Design for A Linear Voltage-controlled 360

Design for A Linear Voltage-controlled 360 -Analogue Phase Shifter M. X. Xiao, S. W. Cheung and T. I. Yuk The Department of Electrical and Electronic Engineering The University of Hong Kong, Hong Kong Abstract — The paper presents the design of a linear voltage-controlled 360 analogue phase shifter operating at 2.2 GHz. It is a reflection-type with a simple and compact structure, employing a /4-coupled-line coupler with the output ports terminated with identical paralleltuned varactor-diode circuits for a full 360 -phase shift. Formulas are derived for making use of the dimensions of the transmission lines to linearize the phase shift against the control voltage. Simulation and measurement results on the linearity and insertion loss are presented. Index Terms — coupled line, linear voltage-controlled, phase shifter, reflection type, serial varactor diodes.

I.INTRODUCTION Phase shifters can be designed using loaded transmission-line techniques to achieve a 360 phase-shift range [1], but these designs require the use of many diodes and transmission lines of several wavelengths and so are bulky and not cost effective. Reflection-type phase shifters can be made small and designed to achieve a 360 phase-shift range by connecting varactor-diode circuits at the ports of the reflection devices such as branch-line couplers [2]. In the design of a reflection-type phase shifter, the following factors should be considered: 1) phase-shift range, 2) attenuation ripple, 3) bandwidth requirement, and 4) linearity of phase shift versus the control voltage. Several methods have been made to satisfy these requirements [3], but none can satisfy all these four requirements in a single circuit. Thus

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the phase shifter designers have to make trade-offs among these requirements. The authors in [2] described a reflection-type phase shifter to provide a full 360 phase shift, but the linearity of phase shift versus control voltage was not considered. The design of reflection-type phase shifters often employs a 3-dB branch-line coupler. In [4], an optically controlled phase shifter using a  / 4 -coupled-line coupler in a reflection-type topology was proposed. Since the size of a  / 4 -coupled-line coupler is much smaller than a branch-line coupler which consists of four branches of  / 4 -transmission lines, the phase shifter had a much compact size. However, the phase shifter could only provide a 120 phase-shift range. In this paper, we propose a new design of a reflection-type analogue phase shifter which is linearly voltage-controlled, with a phase-shift range of 360 at a frequency of 2.2 GHz in microstrip form. It employs a  / 4 -coupled-line coupler, instead of 3-dB 90 branch-line coupler, to reduce the circuit size for implementation. The two output ports of the coupler are terminated with identical reflective loads, containing two parallel branches of tuned varactor-diode circuit. The tuned varactor-diode circuits have purely reactive impedance in order to achieve a phase-shift range of 360 in the phase shifter. The relationship between the phase shift and the control DC voltage is a function of the reactance of the varactor-diode circuits and so can be linearized by using the widths and lengths of the transmission lines on the substrate The remainder of this paper is organized as follows. The design of the proposed reflection-type 360 phase shifter is described in section II. Simulation results using ADS 2008A together with

measurement results are presented in section III . Section IV is conclusions.

II.DESIGN OF LINEAR REFLECTION-TYPE 360◦ PHASE SHIFTER Using  / 4 -coupled-line coupler

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A reflection-type phase shifter often employs a 3-dB 90 branch-line coupler which can be regarded as a two-port network shown in Fig. 1(a) [5]. The input signal to port #1 is equally divided into two signals with 90 out of phase at ports #2 and #3. If each of these two ports is terminated with an identical load with purely reactive impedance, the two reflected signals will combine in phase to produce the output signal at port #4, but cancel with each other at port #1 [4,5] leading to a low insertion loss. This type of phase shifters can be implemented easily and at low cost using microstrip transmission lines. However, one of the drawbacks of such design is that the branch-line coupler requires four  / 4 -transmission lines for implementation, which leads to a relatively larger circuit size. In this paper, we propose to use a  / 4 -coupled-line coupler, instead of a branch-line coupler, to reduce the circuit size. Our proposed

refection-type 360 phase shifter using a  / 4 -coupled-line coupler is shown in Fig. 1(b).

(a)

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(b) Fig. 1 (a) Schematic of reflection-type phase shifter (b) Reflection-type phase shifter using  / 4 coupled-line coupler The signal input to port #1 of the coupled-line coupler in Fig. 1(b) is divided into two signals with 90 out of phase at ports #2 and #3. If these two ports are terminated with identical reflective loads (indicated as the two variable impedances in Fig. 1(b)) having purely reactive impedances, the reflected signals at port #4 will have same phase [5] and so combine together in phase to produce the output signal at port #4. While the reflected signals at port #1 will have 180 out of phase and so cancel off. The basic principle of the phase shifter is to appropriately vary the reactance of the reflective loads terminated at ports #2 and #3, hence to change the phase of the output signal at port #4. Reflective load for a full 360 phase shift Normally varactor diodes are used as the variable capacitance elements in the design of the reflective loads in Fig. 1(b), and a reverse-biased DC voltage is used as the control voltage to vary the varactor capacitance and hence the phase shift of the output signal at port #4. Thus the reflective loads terminated at ports #2 and #3 of the coupler play a very important role in the range of the phase shift. Studies have

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shown that using a single serial-tune varactor-diode circuit as the reflective loads can only provide a limited phase-shift range [6]. For larger phase-shift ranges and low attenuation ripples, a reflective load consisting of two serial-tuned varactor-diode circuits in parallel can be used. In [6], a circuit using two parallel branches, each having a varactor diode in series with a short-circuited microstrip line, as shown in Fig. 2 (a), was proposed to achieve a full 360 phase shift, but the linearity dependency of the phase shift on the control DC voltage was not considered. In Fig. 2(a), the  / 4 -long transformer connects together the two resonant circuits having impedance j ( X di  X si ) , for i  1, 2 . The values of X si are designed and fixed to achieve the required resonances, so there is not much freedom of adjustment in the design. Thus here we propose to use two additional series microstrip transmission lines, TL1 and TL2, in each of the resonant circuits as shown in Fig. 2(b) to give more freedom of adjustment in our design. Moreover, we propose to use two (identical) serial varactor diodes, instead of one varactor diode, in each of the resonant circuits, so that the resultant capacitance is smaller, leading to a smaller controlvoltage range required. This relaxes the minimum capacitance requirement of the varactor diode in the design (as varactor diodes with lower capacitances are more difficult to fabricate and require larger reverse-biased voltages to reach the minimum values).

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Fig. 2

Reflective load (a) using two series-tuned varactor-diode circuits in parallel and (b) adding two

additional transmission lines to the varactor-diode circuits in (a). Linearity optimization From transmission line theory [5], it can be shown that the impedances X i , for i  1, 2 , of the two branches in Fig. 2 (b) are purely imaginary and given by:

X 1  Z t1

( X d 1  X s1 )  Z t1 tan 1 Z t1  ( X d 1  X s1 ) tan 1

(1)

X 2  Zt 2

( X d 2  X s 2 )  Z t 2 tan  2 Z t 2  ( X d 2  X s 2 ) tan  2

(2)

where Z t1 and Z t 2 are the characteristic impedances of the serial transmission lines TL1 and TL2, respectively, with 1 and  2 their respective electrical lengths, X s1 and X s 2 are the reactance of the shorted-stubs TL3 and TL4, respectively, and X d 1 and X d 2 are given by X d1 

X d 11 X d 12 X d 21 X d 22 , Xd2  X d 11  X d 12 X d 21  X d 22

(3)

with X d 11 , X d 22 , X d 21 and X d 22 the reactance of the individual varactor diodes. The capacitance of a varactor diode is inversely proportional to the reverse-biased DC voltage [5]. It can be seen in (3) that the resultant reactance of two varactor diodes connected in series is smaller than that of the either diodes and so requires less bias voltage to reach the minimum capacitance value. As a result, less control voltage is required for a full 360 phase shift. The input impedance seen by the coupled-line coupler is: X

X1 X 2 X1  X 2

(4)

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The reflection coefficient of the reflective load is: 

jX  Z 0 jX  1 X    e j ; X  jX  Z 0 jX  1 Z0

where

    2 tan 1 ( X )

and

X

(5)

(6)

X Z0

(7)

with Z 0 the characteristic impedance of the input and output arms of the coupler. From (6), it can be seen that to have a full 360 phase shift, the variable X needs to be varied from negative infinity to positive infinity. This could be approximately implemented by tuning one varactordiode circuit to resonant at the minimum reverse bias by using the associated series transmission line and the other varactor-diode circuit to resonant at the maximum reverse bias using the associated series transmission line [5]. To design a linear phase shifter, we take partial differentiation in (6)

 X 1 1   2 1  ( X ) V 1  ( X )2 V

X 1 X 2  X 12 V V ( X1  X 2 )2 Z0

X 22

(8)

where X i Z ti ( Z ti  tan 2  i ) X di  i    2 ( Z ti  ( X di  X si ) tan i ) V V If

(9)

 in (8) is kept constant within the operating DC voltage range, the phase shift will be linearly V

proportional to the control voltage. In the design process, to reduce the linear dependency of the phase shift on the applied DC voltage, we should find out the characteristic impedances Z t1 and Z t 2 and the corresponding electrical lengths 1 and  2 of the transmission lines TL1 and TL2, and the impedance

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X s1 and X s 2 of the shorted-stubs TL3 and TL4, respectively, that lead to a constant whole control-voltage range. However, to make

 within the V

 constant is extremely difficult, so we define a V

phase-deviation function:

F

N

 i 1

(  360

Vi 2 ) Vmax

(10)

N

where Vmax is the maximum control voltage for a full 360 phase shift, Vi is a control voltage between 0 V and Vmax , N is the number of points within the control-voltage range used to compute the phasedeviation function, and  is the phase shift given by (6). Then now our design process becomes to find out the values of Z t1 , Z t 2 , 1 ,  2 , X s1 and X s 2 that lead to a minimum value of the phase-deviation function in (10). The schematic of the proposed phase shifter employing a coupled-line coupler is shown in Fig. 3, where port #1 and port #4 are the input port and output port, respectively. Two reflective loads, as shown in Fig. 2 (b), are connected to ports #2 and #3. In each of these reflective loads, a reverse-biased voltage VDC (the control voltage) is used to control the capacitances of the varactor diodes, in turn, the impedance of the varactor diode circuits, and hence the amplitude and phase shift of the coupled signal. The DC voltage is applied to the diodes via a  / 4 -long transmission line (TL0) in series with an open stub (R0) to isolate the high-frequency signals from the biased DC circuit. The inductive transmission lines TL3 and TL4 are connected to the ground through via-holes. In our study, we attempt to design a linear phase shifter for a phase-shift range of 360 at the frequency of 2.2 GHz.

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Fig. 3 Schematic layout of proposed 360 -phase shifter

III.SIMULATION AND MEASUREMENT RESULTS In the design of the phase shifter with the schematic layout of Fig. 3, the computer simulation tool, ADS 2008A, has been used to optimize the dimensions of Z t1 , Z t 2 , 1 ,  2 , X s1 and X s 2 with the objective to minimize the phase-deviation function in (10), i.e., to linearize the relationship between the phase shifter and the control voltage. In the simulation, the substrate used was Rogers’ RO4350B, with a thickness of 30 mil (0.76 mm), dielectric constant of 3.48 and loss tangent of 0.0037. The varactor diodes were Skyworksinc’s SMV1245. The input port #1 and output port #4 were connected with 50-  transmission lines. The optimum parameters obtained from simulation were as follows. The width and spacing of two coupled lines in the coupler were 86 mil and 11 mil, respectively. The characteristic impedances of TL1, TL2, TL3 and TL4 were 48.6  , 56.0  , 46.9  and 46.9  , respectively, with the corresponding electrical lengths of 74.0°, 11.1°, 37.0° and 75.3°. The diameter of the via-holes at the ends of TL3 and TL4 was 32 mil. The characteristic impedance of the  / 4 -transmission line TL0 in the reverse DC biased circuit was 100  at 2.2 GHz. The radius of the open radial stub R0 was 609 mil

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with an angle of 70°. The biased voltages VDC was applied to the circuit via a by-pass capacitor (surfacemounting-technology one) with a value of 2.2 μ F and size of 1208 (120 mil * 80mil).

Fig. 4

Photograph of the phase shifter prototype

(a)

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(b) Fig. 5 Phase shift versus control DC Voltage: (a) Simulated and (b) measured results

The phase shifter of Fig. 3, using the optimized dimensions obtained, has been fabricated on a substrate, Rogers RO4350B, as shown in Fig. 4. The simulated results using ADS 2008 A and measured results on phase shift versus control DC voltage are shown in Fig. 5. It can be seen that both sets of results agree closely with each other. A phase-shift range of 360 can be achieved with a control-voltage range of 0 to 20 V, and the phase shift is very linearly proportional to the control voltage. The maximum linearity errors in the simulation and measured results are only 6 and 8 , respectively. The insertion losses of the phase shifter within the working range of DC voltage have also been simulated and measured. Figure 6 shows that the maximum insertion losses in the simulated and measured results are 6.5 dB and 8 dB, respectively. The measured average insertion loss is about 8 dB with ripples of less than 1 dB.

Fig. 6 Insertion loss versus biased DC voltage

IV.CONCLUSIONS

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A linear voltage-controlled 360 reflective-type phase shifter operating at 2.2 GHz has been designed and fabricated. To reduce the size of the phase shifter, a  / 4 -coupled-line coupler, instead of branchline coupler, has been proposed in the design. Two parallel tuned varactor-diode circuits terminated at the output ports of the  / 4 -coupled-line coupler are used to provide a full 360 phase shift. Formulas have been derived to linearize the relationship between the phase shift and the control DC voltage using the dimensions of the transmission lines on the substrate. Simulation results have agreed well with measurement results which have shown that the phase shift is almost linearly proportional to the control DC voltage with a maximum linearity error and a maximum insertion loss of 8 and 8 dB, respectively.

REFERENCES 1. R. V. Garver, 360 Varactor Linear Phase Modulator, IEEE Transactions on Microwave Theory and Techniques 17 (1969), 137-146. 2. T. W. Yoo, J. H. Song and M.S. Park, 360 Reflection-type Analogue Phase Shifter Implemented with A Single 90 Branch-Line Coupler, Electronic Letters 33 (1997), 224-226. 3. K. Liu, E. Y. B. Pun, and X. J. Tian, L-band 360 Broad-bandwidth Monolithic Analog Phase Shifter, Microwave and Optical Technology Letters 36 (2003), 164-166. 4. M. El Khaldi, F. Podevin, and A. Vilcot, Microstrip Parallel-Line coupler to perform broadband optically controlled phase-shifting, Microwave and Optical Technology Letters 47 (2005), 570-573. 5. A S. Koul and B. Bhat, Microwave and Millimeter Wave Phase Shifters, Vol.2, Artech House, Norwood, 1991. 6. J. S. Tan and P. Gardner, A LINC Demonstrator Based on Switchable Phase Shifters, Microwave and Optical Technology Letters 35 (2002), 262-264.

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