Design Methodologies of LTCC Bandpass Filters, Diplexer, and ...

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718 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006 Fig. 3. filter. Equivalent circuit of the proposed second-order combline bandpass Fig. 5. Transformations for the matching circuit in the source and load ports. (a) Positive J-inverter. (b) Negative J-inverter. is resonance at the central frequency, which will result in . The capacitor can be derived as Fig. 4. Equivalent circuit of the generalized bandpass filter. where and are, respectively, the odd- and even-mode admittances of coupled transmission line, and is the corresponding electric length. Adding two circuits shown in Fig. 2, and shunting with two grounded capacitors at two ports separately yields the complete equivalent circuit of the bandpass filter, as shown in Fig. 3. Thus, we can apply the immittance inverter to analyze and design bandpass filters. The admittance inverter and capacitor are derived as Following the equivalent circuit in Fig. 3, the equivalent circuit of the generalized bandpass filter can also be expressed as Fig. 4, which includes the admittance inverter. The admittance inverters, susceptance, and its slope parameter are, respectively, given by (2) (3) (4) (5) (6) (7) (8) (9) (10) where the ’s are the element values of the prototype lowpass filter, is the fractional bandwidth, and and are the impedances of source and load transmission lines, respectively [19]. (11) where and are electrical length and angular frequency at the central frequency, respectively. The bandpass filter with a transmission zero located at the angular frequency will make . at the center frequency and can be derived as when when (12) (13) The matching circuits located at source and load ports, as shown in Fig. 1, can be implemented using the following methods. Note that the quarter-wavelength transmission line is the simplest form of inverters and, on the other hand, the inductance or capacitance -network to substitute the -inverter is the other method. Since the negative inductance or capacitance cannot be employed to the source or load impedance, a transformation is needed, as shown in Fig. 5. These equations are revealed as III. FILTER DESIGN WITH TRANSMISSION ZERO (14) (15) (16) (17) Here, two examples are presented to explain the location of the frequency of the transmission zero, which will appear at the lower or higher skirt of the passband.
TANG AND YOU: DESIGN METHODOLOGIES OF LTCC BANDPASS FILTERS, DIPLEXER, AND TRIPLEXER WITH TRANSMISSION ZEROS 719 Fig. 6. 2.4-GHz bandpass filter with the transmission zero at the frequency of 1.9 GHz. (a) Filter architecture. (b) Simulated results. A. Circuit Model The first example is a 2.4-GHz bandpass filter. Its center frequency is set at 2.4 GHz and the frequency of the transmission zero is set at 1.9 GHz. The ripple, bandwidth, impedance, and electric length of the coupled transmission line are chosen as 0.01 dB, 6%, 30 , and 12 , respectively. By making use of (1)–(17) derived in Section II, one can show that the parameters of the cross-coupled capacitor , even- and odd-mode impedances and of the parallel-coupled line, and grounded capacitors are equal to 3.93 pF, 39.24 , 24.28 , and 6.47 pF, respectively. Therefore, is 0.0206. A quarter-wavelength transmission line is utilized to form the matching circuit, and, hence, the impedance of this transmission line is 48.47 , which is close to 50 , which is the vale of the system impedance. Therefore, the matching circuit can be neglected and the secondorder combline bandpass filter can be connected directly to the input and output ports, as shown in Fig. 6(a). These derived parameters and are substituted into the circuit simulator such as ADS or equivalent software to carry out the circuit simulation. Simulation results of the 2.4-GHz bandpass filter are presented in Fig. 6(b). Fig. 7. 2-GHz bandpass filter with the transmission zero at the frequency of 2.5 GHz. (a) Filter architecture. (b) Simulated results. A 2-GHz bandpass filter is taken as the second example. Its center frequency is set at 2 GHz and the frequency of the transmission zero is set at 2.5 GHz. The ripple, bandwidth, impedance, and electric length of the coupled transmission line are set as 0.01 dB, 7%, 30 , and 30 , respectively. The structure in Fig. 5(b) can be applied to the transformation for the matching circuit in the source and load ports. Fig. 7(a) shows the equivalent circuit of the bandpass filter with the transmission zero at the higher skirt of the passband. Here, the parameters of the cross-coupled capacitor , even- and odd-mode impedances and of the parallel-coupled line, the grounded capacitors , and source and load capacitors are calculated as 1.26 pF, 54.96 , 20.63 , 2.54 pF, and 0.8 pF, respectively. Simulation results of this 2-GHz bandpass filter are presented in Fig. 7(b). B. EM Simulation and Measurement Prior to designing the circuit, the exact parameter values of ceramic sheets such as the dielectric constant and layer thickness should be known first. These values are very significant to extract physical parameters and can be critical in constructing the equivalent circuit [21].
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