Proceedings of the 5th WSEAS Int. Conf. on Microelectronics, Nanoelectronics, Optoelectronics, Prague, Czech Republic, March 12-14, 2006 (pp64-69) DESIGN OF TRANSFORMER BASED CMOS ACTIVE INDUCTANCES G.SCANDURRA, C.CIOFI Dipartimento di Fisica della Materia e TFA Università degli Studi di Messina Salita Sperone 31, I-98166 Messina ITALY Abstract: - In this paper the design of a transformer based CMOS active inductance to be used for the realization of fully integrated RF CMOS front ends is discussed. The circuit topology employed aims at taking the maximum advantage of the limited transconductance gain of MOS devices for compensating the losses of the integrated magnetic structures. In this way, even if a 0.35 µm technology has been employed, it has been possible to obtain an equivalent “almost ideal” inductance of 6 nH at a center frequency of 2.4 GHz. The circuit operates with a supply voltage of 3.3 V and drives less than 1 mA. Moreover, two control voltages can be used in order to tune the maximum quality factor of the inductance and to change in a relatively wide range the frequency at which it occurs. Key-Words: - Active inductance, Integrated transformer, CMOS, Quality factor, RF, Circuit design 1 Introduction approach is the one in which a bi-pole with a Modern RF front ends to be used for mobile negative resistance behaviour is put in series to the communication and wireless networking require a inductor in order to compensate the losses and considerable amount of digital signal elaboration increase the resulting quality factor Q[8]. A third thus making the CMOS technology the mandatory approach exploits the magnetic coupling between choice if one has to design very low cost fully the spirals of an integrated transformer and a current integrated front ends. In the last few years, amplification between primary and secondary progresses in the CMOS technology have made introduced by an active device in order to obtain a MOSFET with sufficient gain in the GHz frequency purely inductive behaviour[9,10]. As a general rule, range available, and therefore the main obstacle inductorless circuits result in a smaller occupied area toward the fully integration of RF systems is with respect to transformer based ones. However, it represented by the difficulties encountered in the is believed that by resorting to a transformer in integration of high quality inductors. Particularly in which the magnetic coupling controlled by an active the case of CMOS processes, integrated passive device acts in such a way as to increase the quality inductors have typical values of Q that are too low factor of an otherwise passive inductive structure, for implementing several fundamental RF functions one can get better noise and linearity performances (for example highly selective filters) [1,2]. Although with respect to impedance transformation circuit the quality factor can be improved by resorting to such as those based on gyrators. In the case of special fabrication steps[3,4], the additional bipolar technologies, transformer based circuits have processing cost and complication resulting from a allowed the design of LNAs with noise modification in the process flow make such an performances quite close to what would have been approach quite unsatisfactory. For this reason, there obtained in the case of passive, high quality is a strong interest in the possibility of realizing high inductors loads[11]. In this paper it will be discussed quality inductances by employing active circuits. A a new topology that can be used for the realization few topologies of active inductors have been of high quality, transformer based, CMOS active proposed in the literature, which can be classified inductances. The design guidelines will be discussed into three main categories. A first approach is the in detail and simulation results will be presented that one in which no actual inductance is used but an confirm the validity of the followed approach. Open inductive effect is obtained exploiting the questions that need to be addressed in order to make impedance transformation capabilities of circuit the actual design feasible will be discussed as well. such as the “gyrator”[5-7]. A second possible Proceedings of the 5th WSEAS Int. Conf. on Microelectronics, Nanoelectronics, Optoelectronics, Prague, Czech Republic, March 12-14, 2006 (pp64-69) 2 Problem Formulation would be resonant with CGS at the design frequency, In a previous work a new topology for the design of it will be still obtained a purely inductive ZIN. transformer based CMOS inductances was Let us define the impedance ZP as: introduced that was proven to have significant 1 (1) Z P ()()s = RR + sLR || advantages with respect to the one that would have sCR been directly derived from the topology employed in It can be written: the case of bipolar technologies[12]. Here the Vin = VGS = (ZP + R1 + sL1 )iL1 + sMgmVGS (2) properties of the new topology will be discussed in And therefore, in the frequency domain: detail in order to derive guidelines to be used in the ' Z P + R1 + jωL1 design for a specific application. A simplified Z IN = = 1− jωMg diagram of the new topology that has been m (3) developed for the realization of high quality active (Z P + R1 + jωL1 )(1+ jωMg m ) = 2 2 2 inductances is reported in Fig. 1. 1+ ω M g m T C R If now the numerator of Eq.3 is taken into A consideration it may be observed that the term V DD (1+jωMgm) acts in such a way as to increase the phase of Z’IN and therefore it can allow to reach, at a given frequency, a phase quite close or even exactly equal to π/2. Note, however, that as the frequency L R increases, depending on the behaviour of the other terms at the numerator in Eq. 3, it is possible to end V Z IN R up with a bipole whose phase is larger than π/2, that C R is an equivalent impedance with a negative real part. This situation has to be avoided as negative Fig.1: simplified circuit of the CMOS active inductor proposed equivalent resistances may lead to instability. Therefore, it may be stated that the requirements for The parasitic resistances in series with the coils of an equivalent impedance to be regarded as an ideal the transformer are not shown in the figure. These, inductance at a given angular frequency ωD are: however, are shown in the small signal equivalent • The equivalent resistance R of the circuit reported in Fig. 2 in impedance Z’IN has to be 0 at the design frequency ω . iL1 D L 1 • The equivalent resistance Rin has to be 1 v L2 R1 L1 positive in a neighbourhood of ωD. L In other words, it can be accepted as a “good” C R C v i GS R L2 L2 equivalent of an inductance any impedance with V R g V GS R m GS positive imaginary part provided that the real part R2 has a minimum (close or equal to 0) at the desired 2 Z' IN design frequency. The above conditions translate Fig.2: small-signal equivalent circuit of the analytically to the following set of simultaneous CMOS active inductor equations: In order to simplify the discussion the equivalent Rin ()jωD = 0 transconductance (gm) of the cascode stage will be (4) assumed to be purely real. The coupled inductances ∂R ()jω L1 and L2 represent the transformer whereas the in = 0 ∂ω capacitance CR can be realized by means of a MOS ω =ωD varicap and therefore its value can be changed in a given range by means of a proper control voltage. Solving the above problem in our case is not The equivalent impedance ZIN is the parallel of the difficult in principle, but it may become tedious and impedance Z’IN in Fig. 2 and of the input capacitance complicated because of the several parameters that of the MOSFET (CGS). are involved in the design. In order to extract As long as it can be guaranteed a purely inductive general indications on the actual possibility of Z’IN, whose inductance value is below that which designing an ideal inductor with the proposed topology, we may proceed as follows. Proceedings of the 5th WSEAS Int. Conf. on Microelectronics, Nanoelectronics, Optoelectronics, Prague, Czech Republic, March 12-14, 2006 (pp64-69) Let us start by rewriting the impedance ZP in the order to obtain a purely inductive equivalent following form: impedance, from the plots in Fig. 3 we have: s 1+ QR 10,0 ω0R 1 ω0R LR Z P ()s = RR 2 ; ω0R = QR = s s LRCR RR 1+ + 2 Q ω ω ω M g R 0R 0R D m (5) r =0 1 In order not to complicate too much the discussion, 2 1,0 3 let us assume that in any case the inductances L1 and LR is characterized by the very same quality factor, that is: L L 1 = R (6) R R 1 R 0,1 1 2 3 45678910 Now let us define the following quantities: Q D R ω ω 1 D (7) 1,0 r = ; α = ω0R Mg M ; x = ; xD = RR ω0R ω0R With the previous assumptions and position it can be 0,9 ω /ω written: D R ' Z IN 0,8 zn ()x = = 3 R R (8) 2 x 0,7 []r()1− x 2 +1 + jr 1 (1+ jQR x )(1+ jαx ) QR r =0 = 2 2 × 1+α x 2 x 0,6 ()1− x + j QR 0,5 Therefore, finding the conditions for obtaining a 1 2 3 45678910 Q D purely inductive impedance at a given design (angular) frequency ωD, is equivalent to solve the Fig.3: Plots for the design of the active inductance.