# Visualize op amp noise

-March 15, 2013

Picking a low-noise op amp is easier than ever, yet somehow harder also.

How can this be?

Harder – Because there are so many devices to choose from and the noise data is not always presented in the same way.

Easier - Because some very clever engineers have developed some really nice visualization tools so that we can see what's going on [1].

The Basic Problem: Current Noise or Voltage Noise
The main problem with selecting a low-noise op amp is source resistance – this will determine if voltage noise, current noise or a combination of the two is the most important parameter in determining the overall circuit's noise.

For an unbalanced source, op amp noise is modeled as a voltage source and a current source(s) at the input terminals of an ideal / noiseless amplifier as shown in Figure 1 [2].

Figure 1: It is well known that op amp input noise is modeled by inserting uncorrelated voltage sources and current sources at the input terminals of an ideal noiseless amplifier [2].

If your circuit has zero source resistance, then there is no voltage noise generated by the current noise sources, so their contribution is zero and all you are left with is the amplifier's voltage noise. Zero source resistance is hardly ever the case however.

As the source resistance increases, the noise of the source resistance begins to be a factor as all resistors have Johnson noise and the source resistance also interacts with the current noise to produce another voltage noise at the amplifier input. All of these noises are then converted to voltage and RSS (root of the sum-of-their-squares) summed as follows,

Total Noise of figure 1: Note the “4kTRs” term is in V2/Hz units so it is already squared and does not have to be squared again before summing. The total noise is in the units of Volts / Root Hz (commonly nV/rt-Hz or nanoVolts per root-Hz).

Note that the total noise in the above equation is valid for a single frequency. This is because, rather than being constant, the Voltage Noise and Current Noise vary with frequency and get worse the lower in frequency we go because of the 1/f nature of low-frequency noise [2].

This equation, when plotted leads to a very useful visualization tool that has been used for years [1-5]. This is the total input noise versus source resistance graph as seen in Figure 2.

Figure 2: The total noise versus source resistance is plotted for two very different amplifiers at 10Hz. The LT1028 is a very low voltage noise amplifier, whereas the LT1793 is a very low current noise amplifier. It is obvious from this graph that the LT1028 is quieter as long as the source resistance is lower than 2500 ohms and above this source resistance the LT1793 op amp will have less total noise. The resistor noise is plotted for comparison and it shows up as a straight diagonal line.

A few years ago when I was doing some design work on low-noise op amps I made a spreadsheet up that automatically plotted these curves given two simple numbers: The op amp's En and In values at some frequency [6].

Figure 2 plots the noise of two very different types of op amps at 10 Hz – The LT1028 is a low Voltage Noise device and the LT1793 is a JFET op amp designed for low Current Noise. At source resistances below 2500 Ohms the LT1028 will have lower total noise while at source resistances above 2500 Ohms the LT1793 is a lower noise device because of its very low current noise.

Looking at a table of numbers for Vn and In it is very difficult to tell which op amp is going to perform better at any given source resistance, but with a visualization tool like that shown in Figure 2 the results are immediate and conclusive.