# Finding the bandwidth of an FM signal

• tai man
In summary, the given conversation discusses the calculation of bandwidth for a frequency-modulated (FM) signal with a specific formula. The suggested equation for finding bandwidth is (fc+fm)-(fc-fm), but this may not be accurate due to a possible mix-up of fc and fm. The calculation also depends on the frequency deviation, which is not given in the question. The bandwidth can be computed from a normalized curve using the modulation index β.
tai man

## 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)?

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)?
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.

I agree with post #2. Also, the required bandwidth depends on the (constant) frequency deviation Δω; then a bandwidth BW can be computed from a normalized bandwidth curve BW/2Δω vs. β.

## 1. What is bandwidth in relation to an FM signal?

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.

## 2. How do you calculate the bandwidth of an FM signal?

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.

## 3. What factors affect the bandwidth of an FM 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.

## 4. How does the bandwidth of an FM signal compare to that of an AM signal?

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.

## 5. Why is it important to find the bandwidth of an FM signal?

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.

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