Miniaturized Transmission-Line Bandpass Filter: Layout and Measurements.85

CHAPTER 3 Multi-layer Synthetic Quasi-TEM Transmission Line

3.3 Miniaturized Transmission-Line Bandpass Filter: Layout and Measurements.85

(BPF) by mapping the idealized BPF shown in Fig. 3.7 to the four-layer stacked CCS TL filter configuration, as presented in Fig. 3.2. Figure 3.11 shows the three-dimensional view of the miniaturized (BPF), incorporating a multi-layer complementary conducting strip transmission line (CCS TL). The CCS TL is realized by a unit cell with a period of 0.35 mm (P=0.35 mm), and realized in a multi-layer print circuit board (PCB). The permittivity and thickness of each substrate are 4.7 and 0.06 mm with a loss tangent of 0.013. All metal layers are copper with a thickness of 0.0175 mm. The guiding characteristics of CCS TLs, including the propagation constants and the characteristic impedances, are extracted from the theoretical S-parameters, which are calculated by the full-wave EM-simulator [52]. The extracted data are applied to define the width and the meandered shapes of the CCS TLs in different layers. As shown in Fig. 3.11, five TLs, including two series TLs with an electrical length of 64.428^o at 2.5 GHz, two 90^o shunt stubs at 1.88 GHz, and one 90^o shunt stub at 3.19 GHz are in M1 and M2 metal layers. Additionally, two 90^o TLs at 3.95 GHz and one 90^o TL at 1.78 GHz are realized using sandwiched CCS TLs in M2, M3 and M4 metal layers. The minimum and maximum linewidths are 0.11 mm and 0.18 mm, respectively. The reference ground planes (M2 and M4) of the four-layer

configuration are connected by plated-holes filled with copper for proper grounding.

Two external terminals of the BPF are located on the M1 layer, facilitating the interface to the probe tips.

Fig. 3.11 Three-dimensional view of transmission-line bandpass filter realized by multi-layer complementary conducting strip (CCS) transmission line (TL).

SUB1 SUB2 M4 SUB3

M3 M2 M1

Port1

Port2 Plated-hole

Plated-hole

The device under test (DUT) is very thin and small, so measurements cannot be easily made using coaxial connectors or cables. Therefore, two 50Ω G-S-G

CPW-based microwave probes from Picoprote^TM are applied to make the measurements. The chuck, which is a metal plate for supporting the DUT, is grounded to the instruments. Therefore, a piece of paper with a thickness of 0.05 mm is inserted between the DUT and the chuck for proper isolation. Figure 3.12 shows the experimental setups for measuring the multi-layer miniaturized bandpass filter. Before the measurements are made, the whole system, including an Agilent^TM 8510C vector network analyzer (VNA), cables and probes, is calibrated by performing two-port SOLT (Short-Open-Load-Through) procedures with CS-11 standard substrates from Picoprobe^TM. Figure 3.13 compares the measured and theoretical results. The theoretical data include the effects of the junctions, the grounding vias and the plated through-holes, as well as the finite conductivity and dielectric losses.

Fig. 3.12 Experimental setups for measuring miniaturized BPF.

50Ω Probe 50Ω Probe

To 8510C^TM To 8510C^TM

Chuck Paper

DUT

Fig. 3.13 Measured results of miniaturized bandpass filter.

1 1.5 2 2.5 3 3.5 4 4.5 5

Frequency (GHz) -65

-60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0

|S₁₁|

|S₂₁|

Measurement Simulation

The measured data shows four transmission zeros at 1.85 GHz, 1.98 GHz, 3.19 GHz and 3.95 GHz. Notably, the low-side transmission zeros are shifted by approximately 5% (70 MHz) from ideal data in Fig. 3.7 (b). The center frequency of the BPF is slightly shifted from 2.5 GHz to 2.55 GHz, by approximately about 2%.

However, Fig. 3.13 shows that the out-band rejection is highly consistent with the theoretical values predicted by simulation, remaining below 35dB from 3.1 GHz to 4.15 GHz. On the other hand, the measured return-loss, is below -16.8 dB from 2.38 GHz to 2.78 GHz in the passband, exceeds the simulated value by 3.05 dB. Notably, the three reflection zeros are present at approximately 2.42 GHz, 2.58 GHz and 2.74 GHz, offset by only 1% against the idealized design of Fig. 3.7. The measured insertion-loss is approximately 2.46 dB from 2.38 GHz to 2.78 GHz - approximately 0.4 dB above the simulated value. Figure 3.14 shows the photograph of the prototype, whose dimensions are 5.0 X 5.0 X 0.18 mm.

Fig. 3.14 Photograph of 2.4 GHz miniaturized bandpass filter on one Euro (€1).

3.4 Discussion

The miniaturized filter is implemented solely using the stacked complementary conducting strip transmission lines (CCS TLs) so the total volume of the filter can be expressed by the following equation:

N h P

L_t ⋅ ⋅ − ⋅

= 1)

2 (

V_total (2)

Lt is the total length of the all of the transmission lines in the filter design. P is the period of the unit cell of the CCS TL. N is the number of signal layers in the multi-layer system configuration, and h is the thickness of single-layer substrate.

Therefore, the number of substrates is 2N-1. Nz is the number of transmission zeros with a minimum value of two. In the first-order approximation, Lt is inversely proportional to the square root of the relative dielectric constant ( εr ). With reference to Fig. 3.7, the total volume of the three-order 2.4 GHz BPF (with four transmission zeros) can be estimated using (2). Table 3.1 presents the results and lists the relevant parameters in detail, showing good agreement between hand calculations and prototype dimensions.

Table 3.1 Variables for Volume Estimation of Proposed Bandpass Filter

Variable Value f

₀

2.5 GHz

N

4 (1.78 GHz, 1.88 GHz, 3.19 GHz, 3.95 GHz)

N 2

h 0.06 mm

ε

4.7 P 0.35 mm

L

115.1 mm

V

estimate

3.63 mm

V

_prototype

4.5 mm

The parameters in Table 3.1 show that P, h, εr and N, are process-related. These parameters are typical in the present PCB technology. On the other hand, L_t and N_z are related to electric specifications of the proposed miniaturization that incorporates the meandered CCS TL to reduce systematically the volume of BPF, which approaches the limits of state-of-art technology. The estimated V_total is 19% less than that of the prototype, so the approach based on the proposed stacked meandered CCS TL can effectively miniaturize microwave passive circuits, such as the BPF presented here.

On the other hand, the proposed stacked multi-layer complementary conducting strip transmission line (CCS TL) focuses on the miniaturization of the filter to the highest degree of integration density. What follows is the survey of the filters, which include the state-of-the-art discrete filters reported recently in the market [58-62, 64-65, 67-68, 71-72], technical literature [63, 66, 69-70, 73-91], and the filters in advanced SIP [92-97].

Closely examining the statistics shown in Fig. 3.15, supports the following summary. First, the volumes required to realize BPF with three reflection zeros (N_RZ=3) are about one half of those of BPF with two reflection zeros. Second, these commercially available LTCC (low temperature co-fire ceramic)-based filters contain approximately ten layers or more, and so are approximately 0.8 mm thick in most designs. Third, transmission-line-based microwave filters [73-76] are normally large

with volumes of over 14 mm³, independent of the number of reflection zeros in the passband. Figure 3.15 also presents the sizes of the proposed filter integration method with various numbers of dielectric layers adopted for BPF designs for two and three reflection zeros, respectively.

0 2 4 6 8 10 12 14

Fig. 3.15 A Survey of 2.4 GHz ISM band bandpass filter in size (volume) and thickness.

Volume (mm³)

: Two reflection zeros : Three reflection zeros : TL BPF, area over 14 mm³

With reference to Fig. 3.15, the size of the proposed prototype also approaches that of state-of-art technology – approximately 4.5 mm³. In the circumstance, when a designer requires that the area is smaller than that achieved using the presented four-layer prototype, N may be increased from two to four. By doing so, the area will be changed from 5 mm X 5 mm to 1.83 mm X 1.83 mm. The thickness will increase be from 0.18 mm to 1.26 mm, and the volume will change from 4.5 mm³ to 4.23 mm³. (2) also clearly shows that when P and h are reduced, the total volume is scaled down to an extent proportional to the product of P and h. Also, P stands for the periodicity of the unit cell and is the limit on the line pitch, which is the center-to-center distance between the parallel lines associated with particular processes.

CHAPTER 4 EBG Enhanced PCB / Monolithic Spiral Inductors

In this chapter, the microstrip line on the electromagnetic bandgap (EBG) ground plane is introduced for the third kind of synthetic waveguide. Similar to the uniplanar compact photonic bandgap (UC-PBG) reported by Itoh et al. in 1997, the proposed EBG ground plane changes the guiding characteristics of the microstrip, increasing the slow-wave factor (SWF) for the operation frequency below the first stopband [98-99]. Furthermore, this chapter applies those synthesized guiding characteristics presented in Section 4.1 to develop a new planar inductor configuration, so-called EBG enhanced spiral inductors. The EBG enhanced inductor consists of a two-dimensional EBG periodical array beneath the conventional spiral inductor.

Section 4.2 illustrates the physical models of the planar spiral inductor and guiding characteristics of the spiral on EBG ground plane to reconcile the merits offered by

the EBG inductor, which results in higher characteristic impedance (Zc), higher slow-wave factor (SWF), and less attenuation constant (α) of spiral inductor on the

EBG ground plane. The experimental verifications have been carried out by employing modern multi-layered printed-circuit-board (PCB) and standard 0.25um 1P5M CMOS technologies without additional processing requirements. Section 4.3 , SWF and α of the EBG inductor can

be improved simultaneously. Consequently, the main factors of the spiral inductor including the inductance, series resistance, shunt RC parasitic, and Q-factor are improved using proposed inductor configuration.

4.1 Guiding Characteristics of the Microstrip line on the EBG Ground Plane

Electromagnetic Bandgap (EBG) structures are generally the electromagnetic devices made of metal strips, which often conduct DC currents [34, 100-102].

However, such devices can not conduct AC currents within a stopband. Such a structure is occasionally called the “high impedance surface” or a “magnetic conductor”. In contrast to plain conductors, the high impedance surface does not support the propagation of surface waves, and it reflects electromagnetic waves without phase reversal within a stopband. To investigate the effects of EBG ground plane on the microstrip line, the experiment is conducted using multi-layer print-circuit-board (PCB) technology to extract the propagation characteristics of a uniform microstrip on EBG ground plane.

Figure 4.1 shows the multi-layer architecture. The microstrip, as shown in Fig 4.1(a), is 5.0 mm long (L) and 1 mm wide (W₁). The EBG ground plane consists of two-dimensional periodical structures that are similar to those reported in the chapter 2. The top coil at z=h₂ is comprised of a 0.2mm wide (S₁) rectangular loop with a

perimeter of 5.4 mm. Similarly, a 0.2 mm wide bottom coil has a perimeter of 6.2 mm.

Notably both the top and the bottom coils are connected to center via by short metal strips of 0.2 mm (C₁) by 0.2mm (C₂). The diameter of all the via-through holes is 0.25mm (d).

(a)

(b)

(c)

Fig. 4.1 The microstrip line on the EBG ground plane: (a) three-dimensional view, (b) multi-layer EBG ground plane, (c) cross-section view of the multi-layer configuration.

C2 S1

x h₁ z

h₃ via

εr1

εr2

ε_r3

y z x y

z x

Gx h2

The microstrip line and the PBG cells are made on printed RO4003^TM circuit

boards of thickness (h1=h3) 0.2mm, a relative permittivity (εr1=εr2=3.38), and a loss tangent (tanδ1=tanδ2) of 0.002. The prepreg with thickness of 0.05 mm (h1), relative permittivity (εr2) of 4.4, and a loss tangent (tanδ2) of 0.01 is sandwiched between the

microstrip and EBG ground plane. The thickness of the metal through the Fig. 4.1 is 17um with conductivity of 5.8x10⁷ S/m. During the measurements, two microstrip lines, which are identical except in ground planes, were built and test. Notably, the effective substrate thickness of the microstrip line on the PBG ground plane, (h₁+h₂=0.25mm), is thinner than the microstrip line on the uniform ground plane, (h₁+h₂+h₃=0.45 mm). The total circuit size is 5.0 mm (G_x) by 5.0 mm (G_y), corresponding to 3 by 3 EBG cells.

The scattering parameters of the microstrip lines are measured using the WILTRON^TM 3680K test fixture and HP8510C Vector Network Analyzer after

two-port standard calibration procedure so-called short-open-load-through (SOLT).

Then, the complex propagation constant (γ) and the characteristic impedance (Zc) of

the microstrip line extracted from the measured scattering parameters (S_ij) [52].

Figure 4.2 (a) plots the extracted complex propagation constant. The normalized phase constant, β/k0, which is also called the slow-wave factor (SWF), corresponds to the left-hand side of the vertical axis, and the attenuation constant, α, corresponds to

the right-hand side and of the vertical axis. The SWF of the microstrip on the uniform

ground plane is 1.7 in the entire frequency band of interest, whereas the microstrip on the EBG ground plane increases the SWF by 17.6% to 2.0. The propagation loss, α, of

the microstrip line on the uniform ground plane slightly exceeds that of the microstrip on the EBG ground plane. In this work, the effective substrate thickness of the microstrip on EBG ground plane is reduced by 44% smaller than that of the microstrip on the uniform ground plane. Therefore, the characteristic impedance (Zc) of the microstrip line on the EBG ground plane is decreased by 14%, as shown in Fig. 4.2 (b). In the following section, the same PCB fabrication process and the EBG magnetic surface as shown in Fig. 4.1 are applied to the design of EBG-inductor.

Fig. 4.2 Characteristics of the microstrip line on the uniform ground plane and EBG ground plane: (a) complex propagation constant, (b) characteristic impedance.

EBG ground plane Uniform ground plane

4.2 Equivalent Model for the Rectangular Spiral Inductor

The lumped inductor is an extensively used passive device in microwave radio frequency (RF) circuit designs. The properties of inductors also dominate the RF circuit’s performance. For example, Leeson-Cutler’s phase noise model indicates that a higher inductor Q improves the phase noise performance of the oscillator. The above considerations signify the importance of importance of inductors in most RF circuit, and further derive the modeling effort to inductors. From a physical perspective, equivalent circuit models have been developed to characterize inductors [103-105].

Figure 4.3 shows a well-known lumped circuit model of the spiral inductors.

In the lumped model, L_s represents the inductance of the spiral, which is proportional to both the total length and the characteristic impedance of the spiral. R_s is the series resistance of the spiral whose behavior at radio frequency (RF) is governed mainly by the eddy current losses and the skin effect [106-107]. The series capacitance, C_s, which is the capacitance due to the overlap between the spiral and the underpass, is considered independent of frequency. The shunt parasitic of the inductor model include the substrate capacitance and the substrate, named by C_p and R_p, respectively. C_p represents the capacitance between the spiral and the conducting media. R_p represents energy dissipation in the supporting dielectric and conducting media around the spiral. The qualify factor (Q-factor) of the spiral inductor can be

defined by

Based on the equivalent circuit model showed in Fig. 4.3, the Q-factor can be expressed by [103].

⎥⎥

(a)

(b)

Fig. 4.3 The equivalent models for the rectangular spiral inductor: (a) lumped model, (b) transmission line model.

L_s

C_p Rp

⋅l

⋅γ Zc

⋅l γ ^c

Z 2

⋅l γ ^c

Z 2

Z_{0 ,}

γ

l

Factors that contribute to the Q-factor of the spiral inductor are 1) the energy stored in the inductance and the ohmic loss of series resistance; 2) the substrate loss factor, and 3) the self-resonance factor. Moreover, the elements in the lump circuit model can also be represented by equivalent transmission line parameters [104-107].

Where Zc, γ, and _l represent the characteristic impedance, propagation constant, and

overall length of the spiral, respectively. The propagation constant is denoted by γ=α (attenuation constant, Np/m) +jβ (phase constant, rad/m). The series impedance

branch in the lumped model, specified by Ls, Rs, and Cs, equals to the product of Zc, γ, and _l. Cs is extracted using the low-frequency Ls value and the resonant frequency of the series branch [104]. Then, with C_s held constant, L_s, and R_s are determined. The

shunt parasitic can also be extracted from the ratio of 2Zc to γ_l. However, the model in Fig. 4.3 is valid only when |γ_l|is substantially lower than one (refer the Appendix

III for the details). Accordingly, the model in Fig. 4.3 provides a design guideline for the inductors.

Either narrowing the line width or increasing the number of turns of the inductor can increase its inductance. Such approaches correspond to increasing of Zc and _l of the spiral. Other designs for a high-quality spiral inductor include using thick metal strip, high resistivity substrate, or removing the lossy substrate [108-111], but often accompany additional process requirement. One widely accepted approach is to use

the patterned ground shield (PGS) beneath the inductor as an electromagnetic shield [112]. The PGS not only prevents the electric field from penetrating into the lossy substrate, but also inhibits the image eddy currents while simultaneously facilitating

standard IC fabrication.

In an effort to develop a spiral inductor, which can simultaneously increases β

and Zc, and decreases α, section 4.2.2 reports a new methodology to improve the planar spiral inductor by incorporating a photonic bandgap (PBG) structure beneath the inductor as a ground plane substitute. The new spiral inductor, called the EBG inductor, is also fully compatible with standard multi-layer fabrication technologies.

4.3 EBG Enhance-Inductor

4.3.1 EBG Enhanced PCB Spiral Inductor

This section compares the performance of two identical spirals above a uniformly conducting ground plane and an electromagnetic bandgap (EBG) magnetic surface.

Figure 4.4 illustrates the inductor designs. The foregoing observations presented in Section 4.1 conclude that the microstrip line on the PBG ground plane increases SWF and decreases the attenuation constant, thereby a high performance spiral inductor is readily achievable. Figure 4.4 shows two inductor configurations in multi-layered PCB process for verifying the concept of the PBG inductor. Notably the two inductors

appeared in Fig 4.4 (a) and Fig 4.4 (b) are identical except in ground.

The design parameters, including substrate information, thickness and conductivity of the metal strip, and dimensions of the EBG cell are corresponding to Fig. 4.1 (b). The substrate, which together with the metallization patterns on both side of the substrate in Fig. 4.4 (b), is lifted here just for illustration. The spiral inductor, which has 1.5 turns and another via-through-hole connecting an underpass for external circuitry, has the following dimensions. The main body of the spiral is 3 mm (Lx) by 3 mm (Ly) with total spiral length (_l) of 13.1 mm. Total inductor size is 5 mm (G_x) by 5 mm (G_y). The metal width (w₂) and spacing (S₂) are both 0.25 mm wide.

Two short-metal strips of 0.62 mm long and 0.25 mm wide are added at both input and output ports to facilitate the S-parameters measurement. However, the substrate thicknesses of the two kinds of inductor are different. The substrate thickness of the conventional spiral inductor is 0.45 mm (h₁+h₂+h₃), 0.25 mm higher than that of EBG inductor.

(a)

(b)

Fig. 4.4 Spiral inductors on different ground planes; h1=h3=0.2 mm, h2=0.05 mm, Gx=Gy=5.0 mm, Lx=Ly=3.0 mm, S2=0.2 mm, w2=0.2 mm. (a) spiral inductor on the uniform ground plane, (b) spiral on the EBG ground plane.

G_y

h₂

h₁ L_y

L_x

L_y

L_x

S₂ w2

The spiral inductors are fabricated and tested. The precise experiment procedure is carried out as follows. 1), two-port scattering-parameters of the spiral inductors are obtained using the same measurement procedure as described in Section 4.1), input and output pad parasitic are de-embedded using the open dummy pad structure through Y-parameters subtraction. Then the Y-parameters without pads’ parasitic are

converted to ABCD matrix, representing an equivalent transmission line circuit of the two-port spiral inductor [103]. The |γ_l| here is much less than unity for the

frequencies of interests, and hence the spiral inductor model of Fig. 4.3 is applicable.

Following the same extraction techniques described in [103], the measured

de-embedded Y-parameters lead to the following results. The slow-wave factor (SWF) of EBG inductor as shown in Fig. 4.5 (a) is increased by 14% and α approximately

reduced by 20% from 0.1 GHz to 2 GHz. Figure 4.5 (b) shows the characteristic impedance (Z_c) of the EBG inductor is increased by 5% even thought the effective substrate thickness of the EBG inductor is 44% less than the conventional spiral inductor.

The observations mentioned above imply that the geometry of inductor in the case study has strong influence on the characteristics impedance of metal strip above various ground planes. Based on the electric properties of the spiral inductor model shown in Fig. 4.3, EBG inductor property should be significantly improved.

In Fig 4.6, the extracted lumped model elements of inductors are plotted. The series inductance L_s in Fig. 4.6(a) is increased by 7.4% from 0.1 GHz to 2 GHz. The series resistance R_s in Fig. 4.6(b), which is one of the dominant factors determining Q-factor of the spiral inductor, is reduced by 10.2% below 1.4GHz. The series resistance R_s is related to the compound effects of ohmic losses, skin-effect losses and

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