Implementing IIR/FIR Filters

1.3 Analog Highpass Filter
The passive RCL circuit forming a highpass filter
network is shown in Figure 1-3 where the transfer
function, H(s), is again derived from a voltage divider
analysis of the RCL network. The gain and phase
response are plotted in Figure 1-4 for different values
of damping coefficient. As evidenced, the
highpass filter response is the mirror image of the
lowpass filter response.
1.4 Analog Bandstop Filter
The analog RCL network for a bandstop filter network
is simply the sum of the lowpass and highpass
transfer functions shown in Figure 1-5 where the
transfer function, H(s), is again derived from a voltage
divider analysis of the RCL network. The gain
and phase response are plotted in Figure 1-6 for different
values of quality factor, Q, (where Q = 1/d).
Neglecting the departure of real RCL components'
values from the ideal case, the attenuation at the
center frequency, f 0 , is infinite. Also, note that the
phase undergoes a 1 80-degree shift when passing
through the center frequency (zero in the s-plane).
Q for bandpass and bandstop filters is a measure
of the width, ΔΩ, of the stopband with respect to
the center frequency, ΩO , i.e., ΔΩ = Q-1Ωo . ΔΩ is
measured at the points where G(Ω) = 1/ 2
.
1-10 MOTOROLA