An Adaptive Impedance Matching System

EUROPEAN COOPERATION IN THE FIELD OF SCIENTIFIC AND TECHNICAL RESEARCH

COST 273 TD(04)121 Gothenburg, Sweden 2004/June/7-10

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Department of International Development Engineering Tokyo Institute of Technology Tokyo, Japan

An Adaptive Impedance Matching System for Mobile Antennas

Ichirou Ida and Jun-ichi Takada Tokyo Institute of Technology Room 111, South No.6 building 2-12-1, O-okayama, Meguro Tokyo 152-8552 Japan Phone: + 81-3-5734-3288 Fax: + 81-3-5734-3288 Email: [email protected], [email protected] Takeshi Toda and Yasuyuki Oishi Mobile Phones Group, Fujitsu Limited YRP R&D Center, 5-5, Hikari-no-Oka Yokosuka, Kanagawa 239-0847 Japan Phone: + 81-46-839-5373 Fax: + 81-46-839-5560 E-mail: [email protected], [email protected]

An Adaptive Impedance Matching System for Mobile Antennas Ichirou IDA

Jun-ichi TAKADA

Dept. of International Development Engineering Tokyo Institute of Technology Tokyo 152-8552, Japan [email protected], [email protected]

Abstract – An adaptive antenna impedance matching system for mobile communication terminals is proposed. The system adaptively controls two varactors of the pi-network matching circuit detecting the change in the refection coefficient between the matching circuit and the RF front end of a transceiver. This system consists mainly of analog circuits and employs only a simple algorithm for convergence, therefore does not need any complicated mathematical formulation for modeling of the system itself as well as its nonlinear control elements. In this paper, the performance of the adaptive impedance matching system is investigated by simulation. The input impedance of three antennas is alternated assuming the change of the environment due to a human head or a hand and the performance of the impedance matching is compared with fixed capacitance matching systems. As a result, it is found that the input power to the antenna for transmission can be increased by about 2 – 3dB compared with the fixed capacitance matching system. Keywords: Adaptive impedance matching, Varactor, Antenna input impedance, Mobile communication terminals

I. INTRODUCTION The continuous development of the recent mobile communication systems and terminals is vital for our modern life. To meet demands for such high-speed and high-reliable mobile communication systems, efficient ways of signal transmission and reception should be realized. For receivers, it is desired to obtain as high a CNR (Carrier-to-Noise power Ratio) as possible. Also for transmitters, it is necessary to save the battery avoiding the loss caused by an inefficient transmission of the power from the RF circuits to the antenna. Under the mobile environment, however, it is well known that the antenna of the mobile terminal is very much affected by nearby objects such as a human head and hand [1], [2]. Then the input impedance of the antenna changes, and the efficient transmission of the signal is sometimes difficult because of the impedance mismatch between the matching circuit and the RF front end of a transceiver. Furthermore, with a bad impedance matching, a power amplifier in the transmission can be damaged by the unwanted power reflected back from the antenna, and rushing into its output. Therefore, the impedance should be adaptively matched in order to make a mobile system more efficient. There have been several ways to compensate the mismatch. A selective use among several matching circuits [3], and employment of an L, C bank to realize a good impedance

Takeshi TODA

Yasuyuki OISHI

Fujitsu Limited Yokosuka 239-0847, Japan [email protected], [email protected]

matching with combinations of those inductors and capacitors [4], [5] have been reported. These systems, however, have only a limited resolution of the impedance matching. Besides, often seen in the amateur radio apparatus, the use of variable capacitors combined with driving motors has a prohibitive volume for most of mobile communication terminals. The diversity antenna systems [6] are to give multiple antennas to a mobile terminal and to selectively use the antenna, which is least affected by the nearby objects. This method is, however, not easy to implement, increasing the antenna elements and corresponding RF components. The use of the steepest gradient algorithm [7] and the simulated annealing [8] for convergence of the adaptive impedance matching control have been reported. When some mathematical formulation is required, however, a precise modeling of the overall system and control elements is crucial. This is often difficult, therefore sometimes causes the deviation of the theory from the reality. Considering the problems above mentioned, we propose an adaptive impedance matching system, which utilizes mainly analog circuits and only simple digital circuits for generation of the timing signals. The adaptive control is conducted in a sequential manner, and it does not need any complicated mathematical formulation. In this system, only the elements to be controlled are two varactors (varactor diodes) in the pi-matching section. The algorithm of the proposed system has something in common with [9] and [10], both of which exploit what may be called the “test signal” to search for the correct direction of the control. However, components for digital signal processing as well as stepping motors are utilized both in [9] and [10], while our aim is to include no digital signal processing units, but only solid-state components in order to minimize the complexity and area of the system. In this paper, we first show the configuration of the system as well as some merits of the proposed system. Also the proposed adaptive algorithm is illustrated. Second, some simulational results are depicted to show how the adaptive matching system works for various kinds of mobile antennas under effects of a human body or a hand. Finally, it is shown how much the matching performance is improved in terms of input power to the antennas in comparison with a fixed capacitance matching system.

II. CONFIGURATION OF THE SYSTEM Figure 1 shows the configuration of the system. The system is now intended to be used in a transmitting path. It consists of (1) Matching circuit, (2) Mismatch measurement circuit (directional coupler), (3) Switch, (4) Timing generator for switching, and (5) Time constant generator (RC low-pass filter).

Measure Vr(n) at the end of VC2 frame VC1 frame start Increase VC1 voltage by charging the capacitor Measure Vr(n+1) after τd NO

Antenna (1) Matching circuit L

VC2

Reflection measurement

RF source

VC1

Controlled the same as VC1

(5) Time constant generator G2

(4)

(3) Switch

OFF the SW and decrease VC1 voltage until the end of VC1 frame

End of VC1 frame G1

Switching timing generator

S/H

YES

Continue to increase VC1 voltage until the end of VC1 frame

Detected reflection Vr

Detector

(2)

Vr(n+1)>Vr(n) ?

Constant voltage source

Fig. 1 Configuration of the proposed adaptive matching system for transmission. The varactors are used for the control elements in the pi-matching circuit. In this configuration, however, the available information to be used for the impedance matching is only the absolute value of the reflection coefficient between the RF source and the input of the matching circuit. Thus as long as we cannot measure the phase information of the reflection coefficient, we don’t know the correct direction of the control to minimize the mismatch. To solve this problem, we employ a test signal to observe if applying the test signal increases or decreases the mismatch. Then we know for the first time if the direction of the control was correct or wrong. The flowchart of the adaptive matching algorithm is shown in Fig. 2. The detailed explanation for it is as follows: (a) The latest value of the mismatch is measured through the detection circuit (2). (b) The switch (3) is turned on, i.e. the control voltage to the varactor 1 (VC1) is increased (at τf ). (c) The mismatch is again measured right after turning on the switch. Here, if the mismatch has been increased compared with the previous measurement, then the system recognizes that the direction of the control was wrong, and the switch is turned off to decrease the control voltage to the VC1 (at τf + τd). If the mismatch has been decreased compared with the previous measurement, the system recognizes that the direction of the control was correct, and the switch is kept turned on until the end of the control frame for the VC1. During the VC1 frame, the control voltage to the 2nd varactor VC2 is held to the value at the end of the last frame of the VC2. This voltage holding is conducted by the sample and hold circuits. After the VC1 frame is finished, the control voltage for the VC1 is held with the sample and hold circuit and the VC2 frame is commenced. The advantages of the proposed system are as follows: (1) Compared with other systems, which employ some mathematical criteria for optimization, the proposed system does not require such a complicated mathematical modeling.

Hold the current VC1 voltage with Sample & Hold and OFF the SW

The same for VC2 and return to VC1 frame

Fig. 2 Flowchart of the adaptive algorithm. (2) When a mathematical modeling is necessary, the control elements of the matching circuit should also be modeled precisely. In this case, nonlinearity of the varactors and etc. can be very problematic for a good convergence, because formulation of such nonlinear elements is difficult. The proposed system can accept also such nonlinear control elements. (3) In addition, the proposed algorithm can handle multiple controllable elements including various kinds of components such as inductors, capacitors, and resistors, if necessary. (4) The increase and decrease of the control voltages for the varactors are made by charging and discharging the capacitor of the time constant generator. Thus it is rather easy to change the response of the system because we need change either only one resistance or capacitance. III. SIMULATION RESULTS Some simulational consideration was made by using Simulink from The MathWorks Inc. Here, a case of transmission is considered. As shown in Fig. 2, the adaptive control is made on the basis of the reflection, which occurs between the matching circuit and the reflection measurement device, i.e. between (1) and (2) of Fig. 1. To detect the reflection, a directional coupler may be used in an actual implementation of the system. Also in the present simulation, the coupling and isolation of the directional coupler are considered. In addition, we need to investigate the range of the variation of the antenna impedance Za, because it determines constants in the pi-matching section and the time constant of the adaptive matching system. In the present work, three types of variation for the antenna impedance Za are considered as shown in Fig. 3; (a) The Za is alternated between 50 – j50 ohms and 50 + j20 ohms, considering the effect of a human body [1]. These values of the antenna input impedance Za, are approximated values from [1], which gives Za = 50 – j50 ohms as a simulation of a quarter-wavelength monopole antenna mounted on a mobile telephone without the effects of the operator. The Za = 50 + j20 ohms is the value

33

(c)

22 8

0.1λ loop

(c) 39

(a)

71

Unit: mm

39

0.19λ monopole 82

(b)

19

(b)

Fig. 3 Alternation of the antenna impedance Za due to the effects of the human body or hand on the Smith chart; (a) Values from [1], (b) A 0.19λ monopole antenna, (c) A 0.1 λ small loop antenna. (c) A 0.1 λ small loop antenna on a rather small ground plane ((c) in Fig. 3) was measured with and without human hand on the ground plane. The Za is 1 + j70 ohms without human hand and 30 + j100 ohms with it. The measurement was conducted by using an Agilent 8720ES network analyzer and the measurement frequency was 2.45GHz for both (b) and (c) of Fig. 3. The tendency of the antenna input impedance Za with and without hand on the ground plane is that with the hand, the real part of the Za is increased, and at the same time the imaginary part of the Za is also increased. This is because the loss is increased with the introduction of the human hand, and the increase in the current path leads to the increase in the inductive element in the antenna system.

Mismatch Mismatchloss loss(d(dB) B

Fixed Capacitances (2.8pF, 4.9pF) Adaptive matching

2

evaluated by observing the time characteristics of the mismatch loss, i.e. 1/(1–|S11|2): S11 is the reflection occurred between the matching circuit and the RF front end. A fixed impedance matching system with fixed capacitances is also simulated for comparison. The fixed capacitance matching system employs 2.8pF and 4.9pF of the capacitances for the VC1 and VC2, respectively, to obtain a good impedance matching (with about – 28dB of the reflection) at Za = 50 – j50 ohms. The other parameters for the simulation are: operating frequency: 2.45GHz, range of capacitance for varactors: about 3.2pF – 4.2pF, inductance for the matching circuit: 2.0nH. The time constant for the time constant generator is 0.1sec (The selection of an appropriate time constant is a trade off between the quick response and a degree of overshooting). The frequency of the fluctuation for the antenna input impedance Za is 2Hz, i.e. it alternates every one second. The duration of the controlling frame for each varactor VC1 and VC2 is about 60ms. As shown in Fig. 4, the time characteristic of the adaptive matching control oscillates between good and bad matching conditions. In other words, a good matching condition turns to be bad in the next short moment and this deteriorates overall performance of the adaptive matching system. Therefore, it would be desirable to keep the good matching condition once a good matching has been achieved. This function might be realized by stopping the adaptive control and keeping the latest value of the control voltages for the VC1 and VC2, when the mismatch becomes less than a certain threshold value. Figure 5 depicts the result of this control. The threshold value to Fixed Capacitances (2.8pF, 4.9pF) Mismatchloss loss(dB(dB) ) Mismatch

with the effect of the nearby head of the operator. (b) A 0.19λ monopole antenna on a rather small ground plane ((b) in Fig. 3) is measured with and without a human hand. The Za is 10 – j55 ohms without human hand and 25 – j10 ohms with it.

Adaptive Matching

2

1

0 0

1

2

4

6

Elapsed time (sec) Elapsed time (sec)

0 0

2

4

6

Elapsed time Elapsed time(sec) (sec)

Fig. 4 Time characteristics of the mismatch loss for adaptive matching and fixed capacitance systems for (a) in Fig. 3. Figure 4 shows the simulation result for the mismatch loss for (a) in Fig. 3. Here the adaptive matching system is

Fig. 5 Time characteristics of the mismatch loss for the adaptive matching and fixed capacitance systems for (a) in Fig. 3. The adaptive matching system holds the control when the reflection becomes less than about –8.5dB. hold the control is about –8.5dB of the reflection. From Fig. 5 it is observed that the adaptive matching system holds the value of the control voltages for the varactors from the beginning of the simulation, and thus the reflection does not change until the first transition of the antenna input impedance Za. Then at 1sec, the adaptive matching system experiences a

3

Improved power (dB) (dB) Reflection coefficient

Figs. 7 and 8 show the mismatch loss for (b) in Fig. 3 and the amount of the power improvement, respectively. Also, Figs. 9 and 10 depict the same characteristics for (c) in Fig. 3. 3

Improved power Reflection coefficient (dB)(dB)

sudden change of the Za, hence the mismatch loss increases accordingly, and the adaptive matching system tries to reduce the reflection. Then, the reflection becomes less than about –8.5dB, and the system stops controlling and holds the values of the capacitance of the varactors VC1 and VC2.

2 1 0 -1

2 1 0 -1 -2 -3

-2

0

-3 2

4

6

Elapsedtime time (sec) Elapsed (sec)

Fig. 6 The amount of the power improvement by using the adaptive matching system compared with the fixed capacitance matching system for (a) in Fig. 3. This is a simple subtraction between two lines in Fig. 5. Figure 6 shows the amount of the improvement of the input power to the antenna by the adaptive matching system. The amount of the improvement is negative when the mismatch loss by using the adaptive system is larger than that of the fixed capacitance system as shown in Fig. 5. However, what is very important here is that the power is improved by about 2dB under the bad impedance matching condition (1sec – 2sec, 3sec – 4sec, and 5sec – 6 sec) with the introduction of the adaptive impedance matching system. Fixed Capacitances (2.0pF, 7.5pF) Adaptive Matching

6

Fixed Capacitances (3.1pF, 21.0pF)

15

Adaptive Matching

10

5

0 0

2

4

6

Elapsed time Elapsed time(sec) (sec)

5 Mismatch loss(dB) Mismatch loss (dB)

4

Fig. 8 The amount of the power improvement by using the adaptive matching system compared with the fixed capacitance matching system for (b) in Fig. 3. This is a simple subtraction between two lines in Fig. 7.

Mismatchloss loss(dB(dB) ) Mismatch

0

2

Elapsedtime time (sec) Elapsed (sec)

4

Fig. 9 Time characteristics of the mismatch loss for the adaptive matching and fixed capacitance systems for (c) in Fig. 3. The adaptive matching system holds the control when the reflection becomes less than about –8.5dB.

3 2 1 0 0

2

4

6

Elapsed time time (sec) Elapsed (sec)

Fig. 7 Time characteristics of the mismatch loss for the adaptive matching and fixed capacitance systems for (b) in Fig. 3. The adaptive matching system holds the control when the reflection becomes less than about –8.5dB.

The behavior of the power improvement in Figs. 6, 8, and 10 differs rather widely. This is mainly due to the difference in the quality factor (Q) of the antennas. The antenna (a) in Fig. (3) has the lowest Q value among the three antennas, and thus its impedance bandwidth is rather wide so that a stable improved power is obtained as shown in Fig. 6. On the other hand, the antenna (c) in Fig. 3 has the highest Q among the three antennas, therefore the impedance bandwidth is very narrow and the power improvement varies very largely as shown in Fig. 10. In Fig. 8, however, the power improvement shows a moderate behavior, fluctuating approximately between -0.5dB and 2.5dB with the antenna (b) in Fig. 3. This is

3

The system employs mainly analog circuits, and no digital signal processing components as well as no electro-mechanical components are necessary. The improvement of the input power to the antennas using the adaptive matching system was confirmed by about 2 – 3dB in comparison with the fixed matching system. The amount of the power improvement, however, depends on how the antenna impedance fluctuates. Hence the behavior of the antenna impedance should be elaborately investigated on the basis of the applications before an implementation of the proposed system. The experimental study will be reported in the next occasion.

0

ACKNOWLEDGEMENT

-3

This research was supported by the National Institute of Information and Communications Technology of Japan.

Improved power(dB) (dB) Reflection coefficient

because the Q value for the antenna is also moderate compared with other two antennas.

9 6

0

2

4

6

Elapsed time Elapsed time(sec) (sec)

REFERENCES

Fig. 10 The amount of the power improvement by using the adaptive matching system compared with the fixed capacitance matching system for (c) in Fig. 3. This is a simple subtraction between two lines in Fig. 9. It should be mentioned that the time constant of the time constant generator in Fig. 1, the threshold value for the holding the control, and the range of the capacitances for the VC1 and VC2 in each type of the alternation for the antenna impedance (a), (b), and (c) in Fig. 3, are adjusted in order to give considerably good results in Fig. 6, 8, and 10. In particular, how to select the range of the capacitances for VC1 and VC2 may be of interest. In general, a better result of the adaptive matching is obtained by roughly including the values of the capacitances, which realize the impedance matching at both of the alternating antenna impedance, e.g. 50 – j50 ohms and 50 + j20 ohms for case (a) in Fig. 3, and 1 + j70 ohms and 30 + j100 ohms for case (c). The parameters used for each antenna in Figs. 5 – 10 are tabulated in Table I. The capacitances for the fixed capacitance matching systems are also listed. The value of the inductance L is common for both of the adaptive and fixed matching systems. In any case, at first the range of the variation for the antenna impedance Za should be estimated on a basis of the application so that appropriate combination of the parameters is considered. Table I Parameters for calculation in Figs. 5 – 10. Capacitance range Time Threshold (dB) (VC1, VC2) (pF) constant (sec)

L(nH)

Fixed cap. C1, C2 (pF)

(a)

0.01

about – 8.5

3.2 – 4.2, 3.2 – 4.2

2.0

2.8, 4.9

(b)

0.08

about – 8.5

2.0 – 2.6, 5.0 – 6.8

1.9

2.0, 7.5

(c)

0.1

about – 4.0

3.1 – 3.2, 21.0 – 7.3

2.1

3.1, 21.0

IV. CONCLUSIONS An adaptive antenna impedance matching system for mobile communication terminals has been proposed and simulated.

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