Design a bandpass filter using capacitive coupled series resonators, with a 0.5 dB equal-ripple passband characteristic. The center frequency is 2.0 GHz, the band-width is 10%, and the impedance is 50 Ω. At least 20 dB of attenuation is required at 2.2 GHz

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We first determine the order of the filter to satisfy the attenuation specification at 2.2 GHz. Using (8.71) to convert to normalized frequency gives

[latex]\omega \leftarrow \frac{1}{\Delta } (\frac{\omega }{\omega _{0}} - \frac{\omega _{0}}{\omega } ) =\frac{1}{0.1}(\frac{2.2}{2.0}-\frac{2.0}{2.2}) =1.91.[/latex]

Then,

[latex] \left|\frac{\omega }{\omega _{c}} \right|-1 = 1.91-1.0 = 0.91[/latex]

From Figure 8.27a, we see that N = 3 should satisfy the attenuation specification at 2.2 GHz. The low-pass prototype values are given in Table 8.4, from which the inverter constants can be calculated using (8.121). Then the coupling susceptances can be found from (8.134), and the coupling capacitor values as

[latex]C_{n}=\frac{B_{n}}{\omega _{0}} [/latex]

Finally, the resonator lengths can be calculated from (8.135). The following table summarizes these results.Amplitude response for the capacitive-gap coupled series resonator bandpass filter of Example 8.9.

n	[latex]g_{n}[/latex]	[latex]Z_{0}j_{n}[/latex]	[latex]B_{n}[/latex]	[latex]C_{n}(pF)[/latex]	[latex]θ_{n} (deg)[/latex]
1	1.5963	0.3137	6.96 × [latex]10^{-3}[/latex]	0.554	155.8
2	1.0966	0.1187	2.41 × [latex]10^{-3}[/latex]	0.192	166.5
3	1.5963	0.1187	2.41 × [latex]10^{-3}[/latex]	0.192	155.8
4	1.0000	0.3137	6.96 × [latex]10^{-3}[/latex]	0.554	-

The calculated amplitude response is plotted in Figure 8.51. The specifica-tions of this filter are the same as the coupled line bandpass filter of Example 8.8, and comparison of the results in Figures 8.51 and 8.46 shows that the responses
are identical near the passband region.

Question 8.9: Design a bandpass filter using capacitive coupled series res...

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