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2016 Extra Class study guide: E7C - filters

Posted: 03 Feb 2016 01:55 PM PST
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E7C Filters and matching networks: types of networks; types of filters;
filter applications; filter characteristics; impedance matching; DSP
filtering

Because the impedance of inductors and capacitors vary with frequency, we
often make filters out of them. One of the most common is the T-network
filter, so called because it looks like the letter T. An example is shown
in figure E7C-1.
Figure E7C-1. T-network filter.

This particular filter has the characteristic of being a high-pass filter.
That is to say it will pass frequencies above a certain frequency, called
the cutoff frequency, and block frequencies below that frequency. A
T-network with series capacitors and a parallel shunt inductor has the
property of it being a high-pass filter. (E7C02) The reason the circuit
acts this way is that as the frequency of a signal increases, capacitive
reactance decreases and inductive reactance increases, meaning that
lower-frequency signals are more likely to be shunted to ground.

A circuit containing capacitors and inductors can also form a low-pass
filter. A low-pass filter is a circuit that passes frequencies below the
cutoff frequency and blocks frequencies above it.

Pi is the common name for a filter network which is equivalent to two L
networks connected back-to-back with the inductors in series and the
capacitors in shunt at the input and output. (E7C11). The circuit shown in
figure E7C-2 is called a pi filter because it looks like the Greek letter π.

The capacitors and inductors of a low-pass filter Pi-network are arranged
such that a capacitor is connected between the input and ground, another
capacitor is connected between the output and ground, and an inductor is
connected between input and output. (E7C01) The reason the circuit acts
this way is that as the frequency of a signal increases, capacitive
reactance decreases and inductive reactance increases, meaning that
higher-frequency signals are more likely to be shunted to ground.
Figure E7C-2. A low-pass filter is made from two shunt capacitors and a
series inductance.



Pi networks can also be used to match the output impedance of one circuit
to the input impedance of another or the output impedance of a transmitter
to the input impedance of an antenna. An impedance-matching circuit
transforms a complex impedance to a resistive impedance because it cancels
the reactive part of the impedance and changes the resistive part to a
desired value. (E7C04) One advantage of a Pi matching network over an L
matching network consisting of a single inductor and a single capacitor is
that the Q of Pi networks can be varied depending on the component values
chosen. (E7C13)

A Pi network with an additional series inductor on the output describes a
Pi-L network used for matching a vacuum-tube final amplifier to a 50-ohm
unbalanced output. (E7C12) One advantage a Pi-L-network has over a
Pi-network for impedance matching between the final amplifier of a
vacuum-tube transmitter and an antenna is that it has greater harmonic
suppression. (E7C03)

Piezoelectric crystals are also used to build filters. A crystal lattice
filter is a filter with narrow bandwidth and steep skirts made using quartz
crystals. (E7C15) The relative frequencies of the individual crystals is
the factor that has the greatest effect in helping determine the bandwidth
and response shape of a crystal ladder filter. (E7C08) A Jones filter is a
variable bandwidth crystal lattice filter used as part of a HF receiver IF
stage. (E7C09)

Different types of filters have different characteristics. For example, a
Chebyshev filter is a filter type described as having ripple in the
passband and a sharp cutoff. (E7C05) On the other hand, the distinguishing
features of an elliptical filter are extremely sharp cutoff with one or
more notches in the stop band. (E7C06)

Filters have both amplitude and phase-response characteristics. In some
applications, both are important. Digital modes, for example, are most
affected by non-linear phase response in a receiver IF filter. (E7C14)

Often, you’ll choose a filter type for a particular application. For
example, to attenuate an interfering carrier signal while receiving an SSB
transmission, you would use a notch filter. (E7C07) A cavity filter would
be the best choice for use in a 2 meter repeater duplexer. (E7C10)

Today, many of these filters are implemented using digital signal
processing. The kind of digital signal processing audio filter might be
used to remove unwanted noise from a received SSB signal is an adaptive
filter. (E7C08) The type of digital signal processing filter might be used
to generate an SSB signal is a Hilbert-transform filter. (E7C09)

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