DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

8 DESIGN AND ANALYSIS OF ANALOG FILTERS:
inherent buffering, which means that the overall transfer function of several op amp
stages is the product of the individual stage transfer functions, ignoring loading effects
of subsequent stages. This greatly simplifies the theoretical implementation. That is,
for example, a sixth-order op amp filter can be implemented by cascading three
second-order op amp stages, where each second-order stage is implemented
independently of the other two stages. Passive analog filters do not enjoy this
simplification, and the entire transfer function must be implemented as one nonseparable
whole. Passive and active (op amp) filter implementation is presented in
Part II of this book.
1.3 APPLICATIONS OF ANALOG FILTERS
In this section, several examples are given that illustrate the application of
frequency selective analog filters to practical engineering use. Selection of a signal
from others separated in frequency, estimating a signal in noise, frequency selection
decoding, intentionally frequency-limiting a signal, contributing to the demodulation
of signals, rejection of interference signals, and separation of signals according to
frequency bands, are all illustrated.
Examples 1.1 and 1.2
The first two examples were given above in Section 1.1. More specifically,
Example 1.1 illustrates the use of a bandpass filter to extract one desired signal from
the sum of several signals, where the individual signals are separated in the frequency
domain (see Figure 1.2). Example 1.2 illustrates using a lowpass filter to improve
the signal-to-noise ratio of a signal imbedded in noise, but where the noise has a much
wider bandwidth than does the signal (see Figure 1.3).
Example 1.3
Consider a high-gain instrumentation amplifier used to measure electroencephalogram
(EEG) signals. EEG signals are low-level with an equivalent high
source impedance. Electrodes are applied to the scalp of the subject in order to
measure these signals. The electrodes are very high impedance devices so as to not
present much of a load for the measurement signals. Due to the high impedance, the
low-level EEG signal may well be corrupted by additive 60 Hz and/or 120 Hz,
derived from fluorescent lighting and other electrical appliances and equipment. Since
the additive 60/120 Hz noise tends to be mostly common mode, a differential
instrumentation amplifier may significantly suppress the additive noise, but will not
completely remove it, especially since the EEG signal is likely much lower in
amplitude than the additive noise (sometimes referred to as hum). EEG signals, in the
frequency domain, have most of the signal energy below 60 Hz. Since the noise
(hum) components are above the EEG frequency components, a lowpass filter may be
Chapter 1 Introduction