A RF Tunable Impedance Matching Network with a Complete Design and Measurement Methodology C. Hoarau#, P.-E. Bailly, J.-D. Arnould, P. Ferrari, and P. Xavier IMEP (INPG, UJF, CNRS), Minatec, 3 parvis Louis Neel, 38016 Grenoble cedex 1, France #
[email protected]
Abstract— This paper presents the design, fabrication, and measurement of a compact narrow band impedance matching network with hybrid technology: coplanar waveguide transmission lines and surface mounted components. The device is a ∏-structure with tunable components made of varactors in series with inductors. Simulations and measurements are in good agreement. Results are arrived at by two measurement methods. They show that complex impedances with magnitudes varying from 6Ω to 1kΩ can be matched at 1GHz, with a 50% bandwidth.
I. INTRODUCTION Narrow band impedance matching has been an important technique to maximize the power transmission in microwave devices. Literature regarding, basic theoretical concepts for the design of impedance matching networks is easily available. Recently, some tunable matching networks have also been demonstrated. They are mainly applicable in wideband multistandards telecommunication systems or noise measurement systems. These new impedance tuners cover a larger range of impedances although they lead to fresh difficulties in designing and testing. Besides structure dimensions, power reflection, insertion loss, matching bandwidth, maximum power driving, nonlinearity and cost, we have to take into account tunability in frequency and/or in matching impedance, tuning power consumption, tuning delay, and the measurement method to address all the loading impedances. In this paper, an impedance tuner is designed and realized with a very large covered impedance at 1GHz. In addition, a new measurement method is proposed much simpler than the existing ones that required some external tuner. The outline of this paper follows certain design steps. First after a rapid investigation of the existing structures and technologies, the criteria used to choose a particular structure well adapted to a varactor technology are given in section II. Then a theoretical behavior study of the ideal tuner is carried out, and an equivalent electrical model of each component is used to perform an accurate simulation of the structure in section III. Fabrication of the device is outlined in section IV. The measured characteristics of the realized tuner and the methodology used to perform measurement are shown in section V. The comparison with the simulations and a discussion on the device tunability are included in section VI, before the conclusion in section VII.
II. USUAL TECHNOLOGIES FOR TUNABLE IMPEDANCE MATCHING NETWORKS In 1997, JH Sinski et al. studied an impedance transformer with varactors and impedance inverter of quarter wavelength transformer [1]. With this first tunable matching network, the possibility to match loads ranging from 4Ω to 392Ω was demonstrated. Next, other networks, with different tunable technologies, were proposed: semiconductor varactors and switches [1] [7], MEMS varactors [2] [8], capacitors switched by PIN diode [3], capacitors switched by MEMS [4], tunable transmission lines [5], ferroelectric varactors [6]. Results are synthesized in table 1. Even if the order of the magnitude of the returned and transmitted losses are approximately the same for all technologies, some differences can be found for central frequency, maximum power, frequency tuning range, tuning time, and tuning control. III. DESIGN In this study, the hybrid technology with surface mounted components (SMC) and coplanar waveguide (CPW) lumped components was chosen to realize a prototype; A complete methodology of design and measurement of a narrow band tunable impedance matching network is emphasized using an easy fabrication process. The methodology of design and measurement given in this paper can be used in any technology well adapted to other conception criteria. Once the technology is fixed, the topology has to be chosen. To design a narrow band impedance matching network, different topologies can be used [9]: L-structure, ∏-structure [1] [3], T-structure [6], or distributed components [2] [7]. The last one is eliminated because of the length of the lumped components in hybrid technology. For the other structures, the challenge is to introduce tunability: we investigate the frequency and the impedance range of the device. It is wellknown that the L- structure cannot cover the whole Smith chart [9]. To select between a ∏ and a T- structure, a study must be done in terms of impedance and working frequency tunability. The sensitivity to the elements’ quality factor has to be considered too. The simulation method used to address these points is detailed further in this section. Modeling the global structure starts with the creation of an equivalent electrical model of each tunable component and
TABLE I. Ref
Technology
Typical size
Switch
10mm²
Frequency
Tuning Impedance
Control
Maximal Power
Loss
10GHz ∆f /f0= 25%
++ (Discrete)
++
20dBm
>-1dB transmitted -30dB returned
++
++
20dBm
+ (Discrete)
++
30dBm
IC [7]
Hybrid [1] [3]-[5]
Varactor
100mm²
PIN Diode
100mm²
5GHz ∆f /f0= 25% 1GHz ∆f /f0= 5%
>-1dB transmitted -1dB transmitted 30dBm
>-1dB transmitted
++ (Discrete)
––
>30dBm
>-1dB transmitted
2GHz
+
– (100V)
33dBm
-1.1dB transmitted -10dB returned
Ferroelectric [6]
Varactor
100mm²
continues up to the extraction of the reflection and transmission coefficients of the loaded structure. First, a tunable component is chosen. We propose varying the tunable impedance from capacitance to inductance by using a varactor in series with an inductor. Eq (1) gives the ideal theoretical electrical lossless impedance model, where ω0i is the self-resonance of the LiCi structure. If work pulsation ω is greater than the inverse square of LiCi the structure is equivalent to an inductance and if pulsation is lower, the structure is equivalent to a capacitance. ω ω Li Z i = j ⋅ − 0i ⋅ ω ω Ci 0i
Τ=
2 ⋅ s 21 ⋅ ℜ[z L ] 1 + s 22 + z L ⋅ (1 − s 22 )
(2)
(3)
zL − 1 ∗
(4)
zL + 1
However, in practice, the network observes losses. Instead of (1), each impedance of the network can be better represented by (5) where the quality factor Qi is introduced. Zi =
In our structures, three previously presented tunable impedances are used, as shown in Fig. 1. Each impedance is independently tunable. Each tuned possibility of components means a network state. The scattering parameters are deduced from the circuit. To know the power transmitted and reflected by the device, reflection Γ and transmission Τ coefficients are calculated. Equations (2) and (3) gave these coefficients for a load impedance ZL normalized to 50Ω. s 12 ⋅ s 21 ⋅ (1 − z L ) 1 + s 22 + z L ⋅ (1 − s 22 )
∗
s 22 =
(1)
Fig.1. Schematic representation of T-structure with ports (a) and ∏structure (b).
Γ = s 11 −
For lossless impedance matching network, the normalized loaded impedance matched for fixed bias is given by (4), and Γ = 0 and |Τ| = 1.
Li Ci
1 ω ω . + j − 0i Q ω ω 0i i
(5)
In this case, it is mathematically impossible to have Γ = 0 and |Τ| = 1 simultaneously: a compromise between reflection and transmission has to be found. Additionally, it means that no formula gives the best matched impedance directly, (4) does give an order of magnitude, but an iterative method has to be carried out to find the most efficiently matched impedance. The iterative algorithm begins with the computation of all Γ and Τ coefficients corresponding to the combinations of all realistic tunable possibilities with all load impedances. Among all these possibilities, the algorithm selects combinations with Τ higher than -3dB and Γ lower than -20dB. Only these selected combinations are displayed on the Smith chart. Just as it is possible to simulate different structure, this simulation can also be done for several frequencies and/or for several parameters like Q and tunability of components. To choose between ∏ and T-structures, the previous algorithm is used to compare the two using lossy components as well lossless components. The study reveals that the tunabilities of impedance and frequency are equivalent for both structures. An important difference is that the ∏structure is less sensitive to the quality factor of components. This result is due to the topology of the structure; in a T-
structure there are two lossy impedances in series, compared to just one in ∏-structure. Thus, the ∏-structure was chosen to minimize the effect of the low quality factor of the SMC. To bring simulations closer to measurement results, we need a more efficient component-model that takes into account loss and packaging. To elaborate a model, the component manufacturers provide an electrical equivalent circuit. Also in the real structure, a DC block capacitor is needed to isolate different bias of varactors. In order to use the approximation of quasi TEM propagation, symmetry in the propagation direction must be maintained; so on both sides of the CPW ribbon, the same varactor-inductor dipole is connected to the ground. The electrical circuit of the tunable impedance matching network is shown in Fig. 2.
Fig. 2.
Device circuit.
V. MEASUREMENT First, we investigate a common measurement method. It consists of measuring the device with few load impedances by using a programmable tuner from Focus Microwave. Measures are done with SOLT calibration from 0.8 to 1.2 GHz. The device, at fixed reverse bias, is measured in series with the commercial calibrated tuner. With a post-treatment, it is possible to know exactly all the characteristics of transmission and reflection of the loaded device under test. This method is reliable, but fastidious. The loaded impedances measured are: 6+j19Ω, 17-j19Ω, 61+j76Ω, 682Ω, 75-j72Ω, 7+j50Ω, and 6-j50Ω. Measurements carried out using with this method for a few loads are given in Fig. 3 and 4.
Fig. 3. Measurements of ΤdB of the impedance matching network loaded by impedance 61+j76Ω, 682Ω or 75-j72Ω.
With this methodology of network simulation, comparisons can be made between different components of the global structure to select the most efficient device. These results are used to fabricate the tunable impedance matching network. IV. FABRICATION This section enumerates the components, their characteristics, and the fabrication process. The varactor is a MA46H71 from MACOM. The constructor datasheet gives a capacitance ratio of 6:1 with a reverse bias from 0 to 20 V. The value extracted from measurement gives a self resonance frequency of 5GHz and a quality factor around 500 at 1GHz. Inductors are from Coilcraft 0603CS Series and the constructor datasheet gives a self resonance frequency around 3GHz. A quality factor around 20 at 1GHz is extracted from measurement. This measure has to be carried out carefully dye to the presence of parasite element in the process. These measures give a global quality factor, as defined in (5), of 57. The substrate used is a RO4003C from Rogers, the dielectric constant is 3.38 and the tangent loss is 0.0021. CPW line characteristic impedance is calculated to be 50Ω. The classical electronic printed circuit board process is used to fabricate the device. The prototype is 1cm long.
Fig. 4. Measurements of ΓdB of the impedance matching network loaded by impedance 61+j76Ω, 682Ω or 75-j72Ω.
The main originality of this work is to investigate a second measurement method which is much simpler. The purpose is to have an uncomplicated method that takes losses into account. The measure is done with 50Ω ports, and a post treatment computes the devices loaded. Measures are done with TRL calibration on an Agilent HP8510C VNA with a Wiltron test fixture. To reduce the measurement time, measures are done at only one frequency, 1GHz. Once the measures are done, the matched impedances are evaluated by calculating (2) and (3) with the algorithm described in section III. The conditions for transmission and reflection are ΤdB>3dB and ΓdB-3dB and ΓdB
