www.radartutorial.eu www.radartutorial.eu Radar Basics

Noise in Cascaded Amplifiers

G1
F1
G2
F2
G3
F3
Gn-1
Fn-1
Gn
Fn

Figure 1: Noise in cascaded amplifiers

G1
F1
G2
F2
G3
F3
Gn-1
Fn-1
Gn
Fn

Figure 1: Noise in cascaded amplifiers

Reihe von Verstärkerstufen, je mit Verstärkungsfaktor V und Eigenrauschen F.
G1
F1
G2
F2
G3
F3
Gn-1
Fn-1
Gn
Fn

Figure 1: Noise in cascaded amplifiers

A multistage amplifier circuit is often used to achieve the required gain. In this scheme, the amplifier is a series of separate amplifier modules or stages connected in series (Figure 1). Each stage amplifies the signal received by it, which is characterized by the gain of the stage. Each amplification stage, like any active RF component, has its own noise level, which is characterized by a noise figure. The main contribution to the noise of the amplifier stage is its thermal noise, the source of which is the chaotic movement of the electric charge carriers, the intensity of which depends on the temperature of the amplifying elements of the stage. Remember: The noise figure is defined as the value of the signal-to-noise ratio at the input of the cascade, divided by the signal-to-noise ratio at its output.

Let us first consider, for simplicity, an amplifier consisting of only two serially connected stages. If there is no signal at the amplifier input, only the noise of this stage will be observed at the output of the first stage. The noise from the first stage will be amplified in the second stage, and the noise from the second stage will be added to this stage. The formula for determining the noise figure F of a two-stage amplifier is as follows:

F = F1 + (F21)/G1

where:

F represents the noise figure of the cascade,
F1 the noise figure of the first and
F2 the noise figure of the second component and
G1 the power gain of the first component.

It follows from the equation that the noise of the first stage contributes more to the total noise figure. Also, the total noise figure will be lower the higher the first stage gain.

The same is true when the number of gain stages increases. The overall noise figure formula of the stacked amplifier can be written as follows:

Ftotal = Fn + Gn·{Fn-1 + Gn-1·[   ...   F3 + G3·(F2 + G2·F1)]}

Having analyzed the above formula, one can draw such conclusions:

  1. The first stage of amplification should have the lowest noise level. This is because the first stage noise will be amplified sequentially in all subsequent stages, so the smaller they are initially, the smaller their contribution at the amplifier output.
  2. The last amplification stage must have the lowest gain of all stages. This is because all previous amplification stages will be amplified in this stage.

Since the mixers on which the frequency conversion takes place have sufficiently intense noise, the very first amplification stage is performed even before the frequency conversion, that is, at the carrier frequency. This stage is called low noise high frequency amplifier (LNA). Given that the reflected signal often has very little power, LNAs try to be placed closer to the receiving antenna to minimize losses in the transmission path of the signal to the receiver, that is, in the waveguide. Therefore, it is often the case that a low noise amplifier is placed directly on the antenna.


Sponsors: