# Op Amp Noise—but what about the feedback?

-February 11, 2013

Last month we explored noise of the non-inverting amplifier but I dodged the issue of the feedback network’s noise contribution. A reader, Jim, challenged me—he wanted more detail. So what about the noise from R1 and R2 in figure 1?

The noise contribution at the inverting input is comprised of the thermal noise of the feedback resistors and op amp’s current noise reacting with these components. The output contribution of these noise sources can be calculated using basic op amp assumptions:

• R1’s thermal noise voltage is amplified to the output by the inverting gain of the circuit, -R2/R1.
• R2’s thermal noise contributes directly to the output noise.
• The inverting input current noise flows through R2, resulting in an output noise contribution of IN∙R2.

These noise sources are uncorrelated so they “add” by the root sum of the squares.

But there’s a more intuitive way to look at this. It’s handy to refer the noise sources as if they all occur at the non-inverting input. Output noise contributions are divided by the non-inverting gain. This RTI (referred to input) approach makes it easy to compare noise sources and to the input signal.

The noise occurring at the inverting input relates to the parallel combination of R1 and R2. When referred to the non-inverting input, the combined RTI thermal noise of R1 and R2 is equal to the thermal noise of R1//R2. The current noise RTI contribution at the inverting input is equal to IN∙(R1//R2). It’s all about R1//R2.

This result reveals an important factor for a low noise design. Make R1//R2 << RS and the noise contribution at the inverting input is negligible. If R1//R2 = RS then the feedback network contributes equal noise to that of the source resistance. That may be too much for some designs.

In high gains, it’s easy to keep the parallel resistance low—R1 can be made much less than Rs and R2 is big. At moderate gains it gets more difficult. G=2 is the worst case when R1 and R2 are equal. If you want to make the parallel resistance 100Ω, for example, R1 and R2 need to be 200Ω.

The feedback network then imposes a 400Ω load on the op amp—too low in most circumstances.  It gets easy again very close to G=1 when R1 is big and R2 small. This case is not common because you generally want significant gain in the first low noise stage.

Addressing a common concern—there is no noise inherent noise penalty in making R2 a high resistance. If higher gain is achieved by increasing R2 and decreasing R1, while maintaining a constant parallel resistance, noise performance remains constant.

You can download an Excel file to calculate the noise of this commonly used input amplifier stage, including the op amp and source resistance noise. It shows the percentage contribution of each noise source and graphs the total noise over a range of source resistance. It also calculates noise figure, the noise (in dB) that the amplifier adds to thermal noise of the source. This is a handy measure of the noise performance of the amplifier. Tinker with it and you will quickly get a feel for the issues and trade-offs. Download it here.