LOW-PASS FILTER DESIGN COMPARISON Design a maximally flat low-pass filter with a cutoff frequency of 2 GHz, impedance of 50 , and at least 15 dB insertion loss at 3 GHz. Compute and plot the amplitude response and group delay for f = 0 to 4 GHz, and compare with an equal-ripple (3.0 dB ripple) and

Question

LOW-PASS FILTER DESIGN COMPARISON Design a maximally flat low-pass filter with a cutoff frequency of 2 GHz, impedance of 50 , and at least 15 dB insertion loss at 3 GHz. Compute and plot the amplitude response and group delay for f = 0 to 4 GHz, and compare with an equal-ripple (3.0 dB ripple) and linear phase filter having the same order.

Accepted Answer

First find the required order of the maximally flat filter to satisfy the insertion loss specification at 3 GHz. We have that[latex]\ \left|\omega /\omega _{c}\right|-1 =0.5;[/latex] from Figure 8.26 we see that N = 5 will be sufficient. Then Table 8.3 gives the prototype element values as

Then (8.67) can be used to obtain the scaled element values:

[latex]\ C^{\prime}_{1}=0.984pF,[/latex]

[latex]\ L^{\prime }_{2}=6.438nH,[/latex]

[latex]\ C^{\prime }_{3}=3.183pF,[/latex]

[latex]\ L^{\prime }_{4}=6.438nH,[/latex]

[latex]\ C^{\prime }_{5}=0.984pF,[/latex]

The final filter circuit is shown in Figure 8.29; the ladder circuit of Figure 8.25a was used, but that of Figure 8.25b could have been used just as well. The component values for the equal-ripple filter and the linear phase filter, for N = 5, can be determined from Tables 8.4 and 8.5. The amplitude and group delay results for these three filters are shown in Figure 8.30. These results clearly show the trade-offs involved with the three types of filters. The equal-ripple response has the sharpest cutoff but the worst group delay characteristics. The maximally flat response has a flatter attenuation characteristic in the passband but a slightly lower cutoff rate. The linear phase filter has the worst cutoff rate but a very good group delay characteristic.

Question 8.3: LOW-PASS FILTER DESIGN COMPARISON Design a maximally flat lo...

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