CAUTION: Use isolation transformers on the
generator and o-scope to avoid shock hazards and short
circuits that can damage your expensive equipment. If
your o-scope will do ratios, the gain calculation is
simplified. Otherwise, you can calculate the gain by
dividing the Vout on channel 2 by the
Vin on channel 1 for several
frequencies and use the results in a
spreadsheet to draw the Bode Plot.
You can measure the phase shift
by connecting Vin to the vertical
channel (one of the normal inputs)
and Vout to the horizontal channel (sometimes called X or
sweep), and then determine the phase difference from the
resulting Lissajous figures. By substituting potentiometers
for resistors, you can vary the frequency response of these
filters. Any readers out there who are interested, send me
your results and I will try to publish as many as possible.
If there are simple filter circuits, then there are
complex filter circuits. If one filter is good, then adding a
second filter should be twice as good, right? In reality, two
cascaded RC LPFs make the system better than twice as
good. Figure 7 shows the cascaded low pass filter and
Figure 8 shows frequency response curves for the simple
(in blue) and two cascaded (in purple) RC filters which
demonstrate the cascaded filter's cutoff frequency is lower,
and the slope of the "roll off" portion of the curve is
steeper (sharper filter). By adding additional cascaded RC
LPF filter stages, the roll off slope can be made even
steeper, which brings us closer to an ideal filter in which
the roll off portion would be straight up and down.
In reality, adding filter stages can produce
predictability problems since each cascaded stage affects
the other stages (this is beyond the scope of Q&A to
cover, but there are many engineering texts dealing with
this aspect of filter design). The cutoff frequency for the
two-stage cascaded RC LPF is fC = 1/(2Π
If cascading two RC LPF gave us a sharper frequency
response, what about cascading an HPF with an LPF?
Figures 9 and 10 show this arrangement and the
associated frequency response curve. You can easily see
that this filter has both high and low cutoff frequencies,
but it allows frequencies between these two to pass. Thus,
it is called a bandpass filter. The two cutoff frequencies
are: fH = 1/(2ΠR1C1) and fL = 1/(2ΠR2C2). The center
frequency is fCENTER = SQRT(fHXfL). The phase response
can be calculated from ϴ = arc tan((f/( fH - fL))(f/fCENTER -
For the BPF, we define the bandwidth as BW = fH - fL
and the quality factor Q = fCENTER /BW, or Q is the circuit
reactance divided by the circuit resistance. The bandwidth
is inversely proportional to Q; as Q increases, the
bandwidth decreases. So, by decreasing the circuit
resistance, you can decrease the bandwidth. BPFs are
used to eliminate unwanted signals, while allowing wanted
signals such as audio or television signals.
Band Rejection Filters (BRF) are also known as notch
filters or band stop filters, and are used to eliminate
unwanted signals such as a nearby FM radio station that
12 February 2016
■ FIGURE 10.
■ FIGURE 7.
■ FIGURE 8.
■ FIGURE 9.