A carrier is frequency modulated with a sinusoidal signal of ____ KHz resulting in a maximum frequency deviation of 5 KHz. Modulation index and bandwidth of the modulating signal is respectively is given as
mf = 2.5, BW = 14 KHz
The modulating frequency has dropped out of the printed question, so the answer must be recovered from the internal consistency of the options. Two relations must hold together:
\(m_{f}=\dfrac{\Delta f}{f_{m}}\qquad\text{and}\qquad BW=2\left(\Delta f+f_{m}\right)\)
with \(\Delta f=5\ \text{kHz}\) given. Test each option by working out what \(f_{m}\) it implies and then checking whether the quoted bandwidth follows.
| Option | mf | Implied fm = 5/mf | BW = 2(5 + fm) | BW quoted | Consistent? |
|---|---|---|---|---|---|
| 1 | 1 | 5 kHz | 20 kHz | 10 kHz | ✗ |
| 2 | 2 | 2.5 kHz | 15 kHz | 12 kHz | ✗ |
| 3 | 2.5 | 2 kHz | 14 kHz | 14 kHz | ✓ |
| 4 | 1.7 | 2.94 kHz | 15.9 kHz | 14 kHz | ✗ |
Only option 3 closes on itself, and it does so exactly: a modulating frequency of 2 kHz with a 5 kHz deviation gives
\(m_{f}=\dfrac{5}{2}=2.5\qquad BW=2(5+2)=14\ \text{kHz}\)
so 2 kHz is evidently the figure the printer dropped. The answer is flagged for confirmation only because it is reconstructed rather than read.
The technique is worth generalising : when a question is missing a datum, look for the option that satisfies every stated relation simultaneously. A well-set question has exactly one such option, because the distractors are built by breaking one relation at a time — here option 1 uses \(2f_{m}\) for the bandwidth, option 2 mismatches by 3 kHz, option 4 rounds the index wrongly.
What the numbers describe. With \(m_{f}=2.5\) this is wideband FM: the index exceeds unity, so more than one significant sideband pair exists on each side and the bandwidth is genuinely larger than the \(2f_{m}=4\ \text{kHz}\) that AM would need. Carson's rule counts the sidebands carrying about 98 % of the power; the exact spectrum, given by the Bessel functions \(J_{n}(2.5)\), extends further but negligibly.
Hence, mf = 2.5 and BW = 14 kHz.
Similar Questions
In FM
Consider the following :
ST1 : F.M. signal produces more side bands than A.M.
ST2 : The carrier in a F.M. signal can never be dropped to zero amplitude.Which of the following is valid ?
In case of wideband FM, the modulation index value is :
A high frequency signal is frequency modulated by n number of modulating signals. The ideal number of sidebands in the modulated signal will be :
The approximate rule for transmission of an FM signal generated by a single-tone modulating signal of frequency fm, modulation index β and maximum frequency deviation Δf, is defined as :
Assertion (A) : The FM radio broadcast of analog signals provides higher fidelity.
Reason (R) : FM uses significantly larger channel bandwidth for signal transmission.
Select your answer using the codes given below :
What bandwidth is needed for an FM signal that has a peak deviation of ± 3 KHz and handles audio signals from 200 Hz to 5 KHz ?
Which of the following techniques are used to generate frequency modulated signal :
1. Armstrong
2. Foster-Sealy Discriminator
3. Balanced Modulator
4. Reactance ModulatorWhich one of the following is true ?
A fm kc/s modulating frequency provides Mf = 2 (significant Bessel functions i.e. n = 4) in F.M. wave. What bandwidth is required for passing this wave keeping ∆f constant, if frequency of modulating signal is doubled what will be its effect on Mf ?
Which of the following is true ?
Important Questions from Frequency Modulation
Given an angle-modulated signal
$x_c(t) = 10\cos[(10^8) \pi t+5\sin 2\pi (10^3)t]$
The maximum phase deviation and maximum frequency deviation is given byIn FM
Consider the following :
ST1 : F.M. signal produces more side bands than A.M.
ST2 : The carrier in a F.M. signal can never be dropped to zero amplitude.Which of the following is valid ?
In case of wideband FM, the modulation index value is :
A high frequency signal is frequency modulated by n number of modulating signals. The ideal number of sidebands in the modulated signal will be :
