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An FM signal is given as;
Where m(t) is shown in the figure given below.
It is given that carrier frequency (f_{c}) is 1000kHz. Then calculate the value of instantaneous frequency (f_{i}) at t = 1.5 sec and the peak frequency deviation (δf) of the above FM signal.
Concept:
Standard expression of FM signal
Instantaneous frequency (f_{i} in Hz)
Where
From the standard expression
Peak frequency deviation:
Calculation:
Given;
at, t = 1.5 sec ; m(t) = 10
Peak frequency deviation:
m(t)_{max} = 10
A phase modulated wave can be generated from frequency modulator by connecting a ___________ before the modulator and a frequency modulated wave can be generated from phase modulator by connecting a __________ before the modulator.
The output of FM modulator is of form
After passing the modulating signal through the differentiator we give as the input to the frequency modulator, i.e.
The expression of the output signal will be:
The differentiation of the integral will simply give the original signal.
We get a phase modulated signal which is of the form:
Frequency modulated signal with single tone modulation has a frequency deviation of 20 kHz and bandwidth of 60 kHz. The frequency of the modulating signal will be 
Concept:
As per Carson’s rule, the bandwidth of a frequency modulated signal is defined as:
B.W. = 2 (Δf + f_{m})
Δ f = Frequency deviation of the modulated wave
fm = frequency of the modulating signal
Calculation:
Given B.W. = 60 kHz and Δ f = 20 kHz
60k = 2 (20k + f_{m})
30k = 20k + f_{m}
f_{m} = 10 kHz
Frequency Modulation:
Types of FM detection:
Foster Seeley discriminator:
Foster Seeley discriminator is used in the demodulation of FM signal and it uses a doubletuned circuit with primary and secondary tuned to the same frequency.
In a frequency modulation system, maximum frequency deviation allowed is 1000 and modulating frequency is 1 kHz. Determine modulation index β.
Concept:
In FM (Frequency Modulation), the modulation index is defined as the ratio of frequency deviation to the modulating frequency.
Mathematically, this is defined as:
m_{f} = Modulation index
Δf = Frequency deviation
f_{m} = Modulating frequency
Calculation:
Given Δf = 1000 Hz = 1 kHz
f_{m} = 1 kHz
The four basic elements in a PLL are loop filter, loop amplifier, VCO and
The figure shows a schematic of a phaselocked loop:
Determine the bandwidth required for an FM signal having frequency 2 kHz and maximum deviation 10 kHz.
Concept:
According to Carson rule signal, BW is given as:
B.W = (β + 1) 2fm
∵ β = Δf/f_{m}
B.W. = 2[Δf + f_{m}]
If multiple frequencies are available in modulating signal then,
B.W. = 2(β + 1) f_{max }
Calculation:
Given:
Δf = 10 kHz
f_{m} = 2 kHz
B.W. = 2[Δf + fm]
B.W. = 2(10 + 2)
BW = 24 kHz
Hence option (3) is the correct answer.
A wave has 3 parameters Amplitude, Phase, and Frequency. Thus there are 3 types of modulation techniques.
Consider the FM signal x_{c}(t) = 10 cos(2π × 10^{8}t + 0.5 sin(10^{4} πt)). The bandwidth of x_{c}(t) is approximately
The Bandwidth of an FM signal is approximated by Carlson’s rule and is given by
B.W. = 2(Δf + f_{m}).
Where Δf = maximum frequency deviation from the carrier frequency and f_{m} = message signal frequency.
Calculation:
Given, S_{FM}(t) = 10 cos (2π × 10^{8} t + 0.5 sin (10^{4}πt))
The instantaneous frequency is given by:
⇒ Maximum instantaneous frequency
Maximum frequency deviation
So, Approximate bandwidth according to Carson’s rule
⇒ 2(Δf + f_{m}) = 2(2.5 + 5) = 2 (7.5 K) = 15 K
21 docs263 tests

21 docs263 tests
