To paraphrase Daniel Defoe and Benjamin Franklin, there are only two things that are certain in life: death and taxes. Unfortunately for those that deal with electronics, there is another: noise. Although electrical noise cannot be avoided, a better understanding of the various noise sources and how they each contribute to the overall system noise level enables designers to minimize the impact. From the system perspective, noise can originate from a variety of places. There are noise sources that are generated inside the operational amplifier, along with noise from the passive components that are used within the op-amp circuitry. There is also a wide variety of external sources, such as radio waves or ac mains. This article will explore some of these noise sources, as they relate to the internal workings of operational amplifiers.
Flicker Noise
1/f noise, or flicker noise, is a low-frequency phenomenon caused by irregularities in the conduction path and noise due to the bias currents within the transistors. At higher frequencies, flicker noise is negligible as the white noise from other sources begins to dominate; hence the 1/f name. This low-frequency noise can be very problematic if the input signal is near dc, as often occurs in the outputs from strain gauges, pressure sensors, thermocouples or any slow-moving sensor signal.
Although system designers cannot control the internal flicker noise of an amplifier, they can minimize this noise source by selecting the proper amplifiers for the application. If 1/f noise is considered a big concern, then selecting an auto-zero or chopper-based amplifier may be the best solution. In these types of architectures, the 1/f noise is removed as part of the offset correction process. This noise source appears at the input and is relatively slow moving, hence it appears to be a part of the amplifiers offset and gets compensated accordingly.
Shot Noise
Perhaps a lesser-known internal noise source is shot noise, or Schottky noise. This noise source is a result of imperfections in the conduction of charge carriers. Electrical current is electrons moving based on an applied potential. As these electrons run into barriers (imperfections in metals, etc.) the potential energy builds up until the electron shoots across the barrier.
Since shot noise is associated with current flow, if there is no current flowing, there is no shot noise. Shot noise has a Gaussian probability density distribution and is independent of frequency and temperature. Finally, shot noise is inversely proportional to dc current, so less current means more shot-noise voltage. To determine whether shot noise is a factor within a given design, reduce or increase the dc current and see if the noise is affected.
Thermal Noise
Also called Johnson noise, after the person who discovered it, thermal noise is present in all active and passive circuit components. Heat causes electrons to increase their movement, resulting in a random factor to their motion that produces noise. As such, thermal noise is similar to shot noise in that it has a Gaussian probability density distribution and is independent of frequency.
Thermal noise is present in passive components, as well. This is perhaps most notable with resistors, as the thermal noise of the resistor is dependent on the size of the resistance and the temperature. Smaller-sized resistors have less thermal noise, and lower temperatures also help to minimize thermal noise.
Noise Specifications for Operational Amplifiers
We have reviewed several sources of noise that are present within operational amplifiers, all of which contribute to the noise specifications of the actual amplifier. System designers have many choices when it comes to selecting operational amplifiers. However, when it comes to low-noise op amps, a designer must consider a number of factors, including the amplifier’s voltage and current noise, as well as how the amplifier will be used within the application.
In most cases, manufacturers will tout the voltage-noise-density specification of an operational amplifier when discussing noise. Although this is an important specification, it is not the only one. Often, current noise may be a bigger concern. The input-voltage-noise density is specified where the white noise of the amplifier dominates (eliminating the effects of 1/f noise). Current-noise density is also specified where the white noise of the amplifier is dominant, and is critical for applications in which the input resistance is high. Let’s look at a simple example using two equivalent operational amplifiers, Microchip’s MCP621S and Texas Instruments’ LMP7731.
Table 1 highlights some of the key specifications of these two amplifiers.
These two op amps are similar, in terms of offset performance, speed and operating-supply range. Their noise specifications, on the other hand, vary considerably. Operational amplifiers are often promoted as low noise if the voltage-noise density is low. But is the lowest voltage-noise density amplifier always superior in terms of noise performance?
Let’s look at a simple voltage-follower circuit, shown in Figure 1.
Actual circuit design must take into consideration the noise from a multitude of sources, including the internal noise of the ICs, the thermal noise of all components as well as the external noise sources. However, this example will focus only on the noise associated with the amplifier and the thermal noise of the input resistance, noted here as RIN.For the purposes of this exercise, we will specify the thermal noise of this resistorat an ambient temperature of 25ºC.
When the source impedance is zero, there is no noise component due to current noise of the amplifier (since this current must flow through an impedance to cause a voltage error). Likewise, the thermal noise of the input resistor is also zero, when the resistance is zero. In this case, the noise is dominated by the voltage noise of the amplifier;therefore the LMP7731 offers superior performance, as can be seen in the first data column of Table 2.
However, if the source impedance is increased to 10 kΩ, the contribution of the thermal noise associated with this resistance begins to factor in. Recall that the thermal-noise voltage of a resistor is defined as:
V_TH=√4kTRB
Where:
VTH = Thermal Noise Voltage (Vrms)
k = Boltzmann’s constant (1.38 x 10-23)
T = Temperature (ºK)
R = Resistance (Ω)
B = Bandwidth (Hz)
Rearranging this equation to provide the thermal noise as nV/√Hz:
V_TH’=√4kTR
Where:
VTH’ = Thermal noise in nV/√Hz
When multiplied by the source resistance, the amplifier-current noise of the LMP7731 also becomes a factor, which isn’t the case for the MCP621S (see Table 2, second data column). Finally, in the case where the source impedance is increased to 100 kΩ, the thermal noise of the resistance is the dominant factor for the MCP621S. However, in the case of the LMP7731, the amplifier-current noise becomes dominant (see Table 2, third data column).
This simple circuit example highlights the fact that an amplifier’s voltage and current noise must be taken into consideration, when analyzing its noise performance for a given application. For a high-impedance application, such asa pH meter or oven oscillator, using an amplifier with low current noise is critical, as that source can quickly become the dominate noise factor.
In addition to an amplifier’s specified noise parameters, this article explored some of the inherent noise sources that are present within operational amplifiers. Although these noise sources may not be directly accounted for at the system level, an understanding of these various noise sources can assist system designers in minimizing the adverse effects of noise within their applications.
Author
