Dual- Frequency Transformer[19]

Impedance transformers have traditionally been broadly divided into two groups;

those with a continuously tapered impedance distribution and those with a stepped piece-wise impedance distribution. The latter being considerably shorter than the broad-band tapered transformers perhaps because they tend to mimic a traditional lumped-element design.

The feasibility of an electrically small transformer with two sections and capable of achieving ideal impedance matching at two arbitrary frequencies is demonstrated

50

analytically. The parameters of the transformer are presented in explicit closed form.

Figure 3.10 Two-section dual-band transformer.

The input impedance is given by

(3.13)

(3.14) We want the input impedance to be equal to source impedance

Z ₀

at the two frequencies of interest

f ₁

and

f ₂

. Equating

Z _in

to

Z ₀

and solving for

Z ′ _L

from (3.13) leads to

(3.15) From (3.14) and (3.15), after some complicated calculation and we can obtain

(3.16)

(3.17) where

2

(tan(

1 1

))

α

=

β

A (3.18)

Z ′ L

R L

51

Chapter 4

The Proposed Dual-Band Bandpass Filter

We want to design the second and third-order bandpass filters with the function that can operate at two different frequencies corresponding to even- or odd-mode signals respectively. The design procedure and circuit realization as well as the simulation and measurement results will be presented. In the following sections, the filters are classified according to the type of tapping. In addition, the tool we used for circuit simulation is conducted by ADS from Agilent and the EM simulation is completed by Sonnet. All the measurements are obtained by four-port network analyzer E5070. All the filters are fabricated on Rogers RO4003 with a relative dielectric constant of 3.38 and thickness of 20 mil. For the short-end type SIR, the diameter of via hole is chosen as 40mil.

4.1 Design Procedure and Realization with Type I tapping

4.1.1 Second-Order Filter with Open-Ended λ/2 SIR

In this design, we choose the specification that the center frequencies for the higher pass and the lower passband are 3GHz and 2.8GHz respectively. The fractional bandwidth

52

Figure 4.1 The overall circuit diagram. (a) In circuit simulation tool, ADS. (b) In EM simulation tool, Sonnet.

The overall circuit diagram in ADS and Sonnet are shown in Figure 4.1. We utilize the same design procedure as Type III filter in Figure 3.8. First, the filter is considered as two sections consisting of the resonators and the feeding structure at input and output stages.

For the resonators, the center frequency depends on the resonant frequency of the SIR structure while the bandwidths are mainly controlled by the coupling between the resonators. We first design a second-order bandpass filter with the operating frequency 3GHz, fractional bandwidth 5%. The initial parameters for the filter are shown in Table

53

4.1. In our case, a higher characteristic impedance is used to avoid the physical limit in microstirp coupled lines but not deteriorate the coupling required. In Table 4.1,

Z _{oe 12}

and

12

Z oo

represent the characteristic impedances of the coupled line between the resonators.

After that, we design another filter with all the dimensions fixed as previous filter except for the impedance

Z _a

, which is replaced with a higher impedance

Z _{a high _}

. In our case, the impedance is chosen to be 70 ohm. For the characteristics of SIRs mentioned in Section 2.1.3, it’s observed that the fundamental frequency is changeable with the variation of impedance ratio. The smaller the impedance ratio is, the lower the fundamental frequency becomes. That is, the fundamental resonant frequency of the latter filter will be lower than the former one. In our design, a coupled line is employed to realize the segment in the center of each SIR. When excited with even- and odd-mode signals, the segment can perform characteristic impedances

Z _oe

and

Z _oo

relating to

_ a high

Z

and

Z _{a low _}

for the two filters respectively. From the coupled line theory, it’s reasonable that

Z _oe

>

Z _oo

for microstrip coupled lines. In conclusion, when a differential signal is applied, the filter will operate at the high-frequency band whereas the low-frequency band will only perform with a common mode source.

Table 4.1 Initial parameters for the odd-mode filter in Filter A.

So far, the circuit parameters for the resonators are decided. Therefore, the final problem is to find a proper feeding structure to realize the needed coupling between the tapped lines and end resonators. Following Section 3.1, the tapped position should be

f 0

(GHz)

Z _a

(ohm)

Z _b

(ohm)

θ _b θ _a Z _{oe 12}

(ohm)

Z _{oo 12}

(ohm)

3 46 95 60

^o

47.647

^o

133.68 73.67

54

evaluated to give the desired load impedances

R _{L 1}

,

R _{L 2}

at two designed center frequencies. The load impedances

R _{L 1}

and

R _{L 2}

may be different. For convenience, it is assumed that

R _{L 1}

=

R _{L 2}

. In this case, the dual frequency transformer in Section 3.3 can be utilized to carry out the matching circuit. Finally, we use Table 2.1 as a reference to fine tune the full circuit in EM simulation tool, and the total filter is completed which we call Filter A. The circuit layout of Filter A with physical dimensions are shown in Figure 4.2 and listed in Table 4.2. The photograph and measured results are shown in Figure 4.3.

and 4.4.

Figure 4.2 The circuit layout of the proposed Filter A.

Table 4.2 Physical dimensions of the proposed Filter A. (Unit: mil) W1 W2 W3 W4 W5

95 6 12 23 12 L1 L2 L3 L4 L5 180 106 388 170 435 L6 L7 L8 S1 S2 632 328 156 6 5

55

Figure 4.3 Photograph of Filter A

dB(S(1,1)) dB(S(2,1)) dB(S(3,3)) dB(S(4,3))

2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8

2.0 4.0

-40 -30 -20 -10

-50 0

freq, GHz

d B (S(1 ,1 )) d B (S(2 ,1 )) d B (S(3 ,3 )) d B (S(4 ,3 ))

dB(S(1,1)) dB(S(2,1)) dB(S(3,3)) dB(S(4,3))

(a)

56

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

1.0 7.0

-70 -60 -50 -40 -30 -20 -10

-80 0

freq, GHz

dB (S (5 ,5 )) dB (S (6 ,5 )) dB (S (7 ,7 )) dB (S (8 ,7 ))

dB(S(5,5)) dB(S(6,5)) dB(S(7,7)) dB(S(8,7))

(b)

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-50 -40 -30 -20 -10 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(c)

57

FREQUENCY(GHz)

1 2 3 4 5 6 7

S(dB)

-80 -60 -40 -20 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(d)

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-80 -60 -40 -20 0

S11(Common to Differential) S21(Common to Differential) S11(Differential to Common) S21(Differential to Common)

(e)

58

Figure 4.4 Simulated and measured results of Filter A. (a) Simulated

S ₁₁ and S ₂₁

for 2~4 GHz. (b) Simulated

S ₁₁ and S ₂₁

for 1~7 GHz. (c) Measured

S ₁₁ and S ₂₁

for 2~4 GHz. (d) Measured

S ₁₁ and S ₂₁

for 1~7 GHz. (e) Measured isolation between two modes.

Figure 4.4 shows the measured return loss in the passband is better than 15dB and the insertion loss is about 1.5~2 dB. The fractional bandwidths are 6% and 4.7% at 2.7 GHz and 3.19 GHz respectively. The first spurious resonance happens at about 5GHz. The results confirm to the simulation approximately.

4.1.2 Second-Order Filter with Short-Ended λ/2 SIR

MLIN

Figure 4.5 The overall circuit scheme of Filter B. (a) The circuit structure in ADS. (b)

59

The circuit layout in Sonnet.

W1 W2 W3 W4 L1 46 8 44 40 76 L2 L3 L4 L5 L6 200 100 28 300 96

L7 L8 L9 S1 S2 6 472 360 6 6 Table 4.3 Physical dimensions of the proposed Filter B. (Unit: mil)

On the other hand, we can also employ the filter in Figure 3.9 as a main structure to build a second-order bandpass filter with similar function as Filter A. The overall circuit configuration with physical dimensions are depicted in Figure 4.5 in Table 4.3. The filter which we’ll call Filter B is designed with the specification that the two passbands are at 3.3 GHz and 2.9 GHz with ripple level 0.1 dB, and the fractional bandwidth is about 4~6%. Likewise, the structure are partitioned into two parts. The first section corresponds to the SIRs. The same as Filter A, the filter for the higher passband is constructed first.

The initial parameters are shown in Table 4.2.

Table 4.4 Initial parameters of the even-mode filter in Filter B.

Later, for the second filter with a lower passband, we choose a lower impedance

Z _{a low _}

, 37 ohm, to reach the center frequency 2.9 GHz. The decision of

Z _a

is different from that in Filter A. This is because the characteristics of the short-ended λ/2 SIR discussed in Section 2.1 for which the same properties with the open-ended λ/2 SIR

f 0

(GHz)

Z _a

(ohm)

Z _b

(ohm)

θ _b θ _a Z _{oe 12}

(ohm)

Z _{oo 12}

(ohm)

3.3 60 50 60

^o

25.69

^o

58.9298 43.4204

60

can perform while the high- Z and low- Z segments are interchanged.

Finally, we choose a coupled line with the characteristic impedances

Z _oe

and

Z _oo

related to

Z _{a high _}

,

Z _{a low _}

. In the end, the filter will operate at higher passband when applying a common-mode signal. With a differential-mode signal, the lower band can be performed.

Following Section 3.1, we can calculate the load impedance needed of the tapped line when fixing the tapping point. In this case, we choose the tapped position to obtain the same load impedances so that the dual frequency transformer can be utilized to realize the matching circuit. Consequently, we use Table 2.1 as a reference to fine tune the circuit in EM simulation tool. The photograph and measured results are shown in Figure 4.5. and 4.6.

Figure 4.6 Photograph of Filter B.

61

62

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-40 -30 -20 -10 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(c)

FREQUENCY(GHz)

1 2 3 4 5 6 7

S(dB)

-80 -60 -40 -20 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(d)

63

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-80 -60 -40 -20 0

S11(Common to Differential) S21(Common to Differential) S11(Differential to Common) S21(Differential to Common)

(e)

Figure 4.7 Simulated and measured results of Filter B. (a) Simulated

S ₁₁ and S ₂₁

for 2~4 GHz. (b) Simulated

S ₁₁ and S ₂₁

for 1~7 GHz. (c) Measured

S ₁₁ and S ₂₁

for 2~4 GHz. (d) Measured

S ₁₁ and S ₂₁

for 1~7 GHz. (e) Measured isolation between two modes.

Figure 4.7 shows the measured in-band return loss is better than 20 dB and the insertion loss is about 1.2~1.5 dB. The fractional bandwidths are 6.6% and 4.6% at 2.93 GHz and 3.27 GHz. The first spurious occurs at 5.5 GHz. These results consist with the simulated results approximately.

4.1.3 Third-Order Filter with Short-Ended λ/2 SIR

The same procedure in Section 4.1.2 can be utilized to design a higher order bandpass filter. In our case, we try to manipulate a third-order design. The specification of the filter are about 2.9 GHz and 3.2 GHz for center frequencies and 3~5% for the bandwidth with

64

ripple level 0.1 dB . First, focus on the section of the resonators and the coupling causes different resonant frequencies. We use the element values for third-order Chebyshev response to synthesize the initial circuit parameters for the filter with higher passband.

Furthermore, considering the lowest spurious resonance. we choose the impedance ratio of the filter with higher passband is nearly unity which means a UIR filter while the ratio

R of the other one is smaller than unity. It’s for the reason that the SIR filter possesses

the advantage that the first spurious can be much higher than

2 f ₀

; meanwhile, the first spurious of the UIR filter will resonate at

2 f ₀

. Thus, we utilize a coupled line to realize

_ a high

Z

,

Z _{a low _}

. And finally, we can obtain the filter with a higher upper stopband. The initial parameters are presented in Table 4.5.

Table 4.5 Initial parameters of the even-mode filter in Filter C.

For more degrees of freedom, we utilize the transmission line with three sections to accomplish the impedance matching. In addition, Table 2.2 provides a reference to fine tune the circuit during EM simulation. We name the design Filter C. The overall circuit configuration with parameters of physical dimensions are shown in Figure 4.8 and Table 4.6. The photograph and measured results of Filter C are shown in Figure 4.9. and 4.10.

(a)

f 0

(GHz)

Z _a

(ohm)

Z _b

(ohm)

θ _b θ _a Z _{oe 12}

(ohm)

Z _{oo 12}

(ohm)

3.3 37 50 60

^o

25.69

^o

55.6 45.4189

65

(b)

(c)

Figure 4.8 The overall circuit configuration of Filter C. (a) The overall layout. (b) The part of resonators. (c) The part of transformers.

66

W1 W2 W3 W4 W5 W6 54 52 30 44 40 44 L1 L2 L3 L4 L5 L6 900 500 127 151 500 529

L7 L8 L9 L10 L11 L12 1100 470 160 5 151 420

L13 S1 S2

410 6 12 Table 4.6 Physical dimensions of the proposed Filter C. (Unit: mil)

Figure 4.9 Photograph of Filter C.

67

68

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-50 -40 -30 -20 -10 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(c)

FREQUENCY(GHz)

1 2 3 4 5 6 7

S(dB)

-80 -60 -40 -20 0

Evenmode S11 Evenmode S21 Oddmode S11 Oddmode S21

(d)

69

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-80 -60 -40 -20 0

(e)

Figure 4.10 Simulated and measured results of Filter C (a) Simulated

S ₁₁ and S ₂₁

for 2~4 GHz. (b) Simulated

S ₁₁ and S ₂₁

for 1~7 GHz. (c) Measured

S ₁₁ and S ₂₁

for 2~4 GHz. (d) Measured

S ₁₁ and S ₂₁

for 1~7 GHz. (e) Measured isolation between two modes.

Figure 4.10 presents the measured return loss in the passband is better than 10 dB and the insertion loss is about 2.5~3 dB. The fractional bandwidth are 5.2% and 2 % at 2.87 GHz and 3.26 GHz respectively. The first spurious occurs at 6.8 GHz.

70

4.2 Design Procedure and Realization with Type II tapping

4.2.1 Third-Order Filter with Short-Ended λ/2 SIR

In this design, we continue using the design of Filter C with the same specification.

The only difference is the feeding structure. In this case, we employ a coupled-line section in the matching circuit. Since the characteristic impedance of differential-mode and common-mode signal in the coupled line differs, it’s convenient to use the feature to realize the transformer more easily. In addition, the length of the transformer can be effectively shortened as well as the size of the circuit. At the end, the filter is fabricated and called Filter D. The overall circuit scheme with physical dimensions are shown in Figure 4.11 and Table 4.7. The photographs and measured results are shown in Figure 4.12. and 4.13.

Figure 4.11 The overall circuit topology of Filter D.

71

W1 W2 W3 W4 W5 L1 66 24 30 44 40 508 L2 L3 L4 L5 L6 L7 500 625 93 293 114 100

L8 L9 L10 S1 S2 S3 529 420 5 6 6 12 Table 4.7 Physical dimensions of the proposed Filter D. (Unit: mil)

Figure 4.12 Photograph of Filter D.

72

73

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-40 -30 -20 -10 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(c)

FREQUENCY(GHz)

1 2 3 4 5 6 7

S(dB)

-80 -60 -40 -20 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(d)

74

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-80 -60 -40 -20 0

(e)

Figure 4.13 Simulated and measured results of Filter D. (a) Simulated

S ₁₁ and S ₂₁

for 2~4 GHz. (b) Simulated

S ₁₁ and S ₂₁

for 1~7 GHz. (c) Measured

S ₁₁ and S ₂₁

for 2~4 GHz. (d) Measured

S ₁₁ and S ₂₁

for 1~7 GHz. (e) Measured isolation between two modes.

Figure 4.13 presents the measured return loss in the passband is lower than 10 dB.

The insertion loss is about 2.1~2.5 dB and the fractional bandwidth is 7.9% and 4.5 % at 2.79 GHz and 3.21 GHz. The first spurious occurs at the frequency higher than 7 GHz.

75

4.3 Design Procedure and Realization with Type III tapping

4.3.1 Third-Order Filter with Open-Ended λ/2 SIR

Similarly, a third-order Chebyshev filter can be designed with the SIRs used in Filter A. However, as mentioned in Section 2.4, two propagation modes with different effective dielectric constants and phase velocities in a coupled line will degrade the performance of the filter. For that reason, we will consider the influence during the design procedure. The passbands of the filter are designed as 2.7 GHz and 3.5 GHz with ripple level 0.1 dB as well. The fractional bandwidth is about 5~10%. Figure 4.14 shows the overall topology of the filter which we call Filter E.

Term

76

1st 2nd

(b)

Figure 4.14 The overall circuit topology of the Filter E. (a) The circuit scheme in ADS.

(b) The circuit scheme in Sonnet.

W1 W2 W3 W4 W5 L1 44 68 34 18 8 115 L2 L3 L4 L5 L6 L7 500 440 580 390 372 370

L8 S1 S2 S3 S4 430 64 6 6 7 Table 4.8 Physical dimensions of the proposed Filter E. (Unit: mil)

It is noted that we increase the characteristic impedance to 80 ohm to calculate the initial parameters so that the physical limit can be avoided and the required coupling in the second stage can be satisfied as well. The same consideration occurs in Filter A. On the other hand, in order to shift the spurious resonance to a higher frequency more than

2 f 0

, the UIR structure is chosen for the filter with higher passband while another filter is designed using SIRs with

R

< . Moreover, we pay more attention on the separation of 1

the two passbands. That is, the higher the impedance ratio

^_

_

(

^{a high}

)

a

a low

R Z

=

Z

is, the larger the separation becomes. Nevertheless, because of the physical limit for microstrip coupled

77

lines, we finally choose

Z _{a high _}

as 150 ohm. Table 4.9 lists the initial parameters for the filter at 3.5GHz.

Table 4.9 Initial parameters of the odd-mode filter in Filter E.

Moreover, from the coupled line theory, the effective dielectric constants of two propagation modes are different. In other words, the electrical length for even mode will be longer but shorter for odd mode relatively. This situation causes the shift of resonant frequencies for both modes which makes the separation of two passbands become smaller for the filter designed with open-end type SIRs. However, the same property in the filter with short-end type SIRs performs oppositely. Therefore, to reach the specification exaxtly, in this case, the fundamental frequency at higher passband can be chosen to be lower than expected and so does the impedance

Z _{a high _}

with considering the frequency shift.

In the second stage, due to the difference of two propagation modes, the coupling strength will be degraded as well as the bandwidth. To maintain the coupling, it’s necessary to adjust the coupled line.

After the resonators are designed, the problem left is to find a feeding structure. In our case, using the theory in Section 3.1, we first fix the tap point at the stepped junction and obtain the load impedance form (3.5) and (3.12). For the load impedance

R _{L odd _}

and

_ L even

R

relating to two resonant frequencies, it’s necessary to find a matching circuit that can transform source impedance to

R _{L odd _}

,

R _{L even _}

at 3.5 GHz and 2.7 GHz respectively.

f 0

(GHz)

Z _a

(ohm)

Z _b

(ohm)

θ _b θ _a Z _{oe 12}

(ohm)

Z _{oo 12}

(ohm)

3.5 80 80 60

^o

30

^o

110.89 62.57

78

Thus, due to Type II tapping as discussed in previous case, it is apparent that the coupled lines can be a good configuration for our requirement. In this case, we utilize two sections of the quarter-wavelength coupled lines to realize the matching network which is feasible under the condition that

R _{L even _}

is higher than

R _{L odd _}

. Table 4.10 shows the characteristic impedances of the two-section quarter-wavelength coupled lines.

Section Z oe Z _oo

1 ^st 58.14 36.46 2 ^nd 105.21 54.84

Table 4.10 Initial parameters of the two-section transformer in Filter E.

It the end, Filter E is fabricated and the photograph as well as the measured results are shown in Figure 4.15. and 4.17. Furthermore, we modify the layout at the junction between two coupled-line sections in the transformer to be smoother for the concern about implementation. Figure 4.16 and 4.18 shows the modified layout which we call Filter F and the measurement results.

79

Figure 4.15 Photograph of proposed Filter E.

Figure 4.16 Photograph of proposed Filter F.

80

2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8

2.0 4.0

-30 -20 -10

-40 0

freq, GHz

dB (S (1, 1) ) dB (S (2, 1) ) dB (S (3, 3) ) dB (S (4, 3) )

dB(S(1,1)) dB(S(2,1)) dB(S(3,3)) dB(S(4,3))

(a)

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

1.0 7.0

-70 -60 -50 -40 -30 -20 -10

-80 0

freq, GHz

dB (S (1 ,1 )) dB (S (2 ,1 )) dB (S (3 ,3 )) dB (S (4 ,3 ))

dB(S(1,1)) dB(S(2,1)) dB(S(3,3)) dB(S(4,3))

(b)

81

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-40 -30 -20 -10 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(c)

FREQUENCY(GHz)

1 2 3 4 5 6 7

S(dB)

-80 -60 -40 -20 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(d)

82

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-80 -60 -40 -20 0

(e)

Figure 4.17 Simulated and measured results of Filter E. (a) Simulated

S ₁₁ and S ₂₁

for 2~4 GHz. (b) Simulated

S ₁₁ and S ₂₁

for 1~7 GHz. (c) Measured

S ₁₁ and S ₂₁

for 2~4 GHz. (d) Measured

S ₁₁ and S ₂₁

for 1~7 GHz. (e) Measured isolation between two modes.

Figure 4.17 presents the measured return loss in the passband is lower than 10 dB and the insertion loss is about 1.5~3.8 dB. The fractional bandwidths are 5.6 % and 4.9 % at 2.67 GHz and 3.45 GHz. The first spurious occurs near 6 GHz. These results consist with the simulated results approximately.

83

2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8

2.0 4.0

-30 -20 -10

-40 0

freq, GHz

dB (S (1, 1) ) dB (S (2, 1) ) dB (S (3, 3) ) dB (S (4, 3) )

dB(S(1,1)) dB(S(2,1)) dB(S(3,3)) dB(S(4,3))

(a)

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

1.0 7.0

-70 -60 -50 -40 -30 -20 -10

-80 0

freq, GHz

dB (S (1 ,1 )) dB (S (2 ,1 )) dB (S (3 ,3 )) dB (S (4 ,3 ))

dB(S(1,1)) dB(S(2,1)) dB(S(3,3)) dB(S(4,3))

(b)

84

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-40 -30 -20 -10 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(c)

FREQUENCY(GHz)

1 2 3 4 5 6 7

S(dB)

-80 -60 -40 -20 0

Evenmode S11 Evenmode S21 Oddmode S11 Oddmode S21

(d)

85

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-80 -60 -40 -20 0

(e)

Figure 4.18 Simulated and measured results of Filter F. a) Simulated

S ₁₁ and S ₂₁

for 2~4 GHz. (b) Simulated

S ₁₁ and S ₂₁

for 1~7 GHz. (c) Measured

S ₁₁ and S ₂₁

for 2~4 GHz. (d) Measured

S ₁₁ and S ₂₁

for 1~7 GHz. (e) Measured isolation between two modes.

Figure 4.18 shows the measured in-band return loss is lower than 10 dB and the insertion loss is about 1.8~3.7 dB. The fractional bandwidth is 10 % and 5.7 % at 2.71 GHz and 3.49 GHz. The first spurious occurs near 6 GHz. These results have good agreement with the simulation..

4.3.2 Second-Order Filter with Open-Ended λ/2 SIR

Figure 4.19 presents the overall topology of the filter that we call Filter G. In this new design, we now want to set the goal to enlarge the separation of the two passbands. The

86

filter is designed at 2.5/3.5 GHz with ripple level 0.1 dB, and the fractional bandwidth is 4~7%. Apparently, the critical point is the coupling strength of the coupled-line section in the center of each SIR. The stronger the coupling strength is, the more the difference between

Z _oe

and

Z _oo

is, corresponding to the impedances

Z _{a high _}

and

Z _{a low _}

for two passbands respectively. Meanwhile, considering the physical limit of the coupled line in the second stage, we choose

Z _{a high _}

=155

ohm

and

Z _{a low _}

=70

ohm

. Similary, the UIR and SIR structures are employed and operate respectively while exciting differential-mode or common-mode signal. The initial parameters are shown in Table 4.12. The overall circuit configuration with physical dimensions are shown in Figure 4.19 and Table 4.11.

Figure 4.19 The circuit configuration of Filter G.

W1 W2 W3 W4 W5 W6 44 45 24 22 4 15 L1 L2 L3 L4 L5 L6 180 500 588 500 360 360

L7 S1 S2 S3 S4 380 10 15 7 6

87

Table 4.11 Physical dimensions of the proposed Filter G. (Unit: mil)

Table 4.12 Initial parameters of the odd-mode filter in Filter G.

As mentioned, considering the effect of the difference for two propagation modes, the coupled lines in second stage must be adjusted to obtain enough coupling. And we design the first filter with a lower center frequency while the choice of impedance

Z _{a high _}

for the other filter with a lower passband can be lower. In that way, we can approach the specification as expected.

The design procedure of feeding structure is similar with Filter E. With two sections of quarter-wavelength coupled lines, we can easily transform the source impedance into different load impedance required at different passbands. The characteristic impedances of the two-section quarter-wavelength coupled lines are listed in Table 4.13.

Section Z oe Z _oo

1st 67.32 36.05 2nd 137.97 64.12

Table 4.13 Initial parameters of the two-section transformer in Filter G.

Finally, the filter is designed and fabricated as Figure 4.20. The simulated and measurement results are shown in Figure 4.18.

f 0

(GHz)

Z _a

(ohm)

Z _b

(ohm)

θ _b θ _a Z _{oe 12}

(ohm)

Z _{oo 12}

(ohm)

3.5 70 70 60

^o

30

^o

93.392 55.9789

88

Figure 4.20 Photograph of proposed Filter G.

2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8

2.0 4.0

-30 -20 -10

-40 0

freq, GHz

d B (S (1 ,1 )) d B (S (2 ,1 )) d B (S (3 ,3 )) d B (S (4 ,3 ))

dB(S(1,1)) dB(S(2,1)) dB(S(3,3)) dB(S(4,3))

(a)

89

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

1.0 7.0

-70 -60 -50 -40 -30 -20 -10

-80 0

freq, GHz

d B (S (1 ,1 )) d B (S (2 ,1 )) d B (S (3 ,3 )) d B (S (4 ,3 ))

dB(S(1,1)) dB(S(2,1)) dB(S(3,3)) dB(S(4,3))

(b)

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-40 -30 -20 -10 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(c )

90

FREQUENCY(GHz)

1 2 3 4 5 6 7

S(dB)

-80 -60 -40 -20 0

Oddmode S11 Oddmode S21 Evenmode S11 Evenmode S21

(d)

FREQUENCY(GHz)

2.0 2.5 3.0 3.5 4.0

S(dB)

-80 -60 -40 -20 0

(e)

91

Figure 4.21 Simulated and measured results of Filter F. (a) Simulated

S ₁₁ and S ₂₁

for 2~4 GHz. (b) Simulated

S ₁₁ and S ₂₁

for 1~7 GHz. (c) Measured

S ₁₁ and S ₂₁

for 2~4 GHz. (d) Measured

S ₁₁ and S ₂₁

for 1~7 GHz. (e) Measured isolation between two modes.

Figure 4.21 shows the measured in-band return loss is lower than 10 dB and the insertion loss is about 2.5~3 dB. The fractional bandwidth are 6.7 % and 5.4 % at 2.51 GHz and 3.49 GHz. The first spurious occurs at about 6.5 GHz. These results are nearly the same as simulation.

92

Chapter 5 Conclusion

In this thesis, the four-port even- and odd-mode dual band filters are proposed. Three second-order and four third-order filters are designed to approach the specifications. They can perform two different passbands while exciting differential- or common- mode signals respectively. Two types of SIRs as well as UIRs are used as the basic elements in these filters. The resonant frequency as well as the spurious resonance can be fully controlled by choosing proper impedance ratio of SIR. The coupling effect of coupled lines plays an important role in these filters. Based on the difference in phase velocities for two propagation modes, the characteristic impedances

Z and _oe Z can be used to combine _oo

two filters with different operating frequencies. With this property, Filter G is designed to possess wider separation between two passbands. However, applying to the internal stages between resonators, the characteristic will degrade the performance on bandwidth so that the coupled lines need to be adjusted. Moreover, focus on the feeding structure, Filter A,B, and C utilize Type I tapping to transform the same load impedance to source. In these

In this thesis, the four-port even- and odd-mode dual band filters are proposed. Three second-order and four third-order filters are designed to approach the specifications. They can perform two different passbands while exciting differential- or common- mode signals respectively. Two types of SIRs as well as UIRs are used as the basic elements in these filters. The resonant frequency as well as the spurious resonance can be fully controlled by choosing proper impedance ratio of SIR. The coupling effect of coupled lines plays an important role in these filters. Based on the difference in phase velocities for two propagation modes, the characteristic impedances

Z and _oe Z can be used to combine _oo

two filters with different operating frequencies. With this property, Filter G is designed to possess wider separation between two passbands. However, applying to the internal stages between resonators, the characteristic will degrade the performance on bandwidth so that the coupled lines need to be adjusted. Moreover, focus on the feeding structure, Filter A,B, and C utilize Type I tapping to transform the same load impedance to source. In these

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