Enter the peak frequency deviation and maximum baseband message frequency into the calculator to determine the bandwidth of the FM signal.

Carson’s Rule for Bandwidth Calculation

Enter any 2 values to calculate the missing variable

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Carson’s Rule For Bandwidth Formula

The following formula is used to estimate the bandwidth of a frequency modulated (FM) signal according to Carson’s Rule.

B \approx 2(\Delta f + f_m)

Variables:

  • B is the approximate bandwidth of the FM signal (Hz)
  • Δf is the peak frequency deviation (Hz)
  • fm is the maximum baseband message frequency (Hz)

To estimate the bandwidth of the FM signal, add the peak frequency deviation to the maximum baseband message frequency and multiply the result by 2. This gives an approximate FM bandwidth that (by rule of thumb) contains about 98% of the signal power for a sinusoidal modulating signal, and is widely used as a practical bandwidth estimate in FM system design.

What is a Carson’s Rule For Bandwidth?

Carson’s Rule is a mathematical rule of thumb used to estimate the bandwidth of a frequency modulated (FM) signal. It states that nearly all (~98%) of the power of a frequency-modulated signal lies within an approximate bandwidth of B ≈ 2(Δf + fm), where Δf is the peak frequency deviation and fm is the maximum baseband message frequency. The rule provides a simple and reasonably accurate method for predicting the bandwidth requirements for an FM signal, which is crucial for the design and operation of communication systems.

How to Calculate Carson’s Rule For Bandwidth Calculation?

The following steps outline how to calculate Carson’s Rule for Bandwidth Calculation.

  1. First, determine the peak frequency deviation (Δf) in Hz.
  2. Next, determine the maximum baseband message frequency (fm) in Hz.
  3. Next, use the formula B ≈ 2(Δf + fm) to estimate the bandwidth of the FM signal (B) in Hz.
  4. Finally, report the estimated bandwidth value.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

peak frequency deviation (Δf) = 100 Hz

maximum baseband message frequency (fm) = 50 Hz

Bandwidth (B) ≈ 2(100 Hz + 50 Hz) = 300 Hz