Chapter 2 Miniaturized Ultra-Broadband (2-18GHz) Quadrature Hybrid Coupler
2.4 Circuit fabrication and Measurement
(a) (b)
Fig. 2.28 Photos of (a) the fabricated 5-section hybrid coupler and (b) the fabricated 5-section hybrid coupler with dielectric blocks
Based on the previously mentioned design procedures, the proposed 5-section hybrid coupler is fabricated. The photos of the proposed 5-section hybrid coupler are shown in Fig.
2.28. The circuit size is 16.8mm × 6mm and the dielectric blocks at each side of VIP are with the size of 2.5mm × 2.5mm. The thickness of the dielectric block is 60mil.
The measured results of the whole 5-section coupler without dielectric blocks are shown in Fig. 2.29 (a). We see the performance is bad as frequency goes high. Fig. 2.29 (b) shows the phases of the coupled and through port. Fig. 2.29 (c) depicts the amplitude and phase errors between the coupled and through port. The phase error is keeping at 90 -8/+3 degree over the designed frequency of 2-18 GHz. The maximal amplitude error is up to 6.8 dB at 16 GHz and it does not meet the hybrid specifications.
0 2 4 6 8 10 12 14 16 18 20
Frequency (GHz) Graph 3
-50 -45 -40 -35 -30 -25 -20 -15 -10 -5 -11-10-9-8-7-6-5-4-3-2-10
DB(|S(2,1)|) aircoup
DB(|S(2,1)|) airiso
DB(|S(2,1)|) airthr
DB(|S(1,1)|) airthr
Fig. 2.29 (a) The measured results of the total circuit without dielectric blocks
0 5 10 15 20 Frequency (GHz)
Graph 2
-200 -100 0 100
200 10 GHz
141.4 Deg
10 GHz -133.8 Deg
Ang(S(2,1)) (Deg) aircoup
Ang(S(2,1)) (Deg) airthr
Fig. 2.29 (b) Phases of the coupled and through port
0 2 4 6 8 10 12 14 16 18 20
Graph 5
80 85 90 95 100
Phase error (degree)
-4-3 -2-1012345678
Amplitude error (dB)
PlotCol(1,4) air_measurement PlotCol(1,3) air_measurement
Fig. 2.29 (c) The amplitude and phase errors between the coupled and through port Two dielectric blocks at both sides of the VIP substrate are used to improve central section performance. The measured results of the coupler with dielectric blocks are shown in Fig. 2.30. The amplitudes and phases of the coupled and through port are shown in Fig. 2.30 (a) and (b), respectively. It can be seen that the amplitude error is smaller than that of the circuit without dielectric blocks. The performance of return loss and isolation are also better than that of the circuit without dielectric blocks. The phase error is smaller than 10o and amplitude error is less than 2.8dB over 1.8 to 17 GHz bandwidth as shown in Fig. 2.31.
0 2 4 6 8 10 12 14 16 18 20
Fig. 2.30 (a) The measured results of the total circuit with dielectric blocks
0.045 10.05 20.05 26.5
Frequency (GHz)
Fig. 2.30 (b) Phases of the coupled and through port
0 2 4 6 8 10 12 14 16 18 20
Phase error (degree)
-4
Amplitude error (dB)
PlotCol(1,3)
Phase and Amplitude_simulation PlotCol(1,3)
Phase and Amplitude_measurement PlotCol(1,4)
Phase and Amplitude_measurement PlotCol(1,4)
Phase and Amplitude_simulation
Fig. 2.31 The measured and simulated amplitude and phase errors between the coupled and through port
Fig. 2.31 shows the comparison between the measured and simulated amplitude and phase errors. The dotted lines and solid lines are simulated and measured results, respectively.
An acceptable agreement between the simulated and measured results is obtained.
Chapter 3
Multilayer Wideband Bandpass Filter
3.1 Introduction
Wideband bandpass filters are the fundamental building blocks for modern broadband wireless communication systems. Bandpass filters in microwave communication systems are often used to eliminate out-band interference signals. This application requires having steep passband-to-stopband transition, high stopband attenuation, wide stopband range and spurious resonant frequencies far away from passband frequency. The microstrip parallel-coupled filter using resonators with half wavelength has been one of the most commonly used filters [14].
This kind of filter has many advantages such as easy design procedures, a wide bandwidth range (from a few percent to more than 40%) and a planar structure. Influenced by the spurious responses at 2fo, twice the passband frequency, the microstrip parallel-coupled filter may seriously diminish the attenuation of the upper stopband as the bandwidth gets wider.
Stepped impedance resonators (SIR) are composed of transmission lines with different characteristic impedances. They provide an effective way to minimize circuit space and push spurious resonant frequencies away from passband [15]. The resonant frequencies of SIR can be controlled by adjusting the geometrical dimensions, such as the impedance ratio of the high-Z and low-Z segments. Due to the property the first spurious resonant frequency can be much higher than 2fo, it is useful in wideband bandpass filter application.
A quarter-wavelength resonator filters has the spurious passband at 3f0 instead of 2f0, but it is still not enough for wideband application [16]. The wiggly-line filter [17] can reject the harmonic passband of the filter by using a continuous perturbation of the width of the coupled lines following a sinusoidal law, but the circuit layout can not achieve wideband filter and is not suitable for suppression of wide spurious passband. Here, we propose the parallel-coupled
filter using half-wave SIR and multi-layer PCB process to realize the wideband bandpass filter.
3.2 Theory
Firstly, the conditions of fundamental and spurious resonance of a half-wave SIR are discussed. The resonator structure to be considered here is shown in Fig. 3.1. The half-wave SIR is symmetrical and has two different characteristic impedances, Z1 and Z2 in the resonator.
The admittance Yi of the resonator looking into the open end is
2
K = Z is the impedance ratio. The resonance condition is
Yi =0 (3.2) From (3.1) and (3.2) at the fundamental resonant frequency we have
K =tanθ1tanθ2 (3.3)
π
θT = (when K =1) (3.5) When K= 1, this corresponds to a uniform impedance resonator (UIR). The resonator length θT has minimal value when 0 <K< 1 and maximal value when K> 1. This condition can be obtained by differentiating (3.4) by θ1,
0 The above equation is the condition that θT has the maximal or minimal value for constant K. For practical application it is preferable to choose θ1 = because the design equations θ2 can be simplified considerably. Therefore, in the following discussion, the SIR is treated as having θ1 =θ2 =θ, and (3.1) can be expressed as
The resonance condition is then given, using the fundamental frequency f0 and corresponding length θ0, as Taking the spurious resonance frequency to be fsn (n =1, 2, 3,…) and corresponding θ with θsn (n = 1,2,3,…), we obtain from (3.8) and (3.2)
Then, the first three spurious resonance frequencies are given by
⎟⎟⎠
The above results are all a function of the impedance ratio K. Hence, the spurious response can be controlled by the choice of the impedance ratio K, which is a key feature of this type of filter. We can utilize the low impedance ratio K to push the spurious response to high frequency and the length of the resonator will be shortened. The above equations neglect the physical step discontinuity effect at the junction of the two lines.
Next, we consider a parallel coupled transmission line with arbitrary length and its equivalent circuit. For designing bandpass filters with SIR in which lines are coupled in parallel, it is necessary to find the relationship between even- and odd-mode characteristic impedances in the parallel coupled sections and the admittance inverter parameters. Fig. 3.2 (a) shows even- and odd-mode characteristic impedances Zoe, Zoo of a coupled line of electrical length θ , and its equivalent circuit is expressed by two single transmission lines of electrical length θ , impedance Zo and admittance inverter parameter J as shown in Fig. 3.2 (b)
Fig. 3.2 (a) Parallel coupled line and (b) its equivalent circuit The ABCD matrix for Fig. 3.2 (a) and (b) can be expressed as
[ ]
The above simultaneous equations are not independent of each other, and any two equations among the three are valid for solution. Solving (3.14) and (3.16), we obtainθ
These are generalized expressions for parallel coupled lines with arbitrary length. In the special case of quarter-wavelength coupling, by considering the situation
2
θ =π in (3.17)
and (3.18) then the following can be obtained:
The fundamental configuration of n-stage bandpass filter considered here is shown in Fig.
3.3, and slope parameters for all resonators are of equal value, b(b=2θ0Yo). When element values gj and relative bandwidth w are given as fundamental design parameters of a bandpass filter, the admittance inverter parameter Jj,j+1, can be expressed as
1
Fig. 3.3 Bandpass filter using SIR structure
Using (3.17) and (3.18) in the previous section, the design data for coupled lines can be obtained. It is then possible to design a bandpass filter as a SIR structure.
3.3 Design procedure and Simulation
The circuit model of a parallel coupled-line describe above is only good for relatively narrowband and is not suitable for wideband (fractional bandwidth >30％) filter. The fractional bandwidth of the proposed filter is 66.67％ (2-4 GHz). The above method has significant errors.
We utilize the optimization to design the wideband filter. Using the optimization saves our time without analyzing the complicated mathematical formulas to obtain circuit parameters such as impedances and effective dielectric constants etc. The optimization procedures are described as follows. Firstly, we construct the filter model of center frequency 3 GHz and passband 2-4 GHz in Microwave Office. Then, utilize the optimization to obtain the design parameters shown in Fig. 3.4. Fig. 3.5 depicts the simulated wideband bandpass filter response. The first spurious resonant frequency is pushed to about 3.8 times passband frequency.
Fig. 3.4 The wideband bandpass filter model
0 2 4 6 8 10 12 14 16 18 20 Frequency (GHz)
Graph 1
-60 -50 -40 -30 -20 -10 0
DB(|S(1,1)|) Schematic 1 DB(|S(2,1)|) Schematic 1
Fig. 3.5 The wideband bandpass filter response
From the design parameters, we see that high and low impedances of even mode are needed. We propose multilayer broadside coupling structure to achieve high even-mode and low odd-mode characteristic impedances. Fig. 3.6 depicts the proposed 3-layer structure. The 3 layers of metal are the ground metal in the middle layer and signal lines at two outer layers of metal, respectively. Where W is the width of the signal line and G is the overlap (negative symbol) or gap (positive symbol) between ground metal and signal lines.
We can utilize the odd- and even-mode excitations to analyze the structure due to its symmetrical structure. In the odd-mode excitation, we set the middle plane as an electric wall to simplify simulation. We use the same method to solve the even-mode excitation, but set the middle plane as a magnetic wall. Fig. 3.7 shows the odd- and even-mode equivalent circuits.
We can obtain the characteristic impedances and effective dielectric constants of odd and even mode from the simulated results.
8mil 8mil
W W
G G
8mil 8mil
W W
G G
Fig. 3.6 3-layer structure
(a) (b) G W
Electric wall
8mil Co
W G
Magnetic wall Ce
8mil
Fig. 3.7 (a) Odd-mode and (b) even-mode equivalent circuits
Odd- and even-mode characteristic impedances are expressed as
o
oo C
Z = L ,
e
oe C
Z = L (4.21)
Fig. 3.8 shows the 3D diagram of even- and odd-mode circuits in HFSS. The substrate thickness and relative dielectric constant are 8mil and 3.38, respectively. We set the width of the high characteristic impedance line as 10 mil for easy fabrication. The simulated results are shown in Fig. 3.9(a)-(e). It can be observed in Fig. 3.9 (a) that even-mode characteristic impedances increase as G increases and W decreases. Because increase G and decrease W, reduce the even-mode equivalent capacitances (Ce).
Ground Symmetrical plane
Coupled line
Fig. 3.8 The 3D diagram of even- and odd-mode excitations in HFSS
-20 -10 0 10 20 30
Fig. 3.9 (a) Even-mode characteristic impedances versus G and W
-20 -10 0 10 20 30
Fig. 3.9 (b) Even-mode effective dielectric constants versus G and W
Fig. 3.9 (b) depicts that the even-mode effective dielectric constant increases as G and W decrease. Because smaller G and W attract more electric field in the substrate, the even-mode effective dielectric constant increases. For the same reason, we can explain Fig. 3.9 (c)-(e). It should be point out that the characteristic impedances and effective dielectric constants of odd-mode are less influenced by parameter G. From Fig. 3.7 (a), we see the middle plane is electric wall that is similar to a ground plane, so parameter G has less influence on the result.
-20 -10 0 10 20 30
Fig. 3.9 (c) Odd-mode characteristic impedances versus G and W
-20 -10 0 10 20 30
Fig. 3.9 (d) Odd-mode effective dielectric constants versus G and W
0 20 40 60 80 100
120 140 160 180 200 220
Zoh εrh
G (mil) Zoh
(ohm)
1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4
εrh
Fig. 3.9 (e) Characteristic impedances and effective dielectric constants of the high impedance line versus G
According to the simulated results, we can obtain the desired geometrical dimensions.
The circuit diagram in EM simulator HFSS is shown in Fig. 3.10. There are step-junction and open-end effects that affect responses of the circuit. Therefore, the circuit has to be finely tuned. The final geometrical dimensions of the wideband bandpass filter are shown in Table 3.1 and the simulated results are shown in Fig. 3.11.
Fig. 3.10 (a) 3D view of the wideband bandpass filter diagram
Fig. 3.10 (b) Cross-sectional view of the wideband bandpass filter diagram
W1 G1 L1 W2 G2 L2 W3 G3 L3 W4 G4 L4 W50 H50
150 0 240 10 53 144 180 -14 174 10 53 197 18 200
Table 3.1 The geometrical dimensions of the wideband bandpass filter (unit: mil)
Fig. 3.11 Simulated results of the wideband bandpass filter
From Fig. 3.11, we see that the filter bandwidth is slightly reduced. In the tuning process, we have to trade off between the passband return loss and bandwidth. We sacrifice some bandwidth for better return loss.
3.4 Circuit fabrication and Measurement
Fig. 3.12 shows the photos of the multilayer wideband bandpass filter. The circuit size is 1313 mil×366 mil (33.4mm×9.3 mm).
(a) Front-side view
(b) Back-side view
Fig. 3.12 (a) Front-side view and (b) back-side views of the circuit photos
From the circuit photos, we see that the two substrates are fixed by six screws. This can cause fabrication errors because the six screws can not fix every part of the two thin substrates
very tightly. The measured and simulated results are both shown in Fig. 3.13 for comparison.
The solid and dotted lines are measured and simulated results, respectively. The measured and simulated results are matched well, except the measured passband return loss is not as well as the simulated one. The return loss degradation might come from the fabrication errors. The fabrication errors include air gaps between two screw-fastened substrates and misalignment of the circuit. A very wide upper stopband clearance of -23dB up to 20GHz is achieved.
Fortunately, the spurious response at 13GHz in the measured results is not as high as the results in the simulation.
0.01 2 4 6 8 10 12 14 16 18 20
Frequency (GHz)
Graph 1
-60 -50 -40 -30 -20 -10 0
DB(|S(1,1)|) measurement DB(|S(2,1)|) measurement DB(|S(2,1)|) simulation DB(|S(1,1)|) simulation
Fig. 3.13 Comparison between the measured and simulated results
Chapter 4 Conclusion
This thesis has demonstrated two kinds of microwave circuits namely, multi-section ultra-broadband quadrature hybrid coupler and multilayer wideband bandpass filter.
In chapter 2, miniaturized ultra-broadband quadrature hybrid coupler has been realized by using 5-section cascaded CPW coupler structure. The synthesis techniques based on the concept of odd- and even-mode analysis has been developed. The VIP structure to achieve a extremely tight of coupling has been proposed. The unequal modal phase velocities, however, are a serious problem in the VIP structure. Putting two dielectric blocks with the same dielectric constant as the VIP substrate at both sides of the VIP substrate to compensate the modal phase velocities of a VIP coupled-line has been successfully developed. Although two dielectric blocks improve the directivity, they lower the even-mode characteristic impedance.
Tradeoff between directivity and coupling should be made. Finally, the measured results have shown a good agreement with the simulated results. The bandwidth reduction mainly results from the insufficient even-mode characteristic impedance in the tight-coupling section, the discontinuities between each section, and the air gaps between the dielectric blocks and VIP substrate. There still has space to improve the performance.
In chapter 3, the wideband bandpass filter has been realized by using the parallel coupled stepped impedance resonators (SIR). Utilizing the SIR to push the spurious frequency far away from the passband center frequency has been successfully developed. The multilayer structure to achieve a high to low even-mode characteristic impedances has been proposed.
According to the design parameters from the simulated results, a wideband bandpass filter can be easily designed. Finally, the measured and simulated results have been matched well. A very wide upper stopband clearance of -23dB up to 20GHz has been achieved.
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