3066 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 61, NO. 11, NOVEMBER 2014 Current Feedback Linearization Applied to Oscillator Based ADCs Matthias Voelker, Sara Pashmineh, Student Member, IEEE, Johann Hauer, Member, IEEE, and Maurits Ortmanns, Senior Member, IEEE Abstract—A regulation scheme to linearize the tuning curve of CMOS ring oscillators is proposed in this paper. The scheme uses the current consumption of the CMOS ring elements, which is pro- portional to the output frequency to the first order. The design of the feedback loop is presented on system level in conjunction with performance enhancements made on the implementation level. A weakly non-linear ring oscillator model is developed to simplify the control loop design. Model based linearity simulations proof a good agreement with measurements, while the simulation time is significantly reduced. A proof of concept implementation of the proposed linearization technique using CMOS ring oscillators is presented. Operating at 50 MHz sampling frequency, a maximum SFDR of 83.8 dB in a narrow band configuration verifies the effec- tiveness of the linearization. Implemented in a 180 nm process, the active area of the circuit is only 0.03 , which enables the use of this technique for multi-channel, multi-parameter measurement applications. Index Terms—Analog to digital converter (ADC), linearization technique, noise shaping, oscillator based ADC, oversampling, ring oscillator, time-domain signal processing, voltage-controlled oscil- lator (VCO). I. INTRODUCTION G REAT improvements in semiconductor technologies en- abled the ongoing integration of measurement circuits. Fully integrated measurement systems establish the possibility to develop multi-channel systems. Many signal processing strategies, which were originally developed for analog circuits, are transferred into the digital domain to increase the flexibility and to enable the use of complex signal processing. Nowadays, analog to digital con- verters (ADC) are present in nearly every measurement system. Moving the ADC towards the sensor and minimizing the required analog signal processing often lead to cost reduction and performance increase. Application specific ADCs enable the combination of sensor front-end and ADC [1], [2], and the ability to develop optimized multi-parameter measurement systems. Manuscript received November 27, 2013; revised February 22, 2014 and April 09, 2014; accepted April 22, 2014. Date of publication July 10, 2014; date of current version October 24, 2014. This paper was recommended by As- sociate Editor J. M. de la Rosa. M. Voelker and J. Hauer are with the Department of Integrated Circuits and Systems, Fraunhofer Institute of Integrated Circuits IIS, Erlangen, Germany (e-mail: matthias.voelker@iis.fraunhofer.de; johann.hauer@iis.fraunhofer.de). S. Pashmineh is with the Technical University Cottbus, Germany (e-mail: pashmine@tu-cottbus.de). M. Ortmanns is with the University of Ulm, Germany (e-mail: maurits. ortmanns@uni-ulm.de). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCSI.2014.2327302 Positron emission tomography (PET) is one example of this type of measurement system as two different parameters, en- ergy and time of arrival, of individual gamma quanta must be acquired. The different requirements force the implementation of parallel analog signal processing chains [3]. Analog to dig- ital conversion at an early stage can be applied to implement the two different signal processing strategies, for energy and time acquisition, within the digital domain [4], [5]. On one hand, the required ADC has to provide at least 10 effective number of bits (ENOB) at 1 MS/s for energy acquisition of the gamma quanta. On the other hand, 50 MS/s and 5 ENOBs are required to re- alize a timing resolution of 1 ns rms. Additionally, small size and low power consumption are important because more than 100 of such readout channels will be combined for a single readout ASIC [6] and hundreds of readout ASICs are used in the system. The use of typical Nyquist ADC architectures, like succes- sive approximation or pipeline for the combined requirements, lead to an over designed ADC for each individual measurement task. The application of delta-sigma oversampling ADCs could combine the low data rate, high resolution and high data rate, low resolution requirements. Unfortunately, a multi-bit imple- mentation with more than 5 bits of the internal quantizer limits the optimization of such an ADC for low power and area. Noise shaping oscillator (OSC) based ADCs provide the same transfer function as a first order delta-sigma modulator, while achieving more than 5 bits without oversampling [7]. But linearity of this type of ADC is limited by the tuning curve of the oscillator. Advanced digital correction techniques are published to overcome this limitation [8]. At the same time, modern sub-100 nm CMOS technologies, as typically used for OSC based ADCs, cannot be applied, since high volume pro- duction is not anticipated for such PET systems, challenging the designer to achieve small size in a rather mature technology. Consequently, this paper presents a linearization scheme based on the current consumption to frequency relation of the oscillator, which enables an area effective implementation of OSC based ADCs for multi-channel systems. The paper starts in Section II with a short introduction on oscillator based ADCs. The proposed regulation scheme is presented in Sec- tion III together with an analysis of its limitations and possible improvements. A proof of concept implementation in a 180 nm CMOS technology is presented in Section IV to verify the presented approach. Section V summarizes the measurement results. Finally, Sections VI and VII discuss the results and give a conclusion. II. VCO BASED ADC ADCs based on current or voltage controlled oscillators at- tracted increasing attention in recent years [9], [10] because this type of converter moves most of the conversion process into the digital domain, which is very attractive in scaled CMOS tech- nologies. Additional properties like inherent anti-alias filtering, 1549-8328 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. 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