# Bandwidth of FM Signals: Carson’s Rule

• royal084
In summary, FM modulation of an analog voltage on a satellite using a 10,000 Hz per volt constant results in a C/N ratio of 10 dB measured in the Carson's rule bandwidth, and a 3 dB above the FM threshold on the receiver side.

#### royal084

A satellite telemetry link operating in S-band uses frequency modulation to transmit the value of an analog voltage on the satellite to a receiving Earth station. The voltage has a range from -1.0 volts to +1.0 volts, and a maximum frequency of 1000Hz.The FM modulator on the satellite has a constant of 10,000 Hz per volt. At the receiving Earth station the C/N ratio of the signal is 10 dB measured in the Carson’s rule bandwidth, and is 3 dB above the FM threshold of the FM demodulator.

a. What is the Carson’s rule bandwidth for the FM signal?
b. What is the baseband S/N ratio at the Earth station receiver output for the recovered analog signal?

Carson’s rule bandwidth for the FM signal

Question:
A satellite telemetry link operating in S-band uses frequency modulation to transmit the value of an analog voltage on the satellite to a receiving Earth station. The voltage has a range from -1.0 volts to +1.0 volts, and a maximum frequency of 1000Hz.The FM modulator on the satellite has a constant of 10,000 Hz per volt. At the receiving Earth station the C/N ratio of the signal is 10 dB measured in the Carson’s rule bandwidth, and is 3 dB above the FM threshold of the FM demodulator.

a. What is the Carson’s rule bandwidth for the FM signal?
b. What is the baseband S/N ratio at the Earth station receiver output for the recovered analog signal?

Solution:
a.Carson’s rule states that the bandwidth required to transmit an FM signal is given by

B = 2(Δfpk+ fmax) Hz
Where,
Δfpk = the peak frequency deviation
fmax = the highest frequency present in the modulating signal

1. The frequency deviation of the carrier is directly proportional to the modulating signal voltage.

2. The bandwidth required to transmit an FM signal is found from Carson’s rule.

From here don’t know how to calculate the Δfpk ,the peak frequency deviation.

b. (S/N)out = C/N + 10 log10(BRF/fmax) + 20 log10(Δfpeak/fmax) + 1.8 dB (5.11)

Where

BRF = IF bandwidth of receiver = RF B/W of FM signal from Carson’s rule

fpeak = peak frequency deviation at transmitter
fmax = maximum frequency of baseband signal = receiver baseband bandwidth

And the factor of 1.8 dB is equivalent to the numerical ratio 3/2.

Same as here don’t know how to calculate the Δfpk ,the peak frequency deviation.

Khandaker Mosharraf Arafen
g4829517

## 1. What is Carson’s Rule?

Carson’s Rule is a formula used to calculate the bandwidth of an FM (Frequency Modulation) signal. It was developed by John Renshaw Carson, an American engineer, in the early 1920s.

## 2. How does Carson’s Rule calculate the bandwidth of FM signals?

Carson’s Rule takes into account the highest frequency deviation in the FM waveform, the modulation index, and the highest audio frequency in the modulating signal to determine the necessary bandwidth for an FM signal. The formula is bandwidth = 2 * (highest frequency deviation + highest audio frequency).

## 3. Is Carson’s Rule accurate for all FM signals?

No, Carson’s Rule is an approximation and may not accurately estimate the bandwidth for complex FM signals. It assumes a sinusoidal modulating waveform and does not take into account other factors that may affect the FM signal’s bandwidth.

## 4. Why is calculating the bandwidth of FM signals important?

The bandwidth of an FM signal directly affects the amount of spectrum it occupies. Therefore, accurately calculating the bandwidth is crucial for efficient use of the frequency spectrum and reducing interference between different FM signals.

## 5. Can Carson's Rule be used for other types of modulation?

No, Carson’s Rule is specifically designed for FM signals and cannot be applied to other types of modulation, such as AM (Amplitude Modulation) or PM (Phase Modulation). Each type of modulation requires its own formula to calculate the necessary bandwidth.