“IC design engineers and circuit designers are well aware that current noise increases with frequency, but many engineers struggle to understand why due to too little information in this area, or insufficient information from manufacturers.

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IC design engineers and circuit designers are well aware that current noise increases with frequency, but many engineers struggle to understand why due to too little information in this area, or insufficient information from manufacturers.

Many semiconductor manufacturers’ data sheets, including ADI, give the amplifier’s current noise in the spec sheet, typically at 1 kHz. But it is not always possible to indicate where the current noise parameter comes from. Is it by measurement? Or is it a theoretical inference?Some manufacturers clearly state that they do this through a formula

That is, the shot noise formula derives these values. Historically, ADI has provided most of the current noise figures this way. But are these calculated numbers equal to the noise of each amplifier at 1 kHz?

Over the past many years, there has been increasing interest in the relationship between current noise and frequency in amplifiers. Some customers and manufacturers assume that the current noise of a FET input amplifier is similar to that of a bipolar input amplifier, for example, 1/f or flicker noise and flat broadband noise components as shown in Figure 1. This is not the case for FET input amplifiers; as shown in Figure 2, the noise exhibits strange noise shapes that are unfamiliar and ignored in many simulation models.

Figure 1. Current noise of the AD8099 bipolar input amplifier.

Figure 2. Current noise of the AD8065 FET input amplifier.

**Measurement setup is key**

Before we figure out why this is the case, let’s take a quick look at the measurement setup. There is a need to identify easily reproducible, reliable measurements that can be reused in different devices.

The DC417B Single Amplifier Evaluation Board may be required. The power supply used in the device under test (DUT) must have low noise and low drift characteristics. A linear power supply is more appropriate than a switching power supply, so that characteristic changes introduced by the power supply, such as switching artifacts, do not affect the measurement results. The LT3045 and LT3094 are linear regulators with ultra-high PSRR and ultra-low noise positive and negative outputs that can be used to further reduce ripple from linear power supplies. A single resistor configuration allows the LT3045 and LT3094 to achieve output voltages as high as +15V and as low as -15V. Both devices are ideal laboratory power supplies for low noise measurements.

Figure 3. Measurement setup.

A 10 GΩ SMT resistor from Ohmite (HVC1206Z1008KET) was used to convert the current noise on the noninverting pin of the DUT to voltage noise. Typical bias current for FET-input amplifiers is about 1 pA, which equates to a typical noise of 0.57 fA/√Hz.

if the formula

Correct words. The 10 GΩ source impedance thermal noise is

This gives us the noise floor of the measured current

This value can be subtracted in post processing. However, if the current noise in the resistor due to thermal noise dominates the current noise of the DUT, it cannot be measured accurately. Therefore, at least a resistance value of 10 GΩ is required to measure noise. The thermal noise for a 100 MΩ source impedance is about 1.28 μV/√Hz (= 12.8 fA/√Hz), but this is not enough to differentiate between DUT and resistor noise. This noise, if uncorrelated, adds up as a root sum square (RSS). Figure 4 and Table 1 show the RSS effect on the ratio of the two values. n:n increased by about 41%, n:n/2 increased by about 12%, n:n/3 increased by about 5.5%, and n:n/5 increased by about 2%. When the average is sufficient, we might be able to draw 10% from it (0.57 fA/√Hz and 1.28 fA/√Hz RSS).

Figure 4. RSS increase based on the ratio of two numerical values.

Table 1. RSS increase based on two numerical ratios

**Why is the result so strange?**

Figure 5 shows the noise voltage density set up using the AD8065, a 145 MHz FET input op amp with 2.1 pF common-mode input capacitance. The 10 GΩ resistor thermal noise is 12.8 μV/√Hz until the board’s input capacitance and socket stray capacitance roll off the voltage noise. Ideally, it should roll off at C20 dB/dec, but the curve starts to change shape at about 100 Hz and goes flat at about 100 kHz. What’s going on here? Intuition tells us that the only way to stop the C20 dB/dec roll off and achieve flatness is to provide a +20 dB/dec ramp. Current noise is the key to providing this ramp, which increases with frequency and has a +20 dB/dec slope.

Figure 5. Output-referenced voltage noise density.

An SR785 dynamic signal analyzer or FET instrument can be used to measure output voltage noise; however, an instrument with a noise floor below 7 nV/√Hz would be more suitable. As the output voltage noise of the DUT rolls off near 20 nV/√Hz to 30 nV/√Hz, we want the analyzer noise floor to increase as little as possible to the amount of noise being measured. The 3x ratio is only about a 5.5% increase. A maximum of 5% error is acceptable in the noise domain (see Figure 4).

**The subtlety lies in the reverse calculation**

Measuring in this way, the two main parameters needed to map current noise can be obtained in one measurement. First, we get the total input capacitance, which is the sum of the stray capacitance and the input capacitance, which is needed to calculate the roll-off in reverse. Even if there is stray capacitance, its value can be obtained by inverse calculation. The input capacitance is more dominant than the 10 GΩ resistor. The total impedance converts current noise to voltage noise. Therefore, it is very important to grasp the total input capacitance. Second, it shows where the current noise starts to dominate, i.e., where does it start to deviate from the C20 dB/dec ramp.

Let’s take a look at an example in Figure 5 that takes this data. The 3 dB roll-off point corresponds to 2.1 Hz, which is the same as the

Capacitance corresponds. From the data sheet, the common-mode input capacitance is only about 2.1 pF, which means there is about 5.5 pF of stray capacitance. Differential mode input capacitors are bootstrapped by negative feedback, so they will not function at low frequencies. With a 7.6 pF capacitor, the impedance of the current noise is shown in Figure 6.

Figure 6. Total impedance magnitude for a parallel 10 GΩ resistor and 7.6 pF input capacitor.

Taking the voltage noise referred to the output (RTO) measured on the AD8065 (Figure 5) and dividing by the impedance vs frequency (Figure 6), the equivalent current noise of the AD8065 and 10 GΩ resistor combined in the RSS ( Figure 7).

Figure 7. RTI current noise for AD8065 and 10 GΩ resistor.

After removing the 10 GΩ current thermal noise (Johnson noise divided by the resistor value), the input-referred noise of the AD8065 is shown in Figure 8. Below 10 Hz, the noise is heavily distorted because we try to strip 0.5 fA/√Hz to 0.6 fA/√Hz (10% in RSS scale) current noise from 1.28 fA/√Hz, where There are only 100 averages. Between 15 mHz and 1.56 Hz, there are 400 lines with a 4 mHz bandwidth. i.e. 256 seconds/average! 100 averages, 256 seconds each, for a total of 25,600 seconds, a little over 7 hours. Why do you need to measure down to 15 mHz and why does it take so much time? The 10 pF input capacitor and 10 GΩ resistor create a 1.6 Hz low-pass filter. The low noise FET amplifier has large input capacitance, up to 20 pF, corresponding to the 3 dB point at 0.8 Hz. To properly measure the 3 dB point, we need to increase the measurement of the frequency margin forward by a factor of ten, that is, all the way down to 0.08 Hz (or 80 mHz).

If we observe blurry lines below 10 Hz, it can be obtained by the following equation

Confirm 0.6 fA/√Hz. Using this formula to calculate current noise is not entirely wrong. In a first-order approximation, the low-frequency current noise behavior of the part is still shown, because this current noise density value is obtained from the DC input bias current. However, at high frequencies, the current noise does not fit this formula.

Figure 8. RTI current noise of the AD8605.

At higher frequencies, DUT current noise is more dominant than resistor current thermal noise, which is negligible. Figure 9 shows the noise value referred to the input of a FET-type op amp at 10GΩ, measured using the setup shown in Figure 3. It seems that the typical noise performance of most precision amplifiers is: 100 fA/√Hz at 100 kHz.

Figure 9. RTI current noise of selected ADI amplifiers.

There are of course some exceptions: the LTC6268/LTC6269 have a current noise of 5.6fA/√Hz at 100kHz. These parts are ideal for high-speed TIA applications that require high bandwidth, low input capacitance, and femtoamp bias current.

Figure 10. Input-referred current noise of the LTC6268.

**Is this all the current noise in the FET input amplifier?**

The total input current noise in high source impedance applications mainly comes from 4 current noise sources, of which we have covered 2 so far. A simplified equivalent circuit of a TIA amplifier with dominant noise sources is shown in Figure 11 below. The MT-050 is a good reference document for introducing op amp noise sources.

Figure 11. Simplified TIA amplifier with dominant noise source.

**from the FET input amplifier (i _{n_dut}) current noise**

The current noise profile is determined by the amplifier input stage topology. In general, current noise remains flat at low frequencies, but becomes larger as frequency increases. See Figure 8. Finally, as the amplifier runs out of gain at higher frequencies, the noise rolls off at C20 dB/dec.

**from the resistance (i _{n_R}) current thermal noise**

This can be done using resistor e

_{n_R}The thermal noise is divided by the impedance of the resistor value R. 1 MΩ yields about 128 fA/√Hz and 10 GΩ yields 1.28 fA/√Hz.

The thermal voltage noise of the resistor is very flat over frequency until the capacitor rolls off at C20 dB/dec. Figure 5 shows how this behavior behaves in the 10 mHz to 1 Hz range.

**from the sensor (i _{n_source}) current noise**

Sensors also generate current noise, and we have to accept this reality. In the frequency range, noise may appear as various patterns. For example: a photodiode exists from the photocurrent I

_{P}The shot noise I of

_{sn}and the dark current I from the shunt resistor

_{D}and Johnson noise I

_{jn}.

**Current noise from amplifier voltage noise itself**

The current noise from the amplifier voltage noise is called e

_{n}C noise, described in detail in “The Art of Electronics” by Horowitz and Hill (the Chinese translation is “Electronics”). Similar to resistor thermal noise converted from resistors to current noise, amplifier voltage noise e

_{n_dut}Converted to current noise from the total input capacitance, which includes sensor capacitance, board stray capacitance, and amplifier input capacitance.

**In the first order, we use**

From this formula, we can see three points. First, the current noise increases with frequency, and the other current noise component increases with frequency. Second, the greater the input voltage noise of the amplifier, the greater the current noise. Third, the larger the total input capacitance, the larger the current noise. From this, the quality factor enC of the current noise is derived, where the voltage noise of the amplifier and the total input capacitance are the key factors in determining this metric.

The current noise graph for a TIA application (ignoring DUT current noise) is shown in Figure 12.The flat part is mostly resistive noise

**The current noise due to the capacitance is**

Increase with a slope of 20 dB/dec.The formula for calculating the intersection point can be derived from the two equations

Figure 12. enC noise over frequency range.

According to C_{in}e_{n}C may be higher or lower than the DUT current noise. For inverting amplifiers, such as TIA applications, C_{dm}Not bootstrapped; that is:

For example, at 100 kHz, the C of the LTC6244_{cm} = 2.1 pF, C_{dm} = 3.5 pF, e_{n} = 8 nV/√Hz , corresponding to e_{n}C current noise is

**This is well below the 80 fA/√Hz DUT current noise**

However, when the photodiode is connected, an additional C is added to the formula_{source} or C_{pd}, then the current noise needs to be recalculated. even C_{pd} A capacitance value of only 16pF produces the same current noise as the DUT. Low-speed large-area photodiodes have PD equivalent capacitances of 100 pF to 1 nF, and high-speed small-area photodiodes have PD equivalent capacitances of 1 pF to 10 pF.

**Summarize**

IC design engineers and experienced circuit designers are well aware that in CMOS and JFET input amplifiers, current noise increases with frequency, but due to too little information in this area or incomplete information provided by manufacturers, many It is difficult for engineers to understand why. The goal of this article is to help you understand the characteristics of current noise from low frequency to high frequency, and to introduce a method that can repeatably measure op amp current noise.

**appendix**

In a high impedance environment, measuring the FET input with 10 GΩ impedance noise requires attention to the environment and details.

In a typical single amplifier pinout, Pin3 (Vin+) is adjacent to Pin4 (VC). The layout of the board is very important when there are no guard rings. When scanning the power supply, there is a noticeable DC offset at the output. The 10 GΩ SMD was initially soldered in parallel with VC (R10 in Figure 13), so solder paste leakage was unacceptable. Therefore, the 10 GΩ SMD is moved to another position (R8), thereby eliminating leakage. The data sheet for the ADA4530-1 Electrometer Grade Amplifier, 20 fA at 85°C) shows all the error prevention related to solder paste selection, contamination, humidity effects, and other interesting details related to high impedance measurements. The data sheet and user guide UG-865, as well as the circuit note CN-0407, are well worth reading.

Figure 13. Measurement setup.

Devices with high impedance, not soundproofing, are very susceptible to triboelectric, piezoelectric, or microphonic effects. One day, my keys dropped by accident and the noise spectrum displayed by the facility’s equipment showed a spike in the frequency range audible to humans (1 kHz and above). I didn’t think a noise measurement circuit with a 10GΩ resistor in front of a high impedance FET op amp would be very sensitive to sound. But to double check, I whistle. A spike was measured between 1 kHz and 2 kHz. Even with a large number of averages, a single sharp whistle caused a noise spike on the SR785’s CRT screen. The hermetic glass resistors mentioned in CN-0407 are a better choice for eliminating piezoelectric/triboelectric effects.

To confirm, I measured ambient noise in the lab using my laptop’s microphone, processed the data using MATLAB®, and found that the noise corresponds very well to the measurements. The results show a noise spike at 768 Hz and other frequencies as shown in Figure 14. The culprit was a large air-conditioning pipe a few meters away from the workbench. To make sure the noise wasn’t coming from my laptop, I chose to go into the quietest place in the payphone room to collect noise data. The result did not capture the previous noise spike at 768 Hz. Noise spikes at other frequencies are also at least 100 times lower.

Figure 14. Laboratory noise.

Figure 15. Phone booth noise.

Figure 16. Reduced noise voltage density at the output with no noise barrier.

Figure 17. Reduced noise voltage density at the output with a noise barrier.

To attenuate audible noise, a Temptronix box can be used. The box has been thermally isolated and there is no substantial airflow inside. I just need it to isolate enough sound so that the sound effects of the mic don’t get into the measurements. It does exactly that. See Figures 16 and 17.

**Instrument specific questions**

FET input amplifiers have input bias currents in the order of pA. The offset voltage of 10 pA through the 10 GΩ resistor is also only about 100 mV at the output of the amplifier. The SR785 has an AC coupling feature that removes this DC offset and measures the output noise over an optimal range of C50 dB V peak (3.2 mV peak). However, the AC coupling characteristic affects frequencies below 1 Hz, making it difficult to determine the flat 12.8 μV/√Hz frequency range and read the 3 dB roll-off breakpoint. DC coupling must be used, but DC coupling cannot use the optimum sensitivity range in the instrumentation. The 1 mHz passive filter consists of two series-connected 270 μF polarized capacitors (135 μF capacitors) and a 1 MΩ resistor placed between the DUT and the output of the SR785. The longer wire of the capacitor creates a larger current loop area, which causes the magnetic field generated by the harmonics of the SR785 CRT screen at a frequency of 20kHz to interfere with this current loop, resulting in radiated interference noise. . Since the magnetic field is three-dimensional in nature, changing the angle of the passive filter box and rotating it can solve this problem. Notice the angled blue box in Figure 18. Simply E&M Black Magic!

Figure 18. Rotating filter box is less sensitive to magnetic fields.

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