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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