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 ?
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 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
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 byConsider 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 :
