Define signal to noise ratio .Explain the effect of cascade connection on a signal to noise ratio. An amplifier with 10dB noise figure and 4 dB power gain is cascaded with a second amplifier which has a 10dB power gain .What is overall noise figure and power gain.

• Noise Figure (NF) is a measure of how much a device (such an amplifier) degrades the Signal to Noise ratio (SNR).

• Noise Factor (linear not dB) of a receiver is the ratio of the SNR at its input to the ratio of the SNR at its output.

• Note that SNR at the output will always be smaller than the SNR at the input, due to the fact that circuits always add to the noise in a system.

• The Noise Factor, at a specified input frequency, is defined as the ratio of the total Noise Power per unit bandwidth available at the output port when noise temperature of the input termination is standard (290K) to that portion of engendered at the input frequency by the input termination.

• When designing circuits for use with extremely weak signals, noise is an important consideration. The noise contribution of each device in the signal path must be low enough that it will not significantly degrade the Signal to Noise Ratio.

• The Noise level of a system sets the lower limit on the magnitude of a signal that can be detected in the presence of the noise. So, to achieve the best performance you need to have a minimum residual noise level.

• Noise Figure is used to describe the noise contribution of a device. An ideal amplifier would have no noise of its own, but would simply amplify what went in to it.

• For example a 10dB amplifier would amplify the Signal (and the Noise) at its input by 10dB. Therefore, although the noise floor at the output of the amplifier would be 10dB higher than at the input.

• The “ideal noiseless" amplifier would not change the Signal to Noise ratio (SNR).

• A "real world" amplifier will not amplify only the noise at its input, but will contribute its own noise to signal. This reduces the Signal to Noise ratio at the output of the amplifier.

• So, the "real world" amplifier has two major internal components: an "ideal noiseless" amplifier and a noise source. The noise source adds noise to any signal what enters to the amplifier and then the ideal amplifier amplifies the whole thing by an amount equal to its gain, with no noise contribution of its own.

• As an example let's assume that we have an amplifier at room temperature with 10dB of gain which has only a matched resistor at its input and output.

• The noise at the input of the amplifier must be -174dB m/Hz. If the amplifier is known to have a 3dB NF, the internal noise source adds an equal noise to the input noise before amplification. Then 10dB of gain increases the noise by 10dB. Therefore, the noise at the output of the amplifier is 13dB higher than at the input, or (-174dBm/Hz + 10dB gain +3dB NF) =161dBm/Hz.

• The noise contribution of the amplifier's noise source is fixed and does not change with input signal. Therefore, when more noise is present at the amplifier input, the contribution of the internal noise source is less significant in comparison.

• When the noise into an amplifier is higher than kTB (-174dBm/Hz), the amplifier’s Noise Figure plays a smaller role in the amplifier's noise contribution.

• The Noise Figure (NF) of a device is only calculated with the input noise level at kTB.

• The Noise Temperature at the output of an amplifier is the sum of the Noise Temperature of the source and the Noise Temperature of the amplifier itself multiplied by the Power Gain of the amplifier. Tout = G * (Tampl+ Tsource)

• Tout = Noise Temperature at amplifier output in degrees Kelvin. G = Power Gain in linear scale not in dB.Tampl= Noise Temperature of amplifier. Tsource= Noise Temperature of source. The same formula is valid for attenuators. Tout = Gatt* (Tatt+ Tsource)

• The Noise Figure of an attenuator is the same as the attenuation in dB.

• The Noise Figure of an attenuator preceding an amplifier is the Noise Figure of the amplifier plus the attenuation of the attenuator in dB.

If we use cascaded amplifiers:

• For above example both amplifiers has 10dB gain and NF=3dB.

The signal goes in at -40dBm with a noise floor at kTB (-174dBm/Hz).

We can calculate that the signal at the output of the first amplifier is -30dBm and the noise is:

(-174dBm/Hz input noise) + (10dB of gain) + (3dB NF) = -161dBm/Hz.

Let see how many kTBs are entering in the second amplifier:

(-161dBm/Hz) is 13dB greater than kTB (-174dBm13dB is a power ratio of 20x. So, the noise floor at the second amplifier is 20 times kTB or 20kTB.

• Next calculate how many kTBs are added by the noise source of the second amplifier (in this case, 1kTB because the NF=3dB).

• Finally calculate the increase in noise floor at the second amplifier as a ratio and convert to dB. Ratio of (input noise floor) + (added noise) to (input noise floor) is: (20kTB+1kTB) / (20kTB) = 20/21 In dB = 10LOG (21/20) = 0.21dB

• Therefore, the second amplifier only increases the noise floor by 0.21dB even though it has a noise figure of 3dB, simply because the noise floor at its input is significantly higher than kTB. The first amplifier degrades the signal to noise ratio by 3dB, while the second amplifier degrades it only 0.21dB.

• When amplifiers are cascaded together in order to amplify very weak signals, it is generally the first amplifier in the chain which will have the greatest influence upon the Signal to noise ratio because the noise floor is lowest at that point in the chain.