On the Design of Active Downconversion Mixers for Wireless Communications

on a Carbon Nanotube FET Technology Jan Plìva1, Corrado Carta1, Martin Claus2, Michael Schroeter2,3, Frank Ellinger1

1 Chair for Circuit Design and Network Theory, Technische Universität Dresden, Germany 2 Chair for Electron Devices and Integrated Circuits, Technische Universität Dresden, Germany

3 RFNano Corp., Newport Beach, CA, USA

Abstract — Depletion-mode CNTFETs are being fabricated successfully with useable tolerances and compact models are now available for circuit design and engineering. This paper presents the first design study of mixers based on those devices. The impact of peculiar device features and parasitic on analog and RF circuits is discussed in detail and the cascode mixer is selected to overcome challenges specific to the available technology. Circuit performance and design for operation in the 2.4 GHz IMS band are described in detail: while consuming 182 mW and driven with -2 dBm LO power, the mixer provides 8 dB conversion gain to a 10 MHz IF frequency.

Keywords - Carbon nanotube FETs, CNTFET technology, CNTFET mixer, RF circuit design

I. INTRODUCTION Carbon nanotube field effect transistors (CNTFETs) are

emerging semiconductor devices with outstanding intrinsic electrical characteristics, which have been both predicted by physical models [7], [8] and, to some extent, supported by laboratory measurements [12], [13], [14]. The mean free path of charge carriers in the CNT is in the order of 0.1 μm so that ballistic or near-ballistic devices are feasible. Since the CNTFET is a one-dimensional device, bulk effects are effectively suppressed. Low noise, high linearity and operating frequencies surpassing the best of silicon MOS technology are all possible, thanks to one-dimensional transport and good gate control. These characteristics will definitely bring relevant benefits to RF and analog electronics, particularly in the field of wireless communication. With CNT processes still being in their prototyping phase, the research activities focused on challenges of analog high-frequency circuit design have just begun. A number of circuit blocks have to be available in a technology in order to enable effective wireless communication in an integrated system: low-noise and power amplifiers, mixers, oscillators, among others. Most of the published works focus on the design of amplifier circuits: for instance [1] presented a two-stage L-band amplifier with 10 dB gain at 1.8 GHz and [5] presented an amplifier providing 14 dB at 125 MHz. However, in [15], a passive mixer based on the nonlinear resistance of a CNT is presented.

In its first section, this paper reviews the features and performance of the CNTFET technology and compact model, which the circuit designs in this paper are based on. In the following section, two different mixer topologies are discussed and their performance is compared.

Figure 1. The output resistance gds measured and fitted for drain source voltages Vgs={0.5, 1, 1.5} V illustrates the negative impact of metallic tubes.

Figure 2. Model of gm•rds fitted to measurement sweep for Vds = {0.5, 1.0, 1.5} V

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II. DEVICE AND MODEL In spite of the excellent performance predicted by physical

models, fabricated CNTFETs suffer from unresolved technology problems, which impose challenges to analog circuit design. The main problems are the undesired growth of metallic tubes, high contact resistance and the resulting high noise. In multitube devices, about 33% of the tubes are metallic with a zero bandgap [3]. Metallic tubes behave as a low-ohmic nonlinear resistance in parallel to the channel, which cannot be controlled by the gate. Several approaches are possible to mitigate the impact of the metallic tubes; however, none of them has been proven to be applicable for RF CNTFETs. Furthermore, the channel in currently available CNTFETs is usually longer than the mean free path of the carriers and, therefore, the transport is not yet ballistic.

The device available for the design presented in this paper is a multi-finger multi-tube depletion CNTFET with 800 nm channel length and 450 nm gate length consisting of several thousands of tubes in parallel [1], [2]. The CNTFET model is fitted to experimental data for drain-source voltages up to 2.5 V, including parasitics and metallic tubes, for both static and dynamic measurements as shown in Figures 1-3.

The technology is capable of delivering gain of 10 dB at 1.8 GHz [2].

III. CIRCUIT DESIGN For the currently available CNTFET technology, the main

challenge in circuit design is imposed by the unavoidable

presence of the metallic tubes. These increase the off-current and reduce the output resistance. While the off-current merely lowers the power efficiency of the circuit blocks and worsens thermal problems, the low output resistance impairs the performance of analog and RF blocks. In addition, because of extremely low output resistance, many circuit analysis simplifications, typical of established technologies, lose their validity and need some reconsideration.

The impact of the low intrinsic output resistance of CNTFETs on active mixer design can be illustrated by first considering the linear gain of amplifiers, since this is typically proportional to the conversion gain. For this purpose, a very useful figure of merit is the intrinsic voltage gain, which is the upper limit of voltage gain available from a device, defined as the product of its transconductance gm and its output resistance rds. In conventional technologies, such as silicon and III-V ones, this product is typically much larger than unity. In the case of available CNTFETs, however, the intrinsic gain is in the order of 1.5, as shown in Figure 2. and the gds=1/rds are in the order of 40-50 mS as shown in Figure 1.

One practical approach to overcome this limitation is to rely on a circuit topology suitable to increase the effective output resistance. Most notably, a cascode configuration for the amplifier can increase the output resistance at the cost of moderate increase of supply voltage and power consumption. To evaluate the effect of cascode topology for transistors with low output resistance, let us consider the small signal equivalent circuit in Figure 4. Under the assumption that gm and rds of both transistors are approximately the same, then the voltage gain can be expressed as

( )1(1 ) 31

m m dsoutm ds m ds m ds

m dsin

ds L

g g rv g r g r g rg rvr R

⋅ += − ≈ − + ≈ −

+

which, for gm•rds≈2 and RL>>rds, results in an improvement of approximately a factor of three compared to the common source configuration.

Although the cascode topology does improve the intrinsic voltage gain of the available device, the benefit is much less pronounced with respect to conventional technologies, which enjoy a quadratic improvement with respect to the single, common-source connected device. In fact, if gmrds>>1 and RL>>rds, then the voltage gain is approximately –(gmrds)2.

The conversion gain of the active mixer topologies considered in this paper suffers from this limitation as well, as it is proportional to the voltage gain of a corresponding cascode amplifier by a factor 2/π. On the other hand, single-transistor topologies, active or not, become less attractive, as they would attenuate the signal excessively.

Figure 5. shows the schematics of two mixer configurations, suited for monolithic integration [10], that have been considered for design: (a) singly-balanced mixer, (b) cascode mixer. For low-GHz operation, the singly-balanced mixer, Figure 5(a), is an attractive option, as it offers a manageable compromise between conversion gain and port-to-port isolations with low-power operation. The circuit operation, however, is severely

Figure 3. Fitting of the model to experimental data for S-parameter S21 in polar representation. Frequency sweeps 1 GHz...10 GHz for biasVgs=-0.6 V and Vds={0.5, 1.0V, 1.5V}

Figure 4. Small signal equivalent circuit of a cascode amplifier. gm and rds of the two transistors are assumed as same.

iL

gm1·vDS1

gm1·vGS1 vDS1rDS1

rDS2

RL

vout

vGS1

vin

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impaired by the presence of metallic tubes. The mixer core consists of transistors T2,3 and is driven by a large LO signal matched to their gate impedance. This effectively modulates the source impedance seen at the drain of T1, by steering most of its bias current to one side, or the other. In conventional technologies, the small signal current at the collector of T1 is fed into the ~1/gm source impedance of the active transistor (T2 or T3), while its counterpart is off and loads the node with a very high, ideally negligible, impedance. In presence of a low-ohmic connection between source and drain of T2,3 this mechanism is disrupted, as a significant fraction of the RF current is diverted towards the unwanted side of the differential IF output. This, in turn, reduces the conversion gain quite significantly.

A possible solution to this problem is to remove transistor T3 and its IF branch, as done in the cascode mixer of Figure 5(b). The main drawback of this choice consists in the lost suppression of the RF signal at the IF port, and the LO signal at the RF port. With frequency plans typical of operation in the low-GHz band, the suppression of the RF can be performed by the same low-pass IF load used to suppress the LO feed-through. On the other hand, the LO-to-RF isolation remains an open issue, which will have to be dealt with at a system level.

These two circuits have been designed and simulated for operation in the 2.4 GHz IMS band, with a low-IF of approximately 10 MHz. At this moment, only discrete CNTFETs are expected to be available for circuit fabrication. For this reason, the circuit has been designed as microstrip printed circuit board, which would feature surface-mounted unpackaged CNTFETs. The effect of the needed bondwires has been included in simulation. Both designs use narrowband inductive matching of the LO and RF ports to 50 Ω. The matching inductivity is realized by a transmission line and serves as a bias connection at the same time. The bias voltage

is defined by resistive voltage dividers from the supply voltages of +/-5V. Assuming the IF is fed to a voltage amplifier stage with high input impedance, the IF ports are not power matched. The drain current of all the RF transistors is approximately 36mA: this large value makes the use of a resistive IF load rather unpractical. For this reason, a large inductive load LIF has been chosen, with a value suitable for an SMD component. The parasitic capacitance of the component, its self –resonance frequency of approximately 50 MHz and its quality factor have been included in the simulation. In order to suppress the LO and RF feedthrough at the IF port, an additional shunt capacitor CIF has been added to provide, together with the parasitic capacity of LIF, a suitable low-pass load.

In the cascode mixer design, a feedback resistance RFB of 22 Ω has been included to degenerate the drain for better stability. The other design does require a smaller degeneration resistance of 10 Ω, for the same purpose. The source degeneration also contributes to better linearity as well as improving the bandwidth of port matching.

Losses of all components, including bondwires, have been modeled as well.

IV. CIRCUIT PERFORMANCE The conversion gain of the three mixers, shown in Figure 5. has been simulated for an IF frequency of 11 MHz and RF frequency of 2.45 GHz, as a function of the input signal amplitude. As shown in Figure 6. and discussed above, the performance of the cascode mixer is superior with the given CNTFETs, as it provides 8 dB gain, against -1.5 dB for singly-balanced mixer. Given the large difference in this key performance parameter, complete details on the performance will be presented only for the cascode mixer. However, the singly-balanced version has shown a very similar behavior with respect to the other figures of merit.

Figure 5. The two circuit topologies simulated (A: single balanced mixer, B: cascode mixer)

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In Figure7., the conversion gain of the cascode mixer is shown as function of the LO signal power: saturation is reached at about -10 dBm, and all simulations in this section are performed with an LO signal power of -2 dBm.

Figure 8. shows the matching of the high-frequency ports RF and LO. Due to the high quality factor of the SMD components and the high input resistance exhibited at the gate by the CNTFETs, the matching bandwidth is of approximately 5%. Larger matching bandwidths are of course achievable at both RF and LO ports by sacrificing conversion gain or increasing the LO power, respectively.

Figure 9. shows the behavior of the conversion gain as function of the RF frequency, for a fixed IF frequency of 11 MHz. The conversion gain at the matched frequencies for LO and RF signals is 8 dB; however, accepting a slight mismatch at the LO port, the conversion gain can be a few dB higher. Overall, the RF bandwidth is 100 MHz at -3 dB.

The frequency response of the IF port is shown in Figure 10. : the band-pass behavior is the result of the LC-shunt load and allows a 3-dB bandwidth sufficient to accommodate an 11 MHz channel.

The linearity of the mixer can be evaluated with the iP1dB: as shown in Figure 6. , this corresponds to -2 dBm at the input of the RF port. Also the two-tone IP3 test was simulated for IF signals at 10 MHz and 12 MHz: the extrapolation of the iIP3 is shown in Figure 11.

The port-to-port isolations vary with frequency, and reach minimal values in the 2.4 GHz band, as RF and LO port are matched. From a system level perspective, the most critical values are the LO-to-IF and LO-to-RF, because the LO signal is very large. The LO power at the IF port is suppressed by approximately 26 dB, thanks to the low-pass response of the IF load. The signal at the RF port cannot be suppressed with this topology, as it is allocated on the same band. This is a major limitation of the cascode mixer and the optimal solution – a singly-balanced mixer – is not viable with the available technology, as discussed in the previous section. The LO-to-RF isolation is about 2.3 dB and the unwanted signal will have to be dealt with at a system level. The RF-to-LO isolation is only 1.5 dB, but this is less of a concern, as the RF signal is more than 10 dB smaller than the LO signal in normal operation.

Figure 6. Comparison of the conversion gain of the tree designs with fIF=11MHz

Figure 7. Conversion gain versus LO-Amplitude

Figure 8. Matching at the RF and LO inputs of the cascode stage Figure 9. Conversion gain as function of RF frequency for a fixed IF frequecny of 11 MHz

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V. CONCLUSIONS The recent progress in the development of CNTFET

technologies brought the technology to a level of maturity sufficient to initiate circuit design and engineering research. Devices are being produced with useable tolerances and the first compact models are available for circuit analysis and simulation. The devices are functional, although the best fabrication processes developed so far still have difficulties to avoid metallic tubes, which result in low output resistance. Given their specific physical properties, CNTFETs are particularly attractive for analog and RF applications, particularly frontends for wireless communication. This paper presents the first design study of mixers based on this technology. The impact of metallic tubes and the low output resistance on analog electronics block was discussed in detail. In particular, a specific active topology – the cascode mixer – is presented as adequate for implementation with CNTFETs. Circuit operation and predicted performance are presented: a gain of approximately 8 dB can be achieved for the downconversion of several 20-MHz channels from an RF band at 2.4 GHz to an IF of 10 MHz. In combination with a suitable amplifier, already demonstrated at 1.8 GHz with the same

devices, these circuit blocks would offer performance sufficient for the demonstration of a first integrated receiver operating in compliance with existing standards for the 2.4 GHz IMS band.

The performance of those circuit blocks still suffers significantly from the status of the technology; for example, the low output resistance impacts gain and current consumption, but can be dramatically improved by removing metallic tubes. Technology advancements of this kind will lead to significant performance improvements, which will make CNTFET technology very competitive.

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Figure 10. Bandwidth for IF signal – because of inductive load, the mixer shows bandpass behaviour for the IF signal

Figure 11. Third order intercept point

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