Signal flow(details), Block diagram(basics), Transfer function(details), State space analysis

(details), Transient Analysis(details), Nyquist(details), Bode plot(basics)

1. The polar plot of a transfer function passes through -1+j0 point. What is the gain margin?

2. If the Laplace transform of a signal y(t) is Y(s) = 1/s(s-1), then obtain its final value.

3. If the system is represented by G(s) H(s) = k (s+7) / s (s +3) (s + 2), what would be its
magnitude at ω = ∞?

4. Considering unit step response of a unity feedback control system whose open loop transfer
function is G(s) = 1/[s(s+1)], find out the maximum overshoot.

5. For a feedback system of type 2, what is the steady state error for a ramp input?

-- Type 2 gives us zero steady-state error for a ramp input.

6. For the system 2/(s+1), find the approximate time taken for a step response to reach 98% of its
final value.

7. A unity feedback system has the open loop transfer function G(s) = 1/[(s-1) (s+2) (s+3)]. How
many times does Nyquist plot of G(s) encircle the origin?
8. For the system in the given figure, find the transfer function C(s)/R(s).

9. Find out overall transfer function of the following signal flow graph.

10. Find the state transition matrix for the following system.
11. Find out the steady state error of a first order system of G(s) = 1/(1+sT) for unit ramp input.
12. Find out the transfer function V2(S)/V1(S) of the circuit shown below.

13. For which values of K and a, the following feedback system oscillates at 2rad/sec?
14. R-L-C circuit shown in figure. For step input (ei), what will be the overshoot in the output (e0)?
15. Determine the transfer function of the given system
16. Justify that impulse function is a first order derivative of step function.
17. Find out ORDER and TYPE of the system with G(s) = (s-2)/[s.(s+1)].
18. What do you mean by the TYPE of a system?

19. What is the steady state error for a feedback system of TYPE 1 due to a step input?

20. What is the steady state error for a feedback system of TYPE 1 due to a ramp input?

21. What do you mean by maximum over shoot (Mp)?

22. What is settling time (ts) of a system?

23. What do you mean by steady state error?

24. Find out the overall transfer function of the following system.

25. Find out the steady state error of a first order system of G(s) = 1/(1+sT) for unit step
input.
26. Find the transfer function of the following signal flow graph.
27. Find out the steady state error of a first order system of G(s) = 1/(1+sT) for unit ramp input.
--same as 11.

28.Transfer function of a system is G(s) = (s+6)/(ks2+s+6) and damping ratio is 0.5. Find out
the value of k.
29. Considering unit step response of a unity feedback control system whose open loop transfer
function is G(s) = 1/[s(s+1)], find out the maximum overshoot.
--same as 4
30. Find out the open-loop dc gain of a unity negative feedback system with closed-loop
transfer function (s+4)/(s2+7s+13).
31. What is the value of K for a unity feedback system with G(s) = K/s(s+1) to have a peak
overshoot of 50% ?
32. Give the transfer function of the following system
 ……………………………………………………………………………………………………………………………………………………………

1. Find rise time, peak time, maximum overshoot and settling time of the unit step response of a
closed loop system given by C(s)/R(s) = 14/ s2+2s+10.
2. For a closed loop system given by C(s)/R(s) = (ks+c)/ (s2+bs+c) , Show the steady state error
in the unit ramp response is given by ess(t)=(b-k)/c.
3. What is the value of k for which the unity feedback system G(s)H(s) = k / s(s+2)(s+3) crosses
the imaginary axis?
4. Deduce the state variable representation of the system, 5.d3 y/dt3 + 10.d2 y/dt2 + 5.dy/dt + 2y =
u(t).
5. For a system with the transfer function Y(s)/U(s) = 2(s-2) / (s3+3s 2 -2s+1) find out the matrix
A in the state space from x(t) = Ax(t) +Bu(t).
6. For the given transfer function Y(s)/U(s) = 1 / (s2+2s+4), obtain state model.
7. Obtain the transfer function Y(s)/U(s) of a system described by the state equations x(t) = -
2.x(t)+2.u(t) and y(t) = 0.4.x(t).
8. Consider the system represented by the equation as 200/ [s3 (s + 2) (s + 5) (s + 7)]. What would
be the total phase value at ω = 0?
9. Check the stability of the system by Nyquist criteria for the transfer function G(s) = 10/ s 2
(1+0.2s)(1+0.4s).
10. Sketch the Nyquist plot for the open loop system G(s)H(s)= 10/s(s+1)(s+2) and determine the
the stability of it.
11. The open loop transfer function G(s)H(S)= k(1+s)/(1-s) . Comment on stability using Nyquist
plot.
12. Draw the Nyquist plot for 20/s(2-s).
13. Prove that for a multi inputs and multi outputs system transfer function is Y(s)/U(s) = C(sI-
A)-1.B + D.
14. Obtain state equations for d2y/dt2+2.dy/dt+3y=du/dt+2u and find out transfer function.
15. For the transfer function Y(s)/U(s) = (s+2) / (s3+2s2+3s+4), obtain the state equations.

16. For the transfer function Y(s)/U(s) = 1 / (s3+2s2+4s+2), obtain the state equations with signal
flow graph.

17. Explain in details how tachogenerator can be used as feedback sensor for a closed loop
control system.
A tachogenerator, also known as a tachometer or simply a "tacho," is a device that converts
rotational speed into an electrical voltage signal. In a closed-loop control system, the
tachogenerator can be employed as a feedback sensor to provide information about the actual speed
of a rotating component, such as a motor shaft. This feedback is crucial for maintaining precision
and stability in the control system. The tachogenerator output is compared to a reference signal
representing the desired speed, and any difference (error) between the two is used to adjust the
system accordingly. The controller interprets this error signal and generates a control output to
regulate the motor speed, thus minimizing the deviation from the desired setpoint. By continuously
monitoring and adjusting the rotational speed in real-time, the closed-loop control system ensures
accurate and responsive control, making the tachogenerator an essential component for
applications where precise speed regulation is paramount, such as in industrial processes, robotics,
or motor control systems.

18. Write the general form of state variable matrix.

19. Distinguish between controllability and observability.

20. What do you mean by the servomechanism?

21. What is Principle of argument?

22. State Nyquist stability criterion.

23. Define phase crossover frequency.

24. What is state transition matrix?

25. What is Gain Margin of a system?

26. What should be the gain margin for a stable system?

27. Which system has tendency to oscillate among open and closed loop system? Explain.

28. Define rise time for the underdamped system.

29. What do you mean by absolute stability and relative stability?

30. What is synchros?

31. Distinguish between state space analysis and transfer function technique.

….……………………………………………………………………………………………..

Define phase modulation, frequency modulation, amplitude modulation, noise.

What are the advantages of analog and digital communications?

Define percentage modulation.

=> It is defined as the percentage change in the amplitude of the output wave when the carrier is
acted on by a modulating signal.

Give the mathematical expression of phase modulation.

Give the bandwidth of AM.

Give the bandwidth of FM.

Define random process.

Give the Laws of probability.

Define a random variable.

What is Gaussian process?

Find the thermal noise voltage developed across a resistor of 700ohm. The
bandwidth of measuring instrument is 7MHz and the ambient temperature is
270C.
Discuss different techniques used for improving coverage and capacity in cellular systems.

Ans:

Improving coverage and capacity is crucial for enhancing the performance of cellular systems,
especially with the increasing demand for high-speed data services and the proliferation of
connected devices. Various techniques are employed to address these challenges. Here are some
key strategies:

1. Cell Splitting:

- Definition: Dividing a congested cell into smaller cells.

- Advantages: Increases capacity by reducing the number of users per cell and improving frequency
reuse.

- Considerations: Requires additional infrastructure and careful planning to avoid interference.

2. Frequency Reuse:
 - Definition: Efficient allocation of frequency bands to cells in a way that minimizes interference.

- Advantages: Maximizes spectral efficiency and capacity by reusing frequencies across cells.

- Considerations: Requires careful planning to avoid co-channel interference.

3. Microcell and Picocell Deployments:

- Definition: Introducing smaller cells within a macrocell to increase capacity in specific areas.

- Advantages: Enhances coverage and capacity in high-density areas.

- Considerations: Requires additional infrastructure and coordination to avoid interference.

4. Sectorization:

- Definition: Dividing a cell into sectors, each served by a separate antenna.

- Advantages: Improves spatial reuse and capacity by allowing simultaneous transmissions in different
directions.

- Considerations: Requires careful planning to avoid interference between sectors.

5. MIMO (Multiple Input Multiple Output):

- Definition: Using multiple antennas at both the transmitter and receiver to improve spectral efficiency
and capacity.

- Advantages: Increases data rates and improves link reliability by exploiting spatial diversity.

- Considerations: Requires compatible devices and careful design to optimize performance.

6. Carrier Aggregation:

- Definition: Combining multiple frequency bands to increase the overall data rate.

- Advantages: Enhances capacity and data rates by aggregating spectrum from different frequency
bands.
 - Considerations: Requires compatible devices and careful spectrum management.

7. Interference Management:

- Definition: Techniques to mitigate interference between cells and frequency bands.

- Advantages: Improves overall network performance and capacity.

- Considerations: Adaptive resource allocation and advanced algorithms are needed.

8. HetNets (Heterogeneous Networks):

- Definition: Combining different cell sizes and types (macrocells, microcells, picocells) in a network.

- Advantages: Optimizes coverage and capacity in various environments.

- Considerations: Requires efficient handover mechanisms and interference management.

9. Densification:

- Definition: Increasing the number of base stations to improve spatial reuse.

- Advantages: Enhances capacity and coverage in high-demand areas.

- Considerations: Requires additional infrastructure and careful planning to avoid interference.

10. Cloud RAN (Radio Access Network):

- Definition: Centralizing some processing functions in a cloud-based architecture.

- Advantages: Improves resource utilization and allows for centralized optimization.

- Considerations: Requires a robust and low-latency backhaul network.

Implementing these techniques often involves a combination of strategies, and their effectiveness depends
on factors such as the specific network architecture, frequency spectrum availability, and the density of
users in each area. Ongoing advancements in technology, such as 5G and beyond, continue to introduce
new tools and techniques for further improving coverage and capacity in cellular systems.

Derive expression for the AM wave.

With the help of neat diagram explain AM Envelop and equation of AM wave.
Explain and derive the expression of Amplitude Modulation power distribution.

With the help of neat diagram explain VSB signal.

Describe the frequency analysis of angle modulated waves.

Ans:

Frequency analysis of angle modulated waves (AMW) involves examining the

distribution of energy across different frequencies in the modulated signal. This analysis
is crucial for understanding the characteristics of AMW and designing effective
communication systems.
Frequency Spectrum of AMW
The frequency spectrum of an AMW is characterized by a central carrier frequency (fc)
flanked by a pair of sidebands. These sidebands, also known as modulation sidebands,
carry the information about the modulating signal. The bandwidth of the AMW is
determined by the maximum frequency deviation (∆f) and is given by:
BW = 2∆f
Types of AMW
There are two primary types of AMW:
1. Frequency Modulation (FM): In FM, the instantaneous frequency of the carrier
varies proportionally to the modulating signal. The bandwidth of an FM signal is
directly proportional to the maximum frequency deviation and the modulating
signal's bandwidth.
2. Phase Modulation (PM): In PM, the instantaneous phase of the carrier varies
proportionally to the modulating signal. The bandwidth of a PM signal is typically
narrower than that of an FM signal for the same modulation index.
Frequency Analysis Techniques
Various techniques are employed to analyze the frequency spectrum of AMW:
1. Fourier Transform: The Fourier transform decomposes a signal into its
constituent frequency components, providing a detailed representation of the
energy distribution across frequencies.
2. Spectrum Analyzer: A spectrum analyzer directly measures the power spectrum
of a signal, displaying the energy levels at different frequencies.
3. Phase-Locked Loop (PLL): A PLL tracks the instantaneous frequency of a signal,
allowing for precise measurements of frequency deviations.
Applications of Frequency Analysis
Frequency analysis of AMW is essential for:
1. Channel Allocation: Assigning frequency bands for different communication
channels to avoid interference.
2. Receiver Design: Designing receivers capable of demodulating AMW signals and
extracting the modulating information.
3. Error Correction: Identifying and correcting errors introduced during transmission
due to noise or interference.
4. Signal Processing: Developing signal processing algorithms for enhancing the
quality and efficiency of AMW communication.

What do you mean by Nyquist rate?

Explain sampling theorem.

Explain time division multiplexing.

What is ISI? Explain Nyquist’s frist criteria for zero ISI.

Write the advantages of digital communication over analog communication.

Show that the entropy is maximum when all messages are equiprobable.
Describe the procedure of encoding and decoding of linear block codes.
Derive the expression for signal to quantization noise ratio in a PCM system.

A unity feedback system has the open loop transfer function G(s) = 1/[(s-1) (s+2) (s+3)]. How
many times does Nyquist plot of G(s) encircle the origin?

Transfer function of a system is G(s) = (s+6)/(ks 2+s+6) and damping ratio is 0.5. Find out the value of k.

--Already done.

34. Give the expression of steady state error in frequency domain for a feedback system
35. Find out the phase margin of a system with open loop transfer function G(s)H(s) = (1-s) / (1+s)(2+s)

36. The open loop transfer function is given as G(s) = K.s 2 / [(1+0.02s) (1+0.03s)]. what would be the initial
slope for magnitude plot?

37. Sketch the root locus of a feedback system whose open loop transfer function is as

G(s)H(s) = k / s(s+2)(s+3)

38. Write a short note on differentially coherent FSK detection.