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Questions and Answers
Define the standard form of amplitude modulation and derive its equation. Explain each term.
Define the standard form of amplitude modulation and derive its equation. Explain each term.
The standard form of amplitude modulation is given by the equation: $s(t) = A_c [1 + m(t)] imes ext{cos}(2 ext{π}f_ct)$, where $A_c$ is the carrier amplitude, $m(t)$ is the message signal, and $f_c$ is the carrier frequency. The term $A_c$ represents the carrier amplitude, $m(t)$ represents the message signal, and $f_c$ represents the carrier frequency.
Explain the generation of DSBSC waves using a Ring Modulator.
Explain the generation of DSBSC waves using a Ring Modulator.
DSBSC waves are generated using a Ring Modulator by multiplying the message signal by the carrier signal, resulting in the suppression of the carrier and generation of double sidebands.
What will be the frequency content of the AM signal when a 1000 KHz carrier is simultaneously modulated to 300 Hz, 800Hz, and 2KHz audio Sinewaves?
What will be the frequency content of the AM signal when a 1000 KHz carrier is simultaneously modulated to 300 Hz, 800Hz, and 2KHz audio Sinewaves?
The frequency content of the AM signal will include the carrier frequency at 1000 KHz, the upper sideband frequencies at 1000.3 KHz, 1000.8 KHz, and 1002 KHz, and the lower sideband frequencies at 999.7 KHz, 999.2 KHz, and 998 KHz.
Explain the scheme of generation and demodulation of VSB modulated wave with relevant spectrum of signals and mathematical expressions.
Explain the scheme of generation and demodulation of VSB modulated wave with relevant spectrum of signals and mathematical expressions.
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Calculate the sidebands of DSBSC modulated waves appearing at the two product modulator outputs in a two-stage product modulator with given input signal and local oscillator frequencies.
Calculate the sidebands of DSBSC modulated waves appearing at the two product modulator outputs in a two-stage product modulator with given input signal and local oscillator frequencies.
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Explain the working of a FDM transmitter and receiver with a neat block diagram.
Explain the working of a FDM transmitter and receiver with a neat block diagram.
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Find the carrier, modulating frequency, modulation index, and maximum frequency deviation of the given FM wave represented by the voltage equation.
Find the carrier, modulating frequency, modulation index, and maximum frequency deviation of the given FM wave represented by the voltage equation.
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Derive the expression for WBFM and show that the spectrum of WBFM wave contains an infinite number of sidebands.
Derive the expression for WBFM and show that the spectrum of WBFM wave contains an infinite number of sidebands.
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Determine the bandwidth of an FM signal with a fixed maximum frequency deviation and modulation frequency using Carson’s rule and the universal curve.
Determine the bandwidth of an FM signal with a fixed maximum frequency deviation and modulation frequency using Carson’s rule and the universal curve.
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Explain the direct method generation of FM using Hartley Oscillator with relevant equations and diagram.
Explain the direct method generation of FM using Hartley Oscillator with relevant equations and diagram.
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Write the basic block diagram of PLL and derive the expression for the nonlinear model of PLL.
Write the basic block diagram of PLL and derive the expression for the nonlinear model of PLL.
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Derive the expression for the Figure of Merit of a frequency modulated receiver.
Derive the expression for the Figure of Merit of a frequency modulated receiver.
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Define noise and explain Noise Equivalent Bandwidth with relevant equations.
Define noise and explain Noise Equivalent Bandwidth with relevant equations.
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Using the expression for the figure of merit of AM, find the FOM of single tone AM.
Using the expression for the figure of merit of AM, find the FOM of single tone AM.
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Explain the generation and detection of PPM waves with neat block diagrams.
Explain the generation and detection of PPM waves with neat block diagrams.
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Explain the generation and recovery of PAM (Flat-top) signal with necessary equations and spectrum diagram.
Explain the generation and recovery of PAM (Flat-top) signal with necessary equations and spectrum diagram.
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Describe the effect of Noise on a Pulse position modulation System.
Describe the effect of Noise on a Pulse position modulation System.
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State the Sampling theorem and explain the necessity of Digitizing of analog signals.
State the Sampling theorem and explain the necessity of Digitizing of analog signals.
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Explain the effect of Noise on a Pulse position modulation System.
Explain the effect of Noise on a Pulse position modulation System.
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Derive the expression for the output Signal to Noise Ratio of a Quantizer.
Derive the expression for the output Signal to Noise Ratio of a Quantizer.
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Explain the basic elements of a PCM system with a neat diagram.
Explain the basic elements of a PCM system with a neat diagram.
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Calculate the Nyquist rate, number of bits required to encode a sample, and the quantization step for a given PCM system scenario.
Calculate the Nyquist rate, number of bits required to encode a sample, and the quantization step for a given PCM system scenario.
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Study Notes
Amplitude Modulation (AM)
- Standard form of AM:
v(t) = (1 + μ * cos(2πft)) * A_carrier * cos(2πf_carrier * t)
- Where
μ
is modulation index,A_carrier
is amplitude of carrier wave,f
is frequency of modulating signal, andf_carrier
is frequency of carrier wave - Each term in the equation represents:
-
1
: unmodulated carrier wave -
μ * cos(2πft)
: modulation term, which varies the amplitude of the carrier wave -
A_carrier * cos(2πf_carrier * t)
: original carrier wave
-
DSBSC (Double Sideband Suppressed Carrier) Modulation
- Generation using a Ring Modulator:
- Multiply the carrier wave with the modulating signal using a ring modulator
- Produces a DSBSC wave with no carrier component
- Frequency content of AM signal:
- When a 1000 KHz carrier is modulated with 300 Hz, 800 Hz, and 2 KHz audio sinewaves, the frequency content of the AM signal will be:
- Lower sidebands: 998.7 KHz, 999.2 KHz, 998 KHz
- Upper sidebands: 1001.3 KHz, 1000.8 KHz, 1002 KHz
- When a 1000 KHz carrier is modulated with 300 Hz, 800 Hz, and 2 KHz audio sinewaves, the frequency content of the AM signal will be:
VSB (Vestigial Sideband) Modulation
- Scheme of generation and demodulation:
- Generation: filter out one of the sidebands of a DSBSC wave using a filter
- Demodulation: reverse process of generation, using a sync pulse to re-modulate the VSB wave
- Mathematical expressions:
-
v(t) = A_carrier * cos(2πf_carrier * t) + A_sb * cos(2π(f_carrier - f_sb) * t)
-
v(t) = A_carrier * cos(2πf_carrier * t) - A_sb * cos(2π(f_carrier + f_sb) * t)
-
Two-Stage Product Modulator
- Calculation of sidebands:
- Given input signal and local oscillator frequencies, calculate the sidebands at each product modulator output
-
f_sb1 = f_carrier - f_in
,f_sb2 = f_carrier + f_in
FDM (Frequency Division Multiplexing)
- Block diagram of FDM transmitter and receiver:
- Transmitter: multiple modulating signals multiplexed and transmitted over a single channel
- Receiver: demodulates and separates the original modulating signals
FM (Frequency Modulation)
- Equation of FM wave:
v(t) = A_carrier * cos(2πf_carrier * t + β * sin(2πf_mod * t))
- Carrier, modulating frequency, modulation index, and maximum frequency deviation:
- Can be calculated from the given voltage equation
- WBFM (Wideband Frequency Modulation):
- Expression:
v(t) = A_carrier * cos(2πf_carrier * t + β * sin(2πf_mod * t) + ... + β^n * sin(2πnf_mod * t))
- Spectrum of WBFM wave contains an infinite number of sidebands
- Expression:
- Bandwidth of FM signal:
- Calculated using Carson's rule and the universal curve
Direct Method of FM Generation
- Hartley Oscillator:
- Generates an FM wave using a voltage-controlled oscillator
- Relevant equations and diagram:
PLL (Phase-Locked Loop)
- Basic block diagram:
- Consists of a phase detector, low-pass filter, and voltage-controlled oscillator
- Expression for the nonlinear model of PLL:
-
dφ/dt = Δω - K_p * sin(φ)
-
Figure of Merit (FOM)
- Expression for FOM of FM receiver:
-
FOM = Δf / (S/N)
-
- Expression for FOM of AM receiver:
-
FOM = μ / (S/N)
-
Noise and Noise Equivalent Bandwidth
- Definition of noise:
- Random fluctuations in the signal
- Noise Equivalent Bandwidth:
- The bandwidth of an ideal filter that would pass the same noise power as the actual filter
-
NBW = ∫[|H(f)|^2 df]
PPM (Pulse Position Modulation)
- Generation and detection:
- Uses a pulse generator and a delaying circuit to modulate the pulse position
- Demodulated using a synchronizer and a low-pass filter
- Block diagram and equations:
PAM (Pulse Amplitude Modulation)
- Generation and recovery:
- Uses a pulse generator and an amplitude modulator to modulate the pulse amplitude
- Demodulated using a synchronizer and a low-pass filter
- Block diagram and equations:
Quantization and PCM (Pulse Code Modulation)
- Sampling theorem:
-
f_sampling >= 2 * f_max
-
- Necessity of digitizing analog signals:
- To enable digital processing and transmission of analog signals
- PCM system:
- Consists of sampling, quantization, and encoding
- Block diagram and equations:
Q & A
- Calculate the Nyquist rate, number of bits required to encode a sample, and the quantization step for a given PCM system scenario.
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Description
Prepare for the Principles of Communication Systems Fifth Semester B.E. Degree Examination with this model question paper. The paper covers topics like standard form of amplitude modulation, spectral equation of AM wave, and AM spectrum.