Noises from various sources in a circuit can be summed to determine the total noise density.
Note that the noises must be uncorrelated, otherwise measurement errors will rise.
The standard method for noise summing is the Root Mean Square (RMS).
So the total noise in a circuit with severak noise sources is:
$$ \bar{V}_{total}=\sqrt{\bar{v}_{1}^{2}+\bar{v}_{2}^{2}+...} $$
Let as now consider a theoretical example with an amplification stage in the circuit:
Fig.1 Noise in a gain stage
Each gain stage is preceded by a source that has a non-zero output impedance.
Its equivalent circuit is a Voltage source with a series resistor Rs as shown in Fig.1.
Because it has the resistor it produces Johnson noise.
Now there are other two types of noises that are present in an amplifier stage and are produced by that stage component. To model these noises we create the equivalent circuit and place the noise sources at the input of the amp stage. The noises are amplified along with the signal.
These are a voltage noise, depicted as Vn, and a current noise depicted as In.
As the theoretical amplifier has infinite input impedance (practical OpAmps have a very high one)
the current that is induced in the circuit by In is flowing through the source's resistance Rs and that
results in a specific voltage drop across Rs (->voltage noise).
Vn, V caused by In across Rs, and Johnson noise of Rs are amplified with our signal at the output of the stage. Measuring the noise at the output and dividing by the voltage amplification factor Av gives as the Equivalent Input Noise or EIN.
The EIN, is the equivalent circuit that shows the noise sources at the inputs of the amplifier. (That's how Fig.1 is created).
Measuring those noises directly at the input of the stage is very difficult, because it is difficult to distinguish the noises between them (especially Vn and In).
Furthermore, comparing the EIN with the Johnson noise produced by the source's impedance Rs gives as the Noise Figure (NF) that tells us how noisy our circuit is according to a source output impedance.
I wonder why they don't give this measurements in the datasheets of the components. I guess that
the measurements would show a bad value...
Note that the noises must be uncorrelated, otherwise measurement errors will rise.
The standard method for noise summing is the Root Mean Square (RMS).
So the total noise in a circuit with severak noise sources is:
$$ \bar{V}_{total}=\sqrt{\bar{v}_{1}^{2}+\bar{v}_{2}^{2}+...} $$
Each gain stage is preceded by a source that has a non-zero output impedance.
Its equivalent circuit is a Voltage source with a series resistor Rs as shown in Fig.1.
Because it has the resistor it produces Johnson noise.
Now there are other two types of noises that are present in an amplifier stage and are produced by that stage component. To model these noises we create the equivalent circuit and place the noise sources at the input of the amp stage. The noises are amplified along with the signal.
These are a voltage noise, depicted as Vn, and a current noise depicted as In.
As the theoretical amplifier has infinite input impedance (practical OpAmps have a very high one)
the current that is induced in the circuit by In is flowing through the source's resistance Rs and that
results in a specific voltage drop across Rs (->voltage noise).
Vn, V caused by In across Rs, and Johnson noise of Rs are amplified with our signal at the output of the stage. Measuring the noise at the output and dividing by the voltage amplification factor Av gives as the Equivalent Input Noise or EIN.
The EIN, is the equivalent circuit that shows the noise sources at the inputs of the amplifier. (That's how Fig.1 is created).
Measuring those noises directly at the input of the stage is very difficult, because it is difficult to distinguish the noises between them (especially Vn and In).
Furthermore, comparing the EIN with the Johnson noise produced by the source's impedance Rs gives as the Noise Figure (NF) that tells us how noisy our circuit is according to a source output impedance.
I wonder why they don't give this measurements in the datasheets of the components. I guess that
the measurements would show a bad value...
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