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Understanding Excess Noise Ratio (ENR)

enr noise figure y-factor rf amplifier noise measurement

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

Y-Factor vs ENR (Excess Noise Ratio)

  • 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).