THE popularity of cellular communications and wireless

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1 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 41, NO. 9, SEPTEMBER A Low-Voltage Broadband Feedforward-Linearized BJT Mixer Su-Tarn Lim, Student Member, IEEE, and John R. Long, Member, IEEE Abstract A low-voltage, feedforward-linearized bipolar mixer realizes an input IP 3 of+14.3 dbm and an input IP 2 of+54.5 dbm at 2.4 GHz. Conversion (power) gain over the 1 6 GHz RF input range is db, while the input IP 3 is dbm over the same frequency range. The broadband mixer s RF input impedance varies from 60.3-j7.1 at 2.4 GHz to 57.4-j16.6 at 5.8 GHz. Measured SSB (50 ) noise figure is 18.6 db at 2.4 GHz. No on-chip inductors are used in the design, and the 0.14 mm 2 (active area) mixer dissipates 7.2 mw from a (minimum) 1.2 V supply. Index Terms Active mixer, BiCMOS, distortion cancellation, feedforward linearization, SiGe-HBT, silicon radio frequency integrated circuits, third-order input intercept point (IIP 3 ). I. INTRODUCTION THE popularity of cellular communications and wireless local-area networking (WLAN) is increasing the number of users sharing the same frequency spectrum, leading to greater interference levels and lower data throughput because of bit-error limitations. The number of frequency channels available for reuse in a geographic area can be increased by reducing cell sizes. However, this also increases the number of base-stations, and may not be possible when users and their wireless devices share the same office space and expect a reasonable quality of service within m of the same base-station. The problem is exacerbated by new devices using standards that share existing frequency bands and interfere with each other (e.g., IEEE a and a multiband-ofdm ultrawideband). Radio frequency integrated circuits with wide dynamic range and in particular, higher linearity as well as low power consumption are needed to satisfy the constraints imposed by new and evolving portable wireless systems. Fig. 1 illustrates a receiver front-end which supports the b/g, WCDMA, and Group A of the a ultrawideband (UWB) standard. Each standard is provided with its own antenna interface, preselect bandpass filter and low-noise amplifier (LNA) to simplify antenna interfacing and minimize radio-frequency (RF) signal loss between the antenna and LNA input. When all standards share the same mixer and baseband processing circuits, the receiver circuit complexity, parts count and current consumption are all reduced. However, Manuscript received January 5, 2006; revised May 12, This work was supported by the Philips Associated Center at DIMES (PACD). The authors are with the Electronics Research Laboratory/DIMES, Delft University of Technology, 2628 CD Delft, The Netherlands ( s.t.lim@ewi. tudelft.nl). Digital Object Identifier /JSSC the mixer must be capable of operating over a wide range of frequencies and meeting the diverse requirements imposed by multiple standards. The linearity of a radio receiver such as the one shown in Fig. 1 is typically limited by the intermodulation (IM) distortion generated by the first downconverting mixer. Therefore, the mixer must be designed so that its linearity is as high as possible given the supply current/power consumption budget (as linearity and current consumption are usually related). On the other hand, the noise figure target for the mixer may be relaxed when it has sufficient RF-IF gain to suppress baseband noise. This is becoming more feasible as the noise performance of integrated LNAs continues to improve. For example, a mixer with 12 db conversion gain and a double sideband noise figure of 16.5 db (or better) can meet an overall noise figure target for the receiver of 7 db (e.g., for 3G-WCDMA [1]) when the LNA gain and noise figure are 18 db and 1.5 db, respectively. This estimate assumes 3 db loss both before and after the LNA from bandselect filters and other interfacing components. Considering other design aspects, the mixer should maintain robust IM performance at low supply voltages (approaching 1 V for production CMOS). On-chip inductors, which are often used to improve linearity in a mixer, should be avoided if possible because the die area they consume (which may be on the order of transistor equivalents) increases the cost of the radio. Moreover, the mixer should be robust to processing variations and operating temperature shifts. The mixer s RF input impedance should also be close to 50 (broadband) to reduce the components and cost required for a broadband impedance matching network. However, higher impedance levels may be chosen in applications where filtering between the LNA and downconverting mixer and hence a 50 RF interface is not required (e.g., low-if or direct conversion receiver). The most widely used mixer in silicon IC technology is the Gilbert modulator [2], which consists of a differential input amplifier cascoded by a 4-transistor commutating (or quad) circuit. The RF input to the mixer is converted to current by the input pair and then fed to the quad, which is driven by the local oscillator signal. The absolute minimum supply voltage for a bipolar implementation is approximately 2.7 V (two cascode stages biased by tail current sources), making it incompatible with the 0.13 m digital CMOS used in production today which is powered by a 1.2 V supply. IM distortion in the Gilbert modulator is typically limited by the RF input transconductance stage. Improving linearity compromises the conversion gain, current consumption, or noise figure of the mixer. For example, degeneration of the input pair reduces the mixer conversion gain, and complicates impedance matching by increasing the input impedance well above /$ IEEE

2 2178 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 41, NO. 9, SEPTEMBER 2006 Fig. 1. Multi-standard receiver front-end block diagram. Other input stages such as the Class-AB transconductor [3], [4] and multi-tanh input stages [5], as well as out-of-band terminations [6], [7] for harmonic currents have been developed to reduce the distortion and improve the dynamic range of the mixer. However, these alternatives suffer from drawbacks ranging from processing variations and mismatch resulting in sub-optimal linearity (for harmonic terminations), to bandwidth limitations giving rise to asymmetry and even-order distortion for Class-AB and multi-tanh stages. A new low-voltage balanced mixer circuit implemented in IBM s 120 GHz BiCMOS-7HP technology [8] is presented in this paper. Linearity (as measured by the third-order input intercept point, or IIP ) is improved by 4 db over previous circuit realizations through the use of feedforward cancellation of intermodulation distortion. The circuit is inherently broadband, so it can be applied up to 6 GHz, and beyond. The complete circuit (including bias sources) cascodes only two transistors between the supply rails, hence operation supply voltages as low as 1.2 V is possible in most bipolar technologies. Inductors or transformers are not employed, resulting in a very compact design that requires little chip area. A mixer RF-IF conversion gain greater than 12 db is realized using a modest IF load impedance of 470 (at each IF output) and bias current of 6 ma. In addition, the broadband RF input impedance is close to 50 (single-ended), simplifying impedance matching to off-chip components. The main disadvantage of the circuit is its relatively high noise figure (17 18 db SSB-50 ), which is a limitation for receiver, but not for transmitter applications. Section II of this paper briefly reviews the theory and sources of IM distortion in bipolar amplifiers and mixers necessary to understand the feedforward-linearized design. Section III presents the feedforward-linearized mixer circuit, which consists of parallel path mixers with distortion equal in magnitude but opposite in phase resulting in cancellation of the net IM distortion at the IF output. Experimental results for a prototype feedforward-linearized mixer are presented in Section IV, followed by a brief summary. II. BACKGROUND In the conventional Gilbert mixer [2], IM distortion is generated by both the input stage (typically a differential pair) and the mixing quad. Ignoring parasitic capacitances, the third-order intermodulation distortion present in the collector current ( )of the input pair depends upon the square of the differential input voltage ( ). The intercept point (IIP ) can be expressed in terms of input voltage (without emitter degeneration) as, where is the BJT thermal voltage ( ), which is 104 mv at room temperature [9]. This is equivalent to an IIP of 12.9 dbm across a matched (100 ) differential input, which is too low for most radio receiver applications. Since and are related, the intercept point may also be expressed as the ratio of AC and DC collector currents as, which makes it clear that lowering IM distortion requires an increase in bias current and consequently power consumption. The analysis of distortion in a complete mixer requires computer simulation, as the relationships between circuit variables in closed-form expressions are normally obscured by their complexity [10]. A. Feedback and Feedforward Amplifiers Using feedback, it is also possible to design amplifier circuits that have higher linearity, use less bias current, and maintain acceptable noise figure by exploiting the phenomenon of distortion cancellation [11]. It can be shown that third-order IM distortion in a common-emitter amplifier with emitter degeneration is cancelled when the product of transistor transconductance ( ) and degeneration resistance ( ) equals one-half, or. However, perfect cancellation is difficult to realize because of processing variations and component mismatches, even when all devices are fabricated on the same IC chip. Moreover, as the frequency of operation increases, other

3 LIM AND LONG: A LOW-VOLTAGE BROADBAND FEEDFORWARD-LINEARIZED BJT MIXER 2179 Fig. 3. Schematic of modified balanced mixer switching quad. Fig. 2. Schematic of cascade compensated (CasComp) transconductor [13]. sources of distortion (such as bias-dependent capacitors) begin to dominate, and make the local feedback ineffective in reducing the overall IM distortion. Distortion cancellation can also be implemented with a feedforward circuit topology. In the feedforward linearization method, distortion produced by a main and second error amplifier are designed to be equal in magnitude but opposite in phase so that they cancel each other when summed, producing a distortion-free output [12]. Another advantage of the feedforward technique for RF applications is its inherent broadband response [12]. An example of a feedforward-linearized amplifier is shown in Fig. 2. The cascode compensation (CasComp) transconductor [13] uses degenerated common-emitter and common-base stages operating as a parallel-path amplifier. Distortion produced by the base-emitter junctions of input pair is replicated across the base-emitter junctions of. Compensating transistor pair senses the signal across, amplifies it, and then add a compensating anti-phase signal to the collector currents of. The distortion magnitudes are matched by adjusting the gains of the two amplifiers. This requires appropriate selection of both bias currents and feedback resistance values (e.g., 25 /20 ma for and 17 /10 ma for from [13]). Sensitivity to processing variations and component mismatch in a CasComp stage is relatively low, because it depends upon the ratio of the amplifier gains and not on absolute component values. B. Local Feedback and Mixer Linearization Typically, an LO input many times the thermal voltage (e.g., mv-pk differential) is used to drive the switching quad of a balanced mixer (e.g., see Fig. 3). This reduces the period of time when all four transistors (i.e., ) are conducting, and as a result the quad behaves like a common-base amplifier between the RF (input) and IF (output) over most of the LO cycle. Therefore, one might expect intuitively that local feedback from emitter resistor would null or cancel the IM distortion in this mixer, similar to the distortion nulling observed in a common-base stage with local feedback. This is indeed possible, however, the IM distortion generated by the quad is a function of LO amplitude, transistor bias current and the transistor s emitter area in general [14]. As an example, the simulated third-order intermodulation distortion (IM3) phase (relative to the fundamental components) and IIP of the IF output current are plotted in Fig. 4 for the circuit of Fig. 3 as the feedback resistor varies. The transistors in the switching quad are biased at 4 ma and driven by a 235 mv-pk sinusoidal LO for the simulations. The results show that as the feedback increases (i.e., an increase in ), the IM3 components fall to zero (or null), thereby maximizing the mixer IIP. For example, the peak IIP is 9.8 dbm at an RF input frequency of 250 MHz. The behavior at higher frequencies is similar, but parasitic capacitances lower the maximum IIP and change the conditions required to null the IM distortion (e.g., peak IIP occurs at 163 instead of 172 when the frequency increases from 0.25 to 5.75 GHz). The effects of this process variation in the mixer IIP were analyzed using Monte Carlo analysis in Cadence Spectre. The nominal operating conditions of ma,, and mv-pk (single-ended) for the mixer of Fig. 3 produced the desired distortion cancellation and an IIP of 7.93 dbm. The IIP (for constant ) results obtained from the Monte Carlo simulations are plotted as a histogram in Fig. 5. IIP for the linearized mixer follows a Gaussian distribution with a mean of 8.30 dbm and standard deviation of 0.46 db.

4 2180 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 41, NO. 9, SEPTEMBER 2006 Fig. 5. Variation in IIP due to process variation (i.e., fast, normal, slow process) and mismatch from 500 Monte Carlo simulations of a single mixer with distortion nulling. Fig. 4. Phase of IM3 distortion and IIP versus degeneration resistance for the circuit of Fig. 3 (I =4mA and V =235mV-pk). III. FEEDFORWARD DISTORTION COMPENSATION Given the previous example of the CasComp stage and its utility as a linear broadband transconductor, feedforward-linearization of a balanced mixer was attempted in an effort to reduce IM distortion and circuit sensitivity to processing variations and component mismatch. A feedforward scheme used to linearize an amplifier cannot be adapted directly to a mixer because of the frequency translation in the signal path between RF input and IF output. In a classical feedforward linearization scheme, the error is derived from the output current (e.g., from the collector current of and in Fig. 2). If this were attempted in a mixer (i.e., at the IF output), then the original signal (i.e., from the RF input) could not be used to derive an estimate of the distortion without doing another frequency translation. This problem is avoided when the compensating signal is developed independent of the output by using a second, parallel signal path. The feedforward-linearized mixer of Fig. 6 uses two switching quads operating in parallel, where each mixer is producing equal amplitude but anti-phase IM distortion components. Local feedback does not affect the phase of the fundamental at the IF, so when the outputs from the two switching quads are connected in parallel, the fundamental components add in-phase giving a larger output. However, cancellation of the third-order IM distortion components occurs when the IM3 products produced by each mixer are anti-phase. This condition is set by appropriate selection of the bias currents and degeneration resistances (e.g., and in Fig. 6) for each mixer. Degeneration resistors add thermal noise to the RF input giving the mixer a relatively high noise figure. Inductors could be substituted to provide the necessary degeneration impedance because they do not (ideally) add thermal noise. However, inductive degeneration restricts the range of possible bias currents and device sizes where the phase shift between the two RF paths can be matched for IM cancellation, thereby restricting the RF input frequency range. In addition, resistors consume significantly less area than on-chip inductors. In an integrated receiver, the output impedance of the driving stage could also be used to degenerate the mixers (see Section V). Since the emphasis in this design was proof of concept for a broadband mixer with improved linearity, degeneration resistors are used in the following design. For validation of the feedforward-compensation concept, all transistors in the mixer of Fig. 6 were chosen to be m and the total bias current limited to 10 ma. Degeneration resistors were restricted to between 50 and 150 to limit the thermal noise contribution and voltage drop across them. Both mixers are (nominally) driven by a sinusoidal LO of 166 mv-pk at each base terminal, which ensures that the quads switch completely using an LO that is easily sourced from an on-chip oscillator in a wireless application. Feedforward compensation is realized by matching the IM3 magnitudes for mixers A and B. In simulation it was found that 75 and 120 for and, respectively, at a total bias current of 3 ma for mixer A and 5 ma for mixer B set this condition. This selection of degeneration resistors and bias currents gives approximately the same (50 ) input impedance for the two mixers. A differential IF load of 470 and a 2.2 V supply were used for these simulations. The fundamental and IM3 output powers versus the input power for the feedforwardlinearized mixer as well as each mixer individually are plotted in Fig. 7 (RF GHz and IF MHz). There is an

5 LIM AND LONG: A LOW-VOLTAGE BROADBAND FEEDFORWARD-LINEARIZED BJT MIXER 2181 Fig. 6. Feedforward-linearized mixer schematic. Fig. 7. Simulated RF to IF output versus input power for fundamental and thirdorder intermodulation distortion (f = 5:75 GHz, f = 5:60 GHz, 470 IF load, and 2.2 V supply). improvement of more than 7 db in IIP for the feedforward-linearized mixer (overall IIP dbm) compared to either mixer operated stand-alone. These simulations also show that the individual mixers and the feedforward-linearized mixer have approximately the same gain compression point. This is expected, because local feedback only affects distortion generated by the nonlinear transconductance of transistor. It does not affect distortion generated by waveform clipping, which is typically the source of gain compression. Linearity and conversion gain for the feedforward-linearized mixer from a simulation over the RF input frequency range Fig. 8. Simulated conversion gain and third-order intercept point versus frequency (470 IF load, 8 ma total bias current at 2.2 V supply). from 1 10 GHz are plotted in Fig. 8. The conversion gain is approximately 12.3 db at 1 GHz, and decreases gradually with increasing frequency to 11.7 db at 10 GHz. This slight drop in conversion gain is expected as parasitic capacitance dominates the high frequency response. When operated at a lower voltage supply, voltage/current clipping at the IF output lowers the db compression point. However, intermodulation distortion (dominated by nonlinearity of the active devices) remains essentially the same, so an IIP similar to what is achieved at higher supply voltages is expected. Similarly, the third-order output-referred intercept point (OIP ) is highest at lower frequencies; it is 31.6 dbm at 1 GHz and drops to 24.3 dbm at 10 GHz. Simulations predict

6 2182 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 41, NO. 9, SEPTEMBER 2006 Fig. 9. Variation in IIP due to process (i.e., fast, normal, slow) and mismatch from 500 Monte Carlo simulations of the feedforward-linearized mixer. that gain and phase mismatch in IM3 components generated by the two mixers are 0.2 db and 1 at 1 GHz, but increase to 1.7 db and 13 at 10 GHz. Distortion cancellation is affected as parasitic capacitances play a more significant role in the mixer s response at higher frequencies. A single Gilbert mixer operating at 8 ma bias current (3 V supply) is also simulated for comparison. The same LO swing (166 mv-pk) and IF load (470 ) are used. The conversion gain of the mixer is adjusted via a degeneration inductor to equal the feedforward mixer at 5.75 GHz (RF). Simulation predicts that the single mixer with a 10 nh degeneration inductor has a conversion gain and IIP of 12.2 db and dbm ( GHz), respectively. Linearity is still 3 db lower than the feedforward-linearized mixer at GHz, and deteriorates further as the RF decreases below 5.75 GHz. For example, at 2 GHz, simulation predicts a conversion gain and IIP of 20.4 db and 1.7 dbm, respectively, for the single mixer at 8 ma with the same 10 nh degeneration. On the other hand, the simulated IIP for the feedforward-linearized mixer is better than 12.6 dbm for frequencies ranging from 1 10 GHz. Results of Monte Carlo simulation of the complete feedforward-linearized mixer are plotted in Fig. 9 ( ma, and ma). The mean and standard deviation are 14.4 dbm and 0.75 db, respectively. Over 78% of the simulated results for IIP fall between 14 and 15 dbm. Unlike the mixer with feedback distortion nulling (see Fig. 5), the distribution is not Gaussian. This suggests that although the highest IIP cannot be obtained for all samples, high linearity (i.e., within 1 2 db of the max.) is still achieved for the majority of the simulation cases. The second-order intermodulation distortion (IM2) of the feedforward-linearized mixer (important in low/zero-if applications) is primary determined by component matching and the physical layout of the circuit. Monte Carlo simulation results for the mixer IIP (refer to Fig. 10) are Gaussian with a mean and standard deviation of dbm and 7.48 db, respectively. A similar analysis on the circuit of Fig. 3 designed for IM3 nulling gave similar results with a mean IIP of Fig. 10. Variation in IIP due to process (i.e., fast, normal, slow) and mismatch from 500 Monte Carlo simulations of the feedforward-linearized mixer compared to a single doubly balanced mixer with distortion nulling dbm and a standard deviation of 5.94 db, respectively. Fewer components give a slightly smaller spread for a single mixer. Even-order distortion and IIP may be reduced further by correcting for even-order mismatches using a scheme such as that proposed in [6]. IV. EXPERIMENTAL RESULTS The prototype mixer was characterized over the frequency range from 1 to 6 GHz. This covers the spectrum currently occupied by commercial wireless applications (including Groups A and B of IEEE a UWB). The experimental test set-up is shown in Fig. 11. Differential RF and LO signals are derived from single-ended generators using microwave power dividers and 0 /180 hybrid baluns. At the RF input, two differential signals are used such that the individual mixers can be biased individually. The mixer was configured as a downconverter for testing, so 5 pf filtering capacitors (included on-chip) are used to filter the unwanted (upper) sideband at the IF output. The mixer IF is AC coupled to two 470 single-ended loads ( ) and balun-coupled to single-ended test instruments (e.g., a spectrum analyzer). The prototype mixer including the I/O pads occupies mm while the active circuitry of the mixer occupies just m, as seen from the chip micrograph at the center of Fig. 11. The supply voltage was varied between 1.2 V and 2.2 V in testing, although most of the characterization work was performed using the (nominal) 2.2 V supply. The measured IM3 performance is expected to improve when the mixer is used in an integrated transceiver design (i.e., RF integrated with LO and IF/baseband stages), because gain and phase mismatch in the RF, LO and IF paths inherent in the experimental setup can be minimized with an integrated solution. The bias and LO input power that resulted in the highest linearity (IM3) was first determined experimentally from a conventional two-tone test. In each case, 2.4 GHz RF signals spaced 100 Hz apart and with an input amplitude of 13 dbm were downconverted to a 50 khz IF when the mixer was driven by a differential LO power of 1.6 dbm (note: these are the powers

7 LIM AND LONG: A LOW-VOLTAGE BROADBAND FEEDFORWARD-LINEARIZED BJT MIXER 2183 Fig. 11. Test setup for experimental characterization. Fig. 12. Measured difference between fundamental tones and intermodulation distortion (1IM3) at various (I, I ) currents. at the mixer input ports corrected for cable losses, etc.). Close spacing of the RF input tones was used so that the tones could be resolved more accurately at the IF. The largest measured db-difference between the fundamental and third-order intermodulation distortion products (i.e., the IM ) is plotted in Fig. 12 for various combinations of bias current in each quad. The ordered pair of numbers next to each data point represents the bias currents flowing in mixers A and B (from Fig. 6), respectively. From these results, it can be seen that higher IM is consistently achieved by increasing the bias current (as for other active mixers), and that the IIP improves by 11 db (note that IIP IM ) as the total bias current increases from 3 ma to 10 ma. However, for total bias current combinations smaller than 4 ma and larger than 10 ma, each mixer s IM3 distortion tends to add in-phase at the IF rather than cancel, resulting in a lower IM. For example, the bias current combination (3 ma, 3 ma) in Fig. 12 has a IM of 47 db that is comparable to higher bias current combinations such as (3 ma, 4 ma) and (5 ma, 3 ma), but with almost identical IF power at the fundamental (i.e., between 4 and 4.2 dbm). Thus, there is an optimum partitioning of the total bias current for the best IM3 performance, and operation close to the shaded area indicated in Fig. 12 is desirable because less current (and lower power) is consumed while having a relatively large IM. For portable applications, both low power dissipation and high IM is desired. The bias combination (3 ma, 3 ma) from a 2.2 V supply was therefore selected as a compromise between low intermodulation distortion and total current consumption for further characterization. At this bias current, the measured fundamental and IM3 output powers at the IF versus the RF input power are plotted in Fig. 13 (IF khz and RF GHz). An LO input power of 2.6 dbm was used for the measurements. The measured conversion gain and IIP are 12.6 dbm and 14.3 db, respectively. In this case, the measured output-referred intercept point (OIP ) is over 10 db higher than we previously reported in [15], where a 50 IF load was used. It is likely that clipping of the IF waveform (i.e., current limiting) is responsible for the rise in distortion observed for low IF load impedances. The conversion gain can be easily adjusted by modifying the IF load impedance ( in Fig. 11), however, its effect on the linearity and IF bandwidth must also be considered in any design choice. As seen from the transfer curves of Fig. 13, the IF output of the feedforward mixer is linear up to an RF input power of approximately 4 dbm, while the IM3 distortion power expands for input powers larger than about 5 dbm. The measured conversion gain, IIP and OIP of the feedforward-linearized mixer in the frequency ranges from

8 2184 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 41, NO. 9, SEPTEMBER 2006 Fig. 13. power. Measured fundamental and third-order IM distortion versus input Fig. 15. Measured conversion gain and IIP at various supply voltages (I =3mA and I =3mA). Fig. 14. Measured conversion gain and IP from 1 6 GHz (V =2:2 V, I =3mA, and I =3mA) GHz and 4 6 GHz are compared in Fig. 14 (note that frequencies between 2.5 and 4 GHz could not be covered with the present test set-up). The measured values compare favorably with those predicted from simulation. For example, the simulated conversion gain and IIP at 5.7 GHz are 12.1 db and 14.4 dbm, respectively, compared to the measured values of 12.6 db and 13.3 dbm. The conversion gain is relatively constant at approximately 12.5 db between 1 and 6 GHz. The IIP is better than 13 dbm for operating frequencies between 2.1 and 5.8 GHz. IIP varies by 3.5 db across the measured frequency range and is lowest at 1.25 GHz (IIP dbm). Similar performance can be expected over the entire 1 10 GHz RF operating range. Matching between the various single-ended paths in the test set-up is difficult to achieve in-practice. For example, matching the amplitudes of all four mixer RF inputs and ensuring 180 phase difference between signals at each RF input pair over frequency, would require extensive calibration and characterization work and extensive trimming. However, the effects of amplitude mismatch, phase error and phase mismatch are easily studied in simulation. In this way, the differences observed between the measurements and the nominal simulation results may be accounted for. The measured amplitude and phase errors for the external passive components used in the experimental set-up (e.g., power splitters, 0 /180 hybrids, cables, etc.) are frequency dependent, and can cause up to db difference in amplitude, and up to deviation from the nominal phase condition. Simulations predict that such errors cause the conversion gain to vary by up to db, so the conversion gain is relatively insensitive to input amplitude and phase errors. Linearity (enhanced by IM3 feedforward cancellation) is more sensitive to amplitude and/or phase variations at the RF inputs. The simulations show that IIP degrades by up to 5 db at GHz and up to 8 db at GHz. More consistent performance (i.e., similar to that predicted in Fig. 8) could therefore be expected when the mixer is integrated with a low-noise preamplifier and LO synthesizer on the same chip. This would reduce the amplitude variation and phase mismatch with frequency at the RF and LO inputs introduced by the external components used to test the mixer (as predicted by simulation of such variation and mismatch). With only the mixing quads and bias sources connected between the supply rails (i.e., two transistors in series), the feedforward mixer is well-suited to low-voltage operation. The conversion gain and IIP are plotted in Fig. 15 when operating at 2.4 GHz RF from a 1.2 V (minimum) supply. Again, the bias current combination of (3 ma, 3 ma) was used for these measurements. The variation in gain and distortion is minimal due to the decrease in supply voltage. It should also be noted that lower voltage operation (down to approx. 1 V) is possible if the bias current sources were removed and the supply current regulated using the LO common-mode (i.e., bias) voltage. The IIP varies by just to 1.2 V. 0.6 db as the supply voltage drops from 2.2 V

9 LIM AND LONG: A LOW-VOLTAGE BROADBAND FEEDFORWARD-LINEARIZED BJT MIXER 2185 TABLE I PERFORMANCE SUMMARY AND COMPARISON The even-order distortion (i.e., IIP ) was also measured for one sample at 2.4, 5.3, and 5.8 GHz, where it is 54.5, 36.6, and 36.3 dbm, respectively. These values are lower than predicted by simulations (i.e., 67 dbm at 5.8 GHz). It is likely that the difference is caused by mismatching in amplitude and phase of the signals in the RF and LO paths at the inputs to the mixer test circuit (mostly determined by mismatch in the external hybrid baluns and cables). Again, better performance could be expected from a fully integrated solution, where these sources of error are lower and are more tightly controlled. Table I summarizes the measured and simulated results. The data indicates that optimal linearity is achieved when higher LO power and lower bias current are used compared to simulations (i.e., 3 db lower LO power and 2 ma less current). The measured conversion gain is also slightly larger than predicted by simulation (by 0.8 db). The highest linearity observed in the measurements and simulations are comparable, but occur at different LO input powers and bias currents as noted above, which is likely due to processing variations and imperfections in the experimental test setup (e.g., phase inaccuracy of the 0 /180 hybrids). Two other bipolar mixers reported in the recent literature, one developed for receiver base-stations [16] and a second mixer that also uses feedforward-linearization [17], but only in the RF input stage (i.e., the input diff pair of a Gilbert mixer) are included in Table I. Linearity of the mixer developed in this work (i.e., output third-order intercept point) is comparable to the receiver base-station mixer from [16]. Comparing output intercept points (OIP ) removes the effect of conversion gain, which varies widely among the mixers listed in the table. The LT5527 mixer described in [16] uses on-chip transformers at the RF and LO inputs for input coupling and matching purposes. It is designed for use in 3G cellular telecommunication base-stations, where the electronics are not portable or powered from a battery, so current consumption and supply voltage are not important design constraints. As shown in Table I, the feedforward-linearized mixer offers comparable linearity (from the OIP ) but with a current consumption of 6 ma for the core of the mixer compared to 78 ma (total, including LO buffers) from a 5 V supply for the LT5527. The feedforward-linearized design brings higher linearity to portable applications where current consumption and operating time on a fresh battery charge are important. Further power savings are possible for the feedforward design if only one of the two mixers is activated in response to less demanding operating conditions using an adaptive power management scheme. The noise figure of the feedforward design presented in this paper is compromised by the use of resistive degeneration at the RF input, which adds thermal noise. However, this also allows the mixer to work over a wide range of frequencies (from baseband up to 6 GHz), whereas the narrowband RF and LO inputs of the LT5527 chip restrict its operating range to between 400 MHz and 3.7 GHz. The (total) RF input impedance of the mixer is close to 50 (57.4-j16.6 at 5.8 GHz) across most of the 1 6 GHz band, thereby simplifying impedance matching to other components (e.g., an image-reject filter between LNA and mixer). The deleterious effects of high noise figure for the feedforward-linearized mixer are mitigated somewhat by the higher conversion gain of the active mixer, as described in Section I of this paper. However, the feedforward mixer would require

10 2186 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 41, NO. 9, SEPTEMBER 2006 Fig. 16. RF input degeneration using impedances from the preceding stage. VI. CONCLUSION A broadband feedforward-linearized double-balanced bipolar mixer topology was demonstrated. Outputs from two modified switching quads are connected such that fundamental components add but IM3 distortion in their output currents cancels, thereby resulting in a higher mixer IIP. Measured input IP 14.3 dbm and an input IP of 54.5 dbm at 2.4 GHz. Conversion (power) gain over the 1 6 GHz RF input range is db with an input impedance close to 50. On-chip inductors are not used in the design, and the 0.14 mm (active area) mixer draws just 6 ma from a (min.) 1.2 V supply, while exhibiting an IIP better than 13 dbm across the frequency bands commonly used for wireless telephony and high-speed local-area networking applications. greater noise suppression from a low-noise preamplifier in order to realize a given overall receiver noise figure compared to that of the other two mixers listed in Table I. Degradation of the distortion cancellation and IM3 performance due to minor variation in bias current and LO power was also investigated. Each mixer s bias current was varied by 0.5 ma ( 15%), which resulted in a maximal drop of 3.6 db in IIP. Similarly, the maximum change observed in IIP was 6.7 db for a 2 db variation in the LO input power. When compared with the mixer reported in [17], which uses a feedforward transconductor preceding the mixing quad, the feedforward-linearized mixer described in this paper demonstrates 4 db improvement in IIP (8 db improvement in OIP ) and 18 mw lower power dissipation. Moreover, feedforward cancellation using resistive degeneration does not require the phase-shifter implemented in [17] and requires less chip area to implement. V. LOWERING THE NOISE FIGURE The relatively high noise figure of the feedforward-linearized mixer is an impediment to its use in many RF receiver applications. Resistive degeneration at the mixer RF inputs is needed to implement feedforward cancellation of IM distortion over a wide range of frequency. However, thermal noise produced by the degeneration resistors ( and in Fig. 6) is among the largest contributors to the total mixer noise. In order to improve the noise figure, these resistors should be either reduced or eliminated entirely. One way to achieve this is to use the output impedance of the RF driving stage to degenerate the mixers. As seen in Fig. 16, the RF sources for the mixers may be represented by Thevenin equivalent voltage sources ( ) with a series output resistance ( ). The desired values for and can be realized in numerous ways, with one possibility at RF being the use of transformers with different turn ratios (for narrowband applications) to reflect the desired impedance levels at the mixer inputs. A driving stage having a constant output impedance value over frequency (e.g., amplifier with shunt output feedback) can also be used to synthesized the desired and for broadband applications. In both these cases the noise figure is improved, as and are now included as a part of the source impedance. ACKNOWLEDGMENT The authors acknowledge technical support for testing provided by L. van Schie at TU Delft. Fabrication and technology access was facilitated by A. Joseph and D. Harame at IBM Microelectronics, Burlington, VT. REFERENCES [1] O. K. Jensen, T. E. Kolding, C. R. Iversen, S. Laursen, R. V. Reynisson, J. H. Mikkelsen, E. Pedersen, M. B. Jenner, and T. Larsen, RF receiver requirements for 3G W-CDMA mobile equipment, Microw. J., vol. 43, no. 2, pp , Feb [2] B. Gilbert, A precise four-quadrant multiplier with subnanosecond response, IEEE J. Solid-State Circuits, vol. SC-3, no. 4, pp , Dec [3] J. Durec and E. Main, A linear Class AB single-ended to differential transconverter suitable for RF circuits, in IEEE Int. Microwave Symp. Dig., Jun. 1996, vol. 2, pp [4] B. Gilbert, MICROMIXER: A highly linear variant of the Gilbert mixer using a bisymmetric Class-AB input stage, IEEE J. Solid-State Circuits, vol. 32, no. 9, pp , Sep [5], The multi-tanh principle: A tutorial overview, IEEE J. Solid- State Circuits, vol. 33, no. 1, pp. 2 17, Jan [6] L. Sheng and L. E. Larson, An Si-SiGe BiCMOS direct-conversion mixer with second-order and third-order nonlinearity cancellation for WCDMA applications, IEEE Trans. Microw. Theory Tech., vol. 51, no. 11, pp , Nov [7] M. P. van der Hejden, H. C. de Graaff, and L. C. N. de Vreede, A novel frequency-independent third-order intermodulation distortion cancellation technique for BJT amplifiers, IEEE J. Solid-State Circuits, vol. 37, no. 9, pp , Sep [8] A. Joseph, D. Coolbaugh, M. Zierak, R. Wuthrich, P. Geiss, Z. He, X. Liu, B. Orner, J. Johnson, G. Freeman, D. Ahlgren, B. Jagannathan, L. Lanzerotti, V. Ramachandran, J. Malinowski, H. Chen, J. Chu, P. Gray, R. Johnson, J. Dunn, S. Subbanna, K. Schonenberg, D. Harame, R. Groves, K. Watson, D. Jadus, M. Meghelli, and A. Rylyakov, A 0.18 m BiCMOS technology featuring 120/100 GHz (f =f ) HBT and ASIC-compatible CMOS using copper interconnect, in Proc. IEEE Bipolar/BiCMOS Circuits and Technology Meeting (BCTM), Sep. 2001, pp [9] P. Wambacq and W. 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11 LIM AND LONG: A LOW-VOLTAGE BROADBAND FEEDFORWARD-LINEARIZED BJT MIXER 2187 [15] S. T. Lim and J. R. Long, A low-voltage feedforward-linearized broadband mixer, in Proc. IEEE Bipolar/BiCMOS Circuits and Technology Meeting (BCTM), Oct. 2005, pp [16] 400 MHz to 3.7 GHz High Signal Downconverting Mixer, Linear Technology, LT5527 [Online]. Available: [17] S. Otaka, M. Ashida, M. Ishii, and T. Itakura, A +10-dBm IIP SiGe mixer with IM3 cancellation technique, IEEE J. Solid-State Circuits, vol. 39, no. 12, pp , Dec Su-Tarn Lim (S 05) received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Alberta, Canada, in 1999 and 2001, respectively. Currently, he is pursuing the Ph.D. degree at the Delft University of Technology, Delft, The Netherlands. His interests are in the areas of analog and RF circuit design. John R. Long (S 77 A 78 M 83) received the B.Sc. degree in electrical engineering from the University of Calgary, Calgary, AB, Canada, in 1984, and the M.Eng. and Ph.D. degrees in electronics from Carleton University, Ottawa, ON, Canada, in 1992 and 1996, respectively. He was employed for 10 years by Bell-Northern Research, Ottawa (now Nortel) involved in the design of ASICs for Gbit/s fibre-optic transmission systems, and for 5 years as an Assistant and then Associate Professor at the University of Toronto, Canada. He joined the faculty at the Delft University of Technology, Delft, The Netherlands, in January 2002 as Chair of the Electronics Research Laboratory. His current research interests include low-power transceiver circuitry for highly integrated wireless applications, and electronics design for high-speed data communications systems. Prof. Long currently serves on the Program Committees of the IEEE International Solid-State Circuits Conference (ISSCC), the European Solid-State Circuits Conference (ESSCIRC), the IEEE Bipolar/BiCMOS Circuits and Technology Meeting (BCTM), and the European Microwave Conference. He is a former Associate Editor of the IEEE JOURNAL OF SOLID-STATE CIRCUITS. He received the NSERC Doctoral Prize and Douglas R. Colton and Governor General s Medals for research excellence, and Best Paper Awards from ISSCC 2000 and IEEE BCTM 2003.