Kiat T. Ng, Behzad Rejaei, # Mehmet Soyuer and Joachim N. Burghartz

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1 Kiat T. Ng, Behzad Rejaei, # Mehmet Soyuer and Joachim N. Burghartz Microwave Components Group, Laboratory of Electronic Components, Technology, and Materials (ECTM), DIMES, Delft University of Technology, Feldmannweg 17, 2628 CT Delft, The Netherlands, t.kiat@dimes.tudelft.nl. # IBM Research Division, T.J. Watson Reason Center, Yorktown Heights, USA. t I. INTRODUCTION The calls for higher integration levels of radiofrequency (rf) functions on silicon have generated recently interest in optimized monolithic rf transformers. Transformers feature advantages in rf impedance conversion in form of impedance transformers and are available as couplers and baluns, since transformers are 4-port components but inductors are 2-port components. While previous works on transformers have dealt with modeling and characterization based on the scattering parameters [1], [2], which does not relate to an optimized transformer design and demonstrations of the use of monolithic rf transformer in radio-frequency integrated circuits (RFICs) [3], work on rf transformer characteristics such as loss and voltage gain have not been done yet. This work relates the measured scattering parameters and these figures of merit, and characterizes systematically all the three generic spiralcoil transformers. These characterizations are necessary for the systematic design of an optimized transformer for a desired impedance conversion needed in an optimized RFIC design. Similar to spiral inductors on silicon, the generic types of rf transformers, i.e. the stacked, the bifilar, and the nested coil types (Fig. 1), are prone to substrate losses [1], [4]. II. TRANSFORMER STRUCTURES The principal layout of each of the three types is illustrated in Fig. 1. The components were fabricated at IBM Microelectronics on 10 ohm-cm silicon substrates with a 4-level AlCu interconnect process, featuring nominal metal thickness of 0.85 µm and 0.63 µm at the metal levels M2 through M4 and at M1, respectively, with dielectric seperation of 1.2 µm. A metal pitch of 25 µm (width and space between turns were 12.5 µm) and the same inner free coil area of 51x51 µm 2 were used in all cases. Also in each case, the inner terminals of the two spiral coils were connected to ground in order to characterize the devices in two-port configuration (non-inverting transformer). The transformers were modeled using the equivalent lumped-element circuit model in Fig. 2. III. RESULTS The comparison of modeled and measured S- parameters of a transformer with stacked coils at M3 and M4 are shown in Fig. 3a-d. The figures illustrate the good agreement that was obtained overall. The modeling parameters indicate the expected trends, i.e. and S increased, V and R[ decreased, and the total inductances and remained nearly constant with moving port 1 up from M1 to M3 in Table 1. With the increase of the approximated coupling coefficient im(z12 ) *im( 21) = (1) im(z ) *im( ) was found to increase as expected (Fig. 4). Since the three variations of stacked transformers had practically the same transformation ratios they could be used to obtain an insight into the degree of substrate losses. The total losses were determined as 2 2 Loss1 = 1- s - s (2) and ISBN: c STW, :050

2 324 Kiat T. Ng, Behzad Rejaei, Mehmet Soyuer and Joachim N. Burghartz 2 2 Loss2 = 1- s - s (3) for port 1 varying from M1 to M3 and for port 2 fixed at M4 similar to [5]. These two losses would be identical if the transformers were fully symmetrical, i.e. without any substrate losses. Figs. 5a and 5b, however, illustrate that the losses in silicon were considerable and increased when port 1 was moved from M3 to M1. A similar trend was observed if the voltage gains / and /, as defined in [6], were computed as shown in Fig. 6a,b. Thus, substrate losses are significant in transformer design. The characteristics of the three generic types of transformers were compared. The bifilar type was built at M4 with 3, 3.5 and 4 turns, while the three nested transformers had 4 turns for the inner (nested) coil and 2,3, and 4 turns for the outer coil. The voltage gain of the bifilar structure was higher as more turns were used, but with the higher number of turns the larger interwire capacitance became apparent at high frequencies as shown in Fig. 7a,b. As a result of the assymetry of the structure, the voltage gain / was highest with the outer conductor at the output, enclosing completely the generated electromagnetic flux (Fig. 7b). For the nested transformers this assymetry was more pronounced since those structures were strongly ratioed (Fig. 8a,b). With the inner terminal with n=4 at the output, the higher the voltage gain / the fewer turns on the outer coil (Fig. 8a). On the contrary, with the inner terminal at the input, the voltage gain / was higher for a higher number of turns at the outer coil (Fig. 8b). The voltage gains were nearly the same with n=4 for both coils. In comparison, the stacked spiral coil structure had the highest voltage gain and bandwidth, followed by the bifilar and the nested structures, on basis of a 1:1 transformation ratio. This is in part due to the fact that the stacked coil has the highest k in spite of the highest, and the smallest coil area consumed, making the structure less prone to substrate losses. ACKNOWWLEDGEMENTS The authors acknowledge the fabrication of the transformers by IBM Microelectronics, Essex Junction, Vermont, USA. The authors thank Mr Ruud M. de Kok of ECTM-DIMES, TUDelft, for the assistance in the measurements. REFERENCES [1] S. Mohan et al., Modeling and Characterization of On-Chip Transformers, IEDM 98, pp [2] J.N. Burghartz, M. Soyuer, K.A. Jenkins, Integrated RF and Microwave Components in BiCMOS Technology, IEEE Transanctions on ED vol.43, Sept 96, pp [3] J.R. Long, M.A. Copeland, A 1.9 GHz Low- Voltage Silicon Bipolar Receiver Front-End for Wireless Personal Communications Systems, IEEE Journal of Solid-State Circuits, December 95, Vol.30 no.12, pp [4] J.R. Long, Workshop on RF Passives, ISSCC [5] R.F. Drayton, S. Pacheco, J.-G. Yook, L.P.B. Katehi, Micromachined Filters on Synthesized Substrates, IEEE MTT-S vol. 3, Jun 98. Pp [6] R.J. Smith, Circuits, Devices and Systems, 2 nd edition, John Wiley and Sons Inc., IV. CONCLUSIONS The dependence of losses on the distances of transformer coils from the oxide-si interface by the stacked transformers has been confirmed experimentally. The high gains and better-thanexpected bandwidths of the stacked transformers as compared to bifilar and nested transformers were demonstrated experimentally, favouring this type of transformer structure for use in rf circuits. STW/SAFE99

3 Performance of Generic Monolithic Spiral-Coil RF Transformers 325 Table 1 Extracted modeling parameters of stacked transformers "N3" "N2/N4" "Mi/M4" Stacked Bifilar Nested Fig.1 Structural shapes of the transformers & 3 Parameters M1/M4 M2/M4 M3/M4 M (nh) L1 (nh) L2 (nh) RS1 (ohm) RS2 (ohm) CP (pf) COx1 (pf) COx2 (pf) CSi1 (pf) CSi2 (pf) RSi1 (ohm) RSi2 (ohm) CSh (pf) RSh (ohm) / / 0 & 2[ & 2[ & 6K & 0 6L 5 6L & 6L 5 6L 5 6K Fig.2 Lumped element model of stacked transformers Fig.3b Modeled and measured S 12 of the stacked Fig.3a Modeled and measured S 11 of the stacked IEEE/ProRISC99

4 326 Kiat T. Ng, Behzad Rejaei, Mehmet Soyuer and Joachim N. Burghartz Fig.3c Modeled and measured S 21 of the stacked Fig.3d Modeled and measured S 22 of the stacked Fig.4 Extracted coupling coefficients of stacked transformers Fig. 5a Loss1 of stacked transformers, with port2 at M4 Fig. 5b Loss2 of stacked transformers, with port2 at M4 STW/SAFE99

5 Performance of Generic Monolithic Spiral-Coil RF Transformers 327 Fig. 6a Voltage gain V1/V2 of stacked transformers, with port2 at M Fig. 6b Voltage gain V1/V2 of stacked transformers, with port2 at M4 Fig. 7a Voltage gain V2/V1 of bifilar transformers, with port2 as outer coil terminal Fig. 7b Voltage gain V1/V2 of bifilar transformers, with port2 as outer coil terminal Fig. 8a Voltage gain V2/V1 of nested transformers, with port2 at M4 Fig. 8b Voltage gain V1/V2 of nested transformers, with port2 at M4 IEEE/ProRISC99

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