Page 443 - Analog and Digital Filter Design

440 Analog and Digital Filter Design

2.3 Chebyshev and Cauer (elliptic).
2.4 Inverse Chebyshev and Cauer (elliptic).

2.5 Cauer filters have ripple in both passband and stopband. They are
used because they have a very steep skirt (almost a "brick wall"
response).
2.6 Bessel filters have a constant delay in the passband. Unfortunately,
they have a very shallow skirt response.
2.7 Component values are normalized so that one set of data (usually
written in a table) can be applied to any cutoff frequency or load
impedance by simply scaling the values.

Chapter 3

3.1 An output step followed by a smooth exponential decay.

3.2 -0.3 -j0.67.
3.3 Imaginary axis.
3.4 A null in the stopband; otherwise known as stopband ripple. The
presence of two zeroes implies a Cauer (elliptic) or Inverse Chebyshev
response.
3.5 Butterworth poles are located on the unit circle. Each pole is
equidistant from the origin, and they have equal angular distance
between each other.
3.6 Chebyshev poles are located on an ellipse. The Butterworth filter pole
locations are shifted towards the imaginary axis (to the right) and away
from the real axis (up or down). The amount of pole movement is
mathematically derived.

Chapter 4

4.1 An inductor value has to be increased in proportion to the load value,
so to denormalize for impedance we get 0.8212H x 50 = 41.06H. To
scale for cutoff frequency of 20 kHz, remember that we want the
inductor to have an impedance equivalent to a 41.06H inductor at 1
radian per second (which is 41.06ohms at lradls). This means that we
have to divide by 27cF radls, where F is the cutoff frequency. In this
case 2nF= 125,664radls. In summary, L = 0.8212 x R12rtF. This gives a
denormalized value of 327pH, which has an impedance of 41.06ohms
at 20 kHz.