low pass filter design specifications
Passive Low Pass Filter
A Low Pass Filter is a circuit that can be designed to modify,
reshape or reject all unwanted high frequencies of an electrical
signal and accept or pass only those signals wanted by the
circuits designer.Passive RC filters “filter-out” unwanted
signals as they separate and allow to pass only those
sinusoidal input signals based upon their frequency with the
most simple being passive low pass filter network.
In low frequency applications (up to 100kHz), passive filters
are generally constructed using simple RC (Resistor-
Capacitor) networks, while higher frequency filters (above
100kHz) are usually made from RLC (Resistor-Inductor-
Capacitor) components
A simple passive {RC Low Pass Filter} or {LPF}, can be
easily made by connecting together in series a single Resistor
with a single Capacitor as shown below. In this type of filter
arrangement the input signal ( VIN ) is applied to the series
combination (both the Resistor and Capacitor together) but the
output signal ( VOUT ) is taken across the capacitor only.
generally there are many orders of low pass filters but in our
project we going to use
1.first order filter
2.second order filter
3.third order filter
This type of filter is known generally as a “first-order filter”
or “one-pole filter”, because it has only “one” reactive
component, the capacitor, in the circuit.
As mentioned previously in the Capacitive Reactance tutorial,
the reactance of a capacitor varies inversely with frequency,
while the value of the resistor remains constant as the
frequency changes. At low frequencies the capacitive
reactance, ( XC ) of the capacitor will be very large compared
to the resistive value of the resistor, R.
This means that the voltage potential, VC across the capacitor
will be much larger than the voltage drop, VR developed
across the resistor. At high frequencies the reverse is true with
VC being small and VR being large due to the change in the
capacitive reactance value.
While the circuit above is that of an RC Low Pass Filter
circuit, it can also be thought of as a frequency dependant
variable potential divider circuit similar to the one we looked
at in the Resistors tutorial.
We also know that the capacitive reactance of a capacitor in
an AC circuit is given as:
Opposition to current flow in an AC circuit is
called impedance, symbol Z and for a series circuit consisting
of a single resistor in series with a single capacitor, the circuit
impedance is calculated as:
Z = √ R 2 + √ X C2
Second-order Low Pass Filter
Thus far we have seen that simple first-order RC low pass
filters can be made by connecting a single resistor in series
with a single capacitor. This single-pole arrangement gives us
a roll-off slope of -20dB/decade attenuation of frequencies
above the cut-off point at ƒ-3dB . However, sometimes in filter
circuits this -20dB/decade (-6dB/octave) angle of the slope
may not be enough to remove an unwanted signal then two
stages of filtering can be used as shown.
Second-order Low Pass Filter
The above circuit uses two passive first-order low pass filters
connected or “cascaded” together to form a second-order or
two-pole filter network. Therefore we can see that a first-order
low pass filter can be converted into a second-order type by
simply adding an additional RC network to it and the more
RC stages we add the higher becomes the order of the filter.
If a number ( n ) of such RC stages are cascaded together, the
resulting RC filter circuit would be known as an “nth-
order” filter with a roll-off slope of “n x -20dB/decade”.
So for example, a second-order filter would have a slope of -
40dB/decade (-12dB/octave), a fourth-order filter would have
a slope of -80dB/decade (-24dB/octave) and so on. This
means that, as the order of the filter is increased, the roll-off
slope becomes steeper and the actual stop band response of
the filter approaches its ideal stop band characteristics.
Second-order filters are important and widely used in filter
designs because when combined with first-order filters any
higher-order nth-value filters can be designed using them. For
example, a third order low-pass filter is formed by connecting
in series or cascading together a first and a second-order low
pass filter.
But there is a downside too cascading together RC filter
stages. Although there is no limit to the order of the filter that
can be formed, as the order increases, the gain and accuracy
of the final filter declines.
When identical RC filter stages are cascaded together, the
output gain at the required cut-off frequency ( ƒc ) is reduced
(attenuated) by an amount in relation to the number of filter
stages used as the roll-off slope increases. We can define the
amount of attenuation at the selected cut-off frequency using
the following formula.
Passive Low Pass Filter Gain at ƒc
