source: Planet Analog article

**S****ignal Chain Basics**, , 10/8/2015

Many technical documents have been written on noise analysis. Early on in my career I became obsessed with operational amplifier (op amp) noise. Subsequently, I published a series of application notes and a book on the subject. So, why do we need another article? Many engineers don’t want to do the full detailed noise analysis and just need some quick rules of thumb to get their designs “in the ball park.” For those wanting a quick and simple method to minimize noise, this article is for you.

There are three sources of noise in op amp circuits: op amp voltage noise, op amp current noise, and resistor noise (Figure 1). The op amp current noise is translated to noise voltage when it flows through the feedback network and input source impedance.

When doing noise calculations, a common approach is to refer all the noise sources to the amplifiers input. You can calculate input-referred noise for feedback resistors by using the equivalent parallel combination of two resistors (Equation 1). You can calculate noise spectral density using Johnson’s thermal noise equation (Equation 2 and Figure 2 graph), as well as noise from the input resistor (R_{IN}).

**Figure 2**

Using Equation 3, combine noise from the input resistor, R_{IN}, and noise from the equivalent feedback network, R_{EQ}. Use this equation whenever you need to combine any random and uncorrelated noise source.

Generally, you will want to minimize noise generated by the feedback and input resistance to a level much smaller than the op amp voltage noise. In other words, make the op amp voltage noise the dominant source of noise in the circuit. Low-noise amplifiers are expensive and there is no benefit to choosing a low-noise amplifier, if resistor noise dominates. For example, if using a low-noise 1 nV/rtHz amplifier with resistors that have 10 nV/rtHz of noise, total noise is dominated by the resistor (E_{NTOTAL} = 10.05 nV/rtHz).

**Rule 1**

Select the appropriate resistors. In general, resistor noise should be about one-third of the op amp voltage noise. The point is that noise is added as the root sum squared. A factor of three translates to a factor of nine, which is a large enough difference to minimize the effect of the resistor noise (Equations 4, 5).

**Rule 2**

This next rule assures that current noise does not contribute significant noise compared to the amplifier voltage noise. For CMOS amplifiers, bias current noise is rarely a problem. In the case of bipolar devices, however, the effects of bias current noise can be minimized by carefully selecting the input resistors. Translate current noise to voltage noise by multiplying by the equivalent resistance. Make sure that the translated current noise is one-third the voltage noise density.

*Rule 2: Choose an equivalent resistor that sets the current noise to one-third of the amplifier voltage noise:*

**Rule 3**

Engineers want to minimize the total rms noise, which is calculated by integrating the noise spectral density across frequency. For this calculation, the wider the bandwidth the larger the total rms noise. Equation 10 shows how broadband noise spectral density can be translated to rms noise. Nevertheless, this calculation is not necessary to minimize rms noise. Instead, simply choose the lowest possible bandwidth that works for your application.

**Rule 4**

My last rule relates to the 1/f noise region, which often garners a lot of undue concern. In many cases the contribution of 1/f noise is small relative to the broadband noise and can be ignored. If the system’s bandwidth is ten times greater than the 1/f noise corner, ignore the contribution of the 1/f region. Generally, 1/f noise is only problematic in low-frequency systems, such as temperature-monitoring.

*Rule 4: Compare the 1/f noise corner to the closed-loop op amp bandwidth. If the bandwidth is 10 times the noise corner, you can ignore 1/f (Figure 3). If not, search for amplifiers with lower 1/f noise, or use more advanced calculations to estimate the rms 1/f noise. *

**Summary**

These four rules can help you to quickly design a low-noise system. Any calculations required are relatively simple. This method can give you a quick and intuitive way to analyze the circuit, versus getting lost in comprehensive calculations. For a more compressive analysis, TI Precision Labs and the resources provided and can help to broaden your understanding of this subject.

Join us next time when we will discuss the advantages in using current-sense amplifiers in low-side current-measurement applications.

**References**

- A. Kay, Operational Amplifier Noise: Techniques and Tips for Analyzing and Reducing Noise. Elsevier, 2012
- A. Kay and T. Green. Analog Engineer’s Pocket Reference. Texas Instruments, 2015
- A. Kay and Ian Williams, TI Precision Labs, Noise Section, (You will need to register) Texas Instruments, 2015