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A) A DW) A) A DW +: Table 16-2. Values of For Different Filter Types and Different Qs

The document discusses parameters for designing fourth-order bandpass filters using staggered tuning. It provides equations and a table of values for the pole quality (Q), factors (α) by which mid frequencies derive from the overall mid frequency, and coefficients (a1, b1) for different filter types and quality factors.

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80 views1 page

A) A DW) A) A DW +: Table 16-2. Values of For Different Filter Types and Different Qs

The document discusses parameters for designing fourth-order bandpass filters using staggered tuning. It provides equations and a table of values for the pole quality (Q), factors (α) by which mid frequencies derive from the overall mid frequency, and coefficients (a1, b1) for different filter types and quality factors.

Uploaded by

lecuellarq85gmailcom
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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D Ami is the gain at the mid frequency, fmi, of each partial filter

D Qi is the pole quality of each filter


D α and 1/α are the factors by which the mid frequencies of the individual filters, fm1
and fm2, derive from the mid frequency, fm, of the overall bandpass.

In a fourth-order band-pass filter with high Q, the mid frequencies of the two partial filters
differ only slightly from the overall mid frequency. This method is called staggered tuning.

Factor α needs to be determined through successive approximation, using equation


16–13:

ƪ ƫ
2
a·DW·a 1 (DW) 2
a2 ) ) 12 * 2 * +0 (16–13)
b 1ǒ1 ) a 2Ǔ a b1

with a1 and b1 being the second-order low-pass coefficients of the desired filter type.

To simplify the filter design, Table 16–2 lists those coefficients, and provides the α values
for three different quality factors, Q = 1, Q = 10, and Q = 100.

Table 16–2. Values of α For Different Filter Types and Different Qs

Bessel Butterworth Tschebyscheff


a1 1.3617 a1 1.4142 a1 1.0650
b1 0.6180 b1 1.0000 b1 1.9305
Q 100 10 1 Q 100 10 1 Q 100 10 1
∆Ω 0.01 0.1 1 ∆Ω 0.01 0.1 1 ∆Ω 0.01 0.1 1
α 1.0032 1.0324 1.438 α 1.0035 1.036 1.4426 α 1.0033 1.0338 1.39

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