Theoretical and Experimental Characterization of Distributed Analog Phase Shifter

M. Ould-Elhassen, M. Mabrouk, A. Ghazel

CIRTA’COM, SUPCOM-ISETCOM-UC de Tunis Cité Technologique des Communications, 2088, Tunis,

Tunisie mohamed.mabrouk@isetcom.rnu.tn

Ph. Benech IMEP-LAHC, UMR-5130-CNRS-INPG-UJF

MINATEC, 3-Parvis Louis Néel, BP 257, 38016 Grenoble, France

Philippe.Benech@ujf-grenoble.fr

Abstract—This paper describes a theoretical study and experimental characterization of distributed phase shifter based on CPW line loaded by MACOM varactor diode. A circuit simulation combined with electro-magnetic simulation is presented and compared with measurement. In this work, we present also an impedance matching method allows adapting our phase shifter without additional circuit. The expression of phase shifting is obtained through the global ABCD matrix of proposed phase shifter circuit and compared with the measurement. The simulations are carried out on Matlab and ADS (Momentum) software’s, a comparison between two simulations and measurement of fabricated phase shifter is made in order to validate the theoretical modeling and experimental characterization, good agreement is obtained.

Keywords—Phase Shifter, Loaded Line, Coplanar Wave Guide, Analytical modeling, Circuit Simulation.

I. INTRODUCTION With the explosion in recent years of wireless

communications, multi path systems and phased array technologies are becoming very important and need for robust, simple, cheap, digital or analogue solutions [1]. Phase shifter is a microwave device that represents a very important part of microwave system and permits to more flexibility to change the system proprieties. Distributed phase shifter, fabricated on transmission lines periodically loaded by Varactor diode, i.e. lumped components, was characterized and reported by [2-3]. It consists of a high impedance line capacitive loaded by periodic cascaded variable capacitance.

In this paper, we demonstrated by changing a value of loaded capacitance on the line, the phase velocity of the line can be changed and creates a phase shift. The phase shift can be varied in a large variation range depending on the capacitance value and the length of the distributed line.

We have design and fabricated a phase shifted work on 2.4 GHz that can be used for the standard IEEE 802.11, we have used the MACOM varactor diode to load the transmission line and good result was obtained.

II. MODELING AND OPTIMISATION OF DISTRIBUTED PHASE SHIFTER

The figure 1 shows the electrical equivalent circuit of the entire phase shifter. It composed by several units cell, each cell is a 2-ports network. To change the loaded capacitance value, we use varactors diodes polarized by bias voltages, we only have changed the values of these voltage to change the capacitances. The whole of the phase shifter can be easily represented with cascaded networks [4].

C C

iZiZiZiZ

Ω= 500Z Ω= 500Z

Figure 1. Entire phase shifter model

A Coplanar Wave Guide (CPW) transmission line is used for phase shifter. The CPW structure is characterized by its effective permittivity and characteristic impedance.

To maintain a balanced CPW line, a balanced shunt loading topology was chosen with two shunt variable capacitance (Varactor diode) per transmission line cell unit, one to each of the ground planes.

A. Design of Analogue Phase Shifter In order to calculate the phase shift of the studied phase

shifter shown in the figure 1, we use the global matrix ABCD concept, composed by cascaded sub-matrixes [5].

The number of sections that constitute our phase shifter is chosen according to the phase shift desired [3] and is analytically calculated in the following section. Each of central section of the phase shifter is consisting of CPW transmission line portions periodically loaded by parallel C circuit that we can also vary the values. The electrical equivalent circuit of each central section is shown in figure 2 [5] where Zi is the characteristic impedance and θi is the electric length.

dC varC

2dL

2dL

secl

iZ iZ

varC

Figure 2. Equivalent circuit of central section.

The parameters Cd and Ld are the inductance and capacitance of each unit cell [5-7].

ii

d ZvlL sec= and

iid vZ

lC sec= (1)

Where vi is the phase velocity of unloaded transmission line.

The model presented by equation (2) give the matrix of central unit section as function of LC modeling.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

102

1101

102

1 dd Lj

jC

Lj ω

ωω (2)

The model of periodic sections transmission line has a

Bragg frequency defined and shown in equation (3), it is similar to optical Bragg diffraction [5].

( )var

1CCL

fdd

Bragg+

=π

(3)

2

var

1 ⎟⎟⎠

⎞⎜⎜⎝

⎛−

+=

Braggd

dABCD CC

LZω

ω (4)

From equation (4), the characteristic impedance is written

as function of Bragg frequency, it is evident that for frequency well below the Bragg frequency f << fBragg the characteristic can be simplified to the equation (5).

varCCLZ

d

dL +

= (5)

The first key of design relationship is obtained by imposing the constraint that when the varactor is in its maximum capacitance state [3].

We define the ratio:

dClC

x secmax /= and

min

max

CCy = (6)

The phase velocity of distributed loaded line and the section length can be written as function of x and the minimum Bragg frequency as following:

xZZ Li += 1 (7)

xvv i

phase +=

1 (8)

xfvl

Bragg

i

+=

1minsec π (9)

The phase shift generated by one unit cell can be also defined as following:

phasevl

f sec2πϕ = (10)

In order to design our phase shifter, we must consider the cases that we have the minimum and the maximum of varactor capacitor, so the maximum differential phase shifting which can be obtained by one cell unit is:

( )xvl

fi

+= 12 secmax πϕ and ( )xy

vl

fi

+= 12 secmin πϕ (11)

( )xyxvlf

i

+−+= 112 secπδϕ (12)

The equation (13) allows us to determine the number of section of phase shifter. To get a differential phase shifting of 360° at a specified frequency f, the correspondence number of sections is given by:

δϕπ2=n (13)

The global ABCD matrix of entire phase shifter is given by equation (14).

n

global DCBA

DCBA

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛ (14)

The phase shift is the phase of S21 parameter of studied phase shifter. The equation (19) shows the expression of S21 deduced from the global matrix.

DCZZBA

S+++

=0

0

212 (15)

The phase shift is the argument of the S21.

B. Matching Problem Impedance matching is very important to allow a

maximum power transferring coming from a system and entering into the phase shifter. Also at the output, we can have a maximum power transferring using output network impedance matching.

Our phase shifter is a loaded transmission line of characteristic impedance ZL and length n × lsec.

seclnltot ×=

Lphase Zv ,

Figure 3. Entire Phase Shifter.

To insure smooth passage between reference impedance 50Ω and ZL we must use the equation (7) and take ZL=50Ω, that permit to match the phase shifter without additional circuit [3].

C. Varactor Model In this work, we have used the MACOM46H071 varactor

diode to change the capacitance of loaded transmission line. The following figure gives electrical model.

sR sL

pC

jC

Figure 4. Circuit model of diode Varactor

This model of diode varactor has a series resistance Rs, parasitic series inductance Ls, and parasitic parallel capacitance Cp. Equation (16) gives the mathematical expression of variable capacitance.

Mj

jjj

V

CVC

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

φ1

)( 0 (16)

Where Cj is the fitted junction capacitance, Cj0 is the zero-bias junction capacitance, V is the junction potential, φ is the fitted potential barrier and M is the grading coefficient.

TABLE I. VARACTOR DIODE PARAMETERS

Rs Cp Ls Cj0 Q 0.4Ω 0.13pF 1.3 nH 2.45pF 4500

III. FABRICATION For the simulation, we have implemented our Matlab

program for ABCD matrix calculating of the circuit and theoretical modeling, and we have compared our simulated result with the same results calculated with ADS software.

In our first simulation, we used the following key parameters: x=5 and fbragg(min) = 2×fc=4.8Ghz. We also used the same substrate RO4003 with εr =3.36, H=813.0μm and tg(δ)=1.5*10-3. the following figure gives the variation section number and section length as function of the variable x.

The capacitance variation is comprised between Cmax=2.5pF, Cmin=0.5pF.

Figure 5. Section Number and Section Length as function of x.

The figure 5 resumes the variation of section length and number of section that composed our phase shifter versus the x parameter. These values are computed at the frequency f=2.4GHz. We can deduce that if we increase the parameter x we get lower number of section and short length of section.

The parameters values of our phase shifter are given in the following table II, we compute the design parameter at the frequency f=2.4GHz.

TABLE II. DESIGN PARAMETERS

Ld(nH) Cd(pF) Zi(Ω) n lsec(mm) 3.9789 0.2652 122 4 7.7 The figure 6 gives the fabricated phase shifter. We can

see the 4 sections loaded by MACOM varactor diode. The parameters of transmission line are W=1.54mm, G=1.9mm and εeff = 1.6075.

Figure 6. Measured Phase Shifter.

IV. MEASUREMENT The measurement was done in the laboratory IMEP-

LAHC. We used a Vector Network Analyzer with power stability mixed with the RF signal for diode polarization. We have also used ADS circuit simulator, for computing the argument of S21 and validate our analytical model.

These results show a good agreement between our Matlab theoretical end circuit simulation results and ADS circuit simulation. That also confirms the validity of our analytical modeling.

Figure 7. Measurement and Simulation results of phase shifting for

different bias voltage.

The figures 7 show the phase shift variation versus frequency, the capacitance varies between 0.5pF and 2.0pF (obtained from diode datasheet). A linear phase shift variation is realized by the phase shifter for different value of the bias. For Vbias=10V the maximum value of differential phase shift is about 420° while for Vbias=15V the phase shift varies from 0° to 500°. The figure 7 shows a good resemblance between our simulation results and measurement.

Figure 8. Measurement and Simulation results of insertion loss for

different bias voltage.

The figure 8 shows the variation of insertion loss versus frequency for different value of capacitance. The maximum |S21| losses, for Vbias=10V is about |S21(2.4GHz)|=0dB, for Vbias=15V is about |S21(2.4GHz)|=-1dB. If we increase the value of bias voltage we get lower quantity of losses. The results obtained with Matlab and ADS have good agreement with measurement, which confirm again our theoretical modeling.

Figure 9. Measurement and Simulation results of return loss for different

bias voltage.

The figure 9 gives the variation of return loss of our phase shifter versus frequency and for different value of bias voltage. The maximum return loss |S11|, according to the bias voltage variation, for the voltage Vbias=10V and we deduce that if we increase the bias voltage value we can get more efficient phase shifter with less return loss.

V. CONCLUSION In this work, we have developed an analytical modeling

based on ABCD matrix principle for analogue distributed phase shifter. We have used varactors diodes like variable capacitance according to bias voltages. We have implemented Matlab program for computing the coefficients of ABCD matrix and ADS software to perform E/M simulation in order to validate our model. Then we deduced S21 and the phase shifting which is the argument of S21. Good agreements are denoted between all of our simulation results and measurement that confirm the validity of our theoretical modeling.

REFERENCES

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