Many amplifiers exhibit an increase in voltage noise spectral density (NSD) as they approach the unity-gain crossover frequency. This noise peaking can cause your circuits to have 39% higher noise than you expected. This is especially troublesome in unity-gain circuits, also called buffer or voltage-follower applications.
Such peaking occurs when the spot noise becomes greater than the noise floor of the amplifier, and this behavior can extend for several octaves beyond crossover. These effects are present at frequencies well beyond what is shown in most manufactures’ datasheets, and most textbooks don’t discuss the issue at all. The topic remains “out of sight” until you are working with a low-noise, low-gain circuit that seems to have excessive amounts of noise.
The amplifier is set up as a unity gain buffer (Fig. 1). It has a –3-dB bandwidth of 16 MHz, and the noise floor is 16 nV/√Hz at 100 kHz. Notice how the noise density starts to increase around 2 MHz. To make matters worse, the –3-dB noise bandwidth is about 30 MHz.
1. The frequency response of the AD823 op amp in a unity-gain configuration rolls off predictably (red), while the voltage noise spectral density plot shows noise peaking (black).
An academic analysis states that the total noise is equal to the noise floor multiplied by the square root of the noise bandwidth, which is π/2 times larger than the –3-dB bandwidth, for a single-pole rolloff. This calculation shows that the total noise is 80 µVRMS. If you integrate the NSD over the entire bandwidth, the total noise is 111 µV, which is 39 % higher.
Unfortunately, this amount of error is about as good as it gets. Many amplifiers are much worse. Peaks that are 10 times greater than the noise floor are possible. Most amplifiers will have a peak that is 50% to 200% greater than the noise floor.
There are two causes of noise peaking:
- Intrinsic noise peaking: This type of noise peaking is set by the design of a particular op amp. Once a specific model of op amp is chosen for a circuit, the intrinsic noise peaking is set.
- Stability noise peaking: This type is affected by the way the amplifier is used in the circuit.
Most amplifiers are designed so the input stage dominates their noise performance. All of the transistors in an amplifier contribute noise, but their noise is reduced by application of negative feedback. Any gain that precedes a noise generator will reduce the noise that is contributed to the amplifier by that generator.
At most frequencies, there is plenty of gain ahead of all of the transistors except the input stage. Great care and significant amounts of current are spent to make the input stage achieve the noise performance required for the amplifier. This works well enough at lower frequencies.
At higher frequencies around the amplifier’s unity-gain crossover frequency, there is no gain to suppress any noise generated by the transistors inside the amplifier. Any noise that makes its way to the output with a magnitude greater than the noise floor of the amplifier will dominate the total noise. The specific transistors that dominate are unique to every amplifier design.
The stability noise-peaking effect is present in all feedback structures, including the output buffers of voltage references and voltage regulators. A mediocre amplifier may have a noise floor that’s so high that it mask any intrinsic noise peaking. A high-performance, low-noise amplifier has flat-band noise that’s low enough that you can observe the effects of noise peaking.
The feedback-loop stability controls the stability noise peaking. As previously noted, the negative feedback of an amplifier suppresses the noise generated from most of the transistors. As the phase margin degrades, this feedback is no longer negative. The signals near the unity crossover frequency are fed back more in phase with the incoming signal. This causes the closed-loop response to peak near the crossover frequency. The same mechanism responsible for frequency peaking of the signal also causes frequency peaking of the noise.
Avoid destabilizing the feedback loop, because doing so has a detrimental effect on the noise performance. Well-intentioned engineers will place a capacitor at the output of an op amp to “filter” noise. This makes the noise much worse, because the capacitive load adds more phase shift to the feedback loop (Fig. 2).
2. Adding load capacitance at the output intending to filter the noise reduces phase margin and increases noise peaking.
As you load the output of the amplifier with more capacitance, the noise peak grows. The log scales on this plot mask the true severity of the situation. The total noise at the output is the value of the noise spectral density integrated over the entire bandwidth. There is much more bandwidth from 2 MHz to 16 MHz than there is from dc to 2 MHz.
This means the noise is completely dominated by the noise peak and has nothing to do with the thermal noise floor. To compare these results, assume that the rest of the system has limited the –3-dB bandwidth to 16 MHz (25-MHz noise bandwidth). The total integrated noise for CL of 8 pF, 220 pF ,and 470 pF is 95 µVRMS, 110 µVRMS, and 115 µVRMS, respectively.
The proper way to filter the output of a buffer is to place an RC filter at the output (Fig. 3). The resistor makes the amplifier load appear resistive at high frequencies, which avoids adding phase shift to the feedback loop. This technique will reduce the accuracy of the buffer if it is resistively loaded.
This example assumes the entire 16-MHz bandwidth of the buffer is required in the application. The pole frequency of the filter is set approximately 28 MHz. The filter causes a substantial reduction of the out-of-band noise (Fig. 4). The total integrated noise without the filter is 111 µVRMS, while the total noise with the filter is 84 µVRMS. This represents a 25% reduction in noise without affecting the signal bandwidth.
4. Using the RC filter, the noise spectral density improves over frequency as out-of-band noise is reduced.
Better performance can be obtained when the RC filter limits the signal bandwidth of the amplifier. In this case, the filter sets the –3-dB bandwidth of the signal as well as the noise bandwidth of the amplifier.
The lowest-noise results occur when this filter frequency is set before the noise floor starts to peak. This would be approximately 2 MHz in the case of the AD823. Under these conditions, it is possible to approach the theoretical limit of the noise floor, multiplied by 1.57 × f–3dB. The designer must determine if it is appropriate to throw away a significant amount of amplifier bandwidth to improve the noise of the circuit.
At this point, circuit designers may wonder why amplifier data sheets tout their 1/f noise and the thermal-noise performance specifications, when they have nothing to do with total noise in an amplifier. The answer is that they do matter, but only in higher-gain configurations. Great things happen when an op amp is placed in a gain configuration. The loop stability improves, so the noise peaking induced by phase shift is reduced to an insignificant level.
The intrinsic noise peak remains, but it becomes less significant compared to the thermal noise floor (Fig. 5). This is because the intrinsic sources feed directly into the output of the amplifier without any gain. As a result, they remain relatively constant, no matter how the amplifier is set up. The thermal noise floor becomes much more significant because it is “gained up” by the amplifier. The intrinsic noise peaking is visible as bumps in the rolloff region of the higher gain curves.
5. A graph of the AD823 op amp’s output NSD versus frequency clearly shows that the significance of the noise peaking is reduced as the gain increases.
There are many practical implications of noise peaking to consider. First, the noise peak will dominate the total noise in low-gain configurations. Designers should plan for this occurrence and test several amplifiers, if it is critical for the application. Two different amplifiers with the same noise floor can have vastly different amounts of total integrated noise.
Second, filter the outputs correctly with passive RC filters. These filters can have a significant impact on the total system noise. Never add capacitance directly to the amplifier’s outputs (or inputs). This only serves to degrade the feedback-loop stability.
Finally, design the signal path to take as much gain as possible early in a system’s signal chain. This is the best solution if it is possible, since the total noise performance of the system is dominated by the high-gain front-end amplifier.