A Novel Frequency-Independent Third-Order Intermodulation Distortion Cancellation Technique for BJT Amplifiers

Transcription

1 1176 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 37, NO. 9, SEPTEMBER 2002 A Novel Frequency-Independent Third-Order Intermodulation Distortion Cancellation Technique for BJT Amplifiers Mark P. van der Heijden, Student Member, IEEE, Henk C. de Graaff, Member, IEEE, and Leo C. N. de Vreede, Member, IEEE Abstract Second-harmonic control is implemented in a balanced common-emitter configuration to facilitate frequency-independent third-order intermodulation distortion cancellation. Moreover, this circuit configuration facilitates a simultaneous match for either power and linearity or noise and linearity. Experiments demonstrated an improvement of over 15 db in the output third-order intercept point while maintaining freedom in the choice of load and source impedance. Index Terms Bipolar junction transistor, differential amplifier, distortion cancellation, linearization, LNA, matching, third-order intermodulation distortion. I. INTRODUCTION BIPOLAR devices still dominate today s market for high dynamic-range low-noise amplifiers (LNAs) for wireless communication systems. This is due to their high transconductance at low current levels and their relatively good noise performance. Currently, there is a move toward SiGe heterojunction bipolar transistors (HBTs) because they have inherently better low-noise performance and higher cutoff frequency than their more conventional homojunction counterparts. Generally, bipolar devices are strongly nonlinear due to their exponential nature. To meet the increasing demands on linearity made by today s mobile communication standards, linearity is traded off against collector current, which increases the dc power consumption. A common technique to circumvent this and still reduce distortion is to apply series feedback in the emitter of the transistor in a common-emitter (CE) configuration [1]. This reduces the distortion due to the nonlinear exponential current relationship by reducing the available gain of the CE stage. The ultimate goal in LNA design is to obtain a simultaneous device-matching condition for all the amplifier requirements yielding high gain, low noise, and high linearity (IP3 ) as shown in Fig. 1. A simultaneous noise and impedance match has already been reported in [2]. The focus of this work is on the requirements for linearity and impedance matching. This paper presents a novel circuit concept which facilitates excellent linearity at low dc collector current while maintaining excellent noise or gain performance with maximum freedom in Manuscript received December 5, 2001; revised February 28, This work was supported by RF Modules, Philips Semiconductors, Nijmegen, The Netherlands. The authors are with the Laboratory of Electronic Components, Technology and Materials ECTM, DIMES, Delft University of Technology, 2600 GB Delft, The Netherlands ( m.p.vanderheijden@its.tudelft.nl). Publisher Item Identifier /JSSC Fig. 1. Matching triangle for LNAs. sourceandloadmatching. First, toaccomplishthegoalofhighlinearity at low and high frequencies, a fully frequency-independent cancellation technique for third-order intermodulation distortion (IM3) has been developed. The basic principle of this IM3 cancellation relies on the separate treatment of IM3 products generated directly by third-order nonlinearities, and IM3 products that are generated indirectly by mixing of first- and second-order products with second-order nonlinearities. Obviously, cancellation can only occur if both contributions have opposite signs. Essential for this requirement is the presence of shunt or series elementsinthebaseorintheemitterofthedevice. This techniquewas first reported in [3], in which third-order distortion cancellation is achieved via the series resistances in the base and emitter. In practice, however, this effect is masked when the device is operated at RF frequencies, where the reactive components dominate the device and circuit performance[4]. In yet another report, partial IM3 canceling at higher frequencies was attributed to the interaction of the base emitter diffusion capacitance and the exponential current relationship [5]. More recent work also includes the contribution of the base emitter depletion capacitance to the high-frequency nonlinear behavior of a CE stage but does not focus on IM3 cancellation effects [1]. Second, to accomplish the goal of orthogonality in the matching requirements, we propose a differential circuit topology. This topology allows for a simultaneous impedance/ip3 or noise/ip3 match (see Fig. 1). This is accomplished by using the common-mode signal path to tune IP3 and the differential signal path to tune for impedance or noise. Section II describes the theory for the full frequency-span IM3 cancellation by identifying the missing circuit/device requirements by means of a Volterra series analysis. In Section III, these requirements are implemented in a balanced /02$ IEEE

2 VAN DER HEIJDEN et al.: INTERMODULATION DISTORTION CANCELLATION TECHNIQUE 1177 where the Taylor coefficients are Fig. 2. Simplified large-signal model of a bipolar transistor in commonemitter configuration. CE stage and verified using harmonic balance (HB) simulations with a Gummel Poon model of a commercially available double-polysilicon transistor ( GHz). Section IV discusses the implementation and experimental verification of an IM3-compensated balanced CE-amplifier circuit in support of our theory. Conclusions are given in Section V. II. IM3 ANALYSIS OF A COMMON-EMITTER STAGE In this section, the IM3 cancellation requirements are derived as a function of using a Volterra series analysis. First, we calculate the full expression and identify the requirements for lowfrequency IM3 cancellation. Then, the requirements for highfrequency cancellation are calculated and verified by an HB simulation. Fig. 2 shows the large-signal model of a bipolar transistor in CE configuration used in the analysis. and are the source and load impedance, respectively, and and are, respectively, the input and output voltages of the circuit. We assume that the transistor is properly biased at an intermediate and relatively low. For these lower collector currents, exponential distortion dominates [6], whereas quasi-saturation and high injection effects are still negligible. Consequently, the predominant source of distortion is the nonlinear exponential characteristic, which in our analysis, for reasons of simplicity, is set equal to the ideal forward current [7]: Furthermore, we assume the base emitter depletion capacitance and the collector base depletion capacitance to be linear. This is justified as long as the transistor is operated at a relatively low. For the moment, we omit in order to keep the complexity of the equations manageable. Since this assumption is not entirely correct, it will be addressed in Section II-B. A. Volterra Series Analysis of a CE Stage The Volterra series is solved symbolically by calculating the Volterra kernel transforms of the node voltages up to the third order [8]. We do this by computing the voltage transfer functions in increasing order by repeatedly solving a linear network as shown in the Appendix. The linear transfer function of the network is represented by the first-order kernel transform at node 2 of the linearized network (see Fig. 11 in the Appendix) where. The calculation of the third-order Volterra kernel is restricted to the third-order intermodulation frequency at. The complete expression is given by (5), shown at the bottom of the page, where (3) (4) (1) The base current and the diffusion charge are linearly proportional to with the maximum forward current gain and the forward transit time as constants. For the analysis, we assume that. Thus, the basic nonlinearities can be described as a Taylor series expansion up to the third degree, as follows: (2) (6) The magnitude of IM3 at can now be calculated using (3) (5) as in [8], shown in (7) at the bottom of the page. The numerator in (7) has two factors. The first factor depends only on and at the IM3 frequency. Hence, cancellation of this term can only occur at a single frequency (5) IM3 (7)

3 1178 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 37, NO. 9, SEPTEMBER 2002 using an inductor as source impedance [1]. Moreover, it is not possible to obtain orthogonality in the matching requirement for power and IP3. The second factor in the numerator of (7) is expanded into (6). Surprisingly enough, this factor depends only on the linearized transistor parameters and both at the second-order intermodulation (IM2) frequency and the second harmonic (H2) frequency. Note that the zeros of result in a cancellation of the IM3 products. Since the IM3 compensation is in principle based on the canceling of the direct third-order nonlinear terms with the indirect mixing of the second-order nonlinear terms with the fundamental, is considered to be the controlling factor in this process. At low frequencies, (6) reduces to (8) Setting this equation to zero, we obtain the well-known low-frequency IM3 cancellation requirement for the source impedance [3] Substitution of in (6) and setting to zero result in the high-frequency IM3 cancellation requirement (9) (10) If both requirements are fulfilled, this yields a frequency-independent cancellation of the real and imaginary part of.we observe that the current level at which cancellation occurs is fixed for a given intrinsic bipolar transistor by and. Consequently, (9) and (10) reduce to a single requirement for at fixed Fig. 3. Schematic of the single-ended CE amplifier, which is used for harmonic balance simulations with V =1:5 V and swept V. In Fig. 3, the circuit schematic of the CE stage is shown together with a list of parameters used in the model of Q1 [10]. and are the dc blocking capacitor and dc feed inductor, respectively, which are assumed here to be ideal components with infinite values. In the previous calculations, we did not consider the influence of. If we add this capacitance as a linear component to our model, the calculations, as described in the Appendix, yield an extra high-frequency IM3 cancellation requirement for the load impedance in addition to (11). This additional requirement can be found as follows. For higher frequencies, causes a voltage current feedback to the base. Since this feedback disturbs the IM3 cancellation condition at the input, the voltage drop over must be zero for second-order harmonic signals. To accomplish this, the second-order voltage at the base ( ) and the collector ( ) must be equal. where Using (2), (3), (11), and (25), becomes (14) at (11) If we set cancellation, (6) yields another solution for IM3 at (12) However, this solution requires a second-harmonic short at the input of the transistor, which would limit the bandwidth for IM3 cancellation in the circuit. Note that more freedom can be obtained in the choice of by placing a linear capacitor in parallel with the base emitter junction or by scaling the emitter length of the device to increase ( and are in principle independent of the emitter length [9]). B. Harmonic Balance Simulation of a CE Stage As an illustration of the presented theory, we have used the HB simulator of Agilent s Advanced Design System (ADS) to compute the output third-order intercept point (OIP3) versus at different frequencies by using the simplified nonlinear model. The OIP3 is defined as in [8] OIP3 [V] (13) (15) As long as condition (14) is satisfied, IM3 cancellation exists, and in theory, there is no third-order voltage at the output. Since the cancellation process only depends on the proper ratio between fundamental and second-order voltages over the junction, which has been fixed by the proper choice of, the linear feedback will not affect the cancellation. Hence, the requirements for IM3 cancellation of the circuit in Fig. 3 become and according to (11) and (15), respectively. Fig. 4 shows the simulated OIP3 versus at different center frequencies and a fixed delta frequency. It is observed that the peak OIP3 is largely independent of frequency as expected from the theory. A drawback of this configuration is that we cannot obtain a conjugate power match or noise match at the fundamental frequency required in (11) and (15) without introducing harmonic terminations. This fixes the operating frequency and is difficult to implement. Furthermore, the bias circuitry is also part of the load and source impedance. In order to meet the requirements in (11) and (15), the values of and have to be very high. However, a balanced equivalent of the CE stage circumvents the problems related to the bias circuitry and avoids

4 VAN DER HEIJDEN et al.: INTERMODULATION DISTORTION CANCELLATION TECHNIQUE 1179 Fig. 5. Schematic of the balanced CE-amplifier including bias circuitry, which is used for harmonic balance simulations with V =1:5Vand swept V. The transformer impedance ratio from the primary to the secondary winding is 4. Fig. 4. Simulated OIP3 versus collector current I (=I ) of the single-ended CE amplifier at three different center frequencies f, where Z =1500and Z = 10 (solid curves) and Z = Z = 50 (dotted curves) using the simplified large-signal model. the use of harmonic terminations. The proposed configuration uses a center-tapped transformer for second-harmonic control at the input of the device and facilitates orthogonality in the matching requirements for linearity and power/noise. Moreover, even-order harmonics are suppressed at the output, which basically improves the total distortion behavior of the amplifier. Due to the differential nature of the circuit, the second-order Volterra kernel is zero at all nodes except at the base of both transistors (nodes 2 and 3) and at the center tap of the input transformer (node 7). The third-order Volterra kernel is now given by (17) shown at the bottom of the page, where, and III. BALANCED CE AMPLIFIER The balanced CE amplifier configuration and its simplified linearized equivalent circuit are shown in Figs. 5 and 6, respectively. In Section II, we demonstrated that IM3 cancellation depends completely on the proper loading of the IM2 and H2 harmonics. In a balanced configuration, we can discriminate between even- and odd-order frequency components by making use of common-mode (CM) and differential-mode (DM) signal paths. Note that at the input transformer the generated even-order voltages are developed across but not. At the output transformer, the even-order voltages at nodes 4 and 5, and across, are all zero. The odd-order voltages at the input are developed across instead of, and at the output these are developed across. Using the discrimination between the even and odd harmonics in the balanced circuit, we have an extra degree of design freedom. This freedom can be utilized to improve for gain or noise matching. The above can be supported by a Volterra series analysis on the balanced configuration using the simplified large-signal model, in which. This analysis is not included here, but can be performed in a manner similar to that used for the unbalanced CE amplifier. Therefore, only the main results are presented here. The linear transfer function at node 6 (see Fig. 6) becomes (16) where. or Solving (18) for a and (18) independent of frequency, we obtain at (19) at (20) Note that the latter solution is not entirely frequency independent due to the required harmonic short at, and it is therefore discarded. Furthermore, in this situation the inclusion of in our balanced configuration does not lead to an extra IM3 cancellation requirement. This is due to the short-circuit condition for even-order harmonics imposed by the output transformer at (17)

5 1180 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 37, NO. 9, SEPTEMBER 2002 Fig. 6. Linearized equivalent circuit of the balanced CE amplifier. the collector output of the transistors. Consequently, is effectively in parallel with the base emitter depletion capacitance for second-order voltages as given by the Miller approximation, and (19) becomes at (21) If this condition is satisfied, the third-order distortion will cancel. Note that also a higher can be chosen by scaling up the device or by adding a capacitor in parallel with as shown in Fig. 6. One half the value of this capacitor has to be added to and in (21) because it is a CM capacitance. The latter solution will not degrade the linear device performance in terms of gain, noise, and. In Fig. 7, the simulated OIP3 versus is shown for the balanced circuit using the simplified model including. From these results, it is clear that the OIP3 is frequency independent for, calculated from (21). A theoretical improvement of more than 30 db can be achieved compared to a balanced CE amplifier without control of the CM signal, when. In Fig. 8, the independence of the IM3 cancellation technique on the source impedance is demonstrated. Lines of constant OIP3 are plotted on the plane in the Smith chart resulting from a two-tone source-pull analysis for and at GHz. The optimum source reflection coefficient with related minimum noise figure is also indicated on these plots. Note that the very low value of is a consequence of the neglected base resistance and the rather high value of. The figure shows that the OIP3 is well above 40 dbm (peak value in Fig. 7) and that the source impedance basically does not affect the cancellation. The variations found can be explained by numerical deviations of the simulator. The role of with respect to the noise performance of an LNA will not pose a problem. The voltage noise source originating from can be shifted over node 7 toward node 2 and node 3 (see Fig. 6) resulting in two correlated noise sources with equal phase. Ideally, these sources will transform back to the input in antiphase and cancel out due to the differential nature of the transformer balun. In Fig. 9, the simulated OIP3 versus is shown when using the complete Gummel Poon model for the transistors with the parameters found in [10]. In this simulation, is chosen to be 600 to compensate for the presence of base and emitter resistances and some additional capacitive parasitics. For example, additional parasitic capacitance will add Fig. 7. Simulated OIP3 versus collector current I (=2I ) of the balanced CE amplifier at three different center frequencies f, where R = 652 (solid curves) and R = 0 (dotted curves), and Z = Z = 50using the simplified large-signal model. linearly to. This affects both the current level and the value of. The CM resistance of the two base resistors at node 7 is in series with,so must be subtracted. The CM resistance of the emitter resistors at node 7 is approximately and must also be subtracted from. When using the full Gummel Poon model, the OIP3 is less pronounced and less frequency independent than expected from theory. This can be explained by contributions from the weak nonlinearities and, from the base resistance, and from the forward and reverse Early effects that deteriorate the pure exponential behavior of the device. Another observation in Fig. 9 is that the current level at which cancellation occurs is lower than that is observed in Fig. 7. This effect is mainly caused by the reverse Early voltage and the forward Early voltage, which reduces the current gain and the collector current by [7] (22) Since the cancellation technique depends on the ideal forward current rather than, also the current level shifts at which cancellation occurs. Substitution of the Early voltages V and V (see [10]) reduces approximately by 45% as observed in Fig. 9. In support of the theory presented in this paper, Section IV describes the implementation and experimental results of a balanced CE amplifier.

6 VAN DER HEIJDEN et al.: INTERMODULATION DISTORTION CANCELLATION TECHNIQUE 1181 Fig. 8. Simulated constant OIP3 contours plotted in the source reflection plane of the Smith chart for R = 652 and R = 0. The optimum source reflection coefficient 0 for minimum noise figure F is indicated in both charts. Fig. 10. board. Implementation of the balanced CE amplifier on a printed circuit Fig. 9. Simulated OIP3 versus collector current I of the balanced CE amplifier at three different center frequencies f, wherer = 600 (solid curves) and R = 0 (dotted curves), and Z = Z = 50 using the full Gummel Poon model. IV. EXPERIMENTAL VERIFICATION Fig. 10 shows a photograph of a balanced CE amplifier implemented on a RO4003 ( ) high-frequency laminate of Rogers Corporation using two BFG410W wide-band transistors of Philips Semiconductors and Mini-Circuits transformers. The center-tapped transformers of type TC4-14 have an impedance ratio of 4 and are in cascade with a balun of type TCML1-11 to ensure good amplitude and phase balance over a wide frequency range. Note that the IM3 cancellation is based on the proper termination of the second-order products. Therefore, the transformer must have at least one octave of bandwidth. Since the transformer combinations have an upper cutoff frequency of approximately 1 GHz, two-tone measurements were performed at MHz and MHz. In Fig. 11(a) and (b), the OIP3 is shown as a function of the total dc current for MHz and MHz, respectively, at three different frequency spacings. The gain of the amplifier is around 16 db at these frequencies, measured in a 50- environment. The experiment is in agreement with the developed theory that is even more clearly supported by comparing the results for the same circuit with and without the second-harmonic control resistor. An improvement of more than 15 db in OIP3 is obtained by applying the correct resistor value. Fig. 12 shows the output power of the fundamental, IM3, and IM5 as a function of input power for a two-tone test at MHz and MHz. We observe an improvement in IM3 and IM5 of more than 20 and 10 db, respectively, over a wide range of input powers. These results demonstrate that this circuit concept can dramatically extend the spurious-free dynamic range of an amplifier with complete freedom for power or noise matching. Extension of this technique to higher frequencies should be feasible by on-chip IM3- compensating elements in a balanced CE configuration utilizing robust biasing techniques [4]. V. CONCLUSION A novel design technique has been presented for broad-band high-linear low-power LNAs. The technique utilizes exponential IM3 canceling by proper termination of the second-order products, facilitating orthogonality in OIP3 and impedance or noise matching. Experimental data confirms the theory and demonstrates an improvement of more than 15 db in OIP3 compared to a noncompensated design, yielding a dramatic improvement in dynamic range at low dc power consumption.

7 1182 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 37, NO. 9, SEPTEMBER 2002 Fig. 13. Linearized equivalent circuit of the single-ended CE amplifier. (a) APPENDIX The linearized circuit of the unbalanced CE amplifier is shown in Fig. 13. In order to calculate the first-order (linear) response, the circuit is excited with an external voltage source. The solution of the following matrix equation, which results from the compacted MNA method, produces the first-order Volterra kernels [8] (23) Fig. 11. Measured OIP3 versus I at (a) f =225MHz and (b) f = 385 MHz for different tone spacing 1f with R = 600 (solid curves) and R =0(dotted curves). (b) where is the admittance matrix of the circuit, is the vector of the first-order Volterra kernel transforms of the node voltages, and is the vector of excitations with the excitation voltage. Equation (4) can be obtained by solving (23) using Cramer s rule and setting, and. The second-order Volterra kernel transforms of the node voltages in the nonlinear circuit are found by solving the following matrix equation: (24) where are the second-order Volterra kernels and is the vector of nonlinear current sources of order two. These current sources are placed in parallel with their linear equivalents in Fig. 13 and is replaced by a short. The secondorder current sources are (25) The second-order Volterra kernels are now obtained by solving (24) using Cramer s rule as shown in (26) at the top of the next page. The third-order Volterra kernel transforms of the node voltages in the nonlinear circuit are found by solving the following matrix equation: Fig. 12. Measured output power of the fundamental, IM3, and IM5 versus input power at f = 385 MHz with R = 600 and R = 0. Moreover, the technique is effective up to the compression region, making it applicable to medium-power amplifiers. (27) where are the third-order Volterra kernels and is the vector of nonlinear current sources of order three.

8 VAN DER HEIJDEN et al.: INTERMODULATION DISTORTION CANCELLATION TECHNIQUE 1183 (26) These current sources are placed in parallel with their linear equivalents in Fig. 11 and their values are (28) where. Equation (5) can be obtained by solving (27) using Cramer s rule and setting, and. ACKNOWLEDGMENT The authors would like to thank Prof. Dr. J. N. Burghartz and Prof. Dr. L. K. Nanver for their support. REFERENCES [1] K. Leong Fong and R. G. Meyer, High-frequency nonlinearity analysis of common-emitter and differential-pair transconductance stages, IEEE J. Solid-State Circuits, vol. 33, pp , Apr [2] S. P. Voinigescu, M. C. Maliepaard, J. L. Showell, G. E. Babock, D. Marchesan, M. Schroter, P. Schvan, and D. L. Harame, A scalable highfrequency noise model for bipolar transistors with application to optimal transistor sizing for low-noise amplifier design, IEEE J. Solid-State Circuits, vol. 32, pp , Sept [3] J. Reynolds, Nonlinear distortions and their cancellation in transistors, IEEE Trans. Electron Devices, vol. ED-12, pp , Nov [4] G. V. Klimovitch, On robust suppression of third-order intermodulation terms in small-signal bipolar amplifiers, in IEEE MTT-S Int. Microwave Symp. Dig., June 2000, pp [5] S. A. Maas, B. L. Nelson, and D. L. Tait, Intermodulation in heterojunction bipolar transistors, IEEE Trans. Microwave Theory Tech., vol. 40, pp , Mar [6] L. C. N. de Vreede, H. C. de Graaff, J. A. Willemen, W. van Noort, R. Jos, L. E. Larson, J. W. Slotboom, and J. L. Tauritz, Bipolar transistor epilayer design using the MAIDS mixed-level simulator, IEEE J. Solid- State Circuits, vol. 34, pp , Sept [7] P. Antognetti and G. Massobrio, Semiconductor Device Modeling with SPICE. New York: McGraw-Hill, [8] P. Wambacq and W. Sansen, Distortion Analysis of Analog Integrated Circuits. Norwell, MA: Kluwer, [9] L. C. N. de Vreede, HF silicon ICs for wide-band communication systems, Ph.D. dissertation, Delft Univ. Technol., Delft, The Netherlands, [10] NPN 22 GHz wideband transistor, product information. Philips Semiconductors, Eindhoven, The Netherlands. [Online]. Available: Mark P. van der Heijden (S 98) was born in Benthuizen, The Netherlands, in He received the B.S. degree in electrical engineering from The Hague Polytechnic, The Hague, The Netherlands, in 1998, and the Master of Technological Design (M.T.D.) degree in microelectronics from the Delft University of Technology, Delft, The Netherlands, in 2000, where he is currently working toward the Ph.D. degree in electrical engineering. He joined the Laboratory of Electronic Components, Technology and Materials, Department of Information Technology and Systems, Delft University of Technology, in From 1998 to 2000, he worked on isothermal characterization of MOST devices and power amplifier design for linearity. His research interests include design of RF building blocks for linearity and dynamic range. Henk C. de Graaff (M 92) was born in Rotterdam, The Netherlands, in He received the M.Sc. degree in electrical engineering from the Delft University of Technology, Delft, The Netherlands, in 1956, and the Ph.D. degree from the University of Technology, Eindhoven, The Netherlands, in He joined Philips Research Laboratories, Eindhoven, in 1964, where he has been working on thin-film transistors, MOST, bipolar devices, and material research on polycrystalline silicon. His current field of interest is device modeling for circuit simulation. Since his retirement from Philips Research in November 1991, he has been a Consultant to the University of Twente, Twente, The Netherlands (until 1996) and the Delft University of Technology, Delft, The Netherlands. Leo C. N. de Vreede (M 01) was born in Delft, The Netherlands, in He received the B.S. degree in electrical engineering from The Hague Polytechnic, The Hague, The Netherlands, in 1988 and the Ph.D. degree from Delft University of Technology, Delft, The Netherlands, in In 1988, he joined the Laboratory of Telecommunication and Remote Sensing Technology, Department of Electrical Engineering, Delft University of Technology. From 1988 to 1990, he was involved in the characterization and physical modeling of CMC capacitors. From 1990 to 1996, he worked on modeling and design aspects of HF silicon ICs for wide-band communication systems. In 1996, he was appointed as Assistant Professor with the Delft University of Technology, working on the nonlinear distortion behavior of bipolar transistors at the device physics, compact model, and circuit level, at the Delft Institute of Microelectronics and Submicron Technology (DIMES). In the winter of , he was a guest of the High-Speed Device Group, University of San Diego, San Diego, CA. In 1999, he became an Associate Professor, responsible for the Microwave Components Group of the Delft University of Technology. His current research interest is technology optimization and circuit design for improved RF performance and linearity.