Communications Calculator: AM, FM, PCM Sampling, Shannon Capacity and Link Budget

Solve the standard analogue and digital communications problems in one place.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose AM, FM, PCM, Shannon capacity or a radio link. For AM enter the carrier and message voltages and it gives the modulation index, the power in the carrier and sidebands, the efficiency and the bandwidth.

For FM it gives the index and the bandwidth by Carson's rule. For PCM it gives the Nyquist rate, the number of levels, the bit rate and the signal to quantisation noise.

For Shannon it gives the capacity of a channel. For a link it adds the free space path loss to the antenna gains and the losses to find the received power and the fade margin.

Formulas used

  • m = \frac{V_m}{V_c}
  • P_t = P_c\left(1 + \frac{m^2}{2}\right)
  • B_{FM} = 2(\Delta f + f_m)
  • C = B\log_2(1 + S/N)
  • L_{fs} = 20\log d_{km} + 20\log f_{MHz} + 32.44

Worked example

With the default numbers in the calculator above:

  1. Modulation index: 0.60 (60.00 percent)
  2. Carrier power: 1.00 W
  3. Total transmitted power: 1.18 W
  4. Power in each sideband: 0.0900 W
  5. Efficiency (the share of power in the sidebands, which carry the message): 15.25 %
  6. Bandwidth: 30.00 kHz

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? Frequency modulation (FM).

  1. Modulation index: 5.00
  2. Bandwidth by Carson's rule: 180.00 kHz
  3. Type: Wide-band FM

Common questions

What happens if the AM index is above 1?

The signal is over-modulated and the envelope is distorted, so the message cannot be recovered cleanly.

What is Carson's rule?

An estimate that the bandwidth of an FM signal is twice the sum of the peak deviation and the highest message frequency.

What is the Nyquist rate?

The minimum sampling rate, twice the highest frequency in the signal, below which aliasing occurs.

How much fade margin do I need?

At least 10 to 20 dB, more for long paths, rain at higher frequencies, or critical links.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Haykin, Communication Systems; Tomasi, Electronic Communications Systems; ITU-R P.525 free-space attenuation.

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