# Test and Measurement World

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## What is ENR | Excess Noise Ratio definition | Y-factor to ENR

This page describes ENR (Excess Noise Ratio) definition. It mentions formula to convert Y-factor to ENR (Excess Noise Ratio). This guide will help in Excess Noise Ratio measurements from ENR and Y-factor equations.

### Excess Noise Ratio definition

• It is parameter used in the measurement of noise performance of RF amplifier.
• It is mostly used in the connection with noise diodes.
• Noise level at input of receiver is expressed as follows.
➤ Pn = K*T*B
Where,
K = Boltzmann constant = 1.38 x 10-23
T = Temperature in oK
B = Bandwidth (Hz)
• Receivers with less bandwidth will have high sensitivity.

First stage in a receiver dominates overall noise of it. Overall noise can be reduced when first stage is kept at cold or low temperature. Noise diode device has defined ENR (Excess Noise Ratio).
➤Diode is in OFF state: Noise will be thermal noise as calculated using above formula where as bandwidth (B) is the receiver bandwidth.
➤Diode is in ON state: Noise increases from the thermal noise figure by an amount known as "ENR (Excess Noise Ratio)". The ENR value here can be 6 dB or 16 dB depending upon amplifier gain high or less respectively.

### Y-factor to ENR (Excess Noise Ratio) conversion formula ... Equation-1

• The formula or equation-1 above mentions relationship between Y-factor and ENR with respect to NF (Noise Figure). If Noise figure or gain of amplifier is known, Y-factor can be converted to obtain ENR value.

• ENR = {( TsON - TsOFF )/To } ... Numeral form
• ENR (dB) = 10* Log10 { ( TsON - TsOFF )/To } ... decibel form
Where,
TsON = Noise temperature when noise source is in ON state
TsOFF = Noise temperature when noise source is in OFF state
To = Reference temperature, 290 oK

Y-factor is expressed as ratio of two noise power levels as follows.
Y = NON/NOFF
Where,
NON = Noise power level when noise source is ON.
NOFF = Noise power level when noise source is OFF.

➤Y = TON/T OFF, (As noise power is proportional to noise temperature)

• Once we have determined Y-factor and ENR using above formula, NF can be easily calculated or measured using equation-1.

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