Practical Information | How to Characterize Noise in Operational Amplifier Circuits?

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Even considering all known and unknown impedance loads of the op amp, the output of the op amp will always contain signals that cannot be predicted based on the input signal and a completely known closed-loop transfer function. This uncertain signal is called noise.

Noise may be generated by the amplifier circuit itself, by components used in its feedback loop, or by the power supply; it may also be coupled or induced into the input, output, ground return, or measurement circuitry from nearby (or remote) noise sources.

Of course, the degree to which we care about noise depends on two things:

1. The resolution that the circuit needs to achieve in the target frequency band;

2. Avoid noise shifting to non-directly related frequency bands.

Since operational amplifiers are often used as preamplifiers and high-precision signal processors, the accuracy of operational amplifier circuits has received increasing attention. So today we will talk about [Noise and Operational Amplifier Circuits].

From a noise perspective, op amps have unique advantages and are well suited for low voltage and high precision circuits because:

• A specific amplifier transfer function can be chosen to pass only the frequency band of interest.

• The amplifier that meets specific needs can be selected from a wide range of models with different noise characteristics in order to obtain nearly ideal characteristics within the target frequency band.

• If the noise sources are known and properly evaluated, the noise behavior of various amplifier circuits can be predicted with sufficient accuracy to provide a basis for preliminary manual design with some probability of successful verification.

The differential op amp can be considered an ideal noise-free amplifier with noise current sources between each input pin and common-mode ground and noise voltage sources in series with one input pin. This model is very similar to the E _OS - I _{bias model used in offset analysis 2, which is not surprising because E OS} and I _bias can be considered as DC noise sources that can be modulated by parameters such as time and temperature.

Figure 1. Voltage and current noise model

In most practical applications, the noise voltage and noise current sources can be considered independent of each other. If circuit and amplifier dynamic range considerations are temporarily ignored, such as E _OS and I _bias , the instantaneous voltage component of the noise can be measured across a low impedance, high gain circuit (Figure 2), while the instantaneous current component can be measured across a large (ideally "noiseless") resistor. If there is no interaction between e _n and i _n , the noise voltage measurement output will be proportional to (1 + R ₂ /R ₁ ), while the noise current measurement output will be proportional only to R ₂ .

Note that the instantaneous sum of these two types of noise (appearing at the amplifier output) is

And the relative noise contributions of en and in are equal when the following equation holds true

That is, the condition is: the parallel combination of R2 and R1 is equal to the ratio of en _to in _. At impedance levels above en _/ in _{, current} noise _dominates . The ratio of the rms values _{​​of en} and _in is sometimes called the "characteristic noise resistance" of an amplifier at a given bandwidth and can be used as a practical figure of merit when selecting an amplifier to match a given impedance, or vice versa.

Figure 2. Basic measurement of e _n and i _{n (filters are required for narrowband and spot noise measurements)}

In the case of known voltage and impedance, the noise coupled from the external source to the amplifier input pin can be considered as an additional voltage signal, or when the generation of this signal depends on some measurement method of the amplifier, it can also be considered as an additional current signal, as shown in Figure 3.

Figure 3. Contribution of internal and external noise sources

A basic feedback model for an inverting amplifier with several resistive input pins is shown in Figure 4. For large values ​​of loop gain (A β ), the noise gain of the voltage noise is actually 1/ β .

Figure 1. Voltage and current noise model

If A β is not much above unity gain, the following more precise expression can be used

The corresponding current noise expression is:

Note that for passive feedback components, 1/ β will never be less than unity gain and will be greater than the closed-loop gain for any input signal. Therefore, even if the signal gain is less than unity gain or the signal bandwidth is narrow, the total spectrum of en will appear at the output with a value at least equal to unity gain.

Also note that, in general, when A and β are both dynamic expressions, if the phase shift of the loop gain is somewhat above 900, the amplifier is underdamped in the frequency range near A β = 1, and the peak of the noise gain at this frequency may be much higher than unity gain, even though the signal gain rolls off smoothly at lower frequencies. Figure 5 shows a simple, easy to understand example.

Figure 5. Noise bandwidth vs. signal bandwidth

Periodic, repetitive noise can be described based on recurrence rate, waveform, and amplitude (e.g., chopper noise). Irregular noise can only be described by its waveform and amplitude, since its variations are not regular (popcorn noise falls into this category, to some extent). Non -periodic noise, which does not have a repetitive waveform, is usually described by its statistical properties: RMS value, peak value, and frequency content.

RMS value. Most random noise has the following characteristics: if the average interval is long, the resulting RMS value has a large repeatability. Therefore, the target bandwidth RMS value obtained by averaging over a long interval is an effective way to determine the characteristics of this type of random noise. So far, this is the simplest way to estimate the various noise factors that is more acceptable to manufacturers and customers. The voltage RMS value is defined as follows

in

E _rms = root mean square voltage

T = observation time interval

e = instantaneous noise voltage

Substituting the instantaneous current value i for the parameter, we get I _rms , the rms current value. To make rms measurements, you must use a "true rms" meter, or you can multiply the reading of the AC average value (sine wave rms calibrated meter) by a factor of 1.13.

Noise can also be characterized as the difference between the maximum positive amplitude and the maximum negative amplitude observed in any interval. In some applications, the peak-to-peak measurement may be necessary when the peak-to-peak noise may limit the system performance .

However, from a practical point of view, peak-to-peak noise is difficult to measure repeatedly because the noise amplitude distribution is Gaussian, so the probability of the highest noise amplitude is the lowest (but not zero). Since the rms value is easy to measure repeatedly and is the most recognized and commonly used representation of noise data, the following table can be used to estimate the probability of exceeding various peak values ​​for a given rms value.

The peak-to-peak noise values ​​typically observed are between 3 x RMS and 8 x RMS, depending on the observer's patience and the amount of data available. Oscilloscope traces can only be observed at higher intensities, but since a lot of the averaging is done at lower intensities, this will produce a result closer to the RMS value. In addition, there are an increasing number of peak amplitude distribution analyzers on the market that automatically measure this parameter.

The noise of a given circuit can be divided into two basic categories, namely, interference noise (noise picked up from outside the circuit) and intrinsic noise (noise generated inside the circuit).

Interference noise may be periodic, irregularly repetitive, or completely random, and can often be significantly reduced (or prevented) by taking the following precautions. For example, precautions are taken to improve electromagnetic interference caused by power line frequencies and harmonics, radio broadcast stations, mechanical switching arcs, and current or voltage spikes caused by switches in resistive circuits. Such precautions include filtering, decoupling, electrostatic and electromagnetic shielding of leads and components, use of guard potentials, elimination of ground loops, reorientation of leads and components, use of damping diodes in relay coils, and selection of low circuit impedance, low noise power supplies and reference sources whenever possible. Interference noise caused by vibration can be improved by mechanical design. The table in Figure 6 lists some sources of interference noise, their typical values, and how to deal with them.

Figure 6. Typical interference noise sources

However, even if all interfering noise is eliminated, intrinsic noise still exists. Intrinsic noise is usually random in nature and occurs in resistors and semiconductor components such as transistors and diodes. (An example of non-random intrinsic noise is chopper noise in a chopper-regulated amplifier.) Random noise generated in resistor components is called Johnson noise (also called thermal noise). Random noise generated in semiconductor components can fall into one of three categories: Schottky noise (or shot noise), flicker noise (1/f noise), and popcorn noise.

Source: Analog Devices

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