In FM
total power remains constant with respect to modulation index
The defining property of frequency modulation is that its total power never changes — option 3.
Why the power is fixed. An FM wave is
\(s(t)=A_{c}\cos\left(\omega_{c}t+m_{f}\sin\omega_{m}t\right)\)
The amplitude \(A_{c}\) is constant — only the argument of the cosine varies — so the transmitted power is
\(P=\dfrac{A_{c}^{2}}{2R}\)
whatever the modulation index. Modulation redistributes power from the carrier into the sidebands but never adds or removes any, which is expressed by the Bessel identity
\(J_{0}^{2}(m_{f})+2\sum_{n=1}^{\infty}J_{n}^{2}(m_{f})=1\)
Contrast with AM, where total power does depend on the index, \(P_{t}=P_{c}\left(1+m^{2}/2\right)\), because there the amplitude itself is being varied. This difference is the reason an FM transmitter's output stage can be driven into saturation for efficiency, and the reason a limiter at the receiver can strip amplitude noise without harming the signal.
| Option | Verdict |
|---|---|
| Carrier never becomes zero | ✗ It vanishes whenever \(J_{0}(m_{f})=0\), first at mf = 2.405 |
| J-coefficients occasionally negative | True in itself — but only a sign convention |
| Total power constant | ✓ |
| Pulse rate decreases | ✗ FM has no pulses |
Option 1 is plainly false, and instructively so: the carrier amplitude is \(A_{c}J_{0}(m_{f})\), and \(J_{0}\) has zeros at 2.405, 5.52, 8.65 and so on. At those indices the carrier disappears completely while all the power sits in the sidebands — the eigenvalue or carrier-null method, used in the laboratory to set a known deviation precisely.
Why option 2 is flagged rather than dismissed. Bessel functions of the first kind do take negative values, so the statement is literally true. But a negative \(J_{n}\) merely indicates a 180° phase reversal of that sideband pair; the power depends on \(J_{n}^{2}\) and is unaffected. It is an incidental detail of the mathematics, whereas option 3 states the property that characterises FM — which is why option 3 is the intended answer.
Hence, in FM the total power remains constant with respect to the modulation index.
Similar Questions
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 ?
Which of the following is true ?
The FM transmitters have the following blocks as per the following correct sequence :
(A) Crystal Oscillator
(B) Antenna
(C) Frequency multiplier
(D) Phase modulate / Audio source
(E) Power amplifierChoose the most appropriate answer from the options given below :
Consider an FM signal
\(s(t) = 10\sin\left(4\pi \times 10^6 t + 9\cos\left(2\pi \times 10^3 t\right)\right)\)
the frequency deviation and bandwidth of FM wave are
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 ?
Important Questions from Frequency Modulation
Which of the following statements is true for FM?
What is the modulation index in a frequency modulated signal with a modulating frequency of 500 Hz and frequency deviation of 10 kHz?
Which of the following rules states that the bandwidth required to transmit an angle modulated wave is twice the sum of the peak frequency deviation and highest modulating signal frequency?
If f mis modulating frequency and m fis modulation index, then by the Carson's rule, the bandwidth of an FM signal at the input of a conventional discriminator will be:
In FM, "M" stands for
