Active filters are high quality factor based filters that are used in digital as well as analog electrical circuitry

1. Active Electrical Filters
LPF, HPF and BPF
Circuit Analysis II – EE-201

2. Contents
• Electrical Filters
• Active Filters
• Low Pass Filter
• High Pass Filter
• Band Pass Filter
• Resonance Frequency and Q-
Factor
• Butterworth Filter
• Higher Order Filters and its
curves

3. Electrical Filters
• Most electrical filters are circuits that select certain
bands of frequencies to pass along, or accept, and
other bands of frequencies to stop, or reject.
• The frequency at which the transition between
passing and rejecting input signals occurs is called
the “cutoff” frequency, often abbreviated as fC.
• The band of frequencies that is passed is called the
“passband” of the filter, also called the
“bandwidth.”
• Filters can be active filters or passive filters,
depending upon the component it uses.

4. General Design
• The simplest filters are constructed of two passive elements -- either a resistor and capacitor (RC),
or a resistor and inductor (RL)[only in passive].
• The filters that pass low frequencies are referred to as “lowpass” filters and the filters that pass
high frequencies are referred to as “highpass” filters.
• The Inductor is replaced with Active element in Active filters whereas the roll-off gain is
controlled using an Active element such as OPAMP
• Active Filter gives more speedy drop and rise to the amplitude of frequencies on the frequency
response graphs

5. Active Filters
• Active Filters contain active components such as operational
amplifiers, transistors or FET’s within their circuit design. They draw
their power from an external power source and use it to boost or
amplify the output signal.
• Op-amp has a high input impedance, a low output impedance and a
voltage gain determined by the resistor network within its feedback
loop.
• The main difference between a “passive filter” and an “active filter” is
amplification.

6. Active Low Pass Filter
• Its principle of operation and frequency
response is exactly the same as those for
the seen passive filter.
• The only difference this time is that it uses
an op-amp for amplification and gain
control.
• The simplest form of a low pass active filter
is to connect an inverting or non-inverting
amplifier with passive low pass filter
• This first-order low pass active filter, consists
simply of a passive RC filter stage providing
a low frequency path to the input of a non-
inverting operational amplifier

7. Active Low Pass Filter with Amplification
The frequency response of the circuit will be the same as
that for the passive RC filter, except that the amplitude of
the output is increased by the pass band gain, AF of the
amplifier.

8. Voltage gain at various frequencies

9. Active High Pass Filter
• The basic operation of an Active High
Pass Filter (HPF) is the same as for its
equivalent RC passive high pass filter
circuit, except this time the circuit has an
operational amplifier or included within
its design providing amplification and
gain control.

10. Active High Pass Filter with Amplification

11. We can never get a PERFECT high Pass filter
on active devices

12. Active Band Pass Filter
• Active Band Pass Filter can be easily made by
cascading together a single Low Pass Filter with a
single High Pass Filter as shown.
• The cut-off or corner frequency of the low pass
filter (LPF) is higher than the cut-off frequency of
the high pass filter (HPF) and the difference
between the frequencies at the -3dB point will
determine the “bandwidth” of the band pass
filter while attenuating any signals outside of
these points.
• One way of making a very simple Active Band
Pass Filter is to connect the basic passive high
and low pass filters we look at previously to an
amplifying op-amp circuit as shown.

13. Inverting Band Pass filter circuit
• This type of band pass filter is designed to have a
much narrower pass band.
• The center frequency and bandwidth of the filter is
related to the values of R1, R2, C1 and C2. The
output of the filter is again taken from the output of
the op-amp.

14. Resonance Frequency point and the Q factor

15. Butterworth filter
• An ideal electrical filter should not only completely
reject the unwanted frequencies but should also
have uniform sensitivity for the wanted
frequencies
• The Butterworth filter is a type of signal
processing filter designed to have a frequency
response as flat as possible in the passband. It is
also referred to as a maximally flat magnitude
filter.
• The Butterworth filter rolls off more slowly around
the cutoff frequency than the Chebyshev filter or
the Elliptic filter, but without ripple.

16. Higher order filters and its curves

17. Useful Links
Passive Filters
• LPF https://www.electronics-tutorials.ws/filter/filter_5.html
• HPF https://www.electronics-tutorials.ws/filter/filter_6.html
• BPF https://www.electronics-tutorials.ws/filter/filter_7.html
• Butterworth Filter
Class Notes and Webpage
• http://eedmd.weebly.com/ca2/
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