Question 8.8: BANDSTOP FILTER DESIGN Design a bandstop filter using three ...
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.
The fractional bandwidth is Δ = 0.15. Table 8.4 gives the low-pass prototype values, g_{n} , for N = 3. Then the characteristic impedances of the stubs can be found from (8.130). The results are listed in the following table:
Z_{0n}=\frac{4Z_{0}}{\pi g_{n}\Delta }| TABLE 8.4 Element Values for Equal-Ripple Low-Pass Filter Prototypes (g_0 = 1, ω_c = 1, N = 1 to 10, 0.5 dB and 3.0 dB ripple) | |||||||||||
| 0.5 dB Ripple | |||||||||||
| g_{11} | g_{10} | g_{9} | g_{8} | g_{7} | g_{6} | g_{5} | g_{4} | g_{3} | g_{2} | g_{1} | 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 | |||||||||||
| g_{11} | g_{10} | g_{9} | g_{8} | g_{7} | g_{6} | g_{5} | g_{4} | g_{3} | g_{2} | g_{1} | 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 |
g_{n} |
Z_{0n} (Ω) |
|
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.
