SBOA570 may 2023 LMC6061 , LMC6081 , OPA192 , OPA2277 , OPA2350 , OPA277 , OPA320 , OPA328 , OPA350 , OPA391 , OPA392 , OPA4277 , OPA4350

6 Current Noise Correlation

In noise analysis noise sources are typically considered to be random and uncorrelated. For this reason, two noise sources will add as the square root sum of the square (RSS). Equation 1, shows how two random uncorrelated noise sources add. For two completely independent circuit elements you can assume that the noise will be uncorrelated. For example, the noise on two separate resistors will be uncorrelated. However, if a single noise source is coupled through different paths, the noise at the output of each path will be correlated to each other. For example, if a single noise source connects to two different amplifiers, the noise at the output of the amplifiers will be correlated to each other. Equation 2 shows how correlated noise sources add. The correlation factor indicates the degree to which the signals are correlated. If two signals have an identical wave shape they are directly correlated and the correlation factor is +1.0. The equation for this case simplifies to directly adding the two signals to each other ( $e_{n T o t a l} = e_{n 1} + e_{n 2}$ ). On the other hand, when two signals have identical wave shape but one is inverted relative to the other, they are inversely correlated and the correlation factor is -1.0. The equation for this case simplifies to directly subtracting the two signals from each other ( $e_{n T o t a l} = |e_{n 1} - e_{n 2}|$ ).

Equation 1.

e_{n T o t a l} = \sqrt{{e_{n 1}}^{2} + {e_{n 2}}^{2}}

e_n1, e_n1 are random and uncorrelated noise sources

Where

e_nTotal is the combination of these signals

Equation 2.

e_{n T o t a l} = \sqrt{{e_{n 1}}^{2} + {e_{n 2}}^{2} + 2 C e_{n 1} e_{n 2}}

Where

e_n1, e_n1 are random noise sources

e_nTotal is the combination of these signals

C is the correlation factor ranging from -1.0 to +1.0

From an amplifier current noise perspective, there are some cases where the current noise may be correlated. Depending on the internal amplifier design, there may be a common voltage noise source that will couple to the amplifier inputs via the gate to source capacitance. Since this noise couples through capacitance, it acts as an f-squared noise component. In this case, the noise on both inputs originates from the same bias circuitry, so the noise is directly correlated. Matching the impedance, on both the inverting and non-inverting inputs of the amplifier, will translate the current noise into two equal directly correlated voltage noise values. The common mode rejection of the amplifier will effectively subtract the two noise sources from each other and cancel the noise. Of course, any amplifier can have multiple noise sources and not all of the noise will be correlated, so the noise will not completely cancel. Furthermore, many amplifiers will not have any significant correlation in the current noise, so balancing the impedance will not always improve noise.

In general, details on the correlation of noise are not published in amplifier data sheets, so the best way to confirm if balancing the impedance helps is through experimentation. Keep in mind that balancing the impedance can necessarily require adding additional resistors, and the resistors can contain uncorrelated voltage noise. The OPA392 is an example of a device that does have a strong correlation in the current noise.