MIXED SIGNAL LETTER A new robust capacitively coupled second harmonic quadrature LC oscillator Emad Ebrahimi • Sasan Naseh Received: 1 June 2010 / Revised: 6 July 2010 / Accepted: 29 July 2010 / Published online: 10 August 2010 Ó Springer Science+Business Media, LLC 2010 Abstract A study of some reported superharmonic LC quadrature voltage-controlled oscillator (LC-QVCO) is performed in which it is shown that robustness of the quadrature oscillation varies depending on the coupling configuration. Next, a new superharmonic LC-QVCO is proposed in which the common source node in either of two identical cross-connected LC-VCOs is coupled via a capacitor to the node common between the two varactors in the LC-tank of the other LC-VCO. As a result of con- necting common mode nodes, the currents flowing through the two coupling capacitors are comprised of only the even harmonics. In the proposed coupling configuration there exists a closed loop through which the second harmonic signals circulate. A qualitative argument is presented to justify the robustness of the quadrature nature of the pro- posed QVCO by applying the Barkhausen phase criterion to the second harmonic signals in the loop. Since the coupling devices are only two capacitors, no extra noise sources and power consumption are added to the core VCOs. A Monte-Carlo simulation showed that the phase error of the proposed QVCO caused by device mismatches is no more than 1°. Also, generalizing this method to several numbers of VCOs in a loop, multiphase signals can be generated. The proposed circuits were designed using a 0.18-lm RF CMOS technology and simulation results are presented. Keywords LC quadrature voltage-controlled oscillators  Low-phase noise  Low-power  Multiphase  Quadrature robustness  Superharmonic QVCO 1 Introduction Many modern communication systems such as zero-IF receivers, image rejection architectures, clock and data recovery (CDR), and QPSK modulators require oscillating signals with 90° phase differences (I/Q signals) and there- fore, quadrature voltage-controlled oscillators (QVCO) are an indispensable part of these systems. Performance of the QVCO can affect the overall performance of the system and therefore, many efforts have been put on the design of low- phase noise, low-power, highly integrated and robust QVCOs. Some circuits and methods used for quadrature signals generation are [1]: poly-phase RC-CR filters, master-slave flip-flops used as frequency divider, ring oscillators, and QVCOs with LC tanks (LC-QVCOs). Due to their low phase noise and low power consump- tion, LC-QVCOs have received lots of attention in the recent years [2–15]. LC-QVCOs are usually made of coupling two identical cross-connected LC-VCOs in which oscillating signals are injected from one oscillator to the other and vice versa [2]. Depending on their mechanism of operation, LC-QVCOs can be categorized in two main groups. In the first group, two identical LC-VCOs are coupled in an ‘‘in-phase anti-phase’’ manner in such a way that the first harmonic oscillating signals are injected from each of the core oscillator to the other [2–4]. In the second group known as superharmonic QVCOs, the second har- monic oscillating signals, instead of the first harmonics, from a common mode node in each of the core oscillators are injected to the other. In most of the QVCOs in the E. Ebrahimi (&)  S. Naseh Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran e-mail: ebrahimi_em@yahoo.com S. Naseh e-mail: naseh@um.ac.ir 123 Analog Integr Circ Sig Process (2011) 66:269–275 DOI 10.1007/s10470-010-9512-6