(SEM VII) THEORY EXAMINATION 2023-24 FILTER DESIGN

KOE071 – FILTER DESIGN

B.Tech (SEM VII) – Theory Examination
Time: 3 Hours | Max Marks: 100

SECTION A

(Attempt all questions in brief – 2 × 10 = 20 marks)

a. Draw a voltage follower circuit.

A voltage follower is an op-amp configuration where the output is directly connected to the inverting terminal and the input is applied to the non-inverting terminal. It provides unity gain and high input impedance.

b. Define CMRR.

CMRR (Common Mode Rejection Ratio) is the ratio of differential gain to common-mode gain of an op-amp. It indicates the ability of the amplifier to reject common-mode signals.

c. Explain the concept of passband and stopband in filter specifications.

The passband is the frequency range that a filter allows with minimal attenuation, while the stopband is the frequency range that the filter significantly attenuates or rejects.

d. Explain zeros and poles.

Zeros are frequencies where the transfer function becomes zero, reducing output.
Poles are frequencies where the transfer function becomes infinite, influencing stability and frequency response.

e. Give few applications of Integrators.

Applications include:                                                   Analog computers

Signal processing                                                        Ramp generators

Wave shaping circuits

f. Discuss the advantages and disadvantages of FIR filters.

Advantages: Linear phase, stable, simple design
Disadvantages: Higher order required, more computation

g. Define the term “selectivity”.

Selectivity is the ability of a filter to discriminate between desired and undesired frequencies, allowing only a narrow band of frequencies to pass.

h. Discuss the role of feedback in filter design.

Feedback controls gain, improves stability, determines bandwidth, and shapes the frequency response of active filters.

i. Discuss the significance of the Q-factor in filter design.

Q-factor indicates sharpness of resonance. Higher Q means narrower bandwidth and better selectivity.

j. What is the role of ripple in the design of a Chebyshev filter?

Ripple allows faster roll-off in Chebyshev filters by permitting controlled variations in passband magnitude.

SECTION B

(Attempt any three – solved answers provided for ALL)

2(a). What is a filter and its types? Explain ideal and practical filter response.

A filter is a circuit that allows certain frequency components and attenuates others.

Types of filters:                                                   Low-pass

High-pass                                                             Band-pass

Band-stop

Ideal filter:
Sharp cut-off, no attenuation in passband, infinite attenuation in stopband (not physically realizable).

Practical filter:
Gradual transition band, finite attenuation, realizable using active or passive components.

2(b). Explain frequency response of a Bilinear transfer function with advantages and limitations.

Bilinear transfer functions map the s-plane to the z-plane without aliasing. Frequency response is nonlinear but stable.

Advantages:

No aliasing                                                        Stable mapping

Limitations:

Frequency warping                                           Requires pre-warping

2(c). Frequency response of second-order low-pass and band-pass circuits with applications.

Second-order low-pass filter:
Flat response in passband, roll-off of −40 dB/decade.

Second-order band-pass filter:
Passes a narrow frequency band around center frequency.

Applications:
Audio systems, communication receivers, instrumentation.

2(d). Butterworth response vs other low-pass filter responses.

Butterworth filters provide maximally flat magnitude in passband.

2(e). Characteristics of Elliptic response and comparison.

Elliptic filters have ripple in both passband and stopband and the sharpest transition.

Compared to Chebyshev and inverse Chebyshev:                Faster roll-off

More complex design                                                            Lower filter order required

SECTION C

3(a). Inverting and Non-inverting Op-Amp configurations with applications.

Inverting amplifier:                                                             Gain = −Rf/Rin
Applications: Signal conditioning, summing amplifier

Non-inverting amplifier:                                                     Gain = 1 + Rf/Rin
Applications: Voltage amplification, buffers

3(b). Short notes

(i) Circuit elements and scaling
Scaling adjusts component values to practical ranges without changing frequency response.

(ii) Circuit simulation and modelling
Simulation tools (SPICE, MATLAB) help analyze frequency response and stability before hardware implementation.

4(a). Effect of amplifier function A(s) on first-order filter performance.

A(s) determines gain accuracy, bandwidth, phase shift, and stability. Finite gain reduces cutoff sharpness and shifts frequency response.

4(b). Construction and interpretation of Bode plots for first-order filters.

Bode plots represent magnitude (dB) and phase versus frequency.

Key features:

−20 dB/decade slope                                                          −45° phase shift at cutoff frequency

5(a). Biquad filters and frequency response calculation.

Biquad filters are second-order filters implemented using op-amps.

Transfer function:

H(s)=as2+bs+cs2+ds+eH(s) = \frac{as^2 + bs + c}{s^2 + ds + e}H(s)=s2+ds+eas2+bs+c​

Frequency response is obtained by substituting s=jωs = j\omegas=jω.

5(b). Design and parameters of second-order low-pass and band-pass filters.

Design parameters:                                                             Cutoff frequency

Q-factor                                                                                 Gain

Low-pass attenuates high frequencies, band-pass allows a narrow band.

6(a). Arbitrary transmission zeros: advantages, disadvantages, pole effects.

Advantages: Improved selectivity, sharper attenuation
Disadvantages: Increased complexity, sensitivity

Pole location affects stability, bandwidth, and roll-off.

6(b). Summing vs voltage feed-forward approach in second-order filter design.

Trade-off involves complexity vs precision.

7(a). Chebyshev filter design and comparison.

Chebyshev filters use Chebyshev polynomials.

Comparison:

Maximally flat (Butterworth): smooth response             Equal ripple (Chebyshev): sharper cutoff

7(b). Short notes

(i) Chebyshev polynomial
Defined as Tn(x)=cos⁡(ncos⁡−1x)T_n(x) = \cos(n\cos^{-1}x)Tn​(x)=cos(ncos−1x), used in filter design.

(ii) Location of Chebyshev poles
Poles lie on an ellipse in the s-plane, determining ripple and cutoff.