Tab Electronics Guide to Understanding Electricity ... - Sciences Club

392 Chapter Fifteen
parallel with a high-pass filter with a cutoff frequency of 200 hertz.
Since the two filters are in parallel, the input signal would be applied
to the input of both simultaneously. All of the input signal frequencies
up to 100 hertz would be freely passed by the low-pass filter and
appear at the output. Likewise, all input frequencies above 200 hertz
would be freely passed by the high-pass filter and appear at the output.
However, there would be a “notch” formed in the frequency
response, occurring between the frequencies of 100 and 200 hertz. For
example, a frequency of 150 hertz would be too high to be passed by
the low-pass filter and too low to be passed by the high-pass filter.
As in the case of bandpass filters, active op-amp-based low-pass and highpass
filters are often combined to create practical band-reject filters, but this
method is seldom used with common passive filter designs. As you may
have guessed, one method of making a band-reject filter would be to convert
the parallel-resonant circuit of Fig. 15-7c into a series-resonant circuit.
Since a series-resonant circuit exhibits maximum impedance at all frequencies
except the resonant frequency, the output of Fig. 15-7c would be maximum
at all frequencies except those close to the resonant frequency. At this
point, the impedance across the resonant circuit (i.e., the output) would
drop to a low value, causing most of the input signal to be dropped across
R. Consequently, a “notch” in the output frequency response would occur.
Another method of causing the same type of response is illustrated
in Fig. 15-7d. This band-reject filter is identical to the bandpass filter of
Fig. 15-7c, except the output is taken across the resistor instead of the parallel
resonant circuit. The output frequency response graph for this circuit
illustrates how a narrow band of frequencies is attenuated at the
resonance frequency of the parallel circuit, while all other frequencies
either above or below this frequency are passed.
As you may have guessed, the performance variables and the calculations
for the Fig. 15-7d band-reject filter are identical to the bandpass filter
of Fig. 15-7c. The bandwidth is calculated in the same way, but it refers to
the band of frequencies that are blocked rather than passed. All frequencies
attenuated by more than 3 dB are considered to be blocked. Likewise,
the center frequency will be the resonant frequency of the parallel resonant
circuit (calculated the same way as for the bandpass filter of Fig. 15-7c).
Twin-T Filters
The twin-T filter of Fig. 15-7e is another type of passive band-reject filter,
but it is much more commonly used than the type of passive band-