BANDSTOP FILTER DESIGN

Design a bandstop filter using three quarter-wave open-circuit stubs. The center frequency is 2.0 GHz, the bandwidth is 15%, and the impedance is 50 Ω. Use an equal-ripple response, with a 0.5 dB ripple level.

Question

BANDSTOP FILTER DESIGN

Design a bandstop filter using three quarter-wave open-circuit stubs. The center frequency is 2.0 GHz, the bandwidth is 15%, and the impedance is 50 Ω. Use an equal-ripple response, with a 0.5 dB ripple level.

Accepted Answer

The fractional bandwidth is Δ = 0.15. Table 8.4 gives the low-pass prototype values, [latex]g_{n}[/latex] , for N = 3. Then the characteristic impedances of the stubs can be found from (8.130). The results are listed in the following table:

[latex]Z_{0n}=\frac{4Z_{0}}{\pi g_{n}\Delta } [/latex]

TABLE 8.4 Element Values for Equal-Ripple Low-Pass Filter Prototypes ([latex]g_0[/latex] = 1, [latex] ω_c[/latex] = 1, N = 1 to 10, 0.5 dB and 3.0 dB ripple)
0.5 dB Ripple
[latex]g_{11}[/latex]	[latex]g_{10}[/latex]	[latex]g_{9}[/latex]	[latex]g_{8}[/latex]	[latex]g_{7}[/latex]	[latex]g_{6}[/latex]	[latex]g_{5}[/latex]	[latex]g_{4}[/latex]	[latex]g_{3}[/latex]	[latex]g_{2}[/latex]	[latex]g_{1}[/latex]	N
									1	0.6986	1
								1.9841	0.7071	1.4029	2
							1	1.5963	1.0967	1.5963	3
						1.9841	0.8419	2.3661	1.1926	1.6703	4
					1	1.7058	1.2296	2.5408	1.2296	1.7058	5
				1.9841	0.8696	2.4758	1.3137	2.6064	1.2479	1.7254	6
			1	1.7372	1.2583	2.6381	1.3444	2.6381	1.2583	1.7372	7
		1.9841	0.8796	2.5093	1.3389	2.6964	1.359	2.6564	1.2647	1.7451	8
	1	1.7504	1.269	2.6678	1.3673	2.7239	1.3673	2.6678	1.269	1.7504	9
1.9841	0.8842	2.5239	1.3485	2.7231	1.3806	2.7392	1.3725	2.6754	1.2721	1.7543	10
3.0 dB Ripple
[latex]g_{11}[/latex]	[latex]g_{10}[/latex]	[latex]g_{9}[/latex]	[latex]g_{8}[/latex]	[latex]g_{7}[/latex]	[latex]g_{6}[/latex]	[latex]g_{5}[/latex]	[latex]g_{4}[/latex]	[latex]g_{3}[/latex]	[latex]g_{2}[/latex]	[latex]g_{1}[/latex]	N
									1	1.9953	1
								5.8095	0.5339	3.1013	2
							1	3.3487	0.7117	3.3487	3
						5.8095	0.592	4.3471	0.7483	3.4389	4
					1	3.4817	0.7618	4.5381	0.7618	3.4817	5
				5.8095	0.6033	4.4641	0.7929	4.6061	0.7685	3.5045	6
			1	3.5182	0.7723	4.6386	0.8039	4.6386	0.7723	3.5182	7
		5.8095	0.6073	4.499	0.8018	4.669	0.8089	4.6575	0.7745	3.5277	8
	1	3.534	0.776	4.6692	0.8118	4.7272	0.8118	4.6692	0.776	3.534	9
5.8095	0.6091	4.5142	0.8051	4.726	0.8164	4.7425	0.8136	4.6768	0.7771	3.5384	10
Source: Reprinted from G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures, Artech House, Dedham, Mass.,1980, with permission.

n	[latex]g_{n}[/latex]	[latex]Z_{0n} (Ω)[/latex]
1	1.5963	265.9
2	1.0967	387.0
3	1.5963	265.9

The filter circuit is shown in Figure 8.47a, with all stubs and transmission line sections λ /4 long at 2.0 GHz. The calculated attenuation for this filter is shown in Figure 8.49; the ripple in the passbands is somewhat greater than 0.5 dB as a result of the approximations involved in the development of the design equations.

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