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Matching circuit optimization for antenna applicationsImpedance matching is an essential part of antenna design. The input impedance of an antenna needs to be reasonably close to the amplifier impedance (e.g. 50 Ohm), otherwise the signal is reflected back to the amplifier and not radiated by the antenna. In many applications matching circuits consisting of discrete inductors and capacitors, or transmission lines are used to improve the impedance matching characteristics of the antenna. This white paper discusses the optimization of matching circuits especially to antenna applications. Although the design of matching circuits sounds simple, there are many practical considerations that need to be addressed.

Using a matching circuit to change the antenna impedance pres-ents several advantages:

ó Tuning the antenna to operate at a desired frequency range is much easier and faster than modifying the antenna geometry

ó The matching circuits can add additional resonances to the antenna and thus make it more broadband

ó With matching circuits it is easy to incorporate last minute design changes by only changing the values of some discrete components

ó There are fast and easy-to use design tools for matching circuit optimization

However, there are some design issues that need to be addressed in the design of optimal matching circuits. First, all matching components introduce some extra losses into the system and the losses need to be taken into account in the optimization. The commercially sold components are available only as some dis-crete values. The manufactured components always have some parasitic reactances associated with them that need to be taken into account. For example, after a certain frequency (called the self resonance frequency) an inductor has a negative reactance and is thus looking more like a capacitor. Finally, the components have some manufacturing tolerances and thus the designer needs to check how the tolerances affect the performance of the matching circuit.

Somewhat paradoxically, the purpose of matching circuit design is not to obtain the best possible impedance match. A good im-pedance match is easily achieved by adding losses to the match-ing circuit but this naturally results in a poor efficiency of the antenna. The real goal of matching circuit design is to obtain the best possible power transfer between the amplifier and the antenna, resulting in optimal antenna efficiency. Although the above facts are well known to antenna designers, they are easy to forget for example when the antenna system is designed by placing suitable discrete components and measuring the input impedance using a network analyzer.

A matching circuit is actually a filter, but there are significant differences between filter design and antenna matching circuit design. Filters are typically designed to operate in a 50 Ohm

environment, where closed form solutions for optimal filter de-sign are available. In contrast, antenna matching circuits need to take into account the complex antenna impedance that changes rapidly with frequency and thus the closed form solutions are not available any longer. In addition, in matching circuit design it is easy to take into account a complex frequency-dependent ampli-fier impedance (determined e.g. from load-pull measurements). In matching circuit design it is easy to add stop band definitions so that the combination of antenna and the matching circuit is filtering out unwanted interfering signals and improving the an-tenna-to-antenna isolation.

In matching circuit design it is natural to use the power wave definitions of the reflection coefficient and the scattering matrix, because they correctly describe the propagation of power in mi-crowave networks[1, 2]. Standard textbooks typically only express the reflection coefficient and scattering matrix in terms of the traveling waves, which are the physical waves traveling in trans-mission lines. However, due to multiple reflections, the traveling waves do not describe the propagation of power. For example in the case of conjugate matching (which is known to be optimal for power transfer) the traveling wave reflection coefficient is nonze-ro. In contrast, the power wave definition gives zero reflection for the conjugately matched case.

In the power wave theory, the reflection coefficient between a load impedance ZL and a reference (or generator) impedance ZR is given by

where the asterisk denotes complex conjugation. From here it is easy to see that when the load and reference impedances are complex conjugates of each other, the reflection coefficient be-comes zero.

When matching circuits are considered as two-port microwave networks with complex termination (port 1: amplifier, port 2: an-tenna impedance), the transducer power gain of the network is given by |S21|2, when the power wave definition of S parameters is used[2]. The transducer power gain is the ratio of the power delivered to the antenna to the power available from the source and thus it measures the efficiency of power transfer from the

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Matching circuit optimization for antenna applications

amplifier to the antenna. The transducer power gain includes the mismatch losses and the resistive component losses in the matching circuit. To get the total efficiency of the antenna sys-tem, the transducer power gain should be multiplied by the an-tenna radiation efficiency.

Let us now take a look at an example of the matching circuit op-timization process. Figure 1 shows an example antenna simulated using the CST MICROWAVE STUDIO® 3D electromagnetic simu-lator while Figure 2 shows the unmatched S11 of the antenna.

Figure 1 Simple non-resonant antenna for a Bluetooth application. Ground plane size is

15 by 40 mm. The antenna element is 3 by 15 mm and is 2 mm above the ground plane

Figure 2 S parameters of the original unmatched antenna of Figure 1.

To design the matching circuit for this antenna we use the Optenni Lab matching circuit optimization software. The simulated anten-na impedance can be transferred from CST MICROWAVE STUDIO to Optenni Lab using a simple macro command.

Figure 3 shows the matched antenna S11 in Optenni Lab using ideal lossless components. Note that Optenni Lab presents multiple op-timized matching topologies which the user can choose between. The best topology is shown here. Figure 4 shows the S11 and trans-ducer power gain when the components have losses and suitable Murata matching components have been chosen. In general the optimal component values with realistic component models may differ from the optimal lossless component values for the follow-ing reasons: due to the losses and parasitic effects the component

functions differently from the ideal ones; only some discrete nom-inal values are available from the manufacturer.

Figure 3 Impedance matching through an ideal lossless matching circuit. Blue curve:

S11, green curve: transducer power gain

Figure 5 shows the tolerance analysis of the selected topology. This topology is very sensitive to the component variations and therefore the performance could drop by 5 dB due to the compo-nent tolerances. In contrast, Figure 6 shows the tolerance analysis of another topology that has a slightly poorer performance with nominal component values but that is clearly less sensitive to component variations. Finally, Figure 7 shows the tolerance anal-ysis when tight tolerance variants (e.g. 3% instead of 5%) of the components are used.

When the matching circuit has been optimized in Optenni Lab, it can be returned to CST DESIGN STUDIO® (CST DS®) for further processing. The matching circuit is built as a CST DS block so that the components can be edited and further optimized for addi-tional optimization goals. When the matching circuit is in place a joint circuit and electromagnetic simulation can be easily carried out in CST DS.

In the optimization of matching circuits, stop band definitions can be easily added in order to attenuate unwanted interfering signals. Thus, a matching circuit can act as a filter and thereby decrease the requirements of traditional filters. However, the introduction of

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Figure 4 Impedance matching when Murata component models are used

Figure 5 Matching circuit tolerance analysis for the topology in Figure 4. The yield with

respect to -1.5 dB efficiency target is only 40% and the worst-case efficiency is -5.8 dB

Figure 6 Matching circuit tolerance for another matching circuit topology. The yield

is 78% and the worst-case efficiency is -1.7 dB

Figure 7 Same as Figure 6, but with tighter tolerance variants of the inductors. The

yield is now 100% and the minimum performance is -1.3 dB

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Matching circuit optimization for antenna applications

stop band criteria can reduce the performance on the antenna op-eration band and thus the user has to select a compromise between the stop band and pass band operation of the matching circuit.

When using measured data for matching circuit design, it is im-portant to remove the effect of extra measurement cables. The reference plane of the measurement should be exactly at the po-sition where the matching circuit is to be built. Even a few milli-meters of extra transmission line can change the operation of the matching circuit dramatically[3].

In addition to matching circuit design, other important infor-mation can be derived from the antenna impedance data. The concept of bandwidth potential shows for each frequency how much impedance bandwidth can be obtained using an optimized matching circuit. The bandwidth potential can thus be used to rank differently matched or nonresonant antenna prototypes in terms of the obtainable bandwidth. The concept of electromag-netic isolation shows for each frequency the worst-case isolation that is independent of antenna matching. This concept can be used in e.g. antenna placement analysis to see which position gives best antenna isolation or to study the effect of structural changes to improve the isolation between antennas[4].

Figure 8 shows the bandwidth potential of the example anten-na. The bandwidth potential curve shows at each frequency what kind of impedance bandwidth (at the 6 dB return loss level) can be obtained through an optimal lossless two-component match-ing circuit. The example antenna has over 270 MHz of obtainable bandwidth at 2.45 GHz, thus more than enough to cover the Bluetooth band (bandwidth roughly 100 MHz). Put in another way, as the obtainable bandwidth at 6 dB return loss level is more than the required Bluetooth system bandwidth, a two-component matching circuit can cover the Bluetooth system band with much better return loss than 6 dB.

To summarize, matching circuits can be used to speed up the antenna design process and to obtain more wideband antennas provided that proper attention is paid to the losses and tolerances in the matching circuit. In addition, the radiation efficiency of the antenna has to be sufficiently large across the whole operation band to guarantee a sufficient total efficiency.

In practical matching circuit design, please follow these guidelines:

ó Use the correct reference plane in impedance measurements ó Use realistic models of components that include losses

and parasitic effects instead of ideal component models ó Optimize the transducer power gain of the matching

circuit, not the impedance match ó Check the effects of the component tolerances

With modern simulation tools, such as the CST STUDIO SUITE® 3D electromagnetic simulator and the Optenni Lab matching circuit optimization software, the design of a matching circuit can be do-ne within a few minutes, without deep knowledge of the theory of impedance matching.

Figure 8 The bandwidth potential of the example antenna, showing the obtainable

impedance bandwidth through two-component matching circuits as a function of

the center frequency

[1] K. Kurokawa, “Power waves and the scattering matrix,” IEEE Trans. Microw. Theory Tech., vol. MTT-

13, no. 3, pp. 194–202, Mar. 1965.

[2] J. Rahola, “Power waves and conjugate matching,” IEEE Trans. Circuits Syst. II, Express Briefs,

vol. 55, pp. 92–96, 2008.

[3] M. Rütschlin, “Measurement and Simulation in Modern Device Design”, 7th CST EUC 2012,

Mannheim, Germany, http://www.cst.com/Content/Events/EUC-2012-Presentations.aspx

[4] J. Rahola, “Bandwidth potential and electromagnetic isolation: Tools for analysing the impedance be-

haviour of antenna systems,” in Proceedings of the EuCAP 2009 conference, Berlin, March 23-27, 2009.

Author

Jussi Rahola, Optenni Ltd, Espoo, Finlandhttp://www.optenni.com

CST AGBad Nauheimer Str. 1964289 DarmstadtGermany

info@cst.comhttp://www.cst.com

CHANGING THE STANDARDS