Analysis and Design of a GaAs Monolithic Tunable Polyphase Filter in S / C Bands

This paper proposes a new topology of a 2-Stages Ac tive Polyphase Filter (APPF) in MMIC GaAs technology. This new topology, named “radial”, allows a greater balancing of output signals phases and amplitudes, over the actual APPF ’s at the state of the art. In this paper an ex-novo study is shown and synthesis formulas for the APPF are provided. The MMIC simulations in 15GHz bandwidth show a tunable Image Rejection Ratio (IRR) greater than 40dB, a worst case input/output matchi ng of 7.8dB and a maximum insertion loss of 10.8dB. By comparis on with the tandem topology, as will be shown in the following, the radial one allows a significant improvement in the electrical performances.


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wideband operation and it is well suited to be simply integrated in MMIC technologies; hence, it is very attractive for a lot of miniaturized and cost effective electronic systems.Furthermore, it must be considered that the polyphase filter can be used as a phase shifter [11]: by varying the outputs amplitudes, for example using Variable Gain Amplifiers (VGA's), and combining them it's possible to change phase of the output signal. .Unfortunately, at the actual state of the art, multistage APPF's are realized in tandem topology, which are topologically limited by a low balancing of phases and amplitudes of the output signals.
In order to overcome such drawback, in this paper we propose a new PPF topology with synthesis formulas and an useful application example to estimate the powerful of the proposed solution.
This paper is organized as follows: In Section II the analysis of PPF is briefly exposed, giving expressions for input and output differential impedances.In Section III, the strategy used to select the tuning element is reported.In Section IV, the design of the radial and tandem topologies of the APPF 1-5GHz in GaAs technology is shown.Finally, in Section V we report the conclusions of this work.

II. THE POLYPHASE FILTER SOLUTION
The polyphase filter (PPF) is an n-port electric network composed by a series connection of multiple stages of RC sub-networks, each of them is a ring of resistors and capacitors arranged alternately in a closed loop.In the simplest case, the polyphase filter has 4 inputs and 4 outputs (4I/O), but in the most general case it can have n-inputs and n-outputs.For example, a one stage 4 I/O polyphase filter can be seen in Figure 1: the outputs O 1 …O 4 can be considered as 4 unbalanced ones, otherwise as a couple of balanced (or differential) ports O 1 -O 3 and O 2 -O 4 .Between each port and the nearest ones there is a 90° phase difference [1]; for example, the signal taken between the ground and the port O 1 (O 2 ) and the signal taken between the ground and the port O 2 (O 3 ) there is a phase shift of 90°.Hence, by taken as reference for instance the signal between the ground and the port O 1 , the signals taken between the ground at the ports O 2 , O 3 and O 4 have respectively of 90, 180° and 270°: It means that ports O 1 and O 3 and the ports O 2 and O 4 are couples of differential ports and a phase shift of 90° exists between such two couples of differential ports [7].The main application of the PPF in Figure 1 is that to generate 4 quadrature signals at the outputs, a required function in an image reject receiver or in a SSB modulator for example.
An innovative design approach is proposed in this paper, it is based on a "radial topology", which does not introduce phase and amplitude imbalances.The physical layout can be considered as a design requirement as will be described in this paper.APPF have been implemented in CMOS technology, [12][13][14] but until now never in GaAs technology.The range 1-5GHz is easily covered in CMOS technology which is inexpensive and the circuit can be included on the same die with other blocks.Good values of IRR are also achieved with more stages.However, in this project, the GaAs technology has been considered because it is a high reliability process with low losses in the AoP16 microwave region and a low cost process respect Silicon process especially for relatively small volume production [15][16][17][18].The GaAs APPF proposed in this paper has the same performances in terms of covered bandwidth, insertion loss, matching and IIR, but it has many advantages compared to CMOS APPF mentioned above; it can be developed for working at higher frequencies thanks first to GaAs which has less parasitic capacitances and higher charge carriers drift velocity [19][20][21].
Furthermore, there are other two advantages that should be considered, GaAs APPF can work in extreme temperature conditions thanks to larger GaAs band gap and it is radiation resistant thanks to absence of gate oxide [22][23][24], for this reasons it can be used for spatial and military applications.

III. ANALYTICAL APPROACH AND DERIVATION OF THE FORMULAS A. Excitation Mode
There are two ways to excite network in Figure 1: in the first one, named "Type I", only one half of the inputs are excited, while with second way, named "Type II", all the 4 inputs are excited.These excitations modes can be seen in Figure 2 and 3.With "Type I" excitation, the first and third inputs are connected to the generator, i.e. such inputs have 180° phase difference between them, while with "Type II" excitation the first input with the AoP17 second one and the third input with the fourth one are connected together, so that it result in a two input network.The choice of excitation mode determines the characteristics of the differential output signals, as we will show in the following.

B. Transfer Functions
Considering a one stage PPF as those in Figure 1 and that each output is connected to the same load, the two differential output signals are the following expressions (1) and (2): where ∆  and ∆  are differential output signals while ∆  and ∆  are differential input signal and   is load impedance of each output.The pole angular frequency of one stage polyphase filter is From the above equations we obtain, for "Type I" excitation, the relation And for "Type II" excitation the relation With simple circuit analysis used above for (1)-(4), it's possible to calculate transfer functions of multi-stages networks.The previous transfer functions show that with "Type I" excitation the phase difference between the two differential output signal is 90° for all frequencies and load impedances, but they have same amplitude only at each RC pole; instead, while with "Type II" excitation the phase difference between the two differential output signals is 90° only at each RC pole but they have same amplitude for all frequencies and load impedances.Also, network with "Type II" excitation has the insertion loss about 3 dB less than that with "Type I" excitation [1].The theory exposed above is now applied to a two stage APPF.A two stage type II polyphase filter is depicted in Fig. 4.

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The phase difference between differential ports can be seen in Figures 5 and 6 for both excitation modes; we refer to two stages PPF where poles are indicated by f 1 and f 2 , being f 1 the pole of first stage and f 2 the pole of second stage, i.e:

C. Differential Impedances
The overall loss of polyphase filter is composed of two terms: the intrinsic one, and that due to input and output load impedances.Let us indicate with  _ and  _ the source and load differential impedance, and with  _ and  _ the input and output differential impedances.As an example, for the differential impedances the equivalent circuit at the input can be seen in Figure 7. Clearly, in Figure 6 we consider the effect of differential impedance at input; of course, to consider the effect of load termination  _ and  _ must be replaced with  _ and  _ .
Calculating input and output differential impedances for both excitation types, we obtain: for "Type I" excitation, and AoP19 for "Type II" excitation: these expressions are used for input/output matching.

D. Image Reject Ratio, IRR
IRR is the Image Reject Ratio, i.e. it is the ratio between the desired and image signals.IRR depends of the phase and amplitude errors between two differential signals and its relation with them is shown in the following equation derived from Norgaard [5]: where ∆ is phase error respect  2 , while   is amplitude ratio between two differential signals, i.e: The amplitude ratio   is obtained by the ratio between the differential output signals' modulus, the (11) can be write as in (13) : where ∆  and ∆  are defined in ( 14) and (15).
∆  =  22 −  24 (15) Defining the IRR parameter in log scale, yelds: The in-frequency behavior of the IRR in dB Magnitude can be shown as in Fig. 8.An useful information on the character of the proposed circuit can be obtained by observing the behavior of the two parameters from which the IRR depends (∆    ), while changing the frequency of the input signal.As a main feature, there is the complete independence of the amplitude ratio   to the frequency of the signal, as shown in Fig. 9.The phase difference ∆ with respect the 90° phase shift between the two signals is an important figure of merit.Such value should be 0° ( or 180° ) for signals whose phase shift must be 90°; depending on the order into the expression (12).In Fig. 10, the behavior of ∆ is plotted and the operative bandwidth can be observed to have a like constant behavior with a low ripple.The two differential output signals have the same modulus at any frequency but a phase difference between each other of 90° only at the poles' frequency.Analyzing the expression of the IRR is evident that under ideal conditions, which are   = 1 and ∆ = 0 ( or 180° ), the IRR tends approaching the infinity.

A. Technology
The GaAs technology was used to realize the project of a 2-Stage 4I/O APPF.The technology chosen for the project was GaAs mainly because it is a high reliability and low cost process for relatively small volume production.
The design is based on a numerical simulation of the device with several iterative optimization.
Since the simulation has been performed in a factory provided ambient, by employing the library of transistors, microstrips, lumped elements and substrate provided by the foundry, we can consider these result with a nice grade of reliability.
There are two ways to vary the poles in each stage: first, using a FET as a variable transconductance and second, using the FET as a variable capacitance.Our choice was the first and we employed a European Foundry.
Figure 12 shows the transconductance vs. the V GS control voltage ( hereinafter named Vtune ) for a FET with 30 um gate periphery.The FET was connected in parallel to each resistors of the polyphase network, so that we can vary the poles, and consequently the IRR curve translates inside the request band, simply by varying the V GS voltage.
The JFET channel conducts at Vgs=0 because it is a depletion device, as the voltage became more negative the channel starts to close and the resistance increases reaching an opened channel at a voltage of -1V.The FET works into ohmic region where it behaves as a resistor with the following approximated expression (17).
=     (17) where ρ is the resistivity of the channel, L is the length, W is the width while t is the thickness of the channel .The transconductance can be approximated by the following expression (18): In order to compute the transconductance in the factory-provided simulation ambient, the setup shown in Fig. 13 has been implemented.The FET's transconductance behavior in the bandwidth has been measured through the Agilent ADS software, by employing the vendor's library model.

B. Device Design: The Importance of Radial Structure
A schematic of both topologies we have considered, the "modular structure" and the "radial structure", are given in figures 14 and 15.The principal difference in realizing the physical layout of the "radial structure" is the complete symmetrical disposition of components and transmission lines.This is an important issue in the device performances.By employing the radial design, the device

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compactness can be ensured with the minimum encumbrances as a design requirement, from the beginning of the design.This approach could ensure the needed compactness while ensuring the minimum phase error without phase and amplitude imbalances.The spatial arrangement of components can be evaluated in the first step of the design starting by considering the electrical length of the transmission lines and their impact on the physical lengths.The design starts with the choice of an excitation type; the "Type II" excitation mode was our choice because it presents a loss about 3 dB less than a "Type I" excitation way.Next step was the choice of a number of stages to cover the entire band 1-5 GHz: two stages were necessary, as shown in Figure 16.In each stage different poles were chosen to obtain maximum bandwidth.Performing only a circuit analysis it is not evident the effects due to the network's physical asymmetry, while with RF analysis we understand that the layout of the structure is decisive on the whole electrical performances.To     In the following Fig.21 and 22 the reflection scattering parameter are plotted respectively for control voltage Vtune = -1V and Vtune = 0V, relative to the worst case among all possible V GS .The proposed device offers a global performance increase over the classical poliphase filters [6][7][8][9][10][11][12][13],

ASYMMETRICAL PATHS SYMMETRICAL PATHS
such as IRR value and matching that can not be obtained in a classical Modular layout configuration.

V. CONCLUSIONS
In this paper, PPF technology has been investigated, in order to respond to the growing demand for

Fig. 4 .
Fig.4.Two stage type II excitation model for polyphase filter.
maintain the symmetry of the network a new structure was designed named "RADIAL STRUCTURE".This structure has two concentric stages as can be seen in the layout of Figure17.In the left side of the layout, it can be seen the DC power supply line "IN+" and "INand the DC input control voltage Vtune, at top and bottom the inputs and left and right the outputs; its dimensions are 1350 um x 1830 um.For comparison, the modular structure layout is shown in Figure18.It can be seen from Figure12that the band of "RADIAL" layout is greater than "MODULAR" one.

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Fig.23.Phase (deg) vs Frequency (GHz) behavior of the signal O1-O3 (blue) and O2-O4 (red) for Vtune=-1V very wideband and narrow encumbrance telecommunication devices, such as 4 quadrature signals generators and Phase Shifters, suitable for circuits able to transmit a greater amount of data in line with the new requirements of the modern telecommunication devices.The PPF at the actual state of the art are only the Tandem kind, which are limited by a low balancing of phases and amplitudes of the output signals.We have shown a solution to overcome such drawback, by proposing a new PPF topology with direct synthesis formulas for the device design.An example of application has been described and compared to the classical solution.The design and performance of a GaAs MMIC 2-Stages 4I/O Tunable APPF working in 1-5GHz bandwidth has been documented.Two types of layout have been proposed, one being the classical tandem connection of stages, and a new one named "radial" which permits a higher symmetry in the signal paths.The performed simulations show that the radial layout for the Tunable APPF has an output signals with a 0.5° phase unbalance, with an 8 dB of worst case matching and a 16 dB of maximum insertion loss.The tunability is obtained by varying the gate voltage of FET's inside the range 0;-1V, allowing to cover the full 1-5GHz bandwidth.