Three-Dimensional Integration and Modeling Part 6 docx

CAVITY-TYPE INTEGRATED PASSIVES 41

where tan ı is the loss tangent (=0.0015) of the LTCC substrate. The quality factor [Eqs. (5.2)–(5.4)]

of a rectangular cavity can be used effectively in the cavity using via-array sidewalls, which almost

match the performance of the PECs [26,29].

The loaded quality factor (Ql) can be obtained by adding the losses (Qext) of the external

excitation circuit to the Qu as expressed in [61]

Ql =

1

Qu

+

1

Qext −1

(5.5)

The theoretical values of Q can be extracted from the simulated performances of a weakly

coupled cavity resonator using the following equations [61]:

Ql = fres

 f (5.6)

S21(dB) = 20 log10 Ql

Qext

(5.7)

Qu =

1

Ql

− 1

Qext −1

(5.8)

where f is the 3-dB bandwidth. The weak external coupling allows for the verification of Qu of the

cavity resonator as Qu approaches Q l with the weak external coupling as described in (5.8). Also the

weak coupling abates the sensitivity of the measurement on the amplitude of S21. Using the above

definitions, a weakly coupled cavity resonator (S21∼20 dB) has been separately investigated in HFSS

and exhibits a Qu of 367 at 59.8 GHz compared to the theoretical Qu of 372 at 60 GHz from (6)–(8).

All fabricated resonators were measured using the Agilent 8510C Network Analyzer and Cascade

Microtech probe station with 250
m pitch air coplanar probes. A standard short-open-load-through

(SOLT) method was employed for calibration.

5.2 THREE-POLE CAVITY FILTERS

The next topology covered in this chapter has to do with three-pole filters using via walls for 60 GHz

WLAN narrowband (∼1 GHz) applications that consist of three coupled cavity resonators [cavity 1,

cavity 2, cavity 3 in Fig. 5.2(b)]. The three-dimensional (3D) overview and side view are illustrated

in Fig. 5.2(a) and (b), respectively. The three-pole bandpass filter based on a Chebyshev lowpass

prototype filter is developed for a center frequency of 60 GHz, <3 dB insertion loss, 0.1 dB in band

ripple and 1.67% fractional bandwidth.

To meet design specifications, the cavity height [H in Fig. 5.2(a)] was set to 0.5 mm (five

substrate layers) to achieve a higher Qu and consequently to obtain narrower bandwidth. The cavity

resonator with 0.5 mm height has been fabricated in LTCC and measured. The comparison between

the simulation and the measurement is shown in Fig. 5.3. An insertion loss of 1.24 dB at the center