The document defines different types of filters and provides details about their frequency responses. It discusses low-pass, high-pass, band-pass, and band-reject (notch) filters. Specific details are given about the frequency cutoffs, gains, and roll-offs of first and second order low-pass, high-pass, and band-pass filters. Band-reject filters are described as passing most frequencies while attenuating those in a specific range.

1. Prepared by: Nasir Ihsan
Engineering Student 2012-16
Contact No.: 03030743662
MUZAFFARGARH,PUNJAB PAKISTAN

2. DEFINATION
A Filter is an electrical circuit that is designed to pass a
specified band of frequencies while attenuating all the
signals outside that band.
It is a frequency selective circuit.
The filters are basically classified as active filters & passive
filters.
They are used in circuits which require the separation of
signals according to their frequencies.
They are widely use in communication & signal Processing.

3. TYPES OF FILTERS
There are following types of Filters:
• Low-pass(LP)
• High-pass(HP)
• Band-pass(BP)
• Band-reject(BR)

4. 1- LOW PASS FITER
• A low-pass (LP) filter is a filter that passes low-
frequency signals but attenuates (reduces the
amplitude of) signals with frequencies higher
than the cutoff frequency.
• A low-pass (LP) filter is the opposite of a high-
pass (HP) filter.

5. FREQUENCY RESPONSE OF LOW PASS FILTER
IDEAL & PRACTICAL RESPONSE
• A Low Pass Filter has a constant gain from 0 Hz to a high cut-
off frequency, fh.
• Practically, the gain decreases as the frequency increases & at
f= fh, the gain is down by 3 db & after fh; it decreases at a
higher rate.
• After the end of a transition band,
• the gain becomes zero.

6. First Order LP Filter
• A first order filter consists of a single RC n/w connected to I / p terminal of
a non-inverting op-amp.
• Resistors Ri & Rf determine the gain of the filter in the pass band.

7. The voltage across the capacitor
in the s-domain is:-
The closed loop gain of the
op-amp is:-
Let wh= 1/RC
To determine the
frequency response, put
s=jw in above eq.

8. At very low frequency,
i.e. f<<fh
And At very High
frequency i.e. f>>fh, we
have
It has the max. gain at f=0 Hz. At fh the gain falls to .
707 time the max. gain.
Hence gain rolls off at the rate of 20 dB/decade.

9. 2- A HIGH PASS FILTER
• A high-pass (HP) filter offers easy passage to
high-frequency signal and attenuates the low-
frequency signal.

10. A PASSIVE HIGH PASS FILTER:

11. Frequency response of 1st
order HP Filter
• The cutoff frequency for a high-pass filter is that frequency at which the
output voltage equals 70.7% of the input voltage. Above the cutoff
frequency, the output voltage is greater than 70.7% of the input, and vice
versa.

12. 2ND
ORDER HP FILTER
High pass filter is the complement of the low pass filter & can be
obtained simply by interchanging R & C in the low pass
configuration as shown in the fig.
This is the transfer
function:

13. 3- BAND PASS FILTER
• The Band-Pass (BP) filter passes a selected range or band of frequencies
that can be either narrow or wide while attenuating all those outside of
this range.

14. TYPES OF BP FILTER
• Broad-band Band-Pass filter
• Narrow-band Band-Pass filter

15. Frequency Response of a 2nd
order Band-Pass
(BP) FILTER:
• The term "bandwidth" refers to the difference between the lower cut-off
frequency (ƒcLOWER) and the upper cut-off frequency (ƒcUPPER) points.
• A band-pass (BP) filter arrangement commonly consists of a combination
of a Low-pass (LP) and a High-pass (HP) filter.
BW = f2
– f1
Q = f0
/ BW

16. • The "Q" of a BP filter is the ratio of the Resonant Frequency, (ƒr) to the
Bandwidth (BW) and is given as:
• In BP Filter, the width of the pass-band between the upper and lower-3dB
corner points determine the Quality Factor (Q-point) of the circuit. This Q
Factor is a measure of how "Selective" or "Un-selective" the band pass
filter is towards a given spread of frequencies.
• The lower the value of the Q factor the wider is the bandwidth of the filter
and consequently the higher the Q factors the narrower and more
"selective" is the filter.

17. 4- BAND REJECT FILTER
V i n
R 1
R 1
C 1
C 2
R 2
R i
R fb
V O
+
_
+
_
-3dB{
f
f2
f1
Av(dB)
low-pass high-pass
This can also be either as a Narrow or wide band reject filter.
The narrow band reject filter is commonly called a notch filter &
is useful for the rejection of a single frequency, such as 50 Hz
power line frequency hum.

18. BAND STOP FILTER
• A band-stop filter or band-rejection filter passes most frequencies
unaltered, but attenuates those in a specific range to very low
levels. It is the opposite of a band-pass filter.
• A notch filter is a band-stop filter with a very narrow stop band
(high Q factor).Notch filters are used in live sound reproduction (
Public Address systems, also known as PA systems) and in
instrument amplifier (especially amplifiers or preamplifiers for
acoustic instruments such as acoustic guitar, mandolin etc.) to
reduce the noise and unwanted frequencies.
• e.g., Anti-hum filter is used to filter out the mains hum from a 50
Hz power line, though its higher harmonics could still be present.
The filter passes all frequencies, except for the range of 49–51 Hz.

19. Frequency response of BS filters: