An Approach to Simulating Injection-locked Self-Oscillating Active Integrated Antennas Xinping Zeng and Zhizhang (David) Chen Department of Electrical and Computer Engineering Dalhousie University, Halifax, Nova Scotia, Canada B3J 2X4 Eamil:
[email protected] and
[email protected] I. INTRODUCTION Various injection-locked oscillators such as oscillating active integrated antennas have been proposed. They normally presented high frequency stability and clean signal spectra as well as multi-functionality [1-3]. Normally, generating a stable high-frequency locking signal is more costly than generating a low frequency one. Therefore, a locking signal at a subharmonic frequency was also used. Such subharmonic injection locking can achieve the desired stabilizing effect with the use of a single-gate GaAs MESFET; nevertheless, the associated power efficiency is relatively low [4]. To improve the efficiency, two cascaded single-gate FETs were used at the cost of increased circuit complexity [5]. A simple subharmonic injection-locked oscillating active integrated antenna (AIA) structure was then proposed by the authors recently that employed the dual-gate FET [6][7]. It can be used for frequency upconversion and direct RF QPSK modulation/transmission. The dual gates of the FET give one more freedom in optimizing the RF transmitting performance. Although many CAD software packages offer built-in tools for simulation of freerunning oscillators, few of them can be applied directly to an injection-locked oscillating AIA. For a subharmonic injection-locked oscillating AIA, none are capable. The reasons are: (A) solutions obtained with most of existing software packages often become diverge due to matrix singularity or become trivial when injection signals apply [8]; and (B) no effective stability analysis modules have been developed to verify the resulting solutions. In this paper, we propose an approach to solving the problems. In our approach, an auxiliary generator was introduced and adapted for injectionlocked oscillating AIA. In addition, a rigorous and general stability measure, the Nyquist criterion, is implemented to examine stability characteristics of simulation solutions. II. THE AUXILIARY GENERATOR APPROACH The auxiliary generator (AG) approach was developed for phase-locked oscillation [9]. In this paper, the approach is redesigned for simulation of injectionlocked oscillating AIAs as described in the following paragraphs. First, the AG is considered as either a voltage source with a series impedance, or a current source with shunt admittance. It is then inserted into an oscillating AIA circuit at an appropriate location to drive the circuit into a forced regime pertaining to the injection locking. In our case, it is attached to a node between the oscillating device and its resonant load (see Fig. 1).
w
To remove the side effects of AG on the circuit, the AG impedance or admittance should be chosen carefully. They have to be set infinite at all frequencies but zero at the fundamental. The conditions are shown in Fig. 2. Source impedance
Injectedlocking signal
Coupler
Resonator
Output Match Load
Filter Feedback Auxiliary Generator
Fig. 1 An auxiliary voltage generator introduced for simulation of an injectionlocked oscillating circuit that uses dual-gate FET transistor.
Fig. 2 Auxiliary generators: (a) voltage generator; (b) current generator. III. STABILITY ANALYSIS Stability analysis is offers a key measure to check if the simulation solutions are physically realizable and unconditionally sustainable. In a linear simulation, stability factor K (Rollet’s factor) can be used to quantify the stability [10]. However, its application to oscillator simulations is very limited [10] as an oscillation often works in deep nonlinear regions. Therefore, a more rigorous and general stability measure is needed. In our case, the Nyquist criterion is employed. Originally, the Nyquist criterion was developed for small-signal circuits. It has since been extended and applied to the harmonic-balance (HB) based nonlinear analysis [11]. In ADS, the Nyquist criterion based built-in ADS tool, OscTest, is available. However, it can not be applied directly to injection locked oscillations. It needs to be modified. The modified OscTest is shown in Fig. 3. It has two filters: the first filter filters out only the testing signal and lets other frequency components pass without any
attenuation; the second filter filters out all the other frequency components but allows only the testing signal to pass. The modified OscTest enables the tracking of the behaviors of the close-loop gain and there determine the stability [11]. filter1
dc_feed
port1
port2
filter2
Vin
filter2
Vreflect
Fig. 3 The modified Nyquist-criterion based OscTest IV. SIMULATIONS AND MEASUREMENTS The above theory and techniques were applied to simulation of a sub-harmonic injection locked oscillating dual-gate FET active integrated antenna developed recently by the authors [7]. In simulation, the AG was added at the source terminal of the FET. Fig. 4 is the simulated spectrum. As can be seen, the simulated oscillating frequency was 2.079 GHz for Vd = 2.0v ( Vg1 = −0.5v, Vg 2 = 1.0v ). The modified OscTest was then inserted into the active antenna circuit to verify the stability of the solutions. The solutions are found to be stable.
Fig. 4 The simulated spectrum of the injection locked AIA Fig. 5 shows the measured spectrum. It can be seen that in the oscillating frequency is around 2.04 GHz, very close to the simulated 2.079GHz. The phase noise of the injection-locked oscillator was found to be around -99dBc/10 KHz. By comparisons, it can be seen that the harmonics and relative strengths measured (see Fig. 5) are very similar to those simulated (see Fig. 4). For instance, in Fig. 5 the amplitude difference between the 1st and 2nd harmonics is about -17dB while in Fig. 4 it is about -17.3 dB. This is a quite remarkable indication that the proposed approach is effective and accurate in simulation of injection-locked oscillators.
Fig. 5 The measured spectrum V. CONCLUSIONS In this paper, an approach is proposed for the use of the existing commercially available circuit simulators to model injection-locked oscillating active integrated antennas. Experimental results validated the approach. REFERENCES [1] S. Drew and V. F. Fusco, “Phase modulated active antenna”, Electron. Lett., May 1993, pp 835-836. [2] L. Dussopt el. Al., “BPSK and QPSK modulations of an oscillating antenna for transponding applications,” IEE Proc. Microw. Ant. Propag., Oct. 2000, pp 335-338. [3] T. Berceli, W. Jemsion, P. Hertzfeld, A. S. Daryoush, and A. Paolella, “A double-stage injection locked oscillator for optically fed phase array antennas,” IEEE Trans. Microwave Theo. Tech., Feb. 1991, pp. 201-207. [4] Y. Tajima, “GaAs FET application for injection-locked oscillators and self-oscillating mixers,” IEEE Trans. Microwave Theo. Tech., Jul. 1979, pp. 692-693. [5] C. R. Poole, “Subharmonic injection locking phenomena in synchronous oscillators,” Electron. Lett., Oct. 1990, pp.1748-1750. [6] X. Zeng and Z. Chen, “Frequency multiplication and QPSK modulation with subharmonic injection-locked active antenna,” Pro. of the 2nd Annual Conf. Comm. Networks Services Res., May 19-21, 2004, Fredericton, New Brunswick, pp. 329-332 [7] X. Zeng and Z. Chen, “An injection-locked active antenna with direct RF QPSK modulation,” submitted to Intl. J. of RF Microwave Computer-Aided Engineering, John Wiley & Sons [8] Agilent Technologies, Harmonic balance for oscillator simulation, ADS Manuals, 2002. [9] R. Quere, etl. al. , “Large signal design of broadband monolithic microwave frequency dividers and phase-locked oscillators,” IEEE Trans. Microwave Theo. Tech., Nov. 1993, pp. 1928-1938. [10] J. M. Rollet, “Stability and power-gain invariants of linear two-ports,” IRE Trans. Circuit Theory, Vol. 9, 1962, pp. 29-32. [11] S. Mons, et al., “A unified approach for the linear and nonlinear stability analysis of microwave circuits using commercially available tools,” IEEE Trans. Microwave Theo. Tech., Dec. 1999, pp. 2403-2409.
