1. Darshan Institute of Engineering & Technology - Rajkot
Department of Electrical Engineering
ANALOG ELECTRONICS ( )
Topic: Active Filters
Enrollment no. :

2. Filters
A filter is a system that processes a signal in some desired fashion.
A continuous-time signal or continuous signal of x(t) is a function of the continuous variable t. A continuous-time signal is often called an analog signal.
A discrete-time signal or discrete signal x(kT) is defined only at discrete instances t=kT, where k is an integer and T is the uniform spacing or period between samples

3. Types of Filters There are two broad categories of filters:
An analog filter processes continuous-time signals
A digital filter processes discrete-time signals.
The analog or digital filters can be subdivided into four categories:
Lowpass Filters
Highpass Filters
Bandstop Filters
Bandpass Filters

4. Analog Filter Responses
H(f)
H(f) f f fc fc
Ideal “brick wall” filter
Practical filter

5. Ideal Filters Lowpass Filter Highpass Filter Bandstop Filter
M(w)
Stopband
Passband
Passband
Stopband w c w w c w
Bandstop Filter
Bandpass Filter
M(w)
Passband
Stopband
Passband
Stopband
Passband
Stopband w c 1 w c 2 w w c 1 w c 2 w

6. Active filters overcome these drawbacks and are realized using resistors, capacitors, and active devices (usually op-amps) which can all be integrated:
Active filters replace inductors using op-amp based equivalent circuits.

7. Op Amp Advantages Advantages of active RC filters include:
reduced size and weight, and therefore parasitics
increased reliability and improved performance
simpler design than for passive filters and can realize a wider range of functions as well as providing voltage gain
in large quantities, the cost of an IC is less than its passive counterpart

8. Op Amp Disadvantages Active RC filters also have some disadvantages:
limited bandwidth of active devices limits the highest attainable pole frequency and therefore applications above 100 kHz (passive RLCfilters can be used up to 500 MHz)
the achievable quality factor is also limited
require power supplies (unlike passive filters)
increased sensitivity to variations in circuit parameters caused by environmental changes compared to passive filters
For many applications, particularly in voice and data communications, the economic and performance advantages of active RC filters far outweigh their disadvantages.

9. Low-Pass and High-Pass Designs

11. Note that the two asymptotes intersect at fb where
|Av(fb )|dB = -20log f/ fb
Low frequency asymptote
3 dB
Actual response curve
High frequency asymptote

12. Real Filters The approximations to the ideal filter are the:
Butterworth filter
Chebyshev filter
Cauer (Elliptic) filter
Bessel filter

13. Standard Transfer Functions
Butterworth
Flat Pass-band.
20n dB per decade roll-off.
Chebyshev
Pass-band ripple.
Sharper cut-off than Butterworth.
Elliptic
Pass-band and stop-band ripple.
Even sharper cut-off.
Bessel
Linear phase response – i.e. no signal distortion in pass-band.

15. Thank You