1 Introduction
1.4 Organization of the dissertation
In chapter 2, a novel wideband 1800 phase shifter using CPS/interdigital CPS structure is proposed to realize the compact wideband 1800 hybrid coupler. Design equations for stepped-impedance lines and design curves for CPS/interdigital CPS lines are also presented. Chapter 3 describes a single-section cascadable 1800 hybrid coupler is realized by vertically installed planar (VIP) coupler for size reduction and bandwidth enhancement. Then, based on this single-section cascadable 1800 hybrid coupler, a two-section cascadable 1800 hybrid coupler for larger bandwidth and
power- power-division ratios is proposed. Furthermore, the analysis procedures are described in detail for these hybrid couplers. The coupled line using VIP structure is also discussed in this chapter. Chapter 4 presents several novel wideband bandpass filter structures by cascading two 1800 hybrid couplers. The design methods are also given in this chapter. Chapter 5 gives the conclusion.
Chapter 2
A Compact Wideband 180
0Hybrid Coupler Using a Novel Interdigital CPS Phase Inverter
In this chapter, we modify the 1800 hybrid ring in [9] where the phase inverter was implemented by 1800 twist of the high impedance CPS as shown in Fig. 2-1 and the parasitic effect of the twist must be considered. More importantly, the design of the hybrid ring in [9] was mostly try-and-error using EM simulator. Therefore, we propose the 1800 hybrid ring coupler with an wideband phase inverter as shown in Fig.
2-2 where three λ/4 line sections and one λ/4 line section cascading an ideal phase inverter are realized by the configurations in Fig. 2-3(a) and (b) respectively. Note that physical dimensions in Fig. 2-3(a) and (b) have the same dimensions so that the design curves in this chapter are valid for both cases. Also, simple design equations for designing of stepped-impedance line are provided. The method described in this chapter can systematically design a hybrid ring with much better performance than that of [9].
Fig.2-1. Configuration of the wideband phase inverter realized with CPS.
Fig. 2-2. Schematic of the 1800 hybrid ring with an ideal 1800 phase inverter.
(a)
(b)
Fig. 2-3. Proposed configurations of the stepped-impedance 1800 hybrid ring coupler using interdigital CPS (a) λ/4 line section (b) λ/4 line section with a wideband phase inverter.
(a)
(b)
Fig. 2-4. (a) Quarter-wave transmission line (b) Stepped-impedance circuit equivalent to a quarter-wave transmission line
2-1 Analysis of the stepped-impedance line section
The characteristic impedance Z of the hybrid ring corresponding to the specific return loss can be determined by [17]. A quarter-wave transmission line of impedance Z is shown in Fig. 2-4(a) and it serves as a basic building block of the proposed hybrid ring. Its ABCD matrix is given by The quarter-wave transmission line can be replaced by a stepped-impedance structure shown in Fig. 2-4(b) where ZH and ZL are the characteristic impedances of the cascaded sections and θΗ and θL are the corresponding electrical lengths. By choosing ZH>ZL, the overall electrical length of the stepped-impedance section can be shorter than 900. The ABCD matrix of the stepped-impedance section shown in Fig.
2-4(b) is given by
H
Equating the ABCD matrix of the quarter-wave transmission line and the stepped-impedance structure shown in Fig. 2-4, we have
.
2-2 Design steps of the proposed 1800 hybrid ring coupler
The first step to implement the proposed 1800 hybrid ring coupler is to specify the required return loss. The next step is to replace each line section in Fig. 2-2 by the stepped-impedance structure. Followings show the procedures. First, arbitrary choose the θΗ and θL and then use (2-3)-(2-5) to find ZH and ZL. Second, check the obtained ZH and ZL to be realizable or not, if not, redo the first step again. Finally, fine-tuning the obtained circuit parameters might be required to optimize the circuit performance.
In this work, the 1800 hybrid ring coupler with 15-dB return loss is designed as an example and the optimized circuit parameters are shown in Table 2-1.
TABLE2-1
Parameters of the stepped-impedance hybrid ring ZH
Fig. 2-5. Cross-sectional view of the interdigital CPS with N=3.
2-3 Realization and measurement
From [35], we know that the length of a stepped-impedance line can be significantly reduced with larger high- to low-impedance ratios. However, to realize such high and low impedances simultaneously would be a challenge. Fortunately, this can be solved by using CPS (high impedances) and interdigital CPS (low impedances).
The cross-sectional view of the interdigital CPS is shown in Fig. 2-5. Here, N is defined as the number of CPS strip pair (for instance N=2 has 4 strips) and the conductor thickness (t) is assumed to be zero. The proposed hybrid ring coupler is fabricated on an Al2O3 alumina substrate with 15-mil thickness (h) and a dielectric constant (εr) of 9.8. It is designed to operate at the center frequency of 2 GHz.
Fig. 2-6 shows the computed characteristic impedance and effective dielectric constant of CPS as a function of the gap width with the strip width as a parameter. Fig.
2-7 indicates the computed characteristic impedance and effective dielectric constant of interdigital CPS as a function of the gap width with the number of CPS strip pair as a parameter. It can be found that extremely high impedances can be obtained by conventional CPS with large S and small W and extremely low impedances can be implemented by interdigital CPS with large N, small S, and large W. Using the design curves in Fig. 2-6 and Fig. 2-7, parameters of each line section corresponding to Table 2-1 can be obtained. In this design, we choose N=3 and the parameters of each line section are listed in Table 2-2. Fig. 2-8 shows the simulated magnitudes of S11 and S21
and the insertion phase difference between two configurations of Fig. 2-3(a) and (b)
with ZH=184Ω, θH=15.20, ZL=22Ω and θL=16.30 where the S-parameters are based on 50-Ω port impedances. Note that all mentioned curves are computed by EM simulator Sonnet. It can be seen that insertion phase difference is within 10 and S-parameters of them are almost the same. Therefore, the proposed configuration in Fig. 2-3(b) performs perfectly as a wideband phase inverter.
Fig. 2-6. Computed characteristic impedance and effective dielectric constant of CPS as a function of the gap width with the strip width as a parameter, t=0 mil.
TABLE2-2
CPS and Interdigital CPS parameters of the stepped-impedance hybrid ring Line width
W (mil)
Gap width S (mil)
(Ω)Z
Interdigital CPS (N=3) 4 1.6 22
CPS 4 24 184
(a)
(b)
Fig. 2-7. Computed characteristic impedance and effective dielectric constant of interdigital CPS as a function of the gap width with the number of CPS strip pair as a parameter, t=0 mil (a) w=3 mil (b) w=4 mil.
Fig. 2-8. Simulated magnitude of S11 and S21 and insertion phase difference between two configurations of Fig. 2(a) and (b) with ZH=184Ω, θH=15.20,ZL=22Ω and θL=16.30 where the S-parameters are based on 50-Ω port impedances.
(a)
(b)
Fig. 2-9. Fabricated 1800 hybrid ring coupler (a) Layout (b) Photograph.
The layout and photograph of the fabricated 1800 hybrid ring coupler are shown in Fig. 2-9. The size of this hybrid is 404 mil × 404 mil. Fig. 2-10 depicts the measured results of the fabricated hybrid ring coupler and the measured insertion loss is approximately 0.6 dB. The measured return losses are better than 10 dB from 0.98 to 2.93GHz for out-of-phase operation and from 0.97 to 2.96 GHz for in-phase operation, respectively. The measured isolation is better than 30 dB from 0.5 to 4 GHz. The measured amplitude and phase differences are shown in Fig. 2-11. For out-of-phase operation, the amplitude difference is within 0.5 dB from 0.7 to 4 GHz and the phase difference is within 20 from 0.5 to 4 GHz. For in-phase operation, the amplitude difference is within 0.5 dB from 0.5 to 4 GHz and the phase difference is within 30 from 0.5 to 4 GHz. Fig. 2-12 shows the measured and simulated results from 0 to 20 GHz. The measured performances of the 1800 hybrid ring coupler are summarized in Table 2-3.
(a)
(b)
Fig. 2-10. Measured results of the fabricated 1800 hybrid ring coupler (a) Out-of-phase operation (b) In-phase operation
(a)
(b)
Fig. 2-11. Measured phase and amplitude differences of the fabricated 1800 hybrid ring coupler (a) Out-of-phase operation (b) In-phase operation.
Fig. 2-12. Measured and simulated results from 0 to 20 GHz.
TABLE 2-3
Summary of measured performances of the 1800 hybrid ring coupler
Out-of-phase In-phase
Frequency range [GHz] (RL< -10dB) 0.98~2.93 (97.5%)
Phase imbalance [Degree] 180 ± 2 0 ± 3
Frequency range [GHz] 0.5 ~ 4
amplitude imbalance [dB] 0 ± 0.4 0 ± 0.5
Frequency range [GHz] 0.75 ~ 4
Frequency range[GHz] Isolation< -30dB 0.5 ~ 4
Chapter 3
Wideband Multi-section 180
0Hybrid Couplers Using Vertically Installed Planar Couplers
In this chapter, the multi-section 1800 hybrid rings are proposed to overcome the problems of high power-division ratios and broad bandwidth. The basic building block of the proposed multi-section 1800 hybrid ring is the reconfigured ideal 1800 hybrid ring as shown in Fig. 3-1(a) and (b). The proposed single-section hybrid ring can be easily cascaded like the 900 branch-line coupler as depicted in Fig. 3-1(c). The reconfiguration proposed in Fig. 3-1(b) also results in size reduction. Furthermore, the hybrid ring in Fig. 3-1(b) with two output ports on the same side is convenient for the applications such as balanced-mixer, push-pull amplifier, etc. Synthesis procedures to realize Chebyshev-response two-section cascaded 1800 hybrid rings shown in Fig.
3-1(c) with various power-division ratios will be described. The reconfigured single-section 1800 hybrid ring with a unit element at each port [17], [18] can be cascaded to exhibit extended bandwidth as shown in Fig. 3-2. As an example, the 3-dB two-section hybrid ring with 15-dB return loss yields a bandwidth of 5:1.
However, the realization of a broadband phase inverter on microstrip circuits could be a problem. Fortunately, as described in [6] that a short-ended λ/4 coupled line can provide 2700 phase-shift and the ratio of the even- and odd-mode impedance of the
coupled line determines the bandwidth. The higher even- to odd-mode impedance ratio produces wider bandwidth. As the ratio approaches to an asymptotic value, the short-ended coupled line is equivalent to a λ/4 line cascaded with an ideal phase inverter. To achieve an enough bandwidth, a very tight coupled line must be implemented. In this chapter, the VIP coupler described in [36] is proposed to implement the very tight coupled lines. With the VIP coupler, the proposed wideband multi-section hybrid rings can be easily implemented by microstrip circuits. Several design examples show that the proposed multi-section 1800 hybrid rings not only exhibit broad bandwidth but also depict wide range of power-division ratios.
(a)
(b)
(c)
Fig. 3-1. Schematics of hybrid rings using an ideal phase inverter (a) Conventional hybrid ring (b) Reconfigured hybrid ring (c) Proposed two-section hybrid ring.
Fig. 3-2. Schematic of the proposed two-section hybrid ring with a unit element at each I/O port.
(a)
(b)
Fig. 3-3. (a) Even-mode and (b) odd-mode equivalent circuits of the rat-race ring coupler using an ideal phase inverter.
3.1 Theoretical analysis of the two-section hybrid ring
In the reconfigured single-section hybrid ring shown Fig. 3-1(b), the admittance Y1
and Y2 are normalized values with respect to system admittance Y0. Fig. 3-3 shows the even- and odd-mode equivalent circuits of the rat-race ring hybrid using an ideal phase inverter. Using the even- and odd-mode analysis, the ABCD matrices for the even- and odd-mode cascade elements are given by
⎥⎦ where t = jtanθ and the subscripts indicate the degree of the polynomials A(t2), B(t2), C(t2), and D(t2). The reflection and transmission coefficients of the even- and odd-mode cascade elements are
D Therefore, the S-parameters of the single-section hybrid ring can be expressed as
D
The conventional even- and odd- mode analysis method to obtain the S-parameters of the cascaded 900 hybrid ring [20] can not be used in this newly proposed two-section hybrid ring shown in Fig. 3-1(c) because the symmetrical planes for even-
and odd-mode excitation are not exist. Here, the multi-port connection method [37] is used. The results at the center frequency are shown as follows:
2 at the input port will be split between port 3 and port 4. Although all ports can be perfectly matched for the case of Y1=Y4 and Y2=Y3, a zero dB coupler, which means that no signal can be obtained from one of the output ports, is obtained. Therefore, we concentrate our attention in the case of Y1=Y3 and Y2=Y4. Because in this case the two-section hybrid ring consists of two identical single-section hybrid rings, the synthesis procedure can be largely simplified. Again, applying the multi-port connection method to (3-4), we can obtain
)
) It should be noted that the interchange between Y1 and Y2 results in the interchange
between the sum port and the delta port. Assuming that the input is matched well in the passband, we have
2
1
41 2
31
+ S ≈
S
(3-7) The output power-division ratio is2 Now, considering the function
R
where F is approximately equivalent to the reflection coefficient of the two-section hybrid ring over the passband because the denominator is very close to unity [see (3-9)]. Therefore, the insertion loss function PL can be shown as follows:2 As described by Riblet [38], and Carlin and Kohler [39], the insertion loss function of a Chebyshev response has the form
2 where x=cos2θ, xc=cos2θc, Tn(x) is the Chebyshev polynomial of the first kind of degree n ,and m is the parameter to control the ripple level. Substituting A, B, C, and
D in (3-1) into (3-11) and fitting (3-11) to (3-12) with n=3, we obtain The relationship between m and return loss is
dB m
RL=10log(1+1/ 2) (3-15) According to (3-8), (3-13), (3-14), and (3-15), the unknown variables Y1 and Y2 can be solved numerically. It should be emphasized that there exists two set of solutions.
Let us discuss in the following.
Fig. 3-4. Characteristic impedances Z1, Z2, and bandwidth versus return loss for the equal-ripple response 3-dB two-section hybrid ring.
Fig. 3-4 shows the plot of characteristic impedances of Z1, Z2, and bandwidth versus return loss for the 3-dB two-section hybrid ring shown in Fig. 3-1(c). The 96.3% bandwidth for return loss better than 15dB can be achieved. A similar synthesis procedure can be used to solve the unknown variables for the single-section hybrid ring. Fig. 3-5 shows the plots of characteristic impedances of Z1, Z2, and bandwidth versus coupling level, which is defined by the power at coupling port divided by the incident power, for the single- and two-section hybrid rings with 15-dB return loss. It can be seen that, for the single-section hybrid ring, the bandwidth increases with increasing power-division ratios, but the high impedance value of Z1 limits the realizable power-division ratios to about -10dB. The bandwidth of the two-section hybrid ring decreases with increasing of the power-division ratios but the values of Z1 and Z2 are both located in the reasonable range for power-division from as strong as -3dB to weaker than -20dB.
Fig. 3-5. Characteristic impedances Z1, Z2, and bandwidth versus coupling level for the single- and two-section hybrid rings with 15-dB equal-ripple return loss.
Fig. 3-6 shows another set of solutions for the two-section hybrid ring. Comparing to the characteristics of the single-section hybrid ring in Fig. 3-5, it depicts a larger bandwidth, but requires a higher Z1 impedance value. The two-section hybrid ring shown in Fig. 3-2 comprises two single-section units where each unit has a unit element at each I/O port. This two-section hybrid ring can achieve larger bandwidth than above described two-section hybrid ring. However, the analysis method described above is too complicated to obtain similar design equations. Fortunately, values of unknown variables Y1, Y2, Y3, and Y4 can be obtained by optimization with the known relationship between Y1 and Y2. The design curves for a two-section 3-dB hybrid of this type are shown in Fig. 3-7.
Fig. 3-6. Another set of characteristic impedances Z1, Z2, and bandwidth versus coupling level for the two-section hybrid rings with 15-dB equal-ripple return loss.
Fig. 3-7. Characteristic impedances Z1, Z2, Z3, Z4, and bandwidth versus return loss for the equal-ripple response 3-dB two-section hybrid ring with a unit element at each I/O port.
Fig. 3-8. Cross-sectional view of the VIP coupler.
3.2 Characteristics of VIP couplers
Fig. 3-8 shows the cross-sectional view and the parameters of the VIP coupler.
Coupling coefficients can be readily controlled by changing the dielectric constants or the thicknesses of the substrates or the height h and width w of the coupler. Therefore, the newly added vertical substrate can significantly increase the freedom of design.
From [36], we know that the electric field is mainly confined in the vertical substrate for odd-mode excitation and in air and main substrate for even-mode excitation.
The equivalent circuit of a short-ended coupled line is shown in Fig. 3-9 where Z0e
and Z0o are the even- and odd-mode characteristic impedances and θ is the electrical length of the coupled line. When θ=900, the two shunt shorted stubs of the characteristic impedance Z0e are open-circuited. Therefore, at the center frequency, the short-ended coupled line is reduced to a λ/4 transmission line of characteristic impedance 2Z0eZ0o/(Z0e-Z0o) cascaded with an ideal phase inverter. It should be emphasized that previously described theory is based on an ideal single-section 1800 hybrid ring. However, the two shunt shorted stubs in Fig. 3-9 are only open-circuited at the center frequency. Out of center frequency, the influence of this shunt shorted stub decreases as the value of Z0e increases. Until Z0e approaches to infinity, the short-ended coupled line is equivalent to the phase inverting arm required in an ideal single-section 1800 hybrid ring. To obtain higher Z0e, we can increase the height h of the coupler. Comparing Fig. 3-1(b) and Fig. 3-9, it can be found that the value of Z0o
is closed to Z2/2 as long as Z0e is much higher than Z0o. The VIP coupler can not only realize low values of Z0o but also implement high values of Z0e. Here, the main circuit is fabricated on a RO4003 substrate with 20-mil thickness (hs) and a dielectric constant (εr1) of 3.38 and the VIP coupler is implemented on same RO4003 substrate with 8-mil thickness (hv) and same dielectric constant (εr2) of 3.38. The characteristic impedances for even- and odd-modes of the VIP couplers can be obtained by the fully 3-D EM simulator HFSS [40].
Fig. 3-9. Equivalent circuit of a short-ended coupled line.
TABLE3-1
VIP coupler parameters extracted by HFSS (f0=2 GHz)
Z (Ω)
H (mil)
W (mil)
εre εro Z0e (Ω)
Z0o (Ω)
L (mil)
59.0 70 21.5 1.28 2.87 348.0 27.2 894.0
50.8 70 25.9 1.26 2.91 336.0 23.5 886.0
41.3 70 34.0 1.24 2.97 320.6 19.4 875.5
29.8 70 49.0 1.22 3.04 297.5 14.2 862.0
Four cases of VIP couplers are calculated for the prototype circuits in the next section. The physical parameters in Fig. 3-8 and the calculated electrical parameters of the VIP couplers are listed in Table 3-1 where L is the required physical length of the short-ended VIP coupler to provide 2700 phase-shifting at the center frequency of 2GHz. Fig. 3-10 shows the simulated 15-dB equal-ripple return loss bandwidth of a 3-dB single-section hybrid ring with a short-ended coupler versus different Z0e. It can be seen that the bandwidth approaches to an asymptotic value as long as Z0e is higher than about 250Ω. Therefore, if the VIP coupler can have this high Z0e value, a nearly ideal single-section unit can be implemented. Besides, the VIP coupler can also provide a good crossover in the proposed circuit. Because the signal going through the short-ended VIP coupler is mainly odd-mode and the field of odd-mode is mostly confined in the VIP substrate, the crossover has negligible influence on circuit performance.
Fig. 3-10. Simulated 15-dB equal-ripple return loss bandwidth of a 3-dB single-section hybrid ring with a short-ended coupler versus different Z0e.
3.3 Experimental results and discussion
As we mentioned previously, the VIP coupler is a good candidate to realize the phase inverter and the crossover on microstrip circuits. Four prototype circuits are fabricated that all of them are with a 15-dB of equal-ripple return loss. Four prototype circuits are a single-section reconfigured 3-dB hybrid ring to observe the performance of the single-section building block, a two-section 3-dB hybrid ring with the equivalent circuit shown in Fig. 3-1(c) to verify the validity of the theory derived in previous section, a two-section 20-dB hybrid ring to show the high power-division ratio of the proposed design in Fig. 3-1(c), and a two-section 3-dB hybrid ring with the equivalent circuit shown in Fig. 3-2 to depict the bandwidth extension performance.
The 3-D view of the reconfigured single-section hybrid ring is shown in Fig. 3-11
The 3-D view of the reconfigured single-section hybrid ring is shown in Fig. 3-11