High-pass filters
A high-pass filter's task is just the
opposite of a low-pass filter: to offer easy passage of a
high-frequency signal and difficult passage to a
low-frequency signal. As one might expect, the inductive and
capacitive versions of the high-pass filter are just the
opposite of their respective low-pass filter designs:
The capacitor's impedance increases with
decreasing frequency. This high impedance in series tends to
block low-frequency signals from getting to load.
capacitive highpass filter
v1 1 0 ac 1 sin
c1 1 2 0.5u
rload 2 0 1k
.ac lin 20 1 200
.plot ac v(2)
.end
freq v(2) 1.000E-03 1.000E-02 1.000E-01 1.000E+00
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1.000E+00 3.142E-03 . * . . .
1.147E+01 3.602E-02 . . * . .
2.195E+01 6.879E-02 . . * . .
3.242E+01 1.013E-01 . . * .
4.289E+01 1.336E-01 . . . * .
5.337E+01 1.654E-01 . . . * .
6.384E+01 1.966E-01 . . . * .
7.432E+01 2.274E-01 . . . * .
8.479E+01 2.574E-01 . . . * .
9.526E+01 2.867E-01 . . . * .
1.057E+02 3.152E-01 . . . * .
1.162E+02 3.429E-01 . . . * .
1.267E+02 3.698E-01 . . . * .
1.372E+02 3.957E-01 . . . * .
1.476E+02 4.207E-01 . . . * .
1.581E+02 4.448E-01 . . . * .
1.686E+02 4.680E-01 . . . * .
1.791E+02 4.903E-01 . . . * .
1.895E+02 5.116E-01 . . . * .
2.000E+02 5.320E-01 . . . * .
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Load voltage increases with increasing frequency
The inductor's impedance decreases with
decreasing frequency. This low impedance in parallel tends
to short out low-frequency signals from getting to the load
resistor. As a consequence, most of the voltage gets dropped
across series resistor R1.
inductive highpass filter
v1 1 0 ac 1 sin
r1 1 2 200
l1 2 0 100m
rload 2 0 1k
.ac lin 20 1 200
.plot ac v(2)
.end
freq v(2) 1.000E-03 1.000E-02 1.000E-01 1.000E+00
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1.000E+00 3.142E-03 . * . . .
1.147E+01 3.601E-02 . . * . .
2.195E+01 6.871E-02 . . * . .
3.242E+01 1.011E-01 . . * .
4.289E+01 1.330E-01 . . . * .
5.337E+01 1.644E-01 . . . * .
6.384E+01 1.950E-01 . . . * .
7.432E+01 2.248E-01 . . . * .
8.479E+01 2.537E-01 . . . * .
9.526E+01 2.817E-01 . . . * .
1.057E+02 3.086E-01 . . . * .
1.162E+02 3.344E-01 . . . * .
1.267E+02 3.591E-01 . . . * .
1.372E+02 3.828E-01 . . . * .
1.476E+02 4.053E-01 . . . * .
1.581E+02 4.267E-01 . . . * .
1.686E+02 4.470E-01 . . . * .
1.791E+02 4.662E-01 . . . * .
1.895E+02 4.845E-01 . . . * .
2.000E+02 5.017E-01 . . . * .
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Load voltage increases with increasing frequency
This time, the capacitive design is the
simplest, requiring only one component above and beyond the
load. And, again, the reactive purity of capacitors over
inductors tends to favor their use in filter design,
especially with high-pass filters where high frequencies
commonly cause inductors to behave strangely due to the skin
effect and electromagnetic core losses.
As with low-pass filters, high-pass filters
have a rated cutoff frequency, above which the output
voltage increases above 70.7% of the input voltage. Just as
in the case of the capacitive low-pass filter circuit, the
capacitive high-pass filter's cutoff frequency can be found
with the same formula:
In the example circuit, there is no
resistance other than the load resistor, so that is the
value for R in the formula.
Using a stereo system as a practical
example, a capacitor connected in series with the tweeter
(treble) speaker will serve as a high-pass filter, imposing
a high impedance to low-frequency bass signals, thereby
preventing that power from being wasted on a speaker
inefficient for reproducing such sounds. In like fashion, an
inductor connected in series with the woofer (bass) speaker
will serve as a low-pass filter for the low frequencies that
particular speaker is designed to reproduce. In this simple
example circuit, the midrange speaker is subjected to the
full spectrum of frequencies from the stereo's output. More
elaborate filter networks are sometimes used, but this
should give you the general idea. Also bear in mind that I'm
only showing you one channel (either left or right) on this
stereo system. A real stereo would have six speakers: 2
woofers, 2 midranges, and 2 tweeters.
For better performance yet, we might like to
have some kind of filter circuit capable of passing
frequencies that are between low (bass) and high (treble) to
the midrange speaker so that none of the low- or
high-frequency signal power is wasted on a speaker incapable
of efficiently reproducing those sounds. What we would be
looking for is called a band-pass filter, which is
the topic of the next section.
-
REVIEW:
-
A high-pass filter allows for easy passage
of high-frequency signals from source to load, and
difficult passage of low-frequency signals.
-
Capacitive high-pass filters insert a
capacitor in series with the load; inductive high-pass
filters insert a resistor in series and an inductor in
parallel with the load. The former filter design tries to
"block" the unwanted frequency signal while the latter
tries to short it out.
-
The cutoff frequency for a
high-pass filter is that frequency at which the output
(load) voltage equals 70.7% of the input (source) voltage.
Above the cutoff frequency, the output voltage is greater
than 70.7% of the input, and visa-versa.
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