Szhau Lai #1 , Dan Kuylenstierna #2 , Iltcho Angelov # , Klas Eriksson # , Vessen Vassilev # , Rumen Kozhuharov # , Zirath # # GigaHertz Centre, Microwave Electronics Laboratory, Chalmers University of Technology SE-41296 Gothenburg, Sweden 1 szhau@chalmers.se 2 Dan.kuylenstierna@chalmers.se Abstract — This work studies an important area of oscillator operation – VCO biased at varactor breakdown. In this operation, the oscillator’s phase noise is primarily determined by avalanche noise generated in the varactor, i.e., the phase noise can be modulated by the incremental shot noise generated at varactor breakdown. A simple experimental diode model was optimized for modeling varactor-breakdown current and an empirical shot noise model based on Hine’s theory presents good agreement with noise power measurements of varactors. The developed varactor noise-model has successfully been used to simulate the phase noise of a single-ended Colpitts InGaP HBT VCO over and beyond the varactor’s breakdown voltage. The VCO presents a phase noise below -100dBc/Hz for varactor voltages lower than breakdown voltage. Beyond the breakdown the phase noise gradually increases to -60 dBc/Hz@100kHz with a centre frequency deviating less than 0.6% from a 7.38GHz carrier. Index Terms — VCO, varactor breakdown, shot noise. I. INTRODUCTION Low-phase noise voltage-controlled oscillators (VCOs) are key-elements in wireless communication systems. An oscillator’s phase noise is primarily limited by the level of baseband noise in the active device and its upconversion that on a basic level can be said to be governed by the Q-factor of the passive resonator [1, 2]. However, for VCOs, the varactor may contribute significantly to the phase noise not only through Q-factor [3]. Nevertheless, very little efforts have been spent on modeling varactors for better phase noise simulations. In particular, nothing is reported on how the VCOs phase noise changes near the varactor breakdown voltage. The noise induced from the breakdown current can raise the phase noise tremendously. Ignorance of the effect from varactor breakdown noise may lead to erroneous simulation results as low-phase noise VCOs generally have high voltage swing, according to Leeson’s equation [1]. If the voltage swing is too high the varactor may enter the breakdown region during fractions of the VCO cycle. Another motivation for better modeling of the varactor’s noise in the breakdown region is that it can be utilized to design an oscillator with controllable phase noise. Such an oscillator can be used for jamming, but also as a standard with controllable phase noise. This paper presents a varactor-model taking into account avalanche noise in the vicinity of the varactor’s breakdown voltage. The model is based on the Hine’s approach [4-6], originally developed for modeling of Avalanche diodes. Although originally developed for static DC operation, in this work, the Hines model is shown to predict VCO phase noise well beyond the varactor breakdown voltage together with an accurate transistor model. The model is implemented in ADS using the Verilog-A code. The phase noise of a single-ended Colpitts VCO is then simulated, with good agreement to measurements, using ADS’s Harmonic balance tool. II. DEVICE MODEL A. HBT model The HBT model is based on the empirical model presented in [7] and optimized for VCO design. DC and small signal S- parameter measurement were performed for parameter extraction and the extracted model was verified versus large signal network analyzer (LSNA, Maury/NMDG MT4463). Low frequency noise measurements was carried out using ICCAP with standard measurement set-up[8]. Details of HBT model in VCO simulation can be referred to previous work [10]. B. Varactor -DC and small signal model The empirical varactor model focuses on a good fit for the current-slope versus voltage from 0V to reverse breakdown voltage and beyond. Beside good accuracy a reasonably fast extraction is also important, thus only three equations (1)-(3) and a leakage resistance are used for description of current versus voltage slope in breakdown regime. )) tanh( 1 ( 1 1 1 2 1 10 Vrbd rb rc rc Ibd ⋅ ⋅ + ⋅ = (1) ) ( 3 2 4 2 2 3 2 2 3 2 Vrbd rb Vrbd rb Vrbd rb rc Ibd ⋅ + ⋅ + ⋅ ⋅ = (2) ) ( 2 1 Ibd Ibd K Ibd + ⋅ − = (3) In (1)-(3), Vrbd 1 =Vr-Vbd 1 and Vrbd 2 =Vr-Vbd 2 , where Vr is the reverse-bias voltage while Vbd 1 and Vbd 2 are two voltage parameters defining transition between different slopes in the breakdown regime. rc 1,2,3 and rb 1,2,3,4 are fitting parameters. Ibd 1 describes the slope of the breakdown current in the vicinity of breakdown voltage in logarithmic scale (shown in Fig. 1 slope 1), in which the hyperbolic equation is used for better convergence properties in Harmonic Balance simulation when comparing to exponential expression. Ibd 2 is used to model the transition corner between slope 1 and slope 2 in Fig. 1. Herbert A Varactor Model Including Avalanche Noise Source for VCOs Phase Noise Simulation 978-2-87487-022-4 © 2011 EuMA 10 -13 October 2011, Manchester, UK Proceedings of the 41st European Microwave Conference 591