Darshan Institute of Engineering & Technology - Rajkot Department of Electrical Engineering ANALOG ELECTRONICS (2130902) Topic: Active Filters Enrollment no. : 130540109087

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

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

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

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

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.

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

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.

Low-Pass and High-Pass Designs

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

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

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.

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