What you need to know about the noise of operational amplifiers

1 Why is the issue of low-noise amplification emphasized again recently?

　　Part of the problem with low noise amplification has to do with the signal-to-noise ratio (SNR).

　　2 What kind of noise are we talking about?

　　This noise is inherent in the amplifier itself or generated and amplified by corresponding passive components.

　　External noise is a system-level issue.

　　3 What is the source of this noise?

　　Thermal noise comes from the input and feedback resistors (en, R2), the amplifier's inherent voltage noise (en), and current noise (in) (Figure 1). The input-referred noise equation (Noise RTI), shown in Figure 1, shows the contribution of all noise sources. The "k" factor in the resistor noise expression is the Boltzmann constant. T is the absolute temperature and R is the resistance in ohms. A rule of thumb is that a 1kΩ resistor produces 4nV/Hz of noise at room temperature, which is higher than the noise of some modern op amps.

　　4 How to represent noise?

　　To allow all noise sources to be easily combined by taking the square root of the square sum, the baseband noise specification is expressed in nV (or pA)/Hz. This representation is acceptable as long as the noise sources are uncorrelated, so that the probability of any given signal amplitude occurring over the entire spectrum follows a normal (Gaussian) distribution.

　　5. Is noise not truly constant at all frequencies?

　　Indeed, not really. en and in have two components (Figure 2a): low-frequency "1/f" noise, whose spectral density increases at a rate of 3dB/octave as frequency decreases, and "white" noise with a flat spectral distribution at higher frequencies. For applications where 1/f noise is important, peak-to-peak noise specifications over limited bandwidths, such as 0.1 to 10Hz, can be found in product manuals (Figure 2b).

　　6 What is the “corner” frequency and why is it important?

　　The frequency point where the spectral density of 1/f noise equals that of white noise is called the 1/f corner frequency (FC). It can be determined by extending the 1/f and white noise portions of the noise plot to their intersection. It is an important figure of merit. In addition, the 1/f corner frequencies of voltage and current noise are not necessarily the same. However, in general, only voltage noise is specified.

　　7. How should this information be used in the selection of a low-noise amplifier?

　　Consider the frequency band of interest and relate the rms noise within the band to your system requirements.

　　Since noise is expressed as the square root of frequency, the contribution of each noise can be calculated by summing the squares of the noise and then taking the square root.

　　Therefore, within the bandwidth FL~FH, the total rms voltage noise en,rms can be simply expressed as:

　　In the above formula, en,w is broadband white noise, FC is the 1/f corner frequency, and FL and FH define the measurement bandwidth of interest.

　　Generally speaking, any noise component that is 4 to 5 times higher than any other noise component will become the dominant noise, while the remaining components can be ignored. Therefore, at higher frequencies, the effect of FC ln(FH/FL) is no longer significant, and the total rms noise is equal to the white noise multiplied by the square root of the frequency difference. In fact, if FH is much higher than FL, the total rms noise is equal to the white noise multiplied by the square root of FH. On the other hand, when the device operates in the 1/f noise region, the total rms noise is the noise level at the corner frequency (i.e., the white noise level) multiplied by the square root of the corner frequency multiplied by ln(FH/FL).

8 What about current noise?

　　The fourth and fifth terms of the equation in Figure 1 show that when current noise flows through an impedance, it produces a noise voltage that adds to the other noise voltages in the form of a “square root of the sum of the squares.” Furthermore, while voltage noise is the first specification a designer considers, current noise will dominate if the circuit impedance level is higher than en/in (sometimes referred to as the amplifier’s “characteristic noise resistance”).

　　Figure 1: Noise sources (thermal noise, inherent voltage and current noise from external resistors) are all amplified by the circuit’s noise gain (1+R2/R1).

　　Figure 2: Above the corner frequency, the spectral density of the inherent noise is essentially constant. It rises at a rate of 3dB/octave between the corner frequency and 0Hz (a). The actual peak-to-peak noise is available in the data sheet when the 1/f noise becomes critical (b).