I think the question has mixed up fc and fm, which should be probably be 88.1MHz and 3.5kHz respectively. It also does not specify the deviation, which you need to find the bandwidth.tai man said:Homework Statement
Consider the frequency-modulated (FM) signa A(t)=A0sin[2πfct+Δfsin(2πfmt)/fm] , where fc = 3.5 kHz, fm = 88.1 MHz. What is the bandwidth of the signal? [Note: You may take sin≅ and cos≅1 for x (in radian) << 1.]
Homework Equations
A(t)=A0sin[2πfct+Δfsin(2πfmt)/fm]
The Attempt at a Solution
for finding bandwidth, isn't it (fc+fm)-(fc-fm)?
Bandwidth refers to the range of frequencies that an FM signal occupies. It is usually measured in Hertz (Hz) and is an important characteristic of the signal as it determines the maximum amount of information that can be transmitted.
The bandwidth of an FM signal can be calculated using the formula BW = 2(fmax - fmin), where fmax is the maximum frequency deviation and fmin is the minimum frequency deviation. These values can be obtained from the frequency modulating signal.
The bandwidth of an FM signal is affected by the modulation index, which is the ratio of the frequency deviation to the maximum frequency of the modulating signal. It is also affected by the amplitude and frequency of the modulating signal, as well as the carrier frequency and the sensitivity of the receiver.
The bandwidth of an FM signal is typically much wider than that of an AM signal. This is because FM signals use a much larger range of frequencies to transmit information, resulting in a higher bandwidth. AM signals, on the other hand, use a smaller range of frequencies and have a narrower bandwidth.
Knowing the bandwidth of an FM signal is important for several reasons. It helps in the design and optimization of communication systems, as well as in the allocation of frequencies by regulatory bodies. It also ensures that the signal is transmitted and received accurately without any distortion or interference.