Design of a Multiband Microstrip Differential Phase Shifter for Wireless Systems

Transcription

1 Design of a Multiband Microstrip Differential Phase Shifter for Wireless Systems Ali Reza Aboofazeli A thesis presented to Ottawa-Carleton Institute for Electrical and Computer Engineering in partial fulfillment to the thesis requirement for the degree of MASTER OF APPLIED SCIENCE in ELECTRICAL ENGINEERING University of Ottawa Ottawa, Ontario, Canada October 2016 Ali Reza Aboofazeli, Ottawa, Canada, 2016

2 Abstract This thesis investigated the design of a compact multiband differential reflective phase shifter based on slot-coupled coupler layout. Such phase shifter configuration is formed of a hybrid coupler with the coupled and transmission ports ended with elliptically shaped microstrip loads. By optimizing the ending ports of the coupler, we achieved a GHz differential phase from - 90 o to + 90 o, a frequency range that covers most commercial, satellite and personal mobile communication bands. Furthermore, we can obtain different phase ranges by terminating the coupler with suitable reactance loads. Indeed, the simulations showed that the proposed design can achieve ± 30 o, ± 45 o, and ± 90 o differential phase shifts with deviation less than 3 o, as well as return loss and insertion loss better than 10 db and 1 db, respectively. The total size of the designed phase shifter is 25 x 60 mm 2. Measurements results agreed well with the simulations, thus demonstrating the proposed design approach. ii

3 Acknowledgments I would first like to thank my supervisor Professor Mustapha C.E. Yagoub who has supported me throughout my thesis with his patience and knowledge. I attribute the level of my Master s degree to his encouragement and effort and without him this thesis, too, would not have been completed or written. One simply could not wish for a better or friendlier supervisor. Last but the most I would like to thank my family and my friends for their support and encouragements during this thesis work. iii

4 Abstract... ii List of variables... ix List of Acronyms... x Chapter One... 1 Introduction Motivations Thesis contributions Thesis Organization... 3 Chapter Two... 4 Phase Shifters Review Definitions Design Parameters Different Types of Phase Shifters Phase Shifters Design Topologies switched line phase shifters Hybrid-coupled phase shifter Loaded-line phase shifters High-pass-low-pass phase shifters Discussion Planar Couplers Edge coupling configuration Broadside slot coupling configuration Phase Shifter Designs Schifman s phase shifter Mosko-Shelton s constant phase shifter and directional coupler Abbosh wideband phase shifter Conclusions Chapter Three Coupler Design Design Approach Odd and even mode analysis iv

5 3-1-2 Coupler analytical formulation Designing the hybrid coupler Manufactured coupler Conclusion Chapter Four Differential Phase Shifter Design Designing the differential reflective phase shifter Theoretical approach Differential reflective phase shifter s formulation Design Results with Elliptical-Shaped Microstrip Load Parametric Analysis Manufacture and Test Results of the 45 o Differential Phase Shifter comparison of the designed phase shifter with others Conclusion Chapter Conclusions and future works Conclusions Future works References v

6 Table of Figures Figure 2-1. Different electronically phase shifters [14]... 7 Figure 2-2 PIN diode I-V characteristics [15]... 8 Figure 2-3. PIN diode phase shifters can shift the phase with switching signal between two paths with two different lengths l0, l0 + l. [15]... 8 Figure 2-4. Switched line phase shifters [14] Figure 2-5. Hybrid-coupled phase shifters [14] Figure 2-6. High-pass-low-pass phase shifter [21] Figure 2-7. an edge-coupled configuration [26] Figure 2-8. Slot coupling configuration [28] Figure 2-9. Error-correcting network and its two possible differential phase responses [38] Figure Type-B network and its differential phase response Figure Configuration of multi-section directional coupler. a) required coupling response of multi-section coupler. b) decomposition of coupling response Figure Phase shifter a) upper layer b) middle layer c) lower layer d) whole structure [40] Figure 2-13 Phase shifter as a four-port device with two open-circuit ports [40] Figure 3-1. General structure of Tanaka coupler with plane coupling a) transmission lines, gap and sub layers arrangement b) upper view of coupler c) odd and even modes equivalent circuit [42] Figure 3-2. Offered coupler structure s layers with plane coupling Figure 3-3. The coupler model for semi-static analysis [42] Figure 3-4. Conversions to find unit capacitor of coupler s even mode Figure 3-5. the offered wideband structure layers in GHz frequency band with plane coupling Figure 3-6.Simulation results of the hybrid coupler in GHz frequency band a) reflective coefficients b) transmission coefficients c) phase shift d) phase and amplitude unbalance vi

7 Figure 3-7. the manufactured coupler measurement results Figure 4-1 Schematic version of offered reflective phase shifter by using the loaded symmetric directional coupler Figure 4-2 a) General structure of the reflective phase shifter with elliptical load, b) the upper and c) lower transmission lines with elliptical shaped patch and load 43 Figure 4-3 a) phase shift, b) phase ripple, c) return loss, d) insertion loss of the ±30!, ±45!, ±60! and ±90! differential phase shifters with elliptical shaped microstrip load in GHz frequency band Figure 4-4 Simulation results of the 45 o differential reflective phase shifter for parametric analysis a) the effect of changing the load s dimensions on phase shift b) the effect of changing the length of the reference line on the phase shift c) the effect of changing the load s dimensions on the return loss d) the effect of changing the load s dimensions on the insertion loss Figure 4-5 a) Measurement system, b) the manufactured 45 o phase shifter (top, bottom and middle views) Figure 4-6 Measurement results of the 45 o phase shifter, Return and insertion loss 50 Figure 4-7 Comparing measurement and simulation results for S Figure 4-8. Comparing measured and simulated phase shift vii

8 Table of Tables Table 2-1 comparison between slot-coupled and edge-coupled configurations [29] 15 Table 2-2. Comparison between different topologies of phase shifters Table 3-1 Dimensions of the designed coupler in GHz frequency band Table 3-2 Comparison of the designed coupler characteristics vs. existing published works Table 4-1 Designed coupler dimensions for reflective phase shifter Table 4-2 Dimensions of the designed elliptical shaped load to get the ±30!, ±45!, ±60! and ±90! phase shifts Table 4-3 Comparison of the designed phase shifter s specification with other phase shifters with different structures viii

9 List of variables % Phase constant β ef Γ & '(( Effective phase constant Reflection coefficient Effective permittivity ) Electrical length of a uniform line * Wavelength + Phase, Angular frequency b Reflective waves C Te Total unit capacitor of even mode C To Total unit capacitor of odd mode IL Insertion loss - Length l ref Reference line length L L S RL S W W s Length of patch Length of gap Return loss Scattering parameters Width of patch Width of gap. / Characteristic impedance Z 0e Z 0o Characteristic impedance in even-mode Characteristic impedance in odd-mode ix

10 List of Acronyms ADS BW DCS DGS GPS MEMS MMIC PCS S-DMB SIW UMTS WiMax WLAN Advanced Design Systems Software Bandwidth Digital Communication systems Defected Ground Structure Global Positioning System Micro-electromechanical systems Monolithic Microwave Integrated Circuit Personal Communication Systems Satellite-Digital Multimedia Broadcasting Substrates Integrated Waveguide Universal Mobile Telecommunications Systems Worldwide Interoperability for Microwave Access Wireless Local Area Network x

11 Chapter One Introduction 1-1 Motivations In modern communication systems, there is a need to control the direction of signal radiation in order to improve its properties in a particular direction. This is called beam steering [1]. To this aim, phase shifters introduce a configured amount of time delay (or phase at a certain frequency) in the signal passing through it; the amplitude of the radiated signal in each lobe is being controlled by a Variable Gain Amplifier. The radiated waves interact with each other either destructively or constructively. Therefore, by adjusting the phases and amplitudes of the transmitted signals, it is possible to reduce the radiation in all unwanted directions (by destructive interaction) while increasing it in a particular direction (by constructive interaction) [1]- [3]. Phase shifters are then a critical component in many RF and microwave systems. Applications include controlling the relative phase of each element in a phase array antenna in a radar or a steerable communication link, and in cancelation loops used in high linearity amplifiers. Because of their importance in communication systems, a quite impressive number of researches have been already published regarding their design while many others are still ongoing to enhance the phase shifter characteristics such as increasing bandwidth, decreasing ripple phase, reducing size, and/or decreasing losses, to name a few. Depending on how to control the phase shift, phase shifters can be categorized into two main groups: mechanical and electronical, the latter being much popular, especially in 1

12 phase array antennas [1]. Because of the ever-increased need for efficient integrated communication systems with wider bandwidth, the objective of the present work was to design integrated phase shifters with wide bandwidth and minimum attenuation. In this optic, features such as flexibility, availability, and ease to use, have made wireless communication systems unavoidable components in our professional as well as personnel life. We have then focused in this work on the design of a multiband GHz phase shifter, i.e., a frequency range that covers most commercial, satellite and personal mobile communication bands such as Global Positioning System (GPS, GHz), Digital Cellular System (DCS, GHz), Personal Communications Service (PCS, MHz), Universal Mobile Telecommunications System (UMTS, MHz), Wireless Broadband (WiBro, MHz), Bluetooth (2.4 GHz), Wireless Local Area Network (WLAN, GHz), and Worldwide Interoperability for Microwave Access (WiMAX, 2.5 and 5.8 GHz). Slot-coupled structures are a good candidate for wideband applications because of their tight coupling, low phase deviation and reduced size [4]. In addition, among integrated phase shifters, microstrip differential phase shifter are widely used in modern communication systems [4]-[10]. In fact, such phase shifters have broad applications in microwave circuits such as butler matrices, monopulse networks, beam-scanning phased arrays, microwave instrumentation and measurement systems, modulators and many other industrial applications. They can provide suitable phase difference between two different paths with minimum effect on each other. Wideband differential phase shifters are mainly based on the design proposed by Schiffman [6], an edge-coupled stripline transmission configuration. This structure consists of a reference line and two edge-coupled striplines integrated together at their bottom. By choosing the proper length of these lines and the coupling, the phase difference between them can be made constant over one octave frequency band. However, a very narrow gap between the edge-coupled lines is needed for a broadband performance and when this circuit is fabricated in microstrip technology, its operation decreased. So, Abbosh [4] proposed a microstrip-slot-microstrip coupler with an elliptical-shaped broadside coupled structure that shows good wideband properties. 2

13 1-2 Thesis contributions In this thesis, the main contribution has been to propose a modified configuration of Abbosh s phase shifter [4] that can operate over a quite wideband range, covering the GHz band. The proposed enhancements allowed to successfully complete the design of a coupler with suitable characteristic such as 3 db coupling with minimum return loss, phase imbalance and amplitude imbalance and also the design of a phase shifter with high performance in the targeted frequency range, i.e., 137% bandwidth, ((f 2 -f 1 )/f c ) maximum of 3 o phase deviation, as well as return and insertion loss better than 10 db and 1 db, respectively. 1-3 Thesis Organization This thesis is divided into four chapters. After this introductory chapter, the following chapter presents an overview of the existing phase shifters types, designs and requirements. In the third chapter, the design process of a wideband directional hybrid coupler is described including the odd and even modes analysis and related simulations. Chapter Four provides the design, implementation and results of the multiband differential reflective phase shifter. Simulations were performed using both a circuit simulator (Advanced Design System - ADS, from Keysight Technologies) and a fullwave electromagnetic solver (High-Frequency-Simulation-Software HFSS, from ANSYS). The results for phase ripple, phase shift are shown and compared to other works. The manufactured test results for this phase shifter have been brought in this chapter as well. 3

14 Chapter Two Phase Shifters Review In this chapter, we will first review the different topologies of phase shifters, depicting the advantages and disadvantages of each structure. This step will allow us selecting the most suitable for the targeted application. 2-1 Definitions Phase shifters are used to change the transmission phase angle (i.e., the phase of the S 21 parameter) of a network. Ideal phase shifters provide low insertion loss and equal amplitude (loss) in all phase states. Most phase shifters are passive reciprocal networks, meaning that they work effectively on signals passing in either direction [11]. While the applications of microwave phase shifters are numerous, perhaps the most important is within a phased array antenna system (as known as Electrically Steerable Array, or ESA), in which the phase of a large number of radiating elements are controlled to force the electro-magnetic (EM) wave to add up at a particular angle to the array. For this very purpose, phase shifters are often embedded in TR modules [11]. The total phase variation of a phase shifter needs only be 360 o to control an ESA of moderate bandwidth. Networks that stretch phase more than 360 o are often called time delay bits or true time delays (part of a time delay unit or TDU), and are built similar to the switched line phase shifters that will be described below [11]. 4

15 2-2 Design Parameters In recent decades, one of the most important applications of phase shifters is in phase array structures. In antenna theory, a phased array is an array of antennas in which the relative phases of the respective signals feeding the antennas are set in such a way that the effective radiation pattern of the array is reinforced in a desired direction and suppressed in undesired directions. The phase relationships among the antennas may be fixed, as in a tower array, or may be adjustable, as for beam steering. Common phase arrays can have up to thousands radiation elements. In these structures, phase shifters are in the form of constant time delay or phase delay devices [12]. Because of this, phase array structures are in the form of phase scanning and time-delay scan. Phase shifters with small loss, low handling power, continuous adjusting capability and low production costs are among the most fundamental phase array antennas part that direct EM waves with electronically controlling the signal s phase while antenna is not physically moving. In designing a phase shifter, beside cost and tolerances (which we did not consider in this work), different design parameters have to be considered: Insertion Loss: The insertion loss of a phase shifter is largely driven by the number of stages needed and the operating frequency. 4-6dB is a typical range for a design with 360 o of control. The variation with frequency at a given phase is also critical and performance of +/-1dB over an octave bandwidth is often required [13]. Amplitude Imbalance: The magnitude of the RF signal should not be affected by the phase shifter in ideal conditions. In practice, variations are expected in the amplitude of the RF signal over frequency, resulting in unequal distribution of amplitude during the beam steering of the antenna [13]. Return Loss: Return loss is a measure of the input impedance matching of the phase shifter. A typical number for a broadband device would be 10dB to 15dB [13]. 5

16 Transmission coefficient: In telecommunications, the transmission coefficient is the ratio of the amplitude of the complex transmitted wave to that of the incident wave at a given point in a transmission chain. Phase deviation: In phase modulation, the phase deviation is stated as the maximum difference between the instantaneous phase angle of the modulated wave and the phase angle of the unmodulated carrier. Size: Size could be an important issue depending on the application as well as other requirements. However, covering a smaller place is always desired to make room for other components in a system. Power Handling Capability: Although power-handling capability of the phase shifter depends on the application, it can be a very important property in designing the system. Especially in transmitter mode of phased array radars, phase shifters must be capable of handling much power. However, generally each phase shifter in the array is required to handle some portion of the total power since transmitter power is distributed among all the phase shifters [12]. 2-3 Different Types of Phase Shifters In general, phase shifters can be categorized into three groups: Ferrite, Semiconductors and Bulk Semiconductors. Figure 2.1 shows different common categories of electronically phase shifters, in which semiconductor-based ones are the most important [13]. In fact, although Ferrites phase shifters have less input loss, they are complex and expensive. Also they require manual adjusting and have high consumption power [14]. Bulk semiconductor phase shifters are cheaper and smaller but they have limited applications because of high input loss in high frequencies. Also they cannot exhibit continuous phase shift [14]. 6

17 Figure 2-1. Different electronically phase shifters [14]. Semiconductor-based phase shifters can be classified as analog or digital. Analog phase shifters provide a continuously variable phase, usually controlled by a voltage [13], while digital phase shifters provide a discrete set of phase states that are controlled by two-state "phase bits." The highest order bit is 180 o, the next highest is 90 o, then 45 o, etc., as 360 o is divided into smaller and smaller binary steps. A three-bit phase shifter would have a 45 o Least Significant Bit (LSB), while a six-bit phase shifter would have a 5.6 o least significant bit. Most phase shifters are of the digital variety, as they are more immune to noise on their voltage control lines. Considering a semiconductor controlling element as a switch, phase shifters are usually based on PIN diodes or FETs. A PIN diode is a P-N junction with a large depletion region rather than normal diode (Figure 2-2 [15]). Adding this intrinsic region will help controlling the conductance capability in forward bias and also decreasing capacitor in 7

18 reverse bias. In fact, in forward bias, resistance in signal path will become negligible while decreasing capacitor in reverse bias will lead to higher impedance in this track. Figure 2-2 PIN diode I-V characteristics [15] Therefore, PIN diode phase shifters can shift the phase with switching signal between two paths with two different lengths - /, - /01 (Figure 2.3 [15]). Figure 2-3. PIN diode phase shifters can shift the phase with switching signal between two paths with two different lengths - /, - /01. [15] Phase shift is proportional to extra path delay %-, where % is the mean propagation constant and l the difference between lengths. FET phase shifter is used as a two-terminal switch controlled by the gate voltage and has many advantages compared to PIN diode [15]. It has higher switching speed and 8

19 less consumption power. While PIN diode is known as a digital shifter, FET can operate in both analog and digital modes. Note that since semiconductor phase shifters are expensive and have high input loss in microwave frequencies, new technologies are using narrowband linear dielectrics and Micro-Electro-Mechanical Systems (MEMS) to obtain phase shifts with very low input loss (< 2dB). 2-4 Phase Shifters Design Topologies switched line phase shifters The primary kind of phase shifters is the switched-line phase shifter. With this kind of phase shifter, it is conceivable to switch between two (or more) delay lines as shown in Figure 2-4. The phase shift given by this circuit is the distinction between electrical lengths between two transmission lines. There are certain disadvantages for this type. First, an advanced CMOS technology is expected to realize this phase shifter at high frequencies with low insertion loss. Second, the two lines have unequal lengths and different attenuations. This implies that the two lines that the two-time delay states will have different attenuations, resulting in amplitude imbalance between the two states. Third, to realize large time delays, long line lengths are needed which is impractical for integrated circuit realization for most frequency ranges and increases loss for larger time delays [17]. 9

20 Figure 2-4. Switched line phase shifters [14] Hybrid-coupled phase shifter A reflective type phase shifter is composed of a 90 Hybrid coupler with two identical reflective loads as shown in Figure 2.5. The Hybrid coupler divides the input signal at port 1, equally between the two output ports, port 3 and 4, with a phase difference of 90. Signals reflected back from the termination add up at port 2 and no signals returns to port 1 [12]. Since isolation between the input and output ports is improved, there can be better matching at each port. However, the circuit will occupy more chip area and loss is worse because of the coupler [19] Loaded-line phase shifters Another category of phase shifters is the loaded-line phase shifter, often used for 45 o or lower phase shift bits. The loads Z L are synthesized such that they create a perturbation in the phase of the signal when switched into the circuit, while they have only a small effect on the amplitude of the signal. The loads must have a very high reflection coefficient in order to minimize the loss of the phase shifter (they should utilize purely reactive elements). Obviously, the loads must not be too close to a short circuit in phase angle, or the phase shifter will suffer 10

21 from extreme loss. By spacing the reactive loads, approximately a quarter-wavelength apart, the amplitude perturbation can be minimized and equalized in both states [20]. Figure 2-5. Hybrid-coupled phase shifters [14] The phase versus frequency response of a loaded line phase shifter is usually flatter than the switched line phase shifter, but not usually as flat as the high-pass/low-pass phase shifter. Usually only one control signal is required for a loaded-line phase shifter, since the loads can be biased simultaneously. One big issue with this topology is that it is impossible to have a matched circuit in both states. The matching also deteriorates when a larger phase shift is needed. The circuit will also have different attenuations depending on whether the switches are open or closed [19] High-pass-low-pass phase shifters if a constant phase shift is desired over a wide frequency range, the switched line phase shifter isn t going to cut it. A high-pass/low-pass phase shifter can provide near constant phase shift over an octave or more. By high-pass/low-pass we refer to the fact that one arm forms a high-pass filter while the opposite arm forms the low-pass filter. The second advantage of the high-pass/low-pass phase shifter is that it offers a very compact layout because lumped elements are typically used instead of delay lines. This 11

22 is an important consideration for low frequency designs because delay transmission lines can be quite large. The cut-off frequencies of the two filter networks obviously must be outside of the phase shift band for this scheme to work [21]. Figure 2-6. High-pass-low-pass phase shifter [21] Various high-pass-low-pass phase shifters have been reported in different technologies, typically designed as integrated circuits [22]-[23]. They are generally limited to no more than 40% fractional bandwidth. Sometimes, switching transistors are also integrated into the phase shifter, thus reducing size and the number of required components [19] Discussion From the above, all these types have certain advantages and disadvantages. However, reflection phase shifters are still the most suitable in our case because of their high bandwidth. To achieve suitable operation in a wide bandwidth, phase shifters in planar technology (e.g., microstrip lines) use coupled transmission lines working as couplers [24]. 12

23 2-5 Planar Couplers As mentioned, since we chose the reflection type, we need directional hybrid couplers. A simple directional coupler is just two transmission lines put close together, such that the secondary line can absorb energy from the field created around the primary. The resulting structure can have many properties, some of which are desirable and others are not. Coupled line couplers are not "DC connected", as opposed to "direct coupled" couplers such as the Wilkinson and the branch-line. Coupled lines occur when two transmission lines are close enough in proximity so that energy from one line passes to the other. The Through Line, or Main Line, needs to be designed for the best possible match and must be capable of handling whatever the maximum input power level is specified to be. The quality of match for the Coupled Line will affect the directivity of the coupler. Directivity is a measure of how well the coupler isolates two oppositetravelling (forward and reverse) signals [25]. However, some types of couplers will show a greater sensitivity to this than others. For example, if by using both ends of a single coupled line to provide Forward and Reverse coupled output, then the match of this line and also the match of the external components is absolutely critical to directivity. However, if the coupled line will have a termination at one end, then this may be tuned to optimize directivity. It is perfectly feasible to create a dual directional coupler using two separate coupled lines each of which is terminated at one end. Usually we are talking about lines that are coupled over a quarter-wave section, or multiple sections. Bandwidth is greater than in interconnected transmission line (uncoupled line) circuits like the branch-line coupler. Lines can be coupled in at least two ways. Hybrid couplers are the special case of a four-port directional coupler that is designed for a 3-dB (equal) power split. Hybrids come in two types, 90 degree or quadrature hybrids, and 180 degree hybrids. Hybrid couplers are often used in creating reflection phase shifters. 13

24 2-5-1 Edge coupling configuration This structure includes a reference line and two transmission lines connected at the end (Figure 2.7 [26]). By properly choosing the line s lengths and edge-couplings between the two transmission lines, we can find adequate phase shift with one octave wideband [26]. The gap between two lines is one of the important parameters to achieve wideband shift in this edge-coupling structure and for narrower gap we have longer phase shifter s bandwidth. However, producing this structure with narrow gap in microstrip technology would be difficult, thus, application of this type is limited. Figure 2-7. an edge-coupled configuration [26] Broadside slot coupling configuration The slot-coupling approach involving a double-sided substrate, which was first proposed by Tanaka et al. [27]. It can be applied to realizing a tight coupling. The structure is formed by two microstrip lines separated by a rectangular slot in the common ground plane (Figure 2-8 [28]). Table 2.1 summarizes the advantages/disadvantages of each of the above structures highlighting that slot-coupled structures have better performance in phase deviation, bandwidth and size reduction [28]. We will then use this type of devices. 14

25 Figure 2-8. Slot coupling configuration [28] Table 2-1 comparison between slot-coupled and edge-coupled configurations [29] Edge-coupled Slot-coupled Operating bandwidth High Very high Return loss High High Characteristics Insertion loss Low Relatively low Phase ripple Normal Very low Design issues very narrow gap between transmission lines Complexity due to double layers circuit 2-6 Phase Shifter Designs The first published wideband phase shifter based on a Slot-coupled structure was the Schiffman phase shifter [26]. After that, several structures have been proposed [30]- [35]. For instance, in [31], different structures based on Schiffman structure have been 15

26 discussed. In addition to common Schiffman s structures, others configurations such as SIW [36] and loaded transmission line phase shifters [37] have be proposed. Slot coupled transmission signal s structures consist generally on two sub layers. For analyzing these structures, odd and even mode analysis are used. This part will be covered in the next chapter Schifman s phase shifter As mentioned earlier, the Schiffman s phase shifter has been the first published wideband phase shifter design with 90 o difference phase [38]. This differential phase shifter consisted of two transmission lines, a reference transmission line and an edge coupling due to two beside lines. By properly choosing the lines length and coupling rate, the phase difference in the whole bandwidth can be maintained relatively constant, i.e., 90 o. Notice that Schiffman s work was on strip line structure, which scattered odd and even modes in the coupled line have identical phase speed. Therefore, when this type is designed with microstrip lines, unequal speed of odd and even modes will lead to weak phase shifter operation. In [38], two identical parallel-coupled lines were connected at their end and the frequency behavior of the rippled lines network has been evaluated and the image Z r impedance equations and constant phase ϕ defined as Z I = Z 0o Z 0e (2-1) and cos(ϕ) = Z 0e Z 0o tan 2 θ Z 0e Z 0o + tan 2 θ (2-2) 16

27 where Z 0e is the characteristic impedance in even-mode (when equal in-phase currents flow in both lines) and Z 0o represents the characteristic impedance in odd-mode (when equal out-of-phase currents flow in both lines). Also ) = %3 is the electrical length of a uniform line of length - and phase constant %. The most elementary form of such a network is termed Type-A network. The Schiffman s method for reducing the maximum phase error of type-a was to connect another differential phase shifter network to the system, which has symmetric Δϕ to neutralize each other s. This structure, called error-correcting network, consists of two separate structures (Figure 2-9 [38]), a transmission line with the length of 2ml and a coupled-line s part with the length of 2ml, with 4 =. /' /. /6. According to the parameters 4 and m, we can minimize the bandwidth s error [38]. Therefore a type-b structure was designed to reduce the error by taking m = 3, ρ 1 = 4.1 and ρ, leading to a maximum 0.7 o 2 = 2.4 phase error in about one octave bandwidth (Figure 2-10 [38]). In practice, the structure can be simplified by removing equal lengths of uniform transmission line from each branch, without affecting differentialphase response. Such a reduction is illustrated in figure for the Type-B network Mosko-Shelton s constant phase shifter and directional coupler To gain more bandwidth with an acceptable phase ripple by using the edge-coupling method, Mosko and Shelton have proposed an approximate method for making constant phase shifting, which includes different parts of a quarter of parallel coupled wavelength [39]. The main problem with this method, which is generally for edgecoupling phase shifters, is the need of high coupling for gaining large bandwidth. Therefore, it may be impractical. Mosko and Shelton proposed to use series connection to minimize this effect. Another problem of these structures is the large size of these multi-part structures. 17

28 Figure 2-9. Error-correcting network and its two possible differential phase responses [38]. 18

29 Figure Type-B network and its differential phase response. 19

30 Figure Configuration of multi-section directional coupler. a) required coupling response of multi-section coupler. b) decomposition of coupling response Abbosh wideband phase shifter In [40], Abbosh proposed a new approach in designing a phase shifter that exhibits good properties in UWB (which is appropriate to our work). This method was used to design 30 and 45 o UWB phase shifters with size of 2.5cm x 2cm (Figure 2-12, [40]). This structure is formed by two ellipsoid microstrip patch connected to input and output microstrip lines. Upper and lower layers have been placed in front of each other. The coupling between these patches takes place in the ellipsoid gap (ground level, middle layer). Note that the ellipsoid form can provide a constant coupling coefficient in UWB. Results showed a ±3! differential deviation and ripple less than 1 db as well as a return loss better than 10 db. 20

31 Figure Phase shifter a) upper layer b) middle layer c) lower layer d) whole structure [40] Figure 2-13 Phase shifter as a four-port device with two open-circuit ports [40] The analysis starts by assuming the phase shifter as a four-port device. Like figure 2-13 two ports are considered open circuit (with this assumption the reflection coefficient at ports 3 and 4 will be 1). Considering that the designed phase shifter has coupling C 21

32 between upper and lower patches, the scattering parameters of the above structure would be: S 11 = S 21 = 1 C 2 (1+ sin 2 (β ef l)) 1 C 2 cos(β ef l) + j sin(β ef l) j2c 1 C 2 sin(β ef l) 1 C 2 cos(β ef l) + j sin(β ef l) 2 2 (2-3) (2-4) where β ef represents the effective phase constant in the medium of the coupled structure. As mentioned before, edge coupling in single layers structures and the slot-coupled method are two important procedures for band widening [39]. From that, enhanced structures have been proposed [28]-[33]. For instance, in [40], an improved Schiffman s structure with modifying ground plane underneath coupled lines has been proposed. This GHz structure has phase ripple and 0.5 db amplitude ripple. In [31], Sorn has improved the Abbosh s structure by adding a gap in slot-coupled output and gained 90 o phase difference. This structure works in 3-7 GHz bandwidth. A GHz and 90 o phase shifter with stepped impedance open stub and coupled line with 1.1 db amplitude ripple and phase deviation has been proposed in [34]. Also in [35], a 90 o phase shifter, with loaded transmission line and T form open stub, and operating in the GHz frequency range, has been presented. This structure has 6.4! phase deviation and less than 0.6 db loss. In [36], 45 o, 90 o, and 135 o phase shifters with referenced line and coupled lines have been described. Working in the range of GHz, they show phase ripple and loss less than 0.9 db. 5! 5! 5! 2-7 Conclusions In this chapter, we analyzed different wideband differential phase shifters. We reviewed the advantages and disadvantages of conventional methods for phase shifter s 22

33 design (Table 2-2). By comparing different structures, the operating frequency band of slot-coupling structures is higher compared to other structures. The other benefit of this structure is its smaller structure size and lower ripple. We, therefore, opted for a wideband reflective phase shifter based on double layer slot-coupled coupler configuration. From that, we first designed the required coupler as detailed in the next chapter. Table 2-2. Comparison between different topologies of phase shifters type advantages disadvantages Switched-line Perfect for true time delay Variable insertion loss Reflection-type Better matching at each port Occupy more chip area and more loss because of coupler Loaded-line The phase vs frequency is more flatter Impossible to have a matched circuit in both states High-pass-low-pass Provide near constant phase shift over an octave or more Limited to no more than 40% fractional bandwidth 23

34 Chapter Three Coupler Design In the previous chapter, we discussed about the different kinds of phase shifters and retained the reflective phase shifter with slot-coupling configuration. To achieve our design, we will start with the 45! Abbosh s structure, enhancing it to uniform the coupling between transmissions lines on upper and lower sub layers at the minimum and maximum frequencies of the UWB band ( GHz). Then, we will vary the sub layer dimensions to decrease the return loss and insertion loss. To do so, we have to start by designing a wideband hybrid coupler with two loaded ports. 3-1 Design Approach To design a coupler with tight coupling in a so wide frequency range, we retained the plane coupling structure introduced by Tanaka (Figure 3-1, [41]). Its smaller size and wideband operating frequency are the main reasons we selected it. Its smaller size (e.g. compared to Schiffman s structure) is due to the use of a plane coupling between the two transmission lines that are placed on upper and lower sub layers (via the gap on the ground plane). This plane coupling is substituted to the edge coupling in the Schiffman s structure. Also, its phase ripple in the operating band is relatively less compared to other microstrip structures [39]. Figure 3-1-a shows the general form of this structure. Figure 3-1-b depicts the rectangular Tanaka coupler structure. Figure 3-1-c shows the electric field lines for odd and even modes excitation. 24

35 Figure 3-1. General structure of Tanaka coupler with plane coupling a) transmission lines, gap and sub layers arrangement b) upper view of coupler c) odd and even modes equivalent circuit [42] However, one of the issues in designing the Tanaka coupler is its ports location [39]. The solution is usually to change the location of adjacent ports by angulating the connected transmission lines, as seen in figure 3-2. The operating frequency band can be also adjusted by changing the geometric form of the gap on the ground plane (e.g. from rectangular to ellipsoid) and then optimizing the physical dimensions. This approach can be also considered in the Abbosh s coupler. 25

36 Figure 3-2. Offered coupler structure s layers with plane coupling Odd and even mode analysis We designed the hybrid coupler on Rogers RO4003C substrate with 20 mil thickness with dielectric constant ε r =3.38 mainly because of its availability. The first step was to compute the odd and even impedances for a 3 db coupling and 50Ω characteristic impedance Z 0 using the following relations [42] k c (db) = 20log Z Z 0e 0o Z 0e + Z 0o (3-1) Z 0 = Z 0e Z 0o (3-2) 26

37 leading to Z 0e = 120.5Ω and Z 0o = 20.7Ω. Then, it is necessary to analyze the coupler operation in dual modes. When the odd mode is excited, the gap on ground plane can be replaced by a perfect electric conductor (PEC). The upper part of the resulting equivalent coupler converted to a microstrip line with Z 0o characteristic impedance. The related line width, w p, can be then obtained using the standard designing equations for microstrip lines. As for the even mode signal s excitation, the perfect magnetic conductor (PMC) is substituted to the gap on the ground. The magnetic plane will push the electric field from the microstrip ports to the outside area of the parallel planes because the magnetic conductor in the lower plane will not let the electric field to be perpendicular on its surface. Therefore, the even mode signal moves outside the area of parallel planes as shown in figure 3-1-c. To allow the even mode signal moving smoothly from the port to the lines, it is recommended to modify the shape of the upper and lower transmission lines as well as the ground gap from rectangular to ellipsoid (figure 3-2) [42] Coupler analytical formulation As mentioned before, to improve the coupler characteristics, the rectangular form of Tanaka s coupler with dimensions w p and w s was changed to ellipsoid with diameters W and W s (figure 3-2). Since Eqs. (3-1) and (3-2), for finding the dual mode characteristic impedances, are independent of the geometric shape, they are still valid. Then, we found the closed form of analytical equations for dual mode semi static parameters. The results gained by this method are totally similar to Tanaka s expressions, which used the complex numerical Finite element method for semi-static cases. Then, full wave analysis by using spectral domain approach was performed to gain the dispersion characteristics of dual mode coupler s parameters. Note that in this semi static analysis, we assumed the isolation planes, which surround the coupler from up and down, as infinite. Also we assumed that the transmission line thickness and can be neglected. As shown in figure 3-3, the planes that separating the substrate and the air (i.e., AD and A D ) operate as perfect magnetic conductors. 27

38 Figure 3-3. The coupler model for semi-static analysis [42] So the existence of the gap in the mutual ground plane does not affect the coupler s odd mode characteristics. Next, we calculated the coupler s dual mode impedances, Z 0o and Z 0o. Figure 3-4 shows the conversions for the even mode. This was achieved by determining the dual mode capacitance value for each unit. Let the total unit capacitor of even and odd modes, respectively C Te and C To, be: C 1 for the bounded area between the upper shield and the upper microstrip half plane (filled with air), or C 2 for the bounded area between the upper microstrip planes and the common ground (filled with dielectric). C 1 and C 2 are computed for both modes. Note that for the even capacitance, we have K ( k C 1e = 2ε 2 ) 0 K ' (k 2 ) C Te = C 1e + C 2e (3-3-a) K ' ( k and C 2e = 2ε 0 ε 1 ) r K(k 1 ) (3-3-b) 28

39 where K(k) is the type one elliptical integral K '(k) = K(k ') as k ' = 1 k 2 and K(k) K '(k) = 2 1+ k ln 2 π 1 k 2ln π 1+ 1 k k k 1 0 k (3-4) Figure 3-4. Conversions to find unit capacitor of coupler s even mode 29

40 k 1 and k 2 are determined from k 1 = sinh 2 πw sinh 2 s 4h πw s 4h + cosh 2 πw s 4h and k 2 = tanh πw p 4h (3-5) Then, going back to the original design of Tanaka (figure 3-1), it is possible to deduce the length l p and width w p of the middle transmission line, as well as the length l s and width w s of the gap. Finally, the effective dielectric constant ( ε effe ) and the characteristic impedance (Z oe ) for the even mode can be obtained by C ε effe = Te C Te (ε r 1) = ε r K '(k 1 ) K(k 1 ) + K(k ) 2 K '(k 2 ) / K '(k 1 ) K k 1 ( ) + K(k ) 2 K '(k 2 ) (3-6) Z oe = 60π K '(k 1 ) ε effe K(k 1 ) + K(k ) 2 K '(k 2 ) 1 (3-7) Note that, similarly, the BB plane in figure 3-3 works as a perfect magnetic conductor, leading to the total capacitor in the odd mode as: ( ) ( ) K k C 1o = 2ε 4 0 K ' k 4 C To = C 1o + C 2o (3-8) ( ) ( ) K ' k and C 2o = 2ε 0 ε 3 r K k 3 (3-9) with k 3 = tanh πw p 4h and k = tanh πw p 4 4h o (3-10) 30

41 The effective dielectric constant ( ε effe ) and the characteristic impedance (Z oe ) of the odd mode can be then deduced as C ε effe = To C To (ε r 1) = ε r K '(k 3 ) K(k 3 ) + K(k 4 ) K '(k 4 ) / K '(k 3 ) K k 3 ( ) + K(k 4 ) K '(k 4 ) (3-11) Z oo = 60π K '(k 3 ) ε effo K(k 3 ) + K(k ) 4 K '(k 4 ) 1 (3-12) The next step was to determine the coupler s characteristics using MATLAB. The Z oo and Z oe are linked with the values of w s, w p, and the substrate thickness. So, with a coupling ( k c ) of 3 db and a line characteristic impedance ( Z 0 ) of 50Ω, Z oo and Z oe can be achieved by equation (3-1). Now we have two unknown variables w s and w p and two equations. The system was solved after 50 iterations using the newton method in MATLAB. The final results give 7 8 = 6.5<< and 7 = = 4.2 <<. Once the transverse dimensions obtained, we had to compute the longitudinal dimensions. Now we use an approach, which consists to start from the design method described by Schiffman, i.e., to use the concept of two coupled quarter-wavelength transmission lines. Note that the geometric shapes of the transmission lines and the gap on the ground plane were not taken into account during simulations. In fact, the above equations were general and independent of the shapes. We therefore included such information by starting the simulations with the initial design of Tanaka shown in figure 3-1. Then, by considering the operating frequency range, GHz, the central frequency will be 3.6 GHz. For the design, we selected the cost-effective Rogers substrate RO4003C with a relative permittivity & A = 3.38 and 20 mil thickness (equals to mm). The quarter-wavelength length of the transmission line will be: - = = - 8 = D = H = << (3-13) E F G E( F G 31

42 However, the above results are for a rectangular coupler shape. Thus, after determining the equations for the rectangular coupler, we can use the equivalence principle to find the equations for an elliptical coupler, assuming that the length of the rectangular coupler is equal to the elliptical coupler. Let L and L S be the respective lengths of the patch and the gap, and W and W s the corresponding widths (figure 2-2). With the above assumption, converting the gained dimensions from rectangular to ellipsoid can be achieved as: (geometric equivalence) L = l p + l 2 2 ( p + w p ) / 2 L S = l s + l 2 2 ( s + w s ) / 2 (3-14) J 1.273(7 = - = )/P J (7 8-8 )/P 8 (3-15) 3-2 Designing the hybrid coupler The above equations can be used to design a hybrid coupler for different frequencies. As for the operating bandwidth, it is determined based on the application specifications. In this thesis, the purpose is to design a hybrid coupler with suitable characteristics in the GHz operating bandwidth with minimum return loss, phase and magnitude ripple. Designed at a central frequency of 3.6 GHz, the optimized dimensions of the designed coupler (Figure 3-5) are summarized in Table 3-1. The simulated coupler s characteristics, shown in figure 3-6, are a return loss greater than 23 db in the whole GHz frequency bandwidth with 137% frequency bandwidth (BW = Δf / f 0) relatively to the central frequency, as well as a magnitude and phase unbalanced less than 0.75! and 0.4 db, respectively. This design has been also successfully compared to existing designs as summarized in Table

43 Figure 3-5. the offered wideband structure layers in GHz frequency band with plane coupling Table 3-1 Dimensions of the designed coupler in GHz frequency band. Parameters (mm) W m50 W s1 W 1 W s W L s1 L 1 L S L

44 (a) (b) (c) 34

45 (d) Figure 3-6.Simulation results of the hybrid coupler in GHz frequency band a) reflective coefficients b) transmission coefficients c) phase shift d) phase and amplitude unbalance. 3-3 Manufactured coupler in this section we compared the results of manufactured coupler with the simulated ones (Figure 3-7). In the simulation the wave ports are used and the connectors are not included. Also we didn t simulate the holes and screws on the board. We used the Vector Network Analyzer with matched load as our test equipment. Figure 3-7. The manufactured coupler measurement results. 35

46 Table 3-2 Comparison of the designed coupler characteristics vs. existing published works. Couplers characteristics Fractional Bandwidth Frequency band Transmission coefficient Phase ripple Structure Ref. (%) (GHz) (db) (! ) ± 0.4 db ±0.75! Elliptical shaped slotcoupled microstrip coupler our work ± 0.5dB ±1! N-section microstrip tandem structure coupler [43] Vertically installed planar ± 0.65dB ±5! multi section quadrature hybrid coupler [44] Rat-race couplers with dB ±1.5! coupled-line section and impedance transformers [45] 3 ±1dB ±1.4 db 10 ±1.5dB ±1! coupled microstrip coupler Elliptical shaped slot- [46] ±1.5dB ±7! directional coupler CPW slot-coupled 3 ± 0.75dB ±2! coupled microstrip coupler Rectangular shaped slot- [47] [48] Multi section corrugated ± 0.6dB ±0.7! slot-coupled directional coupler [49] 36

47 Note that, to the best of the authors knowledge, there is no microstrip phase shifter in this frequency range with this large bandwidth (137%). Furthermore, the designed phase shifter s characteristics are better than those mentioned articles. 3-3 Conclusion In this chapter, we discussed about the hybrid coupler design approach and analytical formulation. The simulations are performed in HFSS and ADS. The simulated coupler exhibits a return loss greater than 23 db in the whole desired GHz frequency bandwidth (137%) as well as a magnitude and phase unbalanced less than 0.75! and 1 db, respectively for the measured results. 37

48 Chapter Four Differential Phase Shifter Design As already mentioned, the purpose of this thesis is to design a wideband differential phase shifter operating in the GHz frequency band. For this purpose, we used the concept of reflective phase shifters. For building a reflective phase shifter, we used the wideband hybrid coupler we designed in previous chapter, while focusing on the load. In a first step, we designed the required reactance load as a lumped inductor or capacitor. After obtaining its value, the load was connected between the two output ports of the designed coupler while the two other ports were used as input and output of the phase shifter. Thus, the desired differential phase can be obtained by comparison with a reference line. In a second step, we modeled the lumped load as an equivalent microstrip line in order to obtain a planar structure. 4-1 Designing the differential reflective phase shifter Theoretical approach As stated, the purpose was to obtain a reflective differential phase shifter. To start, the analytic expression of the load should be found. Let port 1 and port 2 of the designed 4-ports dual mode coupler be the respective input and output port of the phase shifter 38

49 (Figure 4-1). In order to create a certain coupling k c between the upper and lower patches, the corresponding reflective waves b 1 and b 2 can be computed as: b 1 = jk sinθa + 1 k 2 c 3 c a 4 1 k 2 c cosθ + j sinθ b 2 = jk sinθa + 1 k 2 c 4 c a 3 1 k 2 c cosθ + j sinθ (4-1) with θ the electrical length of the coupled structure, which can be related to the physical length l and the effective physical constant β ef by: θ = β ef l (4-2) leading to β ef = β e + β o 2 = 360! ε r λ (4-3) In the above equation, β e and β o are the dual mode constants, λ is the free space wavelength and ε r the substrate dielectric constant. By assuming that port 2 (output port) is matched, the reflective signal in ports 3 and 4 will be as follows: b 3 = jk c sinθa 1 1 k c 2 cosθ + j sinθ b 4 = 1 k c 2 a 1 1 k c 2 cosθ + j sinθ (4-4) 39

50 If the ports 3 and 4 are open, their reflective coefficients are equal to one, so a 3 = b 3 and a 4 = b 4. Thus, the return loss and insertion loss will be: S 11 = S 22 = 1 k c 2 (1+ sin 2 θ) 1 k 2 c cosθ + j sinθ 2 S 12 = S 21 = j2k c 1 k 2 c (1+ sin 2 θ) 1 k 2 2 (4-5) c cosθ + j sinθ Therefore, the phase shift between the output signal and input signal can be expressed as: S 12 = 90! 2 tan 1 tanθ 2 (4-6) 1 k c To find the differential phase shift, we must compare the structure response to that of a reference line. Thus, a 50Ω microstrip line with physical length l ref, phase constant β ref and effective dielectric constant ε ef has been chosen as reference line with its phase expressed as: S 34 = β ref l ref = 360! l ref ε ef / λ (4-7) The equations relevant to ε ef, brought from [27], lead to tanβ ΔΦ = S 12 S 34 = 90! 2 tan 1 eff l 2 + β eff l ref (4-8) 1 k c 40

51 4-1-2 Differential reflective phase shifter s formulation Following the above equations, we loaded the coupler s ports to determine the phase shift coming from it. Let Γ be the reflection coefficient. The new scattering matrix parameters S (S matrix with loads), will be as follows: ' S 11 ' = S 22 = Γ 1 k c 2 (1+ sin 2 θ) 1 k 2 c cosθ + jsinθ 2 ' S 12 ' = S 21 = Γ j2k c 1 k 2 c (1+ sin 2 θ) 1 k 2 2 (4-10) c cosθ + j sinθ ' The phase of S 12 can be computed by summing the load phase and the phase of S 12. S 12 = S 12 + Γ = 90! 2 tan 1 tanθ 2 + Γ (4-11) 1 k c Then we needed to compare the phase with a reference line with suitable length l ref as its phase is given (equation (3-32)) as S 12 = S 12 + S 34 = β ref l ref (4-12) and the final phase shift of reflective phase shifter will be as follows: tanβ Φ = S 12 S 34 = 90! 2 tan 1 eff l 2 + Γ + β ref l ref (4-13) 1 k c 41

52 Figure 4-1 Schematic version of offered reflective phase shifter by using the loaded symmetric directional coupler As can be seen, we can design different phase shifters only by changing the load. Although loading has most effects on changing the phase, the load also has an impact on the magnitude or phase of other scattering parameters (according to (4-10)). In this case, we had to change the dimensions of the coupler, as it will be discussed later. 4-2 Design Results with Elliptical-Shaped Microstrip Load Following the coupler s design process and formulation described in parts 3-3 and 3-2-2, respectively, its geometrical dimensions were obtained (Figure 4-2 and Table 4-1). As mentioned, the circuit has been designed on a Rogers RO4003C two-layer board with 20 mil thickness, dielectric permittivity ε r = 3.38 and central frequency 3.6 GHz. Table 4-1 Designed coupler dimensions for reflective phase shifter Parameters (mm) Coupler s W m50 W 1 W 1 W s W L s1 L 1 L S L characteristics Values 42

53 Figure 4-2 a) General structure of the reflective phase shifter with elliptical load, b) the upper and c) lower transmission lines with elliptical shaped patch and load Also, by computing the load s reflective coefficient value we can achieve the required phase shift. So, we first determined the Γ value for the desired phase shift in order to get the initial dimensions of the elliptical load using ADS. Then, we optimized its dimensions in HFSS (Table 4-2). As mentioned, the structure should be capable of creating the 90! to +90! phase shift on the GHz frequency band as well as different other phase shifts by changing the dimensions of the elliptical shaped load in coupler s ports. Therefore, the designed load dimensions for ±30!, ±45!, ±60! and ±90! phase shifters have been also brought in Table 4-2. As can be seen in figure 4-3, the reflection and crossing coefficients of the designed structures are less than 10 db and 1 db, respectively. The 90!, 60!, 45!, 30!, 30!, 45!, 60! and 90! phase shifters exhibit a respective 1.6!, 1.2!, 1!, 1.2!, 1.1!, 2.1!, 1.25! and 2! phase deviation in the operating bandwidth. Therefore, the proposed phase shifters have a phase ripple less than 2.1! in a 137% frequency bandwidth (BW = Δf / f 0) relatively to the central frequency. 43

54 Table 4-2 Dimensions of the designed elliptical shaped load to get the ±30!, ±45!, ±60! and ±90! phase shifts a (mm) b (mm) Considered phase shift ! ! ! ! ! ! ! ! 44

55 (a) (b) (c) 45

56 (d) Figure 4-3 a) phase shift, b) phase ripple, c) return loss, d) insertion loss of the ±30!, ±45!, ±60! and ±90! differential phase shifters with elliptical shaped microstrip load in GHz frequency band. 4-3 Parametric Analysis In this part, our purpose is to analyze the effects on coupler s characteristics caused by changing the phase shifter parameters. Let us take the 45 o phase shifter as illustration. Figures 4-4 show the effect of changing a) the load s dimensions on the phase shift, b) the effect of changing the length of the reference line on the phase shift, c) the effect of changing the load s dimensions on the return loss, and d) the effect of changing the load s dimensions on the insertion loss. For all the simulations, the wave ports are used and connectors not included. 46

57 (a) (b) (c) 47

58 (d) Figure 4-4 Simulation results of the 45 o differential reflective phase shifter for parametric analysis a) the effect of changing the load s dimensions on phase shift b) the effect of changing the length of the reference line on the phase shift c) the effect of changing the load s dimensions on the return loss d) the effect of changing the load s dimensions on the insertion loss From these figures, we can note that changing the length and the width of the elliptical load, i.e., the load s reactance, have a significantly impact on the phase shift but much less effect on the return and insertion loss. So, we can control the phase shift by changing the load in the ports. On the other hand, the length of the transmission line has an important role in adjusting the required differential phase shift and choosing the suitable length for the transmission line that would give the desired phase shift for the considered load. 4-4 Manufacture and Test Results of the 45 o Differential Phase Shifter To demonstrate our design, we manufactured the 45 o phase shifter using the parameter values got from simulations (figure 4-5). The dimensions of the designed circuit with the length of the reference line is 24 << 63 << which is equal 0.14* '(( 0.3* '(( based on effective wavelength. The test results of the fabricated phase shifter are shown 48

59 in figure 4-6. From this figure, we can conclude that there is a little difference between measured and simulated results. The return loss and insertion loss are better than 10 db and 1.5 db, respectively, and the maximum phase ripple is 3. For the measurement, we used the Keysight (Agilent/HP) 8720ES Vector Network Analyzer as in figure 4-5. The simulation is carried out considering the holes in where screws are located. We had done simulation by considering the screws as some rod metals. And we have used the wave ports and connectors are not included. It also might be a mismatch between load and connectors. The simulations are performed in HFSS and ADS. The screws can cause resonances. It also might be a mismatch between load and connectors. a) 49

60 b) Figure 4-5 a) Measurement system, b) the manufactured 45 o phase shifter (top, bottom and middle views). Figure 4-6 Measurement results of the 45 o phase shifter, Return and insertion loss 50