Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

11-4 Passive, Active, and Digital Filtersh iK s 2 vzQ zs þ v 2 zT BQ (s) ¼ s 2 þ s þ v 2 pv pQ p(11:16)whereK is a constantv z is the zero frequencyQ z the zero Qv p is the pole frequencyQ p the pole Q11.2.3 Frequency Response (Magnitude and Phase)The magnitude and phase response of the normalized second-order low-pass transfer function is shownin Figure 11.2, where Q is a parameter. In this figure we see that Q influences the frequency response nearv o .IfQ is greater than 0.707, then the normalized magnitude response has a peak value ofQjT n ½v n ( max ) Šj ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(11:17)1 ð1=4Q 2 ÞNormalized magnitude |T LPn (ω n )|20 dB10 dB0 dB–10 dB–20 dB–30 dBQ =0.707Q =0.5Q =5Q =2Q =1–40 dB0.1 1 10(a)Normalized frequency (ω n =ω/ω o )Phase shift (°)0–45–90–135Q =1Q = 0.707Q =0.5Q =5Q =2(b)–1800.1 1Normalized frequency (ω n =ω/ω o )10FIGURE 11.2 (a) Normalized magnitude and (b) phase response of the standard second-order low-pass transferfunction with Q as a parameter.