A Study on RF/Microwave Tunable Inductor Topologies

Volkan Turgul School of Electronics and Computer Science,

University of Westminster, London, United Kingdom

volkan.turgul@my.westminster.ac.uk

Tayfun Nesimoglu Middle East Technical University,

Northern Cyprus Campus, Guzelyurt, Mersin 10, Turkey

ntayfun@metu.edu.tr

B. S. Yarman Istanbul University &

Işık University, Istanbul, Turkey,

yarman@istanbul.edu.tr

Abstract — Recently, tunable structures gained importance due to frequency agile microwave circuits such as tunable filters, matching networks, amplifiers, etc. that are needed to realize reconfigurable radios. Deploying tunable inductors would increase the flexibility in reconfigurable microwave circuits when used in conjunction with variable capacitors. In this paper we investigate several tunable inductor topologies. Each proposed topology has certain advantages/disadvantages and these are addressed throughout the paper.

Keywords—tunability; tunable inductor; varactor; intermodulation distortion, non-linearity

I. INTRODUCTION There has been an increasing demand on radio frequency

(RF) communications through the past few decades. There also has been an increasing interest in the software defined radio (SDR) systems by commercial manufacturers [1], [2]. SDR technology should offer reconfigurability without the necessity of hardware modification or replacement, therefore some of the design challenges have moved to the digital domain such as RF tuning and filtering. Although most of the processing is done digitally in an SDR system, some analog circuitry such as low-noise amplifiers, power amplifiers and antennas are still required. This brings the necessity of flexible (tunable) microwave circuits for the operation of reconfigurable systems [3]. In tunable microwave circuits, varactor diodes are commonly used as variable circuit elements that enable frequency tunability. Usually, the inductors are of fixed values in these circuits, although MEMS structures were used as variable inductances in some applications, these were complex, difficult to realize and had reliability problems [4], [5]. In this study we investigated alternative ways of realizing a tunable inductor using discrete components. Although this study is currently theoretical, the proposed architectures are aimed to be realized using microstrip technology which is easy to fabricate and very cost effective. We considered using varactor stacks in the design of the tunable inductors and investigated the advantages/disadvantages of using different varactor stack topologies on tunability and linearity [6]. The objective is to obtain a large tuning range while keeping the insertion loss and intermodulation distortion as small as possible. The proposed architectures are intended

for low power applications since a high power RF signal would modulate the DC bias of the varactors causing unpredictable operation.

II. TUNABLE INDUCTOR TOPOLOGIES

Tunable inductor design is essentially a tuned circuit where a fixed-value inductor is connected either in series or in parallel with a variable capacitor, i.e. a varactor diode. The circuit takes advantage of the region where the inductive reactance dominates the capacitive reactance. The resulting variable inductor can either be used as a series or parallel component within a resonant circuit. The structure of the tunable inductor is shown in Fig. 1.

Fig.1. Structure of the tunable inductor

The 2.4 GHz industrial, scientific and medical (ISM)

band is selected for the demonstration of the tunable inductor. The variable capacitance is realized using varactor diodes. Since the capacitance range that can be obtained by the varactor is given in the datasheet, the value of the fixed inductor can be calculated by the well-known resonance formula for this band. Varactor model used in the design is SMV2019 from Skyworks Inc [7]. Spice model supplied in the datasheet was used in Agilent Advanced Design System (ADS) [8]. Tunability was investigated for both series and parallel topologies with four possible varactor configurations, namely; single varactor, anti-series varactor stack (VS), anti-parallel VS and anti-series/anti-parallel (ASAP) VS. Each connection type has some advantages as well as disadvantages [3], [6]. Briefly, using a single varactor provides simplicity but its linearity is poor, anti-series connection offers very good linearity and provides smaller capacitance but gives larger series resistance due to the series connection, anti-parallel connection provides larger capacitance and gives reduced series resistance and anti-series/anti-parallel connection offers good linearity but

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occupies a larger circuit area. A more detailed comparison is given in the following sections. All simulations were carried out in ADS.

A. A fixed inductor in parallel with a varactor diode In this topology a fixed-value inductor is connected in

parallel with the varactor. The four possible configurations are shown in Fig.2.

Fig.2. Tunable inductor topologies. a) Single varactor b) Anti-series VS c) Parallel VS d) ASAP VS

When used as a series component these tunable inductor

topologies behave as band-stop filters. At the frequencies below the resonance point, these circuits present inductive impedance and above the resonance they become capacitive. When the resonance is kept at around 2.9 GHz, the lower edge of the stop band is at around 2.5 GHz. This allows us to get the maximum tunability at around 2.4 GHz with minimum insertion loss. The varactors are reverse biased with a variable 0-10 V DC source. Tuning voltage versus obtained variable inductance is given in Fig.3 for the topologies shown in Fig.2.

Fig.3. Inductance vs Tuning voltage.

Nearly all topologies provide similar tunability except for the anti-parallel connection. This is due to the doubling of the capacitance. It is possible to obtain larger overall inductance by adding an additional inductor in series with any of the four topologies however, this is obtained at the cost of increased insertion loss. Then, the resultant inductance can be calculated as in Eq.1;

[ ]nH 2.0)( . ++ tunedadd LL (1)

An excess inductance of 0.2 nH was included in (1) to

represent the parasitic inductance of the varactors independent of the topology. The average insertion loss and return loss values and the value of the fixed inductor are given in Table I for the topologies in Fig.2; on average 0.5 dB insertion loss was obtained.

TABLE I. TUNABLE INDUCTOR PARAMETERS

Topology Parameters

Avg. Insertion Loss Avg. Return Loss Fixed Inductor

Value

Single 0.5dB 11.5dB 1.45nH

Anti-series 0.6dB 11dB 1.45nH

Anti-parallel 0.4dB 15.5dB 0.8nH

ASAP 0.6dB 11.5dB 1.45nH

It was observed that the maximum inductance tunability

is achieved adjacent to the resonance frequency. At lower frequencies below the resonance, the inductance tunability reduces. For example, while the tunability at 2.4 GHz is around 168% the tunability reduces to around 10% at 900 MHz which is another ISM band. The graph showing percentage tunability as a function of percentage deviation from 2.4 GHz is shown in Fig 4. Hence the tunable inductor gives the best results across a narrow band near the resonant frequency.

Fig.4. Tunability vs. Percentage frequency offset from 2.4 GHz

Furthermore, we also have investigated the linearity performanace of the proposed topologies in Fig.2. The results are given in Fig 5.

Fig.5. Fundamental tones and intermodulation products for all topologies

The circuit was injected with two-tones, at 2.40 GHz and

2.45 GHz, respectively at a power of 0 dBm. It can be concluded that the single varactor configuration gives the worst linearity whereas the anti-series configuration provides 50 dB lower third order inter-modulation distortion product (IMD3) compared to the single varactor topology.

B. A fixed inductor in series with a varactor diode In this topology a fixed-value inductor is connected in

series with the varactor. The four possible configurations are shown in Fig.6.

Fig.6. Tunable inductor topologies. a) Single varactor b) Anti-series VS

c) Parallel VS d) ASAP VS

When used as a series component these topologies behave as band-pass filters. The maximum tunability occurs close to the upper edge of the pass-band and the circuit shows overall inductive impedance at frequencies higher than the resonance frequency. For this reason the resonance is kept around 2.1 GHz to obtain good tunability at around 2.4 GHz. The varactors are biased with a variable 0-10 V DC source. Simulated variable inductance performance as a function of tuning voltage is given in Fig.7 for all topologies.

Fig.7. Inductance vs Tuning voltage

It can be observed that the tunability characteristics are

smoother compared to those provided by the parallel topologies. With 0-to-10 V DC control voltage it is possible to obtain a 0-to-6 nH tunable inductor with almost linear tuning characteristics. However, all circuits introduce around 0.8 dB higher insertion loss compared to the parallel configurations. The average insertion loss, return loss and the value of the fixed inductor are given in Table II.

TABLE II. TUNABLE INDUCTOR PARAMETERS

Topology Parameters Avg. Insertion

Loss Avg. Return Loss Fixed Inductor Value

Single 1.2dB 8.5dB 5.6nH

Anti-series 1.5dB 7.5dB 7.3nH

Anti-parallel 1.5dB 9dB 6nH

ASAP 1.2dB 9dB 5.3nH

The linearity characteristics of these topologies were

also investigated; results are shown in Fig 8. Similar to the parallel case, two-tones with a power 0 dBm were injected. The series tunable inductor topologies offer more than 20 dB lower intermodulation distortion than the parallel topologies.

Fig.8. Fundamental tones and intermodulation products for all

configurations

ASAP-VS topology offers excellent IMD3 levels compared to the other topologies whereas the anti-series topology gives the largest inductance tunability range. An increase in the IMD levels is expected if higher power is applied through the varactors

The Q-factor was also investigated for the tunable inductor topologies and for this purpose the anti-series VS configuration was used as the test circuit. For this circuit the fixed inductor value was given as 7.3 nH in Table II. The simulations were carried out using a measurement based 7.5 nH inductor model from CoilCraft Ltd. (model: 0201DS-7N5XJLU) by also using the S-parameters supplied by the manufacturer. Q-factor for this inductor is given as 55 in the datasheet [9]. The Q-factor was obtained from the simulation for the afore mentioned tunable inductor topology and its Q-factor characteristic at 2.4 GHz as a function of tuning voltage is shown in Fig 9.

Fig.9. Q-factor vs. Tuning voltage @ 2.4GHz

The reduction in Q is due to the series resistance of the

varactors and this resistance is largest for the anti-series VS configuration since two varactors are connected in series. It is possible to obtain a higher Q with the single varactor configuration. However, topologies with high Q have the disadvantage of high non-linearity.

III. CONCLUSION Two tunable inductor topologies (parallel/series) were

investigated with four possible varactor configurations for each topology. Inductance tunability, insertion loss and linearity properties were compared and discussed. It has been demonstrated that, tunable inductors may be realized when certain criteria are met. However, proposed tunable inductor topologies have some limitations; they are most suitable for narrow band and low power applications. In this study, the proposed topologies performances were studied by assuming that they are series elements in a circuit, i.e. replacing series inductors in a circuit. It is our intention to validate the operation of the proposed topologies when used as parallel elements as well. It is then our intention to realize these topologies on microstrip technology and obtain experimental results.

ACKNOWLEDGEMENT The work reported here is funded by the Scientific and Technical Research Council of Turkey (TUBITAK) under the project code 110E105.

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[6] K. Buisman, L.C.N. de Vreede, L.E. Larson, M. Spirito, A. Akhnoukh, T.L.M. Scholtes, L.K. Nanver, Distortion-free varactor diode topologies for RF adaptivity, in IEEE International Microwave Symposium Digest, 12---17 June 2005 (2005), pp. 157---160.

[7] http://www.skyworksinc.com [8] http://www.agilent.com/find/eesof [9] www.coilcraft.com/pdf_viewer/showpdf.cfm?f=pdf_store:0201ds.pdf