Dual Coupled Resonator Local Oscillator

Dual Coupled Resonator Local Oscillator

INTRODUCTION

Local oscillators are used in most radio transmitters and receivers. Any phase noise produced by this local oscillator will add to the noise received at the antenna. For low errors in the decoded data, the phase noise of the local oscillator must thus be far less than the other noise sources in a receiver. The local oscillator should be able to be produced at a low cost, since most applications are very cost sensitive. Realising the resonators, which determine the oscillating frequency, as microstrip transmission lines on the same PCB as the active elements of the oscillator results in low cost designs. An oscillator consists of an amplifier and a feedback network containing a frequency selective network, such that positive feedback is obtained at the desired frequency, causing the circuit to oscillate. Many oscillator topologies, such as Colpitts, Hartley, Crystal and Dielectric Resonator oscillators, have a single resonator frequency selective network and are described in standard electronics texts [1]. The frequency selective networks attenuate all signals at frequencies not corresponding to the required oscillation frequency. They have little attenuation and have the required phase shift to cause the positive feedback at the desired oscillation frequency. The primary factors determining the phase noise of the oscillator are the Q of the resonant network, the noise figure of the amplifier and its output power [2]. Leeson's [3] simplified model for phase noise shows the phase noise is inversely proportional to the square of the Q of the resonator.

Fig. 1 shows the block diagram of a typical oscillator. One can determine if this oscillator will oscillate by opening the switch and applying a signal A, at the desired oscillating frequency, to the input of the amplifier and measuring the signal B that is obtained as the feedback signal. When B>A and B is in phase with A then the oscillator will oscillate when the switch is closed. If the real part of the loop gain, being the ratio of B/A, is greater than one, the circuit will oscillate. A frequency selective network with a higher Q has a higher rate of change of phase of the loop gain versus frequency, and a quicker reduction in the real part of the loop gain, as one deviates from the centre frequency. Since the amount of phase noise of the oscillator is directly related to the real part of the loop gain, the higher the rate of change of phase of the loop gain at the oscillation frequency, the smaller the phase noise of the oscillator. The group delay, being the rate of change of phase, of the frequency selective network, is thus an important parameter.

The Q of the frequency selective network is determined by its components. A typical LC resonator has a Q of less than 200 and a Quartz Crystal has a Q of several thousand. The microstrip transmission line resonators used in the designs presented here have a Q of 191.

It is difficult to obtain as high a Q as possible for planar resonators, such as microstrip lines. Laute [4], uses a printed circuit inductor with a Q of 9 for a 900 MHz VCO. Lee [5] describes an oscillator which uses a single resonator. The coupling into the resonator is adjusted to minimize the loading of the resonator and thus maintain as high a Q as possible. It is possible to minimize loading the resonator using tap coupling and that is very suitable for the operating frequencies used in mobile communication systems. In this paper the use of a dual coupled resonator is proposed. Since the Q is defined for single resonator only, the group delay is a better measure of the frequency selective nature of the both the single and coupled resonator network.

II. RESONATOR COMPUTER SIMULATION

In order to accurately compare the phase noise performance of the single and dual coupled resonators, Microwave Office computer simulations are carried out on the oscillators.

Initially a linear simulation is carried out to ensure that the circuit operates at the correct frequency and has a loop gain greater than one, to ensure that oscillations will occur.

Subsequently nonlinear simulations using harmonic balance are carried out to determine the exact oscillating frequency, power output and phase noise of the oscillator designs. To verify those simulations, hardware has been constructed and its performance measured.

Figure 2. Microwave Office circuit of tapped single microstrip resonator.

Fig. 2 shows the Microwave Office circuit model of the microstrip resonator used in the single resonator oscillator design presented in this paper. One end of the resonator is connected to ground and the other end is an open circuit. The input and output signals are coupled to the resonator using

20Ω resistors, connected to the resonator at a specified distance from the ground connection. The resistance value and tapping point are selected to provide a good match at all frequencies into the 50 Ω input and output impedances of the amplifier used and provide a low insertion loss at the desired oscillating frequency. This ensures that the oscillator does not oscillate at other than the designed frequency. The tapping point is chosen to ensure that the loaded Q of the resonator is just sufficient to cause a loop gain greater than one, thus ensuring oscillations.

Fig. 3 shows the Microwave Office circuit model of a tapped two resonator coupled network, which would typically be used in a two resonator filter. To be able to make a good comparison with the single resonator of Fig. 2, the same line widths and the same coupling resistors are used for both these resonators. To obtain a good impedance match at the operating frequency, slightly different tapping points, Ltaps in

Fig. 2 and Ltapd in Fig. 3 were used. Fig. 4 shows the insertion loss and group delay of the two resonators.

The insertion loss and group delay of the dual coupled resonator are governed by the coupling between the two resonators. The bigger the coupling gap, the bigger the insertion loss and the bigger the group delay. To clearly demonstrate the effect of the resonator group delay on the oscillator phase noise, the amount of coupling used for Fig. 4 is such that insertion loss (red curves) for the dual resonator is the same of that for the single resonator, so that the amplifier used for the single resonator oscillator can also be used for the dual coupled resonator oscillator without any changes. It can be seen that the group delay (blue curves) of the dual resonator network is higher than that for the single resonator network. This difference can be increased much more by reducing the coupling between the resonators, however that increases the insertion loss of the dual resonator compared with the single resonator, so that the amplifier gain then needs to be increased for the dual resonator oscillator.