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IEEE TRANSACTIONS ON THEORY AND TECHNIQUES 1 On the Compression and Blocking Distortion of Semiconductor-Based Varactors Cong Huang, Member, IEEE, Koen Buisman, Member, IEEE, Peter J. Zampardi,Senior Member, IEEE, Lawrence E. Larson, Fellow, IEEE,andLeoC.N.deVreede, Senior Member, IEEE

Abstract—The effective capacitance of variable reactors (varac- tors) can be modulated by the magnitude of applied RF signals, resulting in troublesome detuning issues in resonators constructed with these devices. In this paper, the fundamental causes behind these issues are investigated through the use of Volterra series. It is concluded that two major distortion mechanisms, namely, compression and blocking, are responsible for this effective ca- pacitance change under RF excitation. In light of this observation, different varactor configurations are proposed and investigated, yielding novel devices with much smaller capacitance variation, typically on the order of 0.1 0.5 compared to 10 50 for conventional semiconductor-based varactors. With this im- provement, the resonance frequency shift of a 2-GHz resonator is decreased from 300 to 5 MHz for worst case conditions, a Fig. 1. Different frequencies for the intermodulation, compression, and property essential to tunable high- filter applications. Among all blocking distortion under a two-tone signal excitation. analyzed structures, the varactor topology that facilitates cancela- tion of all important distortion products has been experimentally tested. These measurements demonstrate successful cancellation Conventionally, stacking is a useful technique to reduce the of both compression and blocking terms, resulting in capacitance impact of varactor non-linearities. By connecting a number of variation below 0.5% in worst case scenarios. identical varactors in series, the voltage swing on each device Index Terms—Low distortion, microwave devices, power depen- is decreased and accordingly the intermodulation, compression, dency, RF circuits, varactor, varicap. and blocking distortions are all reduced. This approach is simple to implement without changing the base material, but at a cost of device size and quality factor. Although stacking turns out to I. INTRODUCTION be the most efficient way to improve the linearity of ferroelec- tric-material-based varactors [9], [10] due to their high dielectric constants typically 200 ,stringent tradeoffs between quality ARIABLE reactors (varactors) are traditionally non- factor and linearity are found in the semiconductor-based varac- linear devices [1]–[5]. In RF applications this linearity V tors and therefore limit the general utility of the stacking tech- drawback is reflected in compression, blocking/desensitiza- nique. tion and intermodulation distortion phenomena [6], [7] when To address the linearity issues of the semiconductor varactors, operated with large RF signals. Intermodulation distortion research has been directed toward cancellation approaches. In gives rise to in-band and out-of-band interference, which either [11]–[14], the intermodulation distortion of semiconductor var- disturbs the information detection of the adjacent-channel actors has been extensively studied and various varactor topolo- users, or pollutes the transmitted in-band information, causing gies have been proposed to cancel the third-order intermodula- difficulties in signal detection. On the other hand, compression tion components at and under a two-tone and blocking/desensitization phenomena change the effective signal excitation (see Fig. 1). These cancellation techniques capacitance of the varactors under large RF signal excitation yield excellent third-order output intercept point in the and may detune a well-designed RF system by changing its order of 60 dBm, facilitating many varactor-based adaptive RF operation frequency and transfer function, which are both key circuits [15]–[17]. parameters for tunable resonators and filters [8]. In contrast to the previously proposed cancellation tech- niques, the focus of this work will be on the cancellation of Manuscript received May 15, 2012; revised September 06, 2012; accepted detuning related distortion components that appear at the fun- September 13, 2012. This work was supported under the VENI, HEECS, and MEMPHIS projects. damental frequencies and (see Fig. 1). In these scenarios, C. Huang, K. Buisman, and L. C. N. de Vreede are with the Delft Insti- large RF signals present on the varactor might affect the varactor tute of Microsystems and Nanoelectronics (DIMES), Delft University of Tech- operation within the frequency band of interest, a phenomenon nology, Delft 2628 CN, The Netherlands (e-mail: [email protected]; L.C.N. [email protected]). that appears as a variation of the effective varactor capacitance P. J. Zampardi is with Skyworks Solutions Inc., Newbury Park, CA 91320 and in turn detunes the system. In Section II, this phenomenon USA. is investigated using Volterra analysis. It reveals that two dif- L. E. Larson is with the School of Engineering, Brown University, Provi- dence, RI 02912 USA. ferent distortion components may vary the capacitance of var- Digital Object Identifier 10.1109/TMTT.2012.2221139 actors under RF excitation, namely, compression distortion due

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2 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES

TABLE I LINEAR AND NONLINEAR CURRENT PRODUCTS AT &AROUND THE FUNDAMENTAL FREQUENCIES (FIG.2)

Fig. 2. Schematic for the Volterra analysis of the varactors’ capacitance varia- tion due to the RF signals. to the self-mixing of the in-band signal and blocking distortion due to adjacent interferers. In Sections III–V, various cancella- tion mechanisms and solutions to these distortion phenomena are extensively discussed, which not only provide the theoret- ical explanation of the results reported in [18], but also yields the introduction of three new varactor configurations that have in- herent blocking distortion cancellation properties. The practical application fields of these proposed topologies are discussed in Section VI. To experimentally verify the theory, their linearity performance is reported in Section VII followed by conclusions in Section VIII.

II. CAPACITANCE VARIATION ISSUES IN VARACTOR-BASED RF CIRCUITRY Detuning issues in varactor-based RF adaptive circuits mainly arise from the capacitance variations of the varactors due to the presence of large RF signals. To understand this phe- nomenon, we use the Volterra analysis shown in Fig. 2. In this analysis, the voltage-controlled varactor with a given – relationship (with being the capacitance of the varactor and (2) being the reverse applied voltage) is excited by a two-tone RF voltage signal with the amplitudes and and the where is the capacitance under RF excitation and frequencies and , respectively. Due to the nonlinear prop- is the linear capacitance of the varactor. erties of a conventional varactor, the current flowing through It can be found in (1) that the fundamental current at it will consist of many undesired distortion components at flowing through the varactor consists of three terms, i.e., all linear combinations of and . In Table I, all important the desired linear component and two third-order distortion current components at & around the fundamental frequencies components that cause deviations. Although both third-order and are listed for the Volterra kernel orders less than five. distortion components play a role in changing the effective For testing the capacitance variation due to RF signals, only the capacitance of the varactor, as indicated in (2), their mech- distortion products that appear at and play a role. Note anisms are different. Here, we may regard the input voltage that this is different from the intermodulation products, which tone at as the wanted in-band signal and the tone at as appear at and . Consequently, a study related the adjacent blocking signal. It can be observed that the first to detuning must be focused on distortion products appearing third-order distortion component in (1) depends solely on at the fundamental frequencies. The capacitive current flowing and , irrespective of the blocking signal, and therefore it through the varactor at can be written as is a pure self-mixing term. It implies that even if the second jammer tone at is absent, the current flowing through the varactor can be a “compressive” or “expansive” function of the wanted in-band RF signal and is hereafter called compression (1) distortion [6], [7]. In contrast, the second distortion component in (1) is a func- where and are the first- and third-order voltage–current tion of , , ,and ; hence, it arises from the mixing be- transfer functions of the varactor. From (1), the corresponding tween the in-band signal and the blocking jammer signal. This capacitance variation of varactor due to the RF signal type of distortion is called desensitization or blocking distor- is given by tion since the desired weak signal may be desensitized or even This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

HUANG et al.: ON THE COMPRESSION AND BLOCKING DISTORTION OF SEMICONDUCTOR-BASED VARACTORS 3

Fig. 3. Capacitance variation at due to self-mixing and adjacent blockers as a function of input voltage amplitudes for a single . For the compres- sion distortion, capacitance variation is plotted versus voltage amplitude with V. For the blocking distortion, capacitance variation is plotted versus voltage amplitude with V. , where pF and V . GHz, GHz and the dc reverse control voltage V.

blocked due to the existence of a strong interferer [6], [7]. Con- Fig. 4. (a) Single diode configuration. (b) Antiseries configuration. (c) Antis- sequently, as indicated in (2), the compression distortion in- eries/antiparallel configuration. duced capacitance variation depends solely on the amplitude of the in-band signal , while the capacitance variation due to the blocking distortion is proportional to . RF signal amplitude cannot be avoided. This is basically be- To test the contributions of these compression and blocking cause the dc control voltage shares the same terminal with the related distortion products to the capacitance variation, a single applied RF signal(s), as shown in Fig. 4(a). In such a config- nonlinear diode with exponential relationship is simu- uration, the periodic positive and negative RF voltage swings lated using the ADS harmonic-balance simulator. The resulting force the diode to experience an asymmetrical – behavior, capacitance variation is plotted in Fig. 3 as a function of the RF resulting in a variation of effective capacitance and therefore voltage amplitude. The contributions of the self-mixing and ad- raising detuning issues. To address this problem, three-terminal jacent blocker are distinguished using unequal amplitudes for varactor topologies such as antiseries or antiseries/antiparallel the two-tone input signal. By enforcing the amplitude of one configurations shown in Fig. 4(b) and (c) need to be employed. tone to be much smaller than that of the other tone, the capaci- The key approach to cancel the compression and blocking dis- tance variation will be dominated only by one of the distortion tortion is to have a proper combination of the – relation for contributions as suggested in (2). each varactor diode in relation to the chosen center-tap termina- In Fig. 3, the capacitance variation versus voltage amplitude tions at different (harmonic) frequencies, i.e., . has a slope of 2:1 in the logarithmic scale for both distortion For the antiseries configuration shown in Fig. 4(b), the RF cases, differing by a factor of two, which is in agreement signal is applied between the top and bottom terminals, while with the analytical result of (2). In the worst case condition, the center-tap terminal supplies a dc voltage to control the ca- a 40%–50% capacitance variation can occur in the single pacitance of the whole varactor stack. To separate the dc and RF varactor case, a capacitance change that can severely detune signals, the center-tap impedance must be much higher a varactor-based RF adaptive circuit. This phenomenon will than the ac impedance offered by the varactors themselves [i.e., be addressed in detail in Sections III and IV when considering ] at the fundamental frequencies, while being lower than the various distortion cancellation approaches with semicon- that of the varactor at dc for the purpose of biasing. ductor-based varactors. On the other hand, the center-tap impedances around the base- band and second harmonic frequencies ( , , III. LOW-CAPACITANCE VARIATION VARACTOR and ) are, in principle, selectable and this flexibility can CIRCUIT TOPOLOGIES be utilized to cancel the compression and blocking distortion When a single semiconductor diode with given – rela- without influencing the linear operation around the fundamental tion is used as a varactor, its capacitance variation due to the frequency. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

4 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES

current , which contains the third-order compression distortion term and the corresponding capacitance variation relative to the linear capacitance, can be written as

(3)

(4)

where Fig. 5. Cancellation mechanism of the third-order compression term with the transfer function of by using a high center-tap impedance (5) at the second harmonic frequency. (6)

TABLE II (7) OUT-OF-BAND IMPEDANCE SETTINGS FOR COMPRESSION DISTORTION CANCELLATION MECHANISM are the capacitance Taylor coefficients of each varactor diode with being the reverse applied voltage with a positive value, and and are the original linear current and capac- itance with infinitely small RF excitation. It is indicated in (3) that the current flowing through the varactors at the fundamental frequency is modulated by the third-order compression distor- tion product, which is a function of the amplitude of the applied voltage, resulting in capacitance variation, as shown in (4). By setting (4) to zero, we force the cancellation of the third-order compression distortion yielding an exponential relation for the varactor diode, i.e.,

(8) IV. VARACTOR CIRCUIT TOPOLOGY FOR THE CANCELLATION OF COMPRESSION DISTORTION where is the capacitance at zero bias and is the capaci- The compression distortion arises from the self-mixing of the tance grading coefficient. Note that any choice of and will in-band RF signal and is irrespective of the jammer signal. For yield perfect cancellation of the third-order compression term this reason, the focus of the analysis should be on the mixing for Fig. 4(b), providing design flexibility for the tuning range products at dc, fundamental , and second harmonic and maximum control voltage for the varactor diodes. frequencies. In Table II, possible combinations of the center-tap As a proof of cancellation, the proposed compression dis- and varactor impedances at dc and second harmonic frequency tortion cancelled topology [see Fig. 4(b)] is simulated in com- are listed for the circuit of Fig. 4(b) to achieve cancellation of parison with a conventional single diode [see Fig. 4(a)] using compression distortion. From the practical implementation per- the ADS harmonic-balance simulator. The varactor is excited spective, the entry of is not possible because by a single-tone voltage signal in order to test the influence the varactor impedance itself approaches infinity at dc. With of the compression distortion. In Fig. 6, the resulting capaci- this in mind, the analysis can be performed for the remaining tance variation of the proposed topology exhibits a slope of 4:1 condition of . It reveals that the compression versus voltage amplitude in contrast to the slope of 2:1 for the distortion component is composed of the direct mixing product case of the single diode. This 4:1 slope indicates that the capac- of the fundamental signal itself and the indirect mixing product itance variation is dominated by the remaining much smaller between the fundamental signal and the second-order mixing fifth-order compression distortion due to the successful cancel- product at the second harmonic frequency with the mechanism lation of the third-order compression product. As a result, the illustrated in Fig. 5. Considering the fact that there is no dc proposed topology has a maximum simulated capacitance vari- second-order mixing product available at the center-tap node, ation below 0.25% compared to 20 for the conventional we need to utilize the second-order mixing component at to single diode. cancel the third-order direct and indirect mixing products (see To illustrate the reduced sensitivity for detuning when using Fig. 5). Therefore, the center-tap impedance must be higher these improved varactor components, a high- tunable LC par- than that of the varactor impedance at the second harmonic allel resonator with a resonance frequency of 2 GHz (see the frequency [i.e., ]. The Volterra series has schematic in the inset of Fig. 7) is created. The conventional been solved assuming a single-tone voltage excitation, where single diode [see Fig. 4(a)] and the compression distortion can- the varactor is implemented with the antiseries topology shown celled topology [see Fig. 4(b)] are used as the tunable element, in Fig. 4(b). The center-tap impedance is set to be much higher respectively, for comparison. The reverse dc control voltage of than the varactor impedance at while the dc center-tap the diodes is fixed to 5 V, while the input RF voltage is varied impedance remains much lower. The resulting capacitive from 0 to 5 V to test the frequency shift of the resonator. In This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

HUANG et al.: ON THE COMPRESSION AND BLOCKING DISTORTION OF SEMICONDUCTOR-BASED VARACTORS 5

TABLE III IMPEDANCE SETTINGS FOR DIFFERENT BLOCKING DISTORTION CANCELLATION MECHANISMS

V. V ARACTOR CIRCUIT TOPOLOGIES FOR THE CANCELLATION OF BLOCKING DISTORTION

Fig. 6. Simulated capacitance variation relative to the linear capacitance in per- In contrast to the self-mixing induced compression product, centage for the single diode [see Fig. 4(a)] and third-order compression dis- the desired quasi-static capacitance of the varactors can be also tortion cancelled topology [see Fig. 4(b)]. The diodes all have an exponential modulated by the blocking distortion due to the existence of – relationship: V and dc reverse control voltage V. pF for the single diode and pF for the third-order com- adjacent interferers. The blocking distortion product present at pression distortion cancelled topology. arises from the direct mixing of the signals at the funda- mental frequencies (i.e., and ) and the indirect mixing be- ween the fundamental tones and the second-order intermodu- lation terms at and . The approach to cancel the blocking distortion component is to compensate the direct mixing product with the indirect mixing product through the use of a three-terminal varactor device such as the antiseries topology shown in Fig. 4(b) with an appropriate combination between the – relationship for the varactor diodes and the center-tap impedance. Compared to the cancellation of the com- pression distortion where the dc center-tap impedance must be low for biasing, it is now the baseband center-tap impedance at instead of dc that plays a dominant role. Therefore, the baseband impedance provides a degree of freedom in the cancel- lation of the blocking distortion. In Table III, possible combina- tions of center-tap and varactor impedance at and are listed for the cancellation of blocking distortion. Note that there will be no cancellation possible when using low center-tap Fig. 7. Simulated resonance frequency variation of the varactor-based LC par- impedance both at baseband and around the second harmonic allel resonator using a single diode and a third-order compression distortion cancelled topology. The diodes all have an exponential – relationship: frequencies, due to the absence of the indirect mixing products. V and dc reverse control voltage V. pF for Setting one of the baseband or second-harmonic center-tap im- the single diode and pF for the third-order compression product can- pedances to a relatively low value while keeping the other at celled topology. The of the 2.1-nH is set to 500 at 2 GHz. a relatively high value results in the cancellation mechanism showninFig.8(a)and(b).WhensolvingtheVolterraseries,the capacitive current flowing through the varactor stack at Fig. 7, the shift of the resonance frequency of a parallel LC res- that contains the third-order blocking product, and the corre- onator is plotted for the conventional single diode and the com- sponding capacitance variation relative to the linear pression distortion cancelled topology using the same single- capacitance can be written as tone excitation. It reveals that the detuning of the parallel LC resonator is practically eliminated when using the third-order (9) compression distortion cancelled topology. The inset of Fig. 7 highlights the impedance of the resonator in the region close to 2 GHz and it exhibits a resonance frequency shift as small as (10) 2 MHz in the worst case, in contrast to the 175-MHz resonance frequency shift that is found for the resonator using a conven- By solving the differential equation, the required condition tional single diode. to cancel the blocking product will again yield the exponential This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

6 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES

(13)

where is the build-in voltage for varactor diode. Thus far, the antiseries configuration [see Fig. 4(b)] has been used to cancel the compression and blocking distortions. A brief review of the cancellation conditions for the antiseries config- uration reveals that different choices for the center-tap termi- nations can require different – relations, among which the exponential – relationship is the most common solution. This indicates that the antiseries configuration with an exponen- tial – relation can be used in many conditions, except when the center-tap impedance is high at both out-of-band frequen- cies, i.e., and . In this case, varactor diodes with a capacitance power law coefficient of are required, which corresponds to a different doping profile for the varactor diodes, making it more complicate to address all possible varactor so- lutions within a single technology. To address this problem, the antiseries/antiparallel configu- ration of Fig. 4(c) can be used. The antiseries branch with the area ratio of for the varactor diodes redistributes the roles of the direct and indirect mixing products in the mech- anism shown in Fig. 8(c) and enables the exponential – relationship for the cancellation of third-order blocking distor- tion when both out-of-band impedances at and are set to high values. The second antiseries pair with reverse area ratio cancels the even-order nonlinear cur- Fig. 8. Different mechanisms to cancel the third-order blocking distortion rent within the varactor structure and therefore no second-order terms with the conditions listed in Table III. (a) Cancellation mechanism of voltage components will develop across the varactor structure third-order blocking term by using relatively low center-tap impedance at during practical applications, avoiding the secondary mixing and high center-tap impedance at . (b) Cancellation mechanism of third-order blocking term by using relatively high center-tap impedance at that may lead to capacitance variation. By setting the center-tap and low center-tap impedance at . (c) Cancellation mechanism impedance to infinity at both and and using an of third-order blocking term by using relatively high center-tap impedance both exponential – relationship as (8) for the varactor diodes, at and . the current and capacitance variation are given by

relationship. Note that the mechanisms that set one of (14) the out-of-band center-tap impedances at or to a lower value and the other to a higher value [see Fig. 8(a) and (b)] yield identical results, basically because both out-of-band termi- where , nations play the same role in generating the third-order indirect mixing product. (15) On the other hand, when high center-tap impedances are used for and , the cancellation mechanism of Fig. 8(c) can be realized and the resulting current and capacitance varia- which leads to the required area ratio for the cancellation tion are given by of the third-order products, namely,

(16) (11) The resulting antiseries/antiparallel topology with the diode area ratio of (16) allows use of the diode with an exponential (12) – relation when both out-of-band impedances are set to high values, extending the application fieldofsuchadiode. By setting (12) to 0, we can find the required relation To prove the cancellation, the blocking distortion cancelled for the varactor diode to cancel the third-order blocking distor- topologies [see the mechanisms showninFig.8(a)–(c)]aresim- tion component. The required capacitance is ulated and compared with a conventional single diode using the This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

HUANG et al.: ON THE COMPRESSION AND BLOCKING DISTORTION OF SEMICONDUCTOR-BASED VARACTORS 7

Fig. 9. Simulated capacitance variation at in percentage for the single diode and third-order blocking distortion cancelled topologies. pF for the single diode, pF for the Fig. 4(b) topologies. pF and for the Fig. 4(c) configuration. GHz, GHz, V , V, and dc reverse control voltage V. is set to 0.01 V and it is much smaller than .

ADS harmonic-balance simulator. For fair comparison, the var- actor diodes used in the simulation are normalized to have iden- tical capacitance tuning ratio of 11:1 and a maximum control voltage of 10 V. In this test, a two-tone voltage signal is applied to the schematic shown in Fig. 2. The voltage amplitude of the wanted tone at is set to a much smaller value (0.01 V) than the amplitude of the jammer tone at . Under this condition, the blocking distortion component due to the adjacent jammer becomes the dominant contributor to the nonlinear current and capacitance variation. Fig. 9 plots the capacitance variation at versus the amplitude of the jammer signal at .For the blocking distortion cancelled topologies, the slope of 4:1 Fig. 10. Resonance frequency variation due to the RF jammer signal. (a) LC versus voltage amplitude is observed in contrast to the slope resonators using the single diode and four blocking distortion cancelled topolo- gies. pF, and V for the single diode. (b) LC res- of 2:1 for the case of the single diode. The 4:1 slope confirms onator using the antiseries blocking distortion cancellation topology with low the successful cancellation of the third-order blocking distor- ,high , and exponential relationship for the tion, yielding much smaller capacitance variation. varactor diodes. pF, V .(c)LC resonator using the antiseries blocking distortion cancellation topology with high , To investigate the blocking distortion induced detuning phe- low , and exponential relationship for the varactor diodes. nomenon, a two-tone voltage signal is applied to the resonator, pF, V .(d)LC resonator using the antiseries blocking where the jammer frequency is located at 2.1 GHz with distortion cancellation topology with high ,high , and for the varactor diodes. pF, varying RF amplitude . The amplitude of the in-band signal V. (e) LC resonator using the antiseries/antiparallel blocking distortion at is set to a value much smaller than in order cancellation topology with high ,high , and exponential to suppress the influence of compression distortion. The reso- relationship for the varactor diodes. pF, V , and . For all resonators, dc reverse control voltage V and the nance frequency shift of a parallel LC resonator is plotted in of the 2.1-nH inductor is 500 at 2 GHz. issetto0.01Vandismuchsmaller Fig. 10(a) for the conventional single diode and the blocking than . distortion cancelled topologies using the same two-tone exci- tation. Much smaller frequency shifts have been found for the blocking distortion cancelled topologies. Fig. 10(b)–(e) high- cancelled topologies in the region close to 2 GHz and it indicates lights the impedance of the resonators using different blocking that the resonance frequency shifts of the parallel resonators are This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

8 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES

TABLE IV BLOCKING DISTORTION CANCELLED TOPOLOGIES,COMPRESSION DISTORTION CANCELLED TOPOLOGY, AND IM3 CANCELLED TOPOLOGIES

typically less than 8 MHz, compared to 300-MHz frequency becomes difficult to fulfill when the frequency spacing shift for the single diode based resonator. It is worth mentioning becomes very large. that the topology using relatively higher center-tap impedance at On the other hand, when considering the transmitter situation, both and with the mechanism shown in Fig. 8(c) the transmit signal is normally the strongest signal, while other outperforms the rest of the topologies in terms of blocking due jammer interferers are most likely much lower in power. There- to its smaller fifth-order distortion coefficient and transfer func- fore, in this case, the most troublesome detuning issue comes tion. In the worst case, its resulting resonance frequency shift is from the compression distortion. In view of this, the compres- as small as 1 MHz and this property is potentially useful for sion cancelled topology in Table IV is best suited for trans- the most challenging high- filter/duplexer applications subject mitter applications. Through the comparison in Table IV with to high-power jammer signals. the previously published cancelled topologies [12]–[14], it is found that this (highlighted) topology cancels not only the compression and blocking distortion, but also the intermodu- VI. SUMMARY AND COMPARISON OF VARACTOR TOPOLOGIES lation distortion. This property suggests that this topology is In Table IV, the proposed RF power insensitive varactors with also advantageous in terms of much smaller intermodulation the cancellation of the detuning related compression or blocking distortion. In addition, this topology is also potentially useful distortions are summarized. for modern systems that simultaneously transmit signals in mul- For receiver applications, the input signal is typically small tiple bands. In these circumstances, the signals in the different in power 30 dBm while the jammer blocking signals can frequency bands may be regarded by each other as jammers, be much larger at a relatively large frequency spacing (e.g., and therefore the blocking distortion becomes also important MHz). In such conditions, the blocking distortion plays a for transmitters. major role in detuning resonators. In view of this, the first three blocking distortion cancelled topologies (configuration 1–3) in VII. EXPERIMENTAL RESULTS Table IV that require large center-tap impedance at are To evaluate the capacitance variation of the varactor due most suited for adaptive receivers. This can be understood by to the presence of RF signals, an active load–pull system considering the cancelation condition at in these config- [19], [20] is used and the simplified schematic is shown in urations (center tap impedance much larger than the varactor Fig. 11. In this test, the source impedance and load impedance impedance at baseband), which is relatively easy to fulfill at are fixed at 50 . The capacitance of the varactor large tone-spacing. This is in contrast to the configuration that can be accurately extracted through the measured reflection makes use of the complementary solution (center tap impedance coefficient under different RF excitations. Considering the fact much smaller than the varactor impedance at ), which that the varactor under test shares the voltage node with the This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

HUANG et al.: ON THE COMPRESSION AND BLOCKING DISTORTION OF SEMICONDUCTOR-BASED VARACTORS 9

Fig. 11. Measurement setup used to evaluate the capacitance variation of the varactor due to the compression and blocking distortion.

Fig. 13. Measured and simulated capacitance variation versus output RF power for the single diode and third-order compression distortion cancelled topology. DC reverse control voltage V. For the simulation, an ideal exponential – relationship is used. pF for the single diode and pF for the third-order compression distortion cancelled topology. V .

therefore the compression distortion can be solely evaluated. Fig. 13 plots the measured and simulated capacitance vari- ation in percentage with respect to the low-power condition average output power 2dBm as a function of output power. It shows that the compression distortion cancelled topology outperforms the single diode to a large degree. For the single diode, the measurement data match the simulation Fig. 12. (a) Microphotograph and schematic of third-order compres- sion/blocking/intermodulation distortion cancelled varactor circuit. results quite well, while the measured capacitance variation of (b) Microphotograph and schematic of a single diode. the compression distortion cancelled topology are typically less than 0.1%, a level close to the measurement limitation of the characterization system and sufficient for many RF applications load impedance (i.e., in Fig. 11), the output power on such as high- tunable resonators. the 50- load impedance is used to monitor the RF voltage across the varactor. As discussed in Section VI, the highlighted B. Cancellation of Blocking Distortion varactor configuration in Table IV cancels all of the important For the test of capacitance variation due to blocking distor- distortions, and therefore is chosen as the representative for the tion, a two-tone RF signal is used for the schematic shown in compression and blocking distortion cancelled topology. The Fig. 11. In this test, the tone power at is set to a relatively varactor sample is implemented within Skyworks Solutions low level, and therefore the blocking jammer signal at be- Inc.’s GaAs technology [see schematic and microphotograph in comes the main contributor to the capacitance variation at . Fig. 12(a)] and previously showed a successful cancellation of Fig. 14 plots the measured and simulated capacitance variation intermodulation distortion [21]. In this paper, the measurement at with respect to the low-power condition as a function of focus will be on the capacitance variation due to compression the output power at . It suggests that the measured capaci- and blocking distortions. As a counterpart for comparison, a tance variation of the blocking distortion cancelled topology is single diode [see Fig. 12(b)] is implemented on the same wafer 100 times better than that of the single diode at the large output and experimentally tested as well. The implemented varactor power levels. In Fig. 15, the capacitance variation at is plotted diodes all have exponential – relationship with the tuning versus the reverse control voltage with the jammer output power range of 9:1 over a reverse control voltage range from 0 to 15 V at fixed as 20 dBm. It indicates that the blocking distortion [21]. cancelled topology provides a capacitance variation less than 0.5% for the whole exponential – operating range. Under A. Cancellation of Compression Distortion such RF excitation, the blocking distortion cancelled topology To test the capacitance variation due to compression dis- offers a larger effective tuning range ( 6.5 1 over the control tortion, the single-tone RF power at 2 GHz is applied to the voltage range of 0.8–11 V) associated with much smaller ca- schematic in Fig. 11. With the use of a single-tone signal, pacitance variation than that of the single diode, a property at- the blocking distortion due to a jammer signal is absent, and tractive for many RF applications. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

10 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES

tortions has been selected and implemented within Skyworks Solutions Inc.’s GaAs technology. The measurements provide experimental evidence for the predicted cancellation of the compression and blocking distortion, yielding a measured capacitance variation in the order of 0.1 0.5 under large RF excitation. This result is 100 times better than that of the conventional single diode, and therefore very attractive for the RF applications such as high- tunable resonators. Future RF adaptive circuitry using these proposed devices will suffer less from detuning issues, making semiconductor-based varactor an appropriate choice for many large-signal RF applications.

ACKNOWLEDGMENT The authors acknowledge Skyworks Solutions Inc., Newbury Park, CA, for processing the varactor samples. The authors would like to thank S.-J. Park, J. Kim, and C. Zuo, all with Qualcomm Inc., San Diego, CA, for valuable discussions. The authors further acknowledge Anteverta Microwave, Delft, The Fig. 14. Measured and simulated capacitance variation at (1.999 GHz) with respect to the low-power condition versus the output RF power at (2 GHz) for Netherlands, for measurement support. the single diode and third-order blocking distortion cancelled topology. Under the low-power condition, the jammer signal at is turned off and the output REFERENCES power at is kept as 2 dBm. DC reverse control voltage equals to 5 V. For the simulation, ideal exponential – relationship is used. pF for the [1] L. Dussopt and G. M. 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De Man, “An analytic volterra-series-based model for a MEMS variable ,” IEEE Trans. Comput.-Aided Design Integr. Cir- cuits Syst., vol. 22, no. 2, pp. 131–241, Feb. 2003. [6] B. Razavi, RF Microelectronics. Upper Saddle River, NJ: Prentice- Hall, 1998, ch. 2. [7]P.WambacqandW.M.Sansen, Distortion Analysis of Analog Inte- grated Circuit. Norwell, MA: Kluwer, 1998. [8]X.Liu,L.P.B.Katehi,W.J.Chappell,andD.Peroulis,“Powerhan- dling of electrostatic MEMS evanescent-mode (EVA) tunable band- pass filters,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 2, pp. 270–283, Feb. 2012. Fig. 15. Measured and simulated capacitance variation at (1.999 GHz) with [9] J. S. Fu, X. A. Zhu, J. D. Phillips, and A. Mortazawi, “Improving lin- respect to the low-power condition versus reverse control voltage for the single earity of ferroelectric-based microwave tunable circuits,” IEEE Trans. diode and third-order blocking distortion cancelled topology. In this test, the Microw. Theory Techn., vol. 55, no. 2, pp. 354–360, Feb. 2007. output RF power at 2 GHz is kept as 20 dBm. Under the low-power condi- [10] J. S. Fu, X. A. Zhu, D. Y. Chen, J. D. Phillips, and A. Mortazawi, “A tion, the jammer signal at is turned off and the power available from the linearity improvement technique for thin-film barium strontium titanate source at is 2 dBm. Note that the simulation is based on the fitted – mea- capacitors,” in IEEEMTT-SInt.Microw.Symp.Dig., San Francisco, surement data and the – deviates from the exponential relation at 12.5 V. CA, Jun. 2006, pp. 560–563. pF for the single diode and pF for the third-order blocking [11] R. G. Meyer and M. L. Stephens, “Distortion in variable-capacitance distortion cancelled topology. diodes,” IEEE J. Solid-State Circuits, vol. SC-10, no. 2, pp. 47–55, Feb. 1975. [12] K. Buisman, L. C. N. de Vreede, L. E. Larson, M. Spirito, A. Akhnoukh, T. L. M. Scholtes, and L. K. Nanver, “Distortion free VIII. CONCLUSIONS varactor diode topologies for RF adaptivity,” in IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, Jun. 2005, pp. 157–160. For the first time, the fundamental mechanisms that induce [13] C. Huang, L. C. N. de Vreede, F. Sarubbi, M. Popadić,K.Buisman,J. capacitance variation of semiconductor varactors under large Qureshi, M. Marchetti, A. Akhnoukh, T. L. M. Scholtes, L. E. Larson, RF excitation have been investigated. Both compression and and L. K. Nanver, “Enabling low-distortion varactors for adaptive transmitters,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 5, pp. blocking distortion may play a role in changing the capacitance. 1149–1163, May 2008. Based on this information, various varactor configurations have [14] C. Huang, K. Buisman, M. Marchetti, L. K. Nanver, F. Sarubbi, M. been proposed to cancel the third-order compression and Popadić,T.L.M.Scholtes,H.Schellevis,L.E.Larson,andL.C.N.de Vreede, “Ultra linear low-loss varactor diode configurations for adap- blocking distortion. For the experimental verification, the tive RF systems,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 1, varactor configuration that cancels all of the important dis- pp. 205–215, Jan. 2009. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

HUANG et al.: ON THE COMPRESSION AND BLOCKING DISTORTION OF SEMICONDUCTOR-BASED VARACTORS 11

[15] W. C. E. Neo, Y. Lin, X. D. Liu, L. C. N. de Vreede, L. E. Larson, M. Peter J. Zampardi (S’93–M’96–SM’02) received Spirito, M. J. Pelk, K. Buisman, A. Akhnoukh, A. de Graauw, and L. the B.E. degree in engineering physics from the K. Nanver, “Adaptive multi-band multi-mode power amplifier using Stevens Institute of Technology, Hoboken, NJ, in integrated varactor-based tunable matching networks,” IEEE J. Solid- 1986, the M.S. degree in applied physics from the State Circuits, vol. 41, no. 9, pp. 2166–2176, Sep. 2006. California Institute of Technology, Pasadena, in [16] K. Buisman, L. C. N. de Vreede, L. E. Larson, M. Spirito, A. 1988, and the Ph.D. degree from the University of Akhnoukh, Y. Lin, X. D. Liu, and L. K. Nanver, “A monolithic California at Los Angeles (UCLA), in 1997. low-distortion low-loss silicon-on-glass varactor-tuned filter with While with the California Institute of Technology, optimized biasing,” IEEE Microw. Wireless Compon. Lett.,vol.17, he studied molecular-beam epitaxy (MBE)-grown no. 1, pp. 58–60, Jan. 2007. GaAs/AlGaAs structures and investigated tellurium [17] J. H. Qureshi, S. Kim, K. Buisman, C. Huang, M. J. Pelk, A. Akhnoukh, clustering in ZnSe:Te for use in visible light emit- L.E.Larson,L.K.Nanver,andL.C.N.deVreede,“Alow-losscom- ters. In 1988, he joined the Ring Laser Gyroscope Test Laboratory Rockwell pact linear varactor based phase-shifter,” in IEEE Radio Freq. Integr. Science Center, where he was responsible for development and testing of Circuits (RFIC) Symp., Honolulu, HI, Jun. 2007, pp. 453–456. ring laser gyros for use in inertial measurement units. In 1990, he joined the [18] K. Buisman, C. Huang, P. J. Zampardi, and L. C. N. de Vreede, “RF Optics Technology Department, Rockwell Science Center, where he developed power insensitive varactors,” IEEE Microw. Wireless Compon. Lett., processes and procedures for the characterization and fabrication of infrared vol. 22, no. 8, pp. 418–420, Aug. 2012. (IR) etalon filters. In 1991, he joined the High Speed Circuits Department, [19] M.Spirito,M.J.Pelk,F.vanRijs,S.J.C.H.Theeuwen,D.Hartskeerl, Rockwell Science Center, where he performed device and circuit development, and L. C. N. de Vreede, “Active harmonic load–pull for on-wafer characterization, and modeling of GaAs, InP, and SiGe HBTs, and MESFET, out-of-band device linearity optimization,” IEEE Trans. Microw. HEMT, BiFET, and RTD technologies. In 1999, he led the technical develop- Theory Techn., vol. 54, no. 12, pp. 4225–4236, Dec. 2006. ment of SiGe RF models for the Analog and Mixed Signal Foundry business [20] M. Marchetti, M. J. Pelk, K. Buisman, W. C. Edmund, M. Spirito, and of IBM, Burlington, VT. Since 2000, he has been with Skyworks Solutions L. C. N. de Vreede, “Active harmonic load–pull with realistic wideband Inc., Newbury Park, CA, where he is Technical Director for Device Design, communication signals,” IEEE Trans. Microw. Theory Techn., vol. 56, Modeling, and Characterization. The group’s interests are technologies, char- no. 12, pp. 2979–2988, Dec. 2008. acterization, modeling, and circuit design for wireless applications. He has [21]C.Huang,P.J.Zampardi,K.Buisman,C.Cismaru,M.Sun,K. authored or coauthored over 170 papers related to circuits and devices and two Stevens, J. Fu, M. Marchetti, and L. C. N. de Vreede, “A GaAs book chapters. He holds six U.S. patents. junction varactor with a continuously tunable range of 9:1 and an Dr. Zampardi actively participates in several IEEE technical conference com- of 57 dBm,” IEEE Electron Device Lett., vol. 31, no. 2, pp. mittees. 108–110, Feb. 2010.

Lawrence E. Larson (S’82–M’86–SM’90–F’00) Cong Huang (S’07–M’12) was born in Shanghai, received the B.S. degree in electrical engineering China, in 1980. He received the B.S. degree in micro- from Cornell University, Ithaca, NY, and the Ph.D. from Fudan University, Shanghai, China, degree from the University of California at Los in 2002, the M.Sc. degree (with honors) in micro- Angeles (UCLA). electronics from the Delft University of Technology, From 1980 to 1996, he was with Hughes Research Delft, The Netherlands, in 2005, the M.Sc. degree in Laboratories, Malibu, CA, where he directed the microelectronics from Fudan University, in 2005, and development of high-frequency microelectronics the Ph.D. degree from the Delft University of Tech- in GaAs, InP, Si/SiGe, and MEMS technologies. nology, in 2010. In 1996, he joined the faculty of the University of He is currently, he a Postdoctoral Researcher/As- California at San Diego (UCSD), La Jolla, where he sistant Professor with the Delft University of Tech- was the inaugural Holder of the Communications Industry Chair. From 2001 nology. In 2001, he joined the State Key Laboratory of ASIC and System, to 2006, he was Director of the Center for Wireless Communications, UCSD. Fudan University, where he developed piezoelectric-material-based cantilevers From 2007 to 2011, he was chair of the Department of Electrical and Computer for microelectromechanical systems (MEMS) applications. In 2003, he joined Engineering, UCSD. In 2011, he joined Brown University, Providence, RI, the Laboratory of High Frequency Technology and Components (HiTeC), Delft where he is Founding Dean of the School of Engineering. During the academic University of Technology, where he developed low phase-noise voltage-con- year from 2000 to 2001, he was on leave at IBM Research, San Diego, CA. trolled oscillators for RF applications. Since 2006, he has been with the Elec- During the academic year from 2004 to 2005 , he was a Visiting Professor with tronics Research Laboratory (ELCA), Delft University of Technology, where he the Delft University of Technology, Delft, The Netherlands. He has authored is involved with high-performance varactors for RF adaptivity and the develop- or coauthored over 300 papers. He coauthored three books. He holds 40 U.S. ment of RF integrated circuits (RFICs) for next-generation wireless systems. patents. Dr. Huang was the recipient of the 2010 Else Kooi Prize (Dutch best Ph.D. Dr. Larson was the recipient of the 1994 Hughes Sector Patent Award for thesis in microelectronics). In 2011, he was recognized for academic excellence his work on RF MEMS. He was a corecipient of the 1996 Lawrence A. Hyland and received a VENI Grant from the Dutch Scientific Foundation (NWO). Patent Award of Hughes Electronics for his work on low-noise millimeter-wave high electron-mobility (HEMTs) and the 1999 IBM Microelectronics Excellence Award for his work on Si/SiGe HBT technology.

Koen Buisman (S’05–M’09) received the M.Sc. and Ph.D. degrees in microelectronics from the Delft University of Technology, Delft, The Netherlands, LeoC.N.deVreede(M’01–SM’04) was born in in 2004 and 2011, respectively. Delft, The Netherlands, in 1965. He received the He is currently a Postdoctoral Researcher with the B.S. degree (cum laude) in electrical engineering Delft University of Technology. Since 2004, he has from The Hague Polytechnic, The Hague, The been with the Delft Institute of Microsystems and Netherlands, in 1988, and the Ph.D. degree (cum Nanoelectronics (DIMES), Delft University of Tech- laude) from the Delft University of Technology, nology, where he was involved in the development Delft, The Netherlands, in 1996. of a pulsed dc and RF measurement system, an active In 1988, he joined the Laboratory of Telecom- harmonic load–pull system and the development of munication and Remote Sensing Technology, a custom in-house DIMES technology for high performance “distortion-free” Department of Electrical Engineering, Delft Uni- varactors. From March 2009 to February 2010, he contributed to the develop- versity of Technology. From 1988 to 1990, he was ment of extremely shallow junctions for EUV . He has authored involved in the characterization and physical modeling of ceramic multilayer or coauthored over 30 refereed journal and conference papers. His research capacitors (CMCs). From 1990 to 1996, he was involved with the modeling interests are varactors for RF adaptivity, nonlinear device characterization, and and design aspects of high-frequency (HF) silicon integrated circuits (ICs) technology optimization for wireless systems. for wideband communication systems. In 1996, he became an Assistant This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

12 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES

Professor with the Delft University of Technology, where he is involved with visor of Anteverta-mw. He has coauthored over 80 IEEE refereed conference the nonlinear distortion behavior of bipolar transistors with the Delft Institute and journal papers. He holds several patents. His current interest includes of Microsystems and Nanoelectronics (DIMES). In Winter 1998–1999, he RF measurement systems, technology optimization, and circuit concepts for was a guest with the High Speed Device Group, University of San Diego, San wireless systems. Diego, CA. In 1999, he became an Associate Professor responsible for the Dr. de Vreede was a corecipient of the 2008 IEEE Microwave Prize. He was Microwave Components Group, Delft University of Technology, where, since mentor of the Else Kooi Prize awarded Ph.D. work in 2010 and a mentor of the that time, he has been involved with RF solutions for improved linearity and Dow Energy Dissertation Prize awarded Ph.D. work in 2011. RF performance at the device, circuit, and system levels. He is cofounder/ad-