(SEM VII) THEORY EXAMINATION 2024-25 FILTER DESIGN

SECTION A

(2 × 10 = 20 marks | Short Answers)

a) Analog Filter

An analog filter is an electronic circuit that processes continuous-time signals to allow certain frequency components to pass while attenuating others.

b) Circuit simulation vs circuit modeling

Circuit modeling: Mathematical representation of a circuit using equations

Circuit simulation: Computer-based analysis of circuit behavior using models (e.g., SPICE)

c) Bilinear transfer function

A bilinear transfer function is obtained using bilinear transformation, which maps the s-plane to the z-plane while preserving stability.

d) Bode plot

A Bode plot is a graphical representation of frequency response, showing:

Magnitude (in dB) vs frequency

Phase vs frequency

e) Design parameters for a second-order low-pass filter

Cutoff frequency (ωc)                                        Quality factor (Q)

Gain (K)                                                              Damping ratio (ζ)

f) Function of integrators in second-order filters

Integrators provide frequency-dependent gain and help realize the second-order differential equation required for filter operation.

g) Butterworth pole location (2nd order)

Butterworth poles are equally spaced on a circle in the left half of the s-plane, ensuring a maximally flat response.

h) Chebyshev polynomial

Chebyshev polynomials define equal-ripple behavior in the passband and are used in Chebyshev filter design.

i) Voltage feed-forward

Voltage feed-forward is a technique where input signal is directly fed to later stages to improve stability and frequency response.

j) Cauer filters

Cauer (Elliptic) filters provide ripple in both passband and stopband, offering the sharpest transition band.

SECTION B

(Attempt any 3 | 10 marks each)

a) Voltage follower using feedback

A voltage follower uses 100% negative feedback where output is directly connected to the inverting terminal.
It provides:                                                    Unity gain

High input impedance                                  Low output impedance

b) First-order active filter using op-amp

A first-order active filter consists of:             Op-amp

One resistor                                                   One capacitor

Depending on configuration, it can act as low-pass or high-pass with gain.

c) Design of second-order low-pass filter

Steps:

Select cutoff frequency                                 Choose filter type (Butterworth, Chebyshev)

Determine Q and gain                                   Calculate R and C values

Implement using op-amp

d) Cascade design for Butterworth filter

Higher-order Butterworth filters are designed by cascading second-order sections.
Steps:                                                             Determine order

Find pole locations                                        Group into 2nd-order stages

Implement stage-wise

e) Inverse Chebyshev filter                         Ripple in stopband

Flat passband

Sharper roll-off than Butterworth                  Used where high stopband attenuation is required.

SECTION C

Q3 (Attempt any one)

a) Effect of scaling & terminology

Scaling: Adjusts resistance and capacitance values without changing frequency response

Descriptive terminology: Based on response shape

Functional terminology: Based on signal behavior

Scaling improves practical realizability.

b) Resistive feedback in op-amps

Resistive feedback:                                           Improves stability

Controls gain                                                   Reduces distortion

Block diagram:
Input → Amplifier → Feedback network → Output

Q4 (Attempt any one)

a) Non-inverting op-amp                              In a non-inverting amplifier:

Input is applied to + terminal                          Gain > 1

High input impedance

Applications: Signal conditioning, voltage amplification, filters.

b) LPF to band-stop filter (frequency transformation)

Using frequency transformation:                     Replace s with suitable function

Shift cutoff frequency                                      Introduce zeros in passband

This converts LPF response into band-stop behavior.

Q5 (Attempt any one)

a) Effect of increasing Q in band-pass filter

As Q increases:                                                 Bandwidth decreases

Selectivity increases                                         Peak gain increases

High Q gives narrow, sharp frequency response.

b) Poles and zeros in notch filter

Zeros placed at notch frequency                     Poles placed near zeros
This results in deep attenuation at specific frequency.

Q6 (Attempt any one)

a) Frequency warping in bilinear transformation

Bilinear transformation causes non-linear frequency mapping, known as frequency warping.
Pre-warping is used to correct this effect.

b) Arbitrary transmission zeros

Transmission zeros are added intentionally to:     Improve stopband attenuation

Suppress unwanted frequencies                           Shape frequency response

Q7 (Attempt any one)

a) Butterworth vs Chebyshev (Audio application)

Butterworth is preferred for high-quality audio.

b) Cauer filter design process                 Cauer filter design balances:

Passband ripple                                          Stopband attenuation

Pole-zero placement

Interaction of these gives sharpest cutoff with minimum order.

SEM VII – ALL SUBJECTS COMPLETED (SECTION-WISE)

You now have complete exam-ready answers for:            HVAC Systems

Mathematical Modeling of Manufacturing Processes          Machine Learning

Maintenance Engineering & Management                           Power Plant Engineering