Understanding Excess Noise Ratio (ENR)

This article explains what Excess Noise Ratio (ENR) is, how it’s used, and how it relates to the Y-factor. We’ll also cover the formulas needed for ENR measurements.

What is Excess Noise Ratio (ENR)?

• ENR is a key parameter for measuring the noise performance of RF amplifiers.

• It’s frequently used in the context of noise diodes.

• The noise level at the input of a receiver is generally expressed as:

  Pn = K * T * B

  Where:

  • K = Boltzmann constant (1.38 x 10^-23^)
  • T = Temperature in Kelvin (K)
  • B = Bandwidth in Hertz (Hz)

• Receivers with narrower bandwidths tend to be more sensitive. The first stage of a receiver is usually the biggest contributor to overall noise. Keeping this first stage at a low temperature can significantly reduce the overall noise.

• Noise diodes have a defined ENR.

  • Diode OFF: The noise will be thermal noise, calculated using the formula above, where B is the receiver’s bandwidth.
  • Diode ON: The noise increases above the thermal noise level by an amount called the “Excess Noise Ratio” (ENR). This ENR value can vary, typically being 6 dB or 16 dB depending on whether the amplifier gain is high or low, respectively.

Converting Y-factor to ENR

• The formula (Equation-1, shown in the image) relates Y-factor and ENR to Noise Figure (NF). If the Noise Figure or gain of the amplifier is known, you can convert the Y-factor to find the ENR value.

• ENR Formula:

  • Numerical Form: ENR = (Ts ON - Ts OFF) / To
  • Decibel Form: ENR (dB) = 10 * Log10 { (Ts ON - Ts OFF) / To }

  Where:

  • Ts ON = Noise temperature when the noise source is ON.
  • Ts OFF = Noise temperature when the noise source is OFF.
  • To = Reference temperature, typically 290 Kelvin.

• Y-factor: The Y-factor is a ratio of two noise power levels. It is expressed as:

  Y = N ON / N OFF

  Where:

  • N ON = Noise power level when the noise source is ON.
  • N OFF = Noise power level when the noise source is OFF.

  Since noise power is proportional to noise temperature, we can also say: Y = T ON / T OFF

• Once you determine both the Y-factor and the ENR using these formulas, you can then easily calculate or measure the Noise Figure (NF) using Equation-1 (as shown in the image).