MATCHING CIRCUIT OPTIMIZATIONFOR ANTENNA APPLICATIONSWHITEPAPER

Impedance 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 of transmission lines are used to improve the impedance matching characteris-tics of the antenna. This whitepaper discusses the optimization of matching circuits especially to antenna applications. Although the design of matching circuits sounds simple, there are many practical considera-tions that need to be addressed.

Using a matching circuit to change the antenna impedance presents several advantages:

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

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

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

• 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 discrete 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 impedance match is easily achieved by adding losses to the matching 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 design 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, it is straightforward to take into account a complex frequency-dependent amplifier 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 the antenna and the matching circuit is filtering out unwanted interfering signals and improving the antenna-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 microwave 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 transmission 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 nonzero. 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 becomes zero. When matching circuits are considered as two-port microwave networks with complex termination (port 1: amplifier, port 2: antenna 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 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 system, the transducer power gain should be multiplied by the antenna radiation efficiency.

Let us now take a look at an example of the matching circuit optimization process. Figure 1 shows an example antenna simulated using the CST Studio Suite®[3] 3D electromagnetic simulator while Figure 2 shows the unmatched S11 of the antenna.

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

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.

Figure 3: Impedance matching through an ideal lossless matching circuit. Blue curve: S11, green curve: transducer power gain.

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 3 shows the matched antenna S11 in Optenni Lab using ideal lossless components. Note that Optenni Lab presents multiple optimized matching topologies which the user can choose between. The best topology is shown here. Figure 4 shows the S11 and transducer 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 following reasons: due to the losses and parasitic effects the component functions differently from the ideal ones; only some discrete nominal values are available from the manufacturer.

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 component 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 analysis 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 Studio Suite for further processing. The matching circuit is built as a schematic circuit model block so that the components can be edited and further optimized for additional optimization goals. When the matching circuit is in place a joint circuit and electromagnetic simulation can be easily carried out.

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 stop band criteria can reduce the performance on the antenna operation 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 important to remove the effect of extra measurement cables. The reference plane of the measurement should be exactly at the position where the matching circuit is to be built. Even a few millimeters of extra transmission line can change the operation of the matching circuit dramatically[4].

In addition to matching circuit design, other important information 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 electromagnetic 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[5].

Figure 8 shows the bandwidth potential of the example antenna. 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 matching 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.

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.

CONCLUSION

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:

• Use the correct reference plane in impedance measurements.

• Use realistic models of components that include losses and parasitic effects instead of ideal component models.

• Optimize the transducer power gain of the matching circuit, not the impedance match.

• 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 done 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.

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REFERENCES

[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] CST Studio Suite, https://www.3ds.com/products-services/simulia/products/cst-studio-suite/

[4] 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

[5] J. Rahola, “Bandwidth potential and electromagnetic isolation: Tools for analysing the impedance behaviour of antenna systems,” in Proceedings of the EuCAP 2009 conference, Berlin, March 23-27, 2009.

AUTHOR

Jussi Rahola, Optenni Ltd, Espoo, Finland