lektor January & February 2021 75Figure 2 shows the basic structure of Cauer (elliptical) and inverse
Chebyshev filters (also known as type 2). Here the inductors or
capacitors are replaced with parallel or series resonant circuits.
Drawn are low- and high-pass filters in PI and T configurations
from the third through to sixth order.Figure 3 shows the basic structure of band-pass and band-stop
filters with a Bessel, Butterworth or Chebyshev characteristic (from
third through to seventh order), and in Figure 4 we see the more
complex structures with Cauer and inverse Chebyshev characteris-
tics (fifth and seventh order). Here too there are PI and T variants.Dimensioning
A Bessel or Butterworth filter is entirely determined by the filter
characteristic, the -3dB corner frequency, the chosen structure, the
order, and the input and output impedances. In contrast to the active
filters, with passive filters there is no freedom at all when it comes to
choosing component values. If you would like to select, for example,
a standard value from an E-series for an inductor, then you will have
to adjust the corner frequency of the filter at a given impedance a
little. Of course this is only possible if the application allows it.How the characteristics of a Butterworth filter change for the differ-
ent orders has already been discussed in part 1 of this series [1]. Now
we can see how the component values change depending on the
chosen corner frequency. In Figure 5 we see the fully dimensioned
schematic of a fifth-order Butterworth low-pass filter with a corner
frequency of 1 MHz. If we want to double the corner frequency
to 2 MHz we only need to halve the values of the inductors and
the capacitors. This is no surprise because the corner frequencyoutput impedances (which do not have to be identical). It should
be noted that deviations from the expected source or load imped-
ance can have a strong influence on the filter characteristic. In
this article we will take a look at the types of passive filters that
are commonly used and what needs to be considered.Structures
In Figure 1 you can see the basic structure of high- and low-pass
filters of the first through the sixth order. By choosing the correct
values for the components, these structures allow filters with Bessel,
Butterworth and Chebyshev characteristics to be realised. You can
choose whether a filter starts with a component in series with the
others (T-structure) or with a component to ground (PI-structure).In the leftmost column of Figure 1 are the PI low-pass filters that
all begin with a capacitor to ground at their inputs. In the second
column are the T low-pass filters that start with an inductor in series.The high-pass filters are exactly the other way around. In the third
column we see the PI high-pass filters with an inductor to ground
and, in the rightmost column, the T high-pass filters with a capac-
itor in series.At the higher orders components are added alternating between
longitudinal (in series) and transversal (to ground). These additional
components have different values than the first components. For
the desired functionality it does not matter whether we choose
a T or PI structure. But, because inductors are not popular with
electronics designers, it is common to attempt to use as few of
these as possible.L1R 1 C 1
L2 R 2C 2L3C 3L1R 1
L2 R 2C 1
L3C 2 C 3L1
C 1R 1 L2
C 2L3
C 3 R 2
C 1R 1 L1
C 2L2
C 3 R 2L3L1R 1 C 1
L2 R 2C 2 C 3L1R 1
L2 R 2C 1
L3C 2L1
C 1R 1 L2
C 2L3
R 2
C 1R 1 L1
C 2L2
C 3 R 2L1R 1 C 1L2 R 2C 2L1R 1
L2 R 2C 1 C 2L1
C 1R 1 L2C 1 C 2 R 2R 1 L1
C 2L2
R 2L1R 1 C 1
R 2C 2L1R 1
L2 R 2C 1L1
C 1R 1 L2
R 2
C 1R 1 L1
C 2 R 2LP Shunt First LP Series First HP Shunt First HP Series First- Order
- Order
200522-002C 4 C 5C 4 C 5C 3C 3L4 L5L4 L5L3L3L4 L5 L6L4 L5L3L3C 4 C 5C 4 C 5C 3C 3- Order
- Order
Figure 2: Basic schematics for low-pass and high-pass filters of third through to sixth order with Cauer or inverse Chebyshev characteristics in PI and T
configurations.