What Are the Noise Parameters of a Very-Low-Noise Amplifier?

[kaancelebi]

We need a very-low-noise amplifier for a special application, and we buy such an amplifier with a noise bandwidth of 2.4 MHz and an amplification of 1000. To test it, we take a set of "perfectly" shielded standard resistors, connect each if these to the amplifier input, and measure the rms output noise voltage in each case. The data are given in the Table below. Calculate the following noise parameters of the amplifier: Equivalent noise input voltage, equivalent noise input current, optimum source resistance Ro, and noise factor F at Ro.
Table of output noise voltages:
R (Ω) ---- Urms (mV)
1 ----- ----- 2.0
10 -------- 2.0
10^2 ----- 2.4
10^3 ----- 4.6
10^4 ----- 15
10^5 ----- 90
10^6 ----- 8.1x10^2
10^7 ------ 8x10^3

i really don't understand what i will do. i know some formula Unoise=(4kBTf)^1/2 ,optimum source resistance , and noise factor but i don't know how i can do circuit , use formula or where can i use these table.
i need help !

 

[marcusl]

Amplifiers are modeled with two effective noise sources, a voltage and a current source. The current source is connected directly across the amplifier terminals. The voltage source in series with the input resistance is also across the terminals, in parallel with the current source. (It's hard to describe, easy to grasp if you see a diagram. Is it in your book?)

When the input R = 0, the current source develops no noise voltage drop so all noise comes from the voltage source. The opposite is true for R=infinity. Your data shows directly the noise voltage, and I think the last two terms give you the current noise. From there you can calculate the optimum source resistance, and the total noise there. That should give you noise factor.

 

[kaancelebi]

diagram mean =
www.resimupload.com/ds271573906_diagram.html[/URL]

i have a book its name is Principles-of-Measurement-Systems and i tried to find it but i didnt find :S

also i understood thanks a lot. it is really good information.
(((((((((When the input R = 0, the current source develops no noise voltage drop so all noise comes from the voltage source. The opposite is true for R=infinity.))))))))

i solved question .thanks again

 

[marcusl]

Yes, it looks like you got it exactly. Good job!

 

[paranormal]

I can provide some guidance on how to approach this problem. First, let's define some terms and equations that will be useful in calculating the noise parameters of the amplifier.

1. Equivalent noise input voltage (En): This is the voltage that would produce the same output noise as the amplifier. It can be calculated using the following equation:
En = √(4kTΔf)
where k is the Boltzmann constant (1.38x10^-23 J/K), T is the temperature (in Kelvin), and Δf is the noise bandwidth (2.4 MHz in this case).

2. Equivalent noise input current (In): This is the current that would produce the same output noise as the amplifier. It can be calculated using the following equation:
In = En / Ro
where Ro is the optimum source resistance.

3. Optimum source resistance (Ro): This is the resistance value that would minimize the noise of the amplifier. It can be calculated using the following equation:
Ro = √(4kTBΔf)
where B is the amplifier bandwidth (2.4 MHz in this case).

4. Noise factor (F): This is a measure of how much the amplifier degrades the signal-to-noise ratio. It can be calculated using the following equation:
F = 1 + (En^2 / In^2)
where En and In are the equivalent noise input voltage and current, respectively.

Now, let's use the data provided in the table to calculate these noise parameters. We can plot the output noise voltage (Urms) against the resistance (R) on a logarithmic scale to get a better understanding of the data.

From the graph, we can see that the output noise voltage remains constant for resistances up to 10^3 Ω, after which it starts to increase significantly. This indicates that the amplifier is designed to work best with a source resistance of 10^3 Ω or higher.

Using the equation for equivalent noise input voltage, we can calculate the En for the given noise bandwidth (Δf = 2.4 MHz) and temperature (T = 300 K):
En = √(4kTΔf) = √(4x1.38x10^-23x300x2.4x10^6) = 1.74x10^-7 V

To calculate the optimum source resistance (Ro), we can use