## 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 ^{o}K

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 = {( Ts^{ON} - Ts^{OFF} )/To } ... Numeral form

• ENR (dB) = 10* Log_{10} { ( Ts^{ON} - Ts^{OFF} )/To } ... decibel form

Where,

Ts^{ON} = Noise temperature when noise source is in ON state

Ts^{OFF} = Noise temperature when noise source is in OFF state

To = Reference temperature, 290 ^{o}K

Y-factor is expressed as ratio of two noise power levels as follows.

Y = N^{ON}/N^{OFF}

Where,

N^{ON} = Noise power level when noise source is ON.

N^{OFF} = Noise power level when noise source is OFF.

➤Y = T^{ON}/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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