Carrier-to-Noise Ratio (CNR)

What is this formula?

Carrier-to-Noise Ratio (CNR) measures the strength of a received carrier relative to the noise power present in the receiver bandwidth. It is a fundamental performance metric in analog and digital communication systems.

When to use it

Use this formula when evaluating satellite links, microwave systems, radio receivers, broadcast transmitters, and communication channels where carrier quality must be assessed.

Example

A satellite receiver measures a carrier power of 5×10^-10 W and a noise power of 1×10^-12 W.

Formula:

CNR = Pc/Pn

Substitution:

CNR = (5×10^-10)/(1×10^-12)

Result:

CNR = 500

CNR = 26.99 dB

Applications

Satellite communications, microwave links, radio astronomy, broadcast systems, wireless communications, RF receiver design, and link performance analysis.

Note

CNR is commonly expressed in decibels using CNRdB = 10·log10(CNR). Although related, CNR, SNR, and Eb/N0 are not identical metrics. The appropriate parameter depends on the modulation method, receiver bandwidth, and communication system architecture.