(SEM VII) THEORY EXAMINATION 2022-23 FILTER DESIGN

SECTION A – Short Answers (2 Marks Each)

(a) Why do we use Analog Filters?

Analog filters are used to remove unwanted frequency components from signals and to allow only desired frequency bands for processing.

(b) Applications of Op-amp

Op-amps are used in amplifiers, integrators, differentiators, filters, oscillators, and voltage regulators.

(c) Passive elements

Passive elements are components that do not generate energy, such as resistors, capacitors, and inductors.

(d) Frequency response

Frequency response describes how the magnitude and phase of a system output vary with frequency.

(e) Use of band-pass filters

Band-pass filters allow signals within a certain frequency range and reject frequencies outside that range.

(f) Applications of integrators

Integrators are used in ramp generators, analog computers, waveform shaping, and signal processing.

(g) Difference between first and second order filters

First order filters have one energy storage element and a roll-off of 20 dB/decade, while second order filters have two storage elements and a roll-off of 40 dB/decade.

(h) Low-pass filter

A low-pass filter allows frequencies below a specified cutoff frequency and attenuates higher frequencies.

(i) Chebyshev polynomial

Chebyshev polynomials are mathematical functions used in filter design to achieve sharper cutoff with ripple in passband or stopband.

(j) Chebyshev coefficient

Chebyshev coefficients are calculated using Chebyshev polynomial equations based on filter order and ripple factor.

SECTION B – Long Answers (10 Marks Each)

(a) Non-inverting operational amplifier

In a non-inverting amplifier, input is applied to the non-inverting terminal. The output is in phase with input and gain is given by
Av = 1 + (Rf / Rin).
Applications include voltage followers, signal conditioning, and audio amplifiers.

(b) Frequency transformation in filter design

Frequency transformation converts a normalized low-pass filter into high-pass, band-pass, or band-stop filters by substituting frequency variables. A band-pass filter is obtained by replacing s with (s² + ω₀²) / Bs.

(c) Butterworth low-pass filter

Butterworth filter has maximally flat magnitude response in passband. Filter order is calculated using attenuation and cutoff frequency specifications.

(d) Filters with arbitrary transmission zeros

These filters allow placement of transmission zeros at desired frequencies. Poles of Butterworth filters lie on a circle in the left half of the s-plane.

(e) Elliptic (Cauer) filter

Elliptic filters have ripple in both passband and stopband and provide sharpest transition. They are used where high selectivity is required.

SECTION C – Long Answers (10 Marks Each)

(3a) Filter and its importance

A filter is a circuit that selects desired frequencies and rejects unwanted ones. Ideal filters have sharp cutoffs, while practical filters show gradual roll-off due to physical limitations.

(3b) Operational amplifier

An op-amp is a high-gain differential amplifier. Op-amp resistor circuits include summing amplifiers, difference amplifiers, integrators, and differentiators.

(4a) Conversion of LPF to band-stop filter

A band-stop filter is obtained using frequency transformation by replacing s with Bs / (s² + ω₀²) in the LPF transfer function.

(4b) Bandwidth of non-inverting amplifier

For IC-741, bandwidth is calculated using Gain-Bandwidth Product (GBP).
Bandwidth = GBP / Gain.

(5a) Second order filter responses

Second order filters include low-pass, high-pass, band-pass, and band-stop. Their pole locations determine response characteristics.

(5b) Biquad filters

Biquad filters are second-order active filters implemented using op-amps. Frequency response is calculated using transfer function parameters.

(6a) Frequency warping

Frequency warping occurs in bilinear transformation due to nonlinear frequency mapping. Pre-warping compensates for this effect.

(6b) Features of Butterworth filters

Butterworth filters have flat passband, smooth response, and poles equally spaced on a circle. Cascade design improves stability.

(7a) Inverse Chebyshev filter

Inverse Chebyshev filters have ripple in stopband and flat passband. They provide sharper cutoff than Butterworth filters.

(7b) Elliptical response characteristics

Elliptic filters show ripple in both passband and stopband and provide steepest transition compared to Chebyshev and inverse Chebyshev filters.