关键词: 0.1 to 10 Hz noise of voltage reference, low frequency noise or flicker noise of voltage reference, ultra low noise measurement of voltage reference
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Simple, Effective Method and Circuit to Measure VeryLow 1/f Voltage Reference Noise (< 1µV_{PP}, 0.1Hz to 10Hz)

Eliminating expensive components needed as part of a highpass filter after voltage reference can be accomplished by using two identical voltage references and a differential amplifier to measure ultralow (0.1Hz to 10Hz) noise of one voltage reference.
The voltage noise and temperature drift of a voltage reference usually determine the measurement limits of a data acquisition system (DAS). Voltage reference data sheets generally specify the noise by two separate categories: 1) lowfrequency (0.1Hz to 10Hz) as µV_{PP}; 2) wideband noise as µV_{RMS} for a given band (e.g., 10Hz to 1kHz), or spectralvoltage noise density at a frequency where the noise spectral density has reached its flatness, specified as nV/√Hz .
Data sheets specify lowfrequency and wideband noise separately because the latter can be greatly reduced in the system application using lowpass filtering. Filtering of lowfrequency noise, however, is cumbersome and not practical, as large capacitors are needed to filter out lower frequencies.
Voltagereference noise also affects outputvoltage accuracy since it is a random signal. For example, if there is 1mV_{PP} output noise, then for a 3V reference that noise translates into 0.033% voltage randomness which affects the reference's initial accuracy. This application note presents a simple and effective way to measure and reduce lowfrequency noise in a voltage reference. The application example aims to achieve lowfrequency noise (0.1Hz to 10Hz) below 1µV_{PP}.
A standard way of measuring the noise of a voltage reference is shown in Figure 1. The output of the voltage reference is fed into a highpass filter to pass frequencies of 0.1Hz and above. The highpass filter also performs two beneficial tasks: provides DCblocking of the voltage reference output, and allows only the ACsignal content above the highpass filter corner frequency to reach the lownoise preamplifier.
Figure 1. Typical setup for measuring the noise of a voltage reference.
There are design considerations that affect, even limit, the performance of the above circuit:
The Figure 2 setup employs two identical voltage references to accurately determine their lowfrequency noise. This is an indirect method to measure noise. It operates on the assumption that two different units (from the same manufacturing batch) exhibit very similar noise performance while their noise is uncorrelated.
Figure 2. Proposed setup to evaluate a voltage reference noise performance.
In our experiment, the setup employs a pair of MAX6126 ultralownoise voltage references. The dotted line in the Figure 2 detailed setup shows that all the test circuit is shielded from the outside environment in a Faraday metal cage. Our detailed bench setup can be seen in Figures 6 and 7.
Uncorrelated noise of each voltage reference adds up such that the resulting total noise at the input of the preamplifier can be expressed as in Equation 1:
eN^{2} ＝ e1^{2} + e^{2}  (Eq. 1) 
where,
eN is the total noise of the two voltage references combined, and
e1, e_{2} is the noise associated with each voltage reference.
e_{N} ＝ 2 × e  (Eq. 2) 
To determine the noise contributed by one voltage reference, a correction factor will be used based on the above formula. The total input noise of the differential amplifier in the setup (e_{in}) is calculated with Equation 3. The noise signal e0 incorporates the contributions of the circuit noise sources (excepting the voltage references). It is assumed that all noise sources are uncorrelated:
e_{in}^{2} ＝ 2 × e^{2} + e0^{2}  (Eq. 3) 
The total input noise is amplified and filtered. The resulting noise signal e_{out} is applied at the input of the spectrum analyzer. This noise signal can be expressed with Equation 4, where G and F are the transfer functions of the differential amplifier and filter, respectively:
e_{out}^{2} ＝ G × F × e_{in}^{2}  (Eq. 4) 
Using the results of Equations 3 and 4 we can express the setup output noise signal e_{out} as given by Equation 5 below:
e_{out}^{2} ＝ G × F × 2 × e^{2} + G × F × e0^{2}  (Eq. 5) 
We can separately measure the setup noise by removing the voltage references and connecting the differential amplifier inputs to ground. In that case, the output noise signal e_{out}0 is the result of e0 only. It can be expressed as in Equation 6:
e_{out}0^{2} ＝ G × F × e0^{2}  (Eq. 6) 
With the results from Equations 5 and 6 we can calculate the reference noise voltage as shown below in Equation 7:
E^{2} ＝(e_{out}^{2}  e_{out}^{2})/(2× G × F)  (Eq. 7) 
The transfer function of the setup (G × F) can be easily evaluated with a network analyzer.
The MAX6126 has a noisereduction pin NR, where an external capacitor can be connected to ground. This capacitor in conjunction with the onchip resistor (20kΩ typ.) creates a lowpass filter which reduces the noise of the internal reference. With a 0.1µF noisereduction capacitor we can filter out spectral components at frequencies above 100Hz. In this application note, we show that a 100µF noisereduction capacitor can be used to reduce 1/f noise (0.1Hz to 10Hz) since the filter cutoff frequency is ≈ 0.1Hz.
The MAX9632 opamp has been chosen for its ultralow noise, both 1/f and wideband. The MAX9632 is used in a differential amplifier configuration. The differential voltage gain is by the ratio of wellmatched 5KΩ and 50Ω resistors. These 0.01% matched resistors were chosen to improve the CMRR performance and, consequently, reject unwanted commonmode noise injected by parasitic coupling of external RF and/or ACline signals. A gain of 100V/V is used, but it can be set higher, if desired. However, the differential amplifier bandwidth BW will be reduced, since BW = GBW/gain.
The output of the differential amplifier is applied to a highpass filter. This filter allows proper setting of the filtercutoff frequency based on resistor and capacitor values. A combination of 100µF and 50kΩ are used to pass frequencies of 0.03Hz and higher. There are several advantages to using a highpass filter after the lownoise preamplifier. Now we can use generic capacitor and resistor components since their noise is not that critical because the filter is placed after the gain stage. Also, we can customize the filter cutoff frequency as desired. It is important to note that the signal analyzer input is set for DCcoupling mode. Thus, the measurement is not limited by the highpass filter frequency corner of ACcoupling mode in the signal analyzer.
The setup shown in Figure 3 below is used to evaluate the frequency response of the noise measurement setup from Figure 2. In this case, the test signal is applied to one input of the differential amplifier while the other input is connected to ground.
Figure 3. Test setup (correspondent to Figure 2) to measure the frequency response.
The frequency response function is G × F (see Equation 7 above). Figure 4 shows that within the lowfrequency band (0.1Hz to 10Hz) we may assume that the noise referred to output is gained up by 40dB or 100V/V. Since 0.1Hz and 10Hz are corner frequencies of the external bandpass filter used, they are 3dB points on the gain response.
Figure 4. AC gain frequency response (G × F) of the noise measurement setup.
Figure 4 shows that within the band of frequencies (0.1HZ to 10Hz) it is safe to assume that the noise referred to output will be gained up by 40dB or 100V/V. Figure 5 below shows a timedomain output setup for calibration noise. The setup inputs are connected to ground. The output noise is recorded within a 64s time slot, clearly beyond 10 seconds which corresponds to 0.1Hz in frequency domain. This is useful, as it shows that there is little change of the peaktopeak values of any 10s window within 64 seconds total time.
Figure 5. Timedomain setup for calibration noise eout0 (see Equation 6).
Figure 6 shows a picture of the bench setup and the equipment used. Figure 7 is a detail of the setup.
Figure 6. Picture of the detailed bench setup.
Figure 7. Setup inside Faraday cage shown in Figure 6.
Figure 8 below shows the timedomain output noise corresponding to two MAX6126 units. The measurement setup is shown in Figure 2 above. Just as for the setup calibration noise, the output noise is recorded within a 64s time slot.
Figure 8. Setup for output noise using two MAX6126 units. (Refer to the test setup in Figure 2.)
Equation 7 below is used to calculate the noise contributed by one voltage reference:
e^{2} ＝ (e_{out}^{2}  e_{out}0^{2})/(2 × G × F)
√e_{out}^{2} = 130µV_{PP}
√e_{out}0^{2} = 22.4µV_{PP}
G × F = 100V/V or 40dB
Substituting these results in Equation 7 shown above yields: = 0.9055µV_{PP} The reference noise calculated without the correction term (e_{out}0^{2}) is e = 0.919µV_{PP}. Therefore, the setup calibration noise is negligible compared to the voltage reference noise.
In Figure 9 below, the NR capacitor used in the Figure 2 setup was changed to a 100µF (X5R, 10V, 1206 size) capacitor purchased from Digikey® distribution. This largevalue capacitor improves the 0.1Hz to 10Hz noise (Figure 10).
Figure 9. MAX6126 noise setup using a 100µF NR capacitor.
Figure 10. Output noise of test setup shown in Figure 9.
Equation 7 is used again to calculate the noise contributed by one voltage reference:
e^{2} ＝ (e_{out}^{2}  e_{out}0^{2})/(2 × G × F)
√e_{out}^{2} = 84.6µV_{PP}
√e_{out}0^{2} = 22.4µV_{PP}
G × F = 100V/V or 40dB
Substituting these results in Equation 7 shown above yields: = 0.5769µV_{PP}.
The reference noise calculated without the correction term (e_{out}0^{2}) is e = 0.5982µV_{PP}. Therefore, the setup calibration noise is negligible compared to the voltage reference noise.
Figure 11 shows the performance of a competitive voltage reference with the same test setup (see Figure 9) using two of their units. The C_{LOAD} was replaced with 10µF instead of the 0.1µF used in MAX6126 setup. The competitive part exhibits the best noise performance when C_{LOAD} = 10µF.
Figure 11. Setup output noise using competitive part with C_{LOAD} =10µF.
Equation 7 is used again to calculate the noise contributed by one voltage reference:
e^{2} ＝ (e_{out}^{2}  e_{out}0^{2})/(2 × G × F)
√e_{out}^{2} = 84.7µV_{PP}
√e_{out}0^{2} = 22.4µV_{PP}
G × F = 100V/V or 40dB
Substituting these results in Equation 7 yields: e = 0.5776µV_{PP}. The reference noise calculated without the correction term (e_{out}0^{2}) is e = 0.5989µV_{PP}. Therefore, the setup calibration noise is negligible compared to the voltage reference noise.
We have shown that the 0.1Hz to 10Hz noise of the MAX6126 is significantly reduced when a largevalue NR capacitor is used. However, we need to ensure that the reference outputvoltage temperature drift is negligibly affected by the leakage of the capacitor (connected between the NR and GND pins). Figure 12 shows MAX6126 temperature drift performance in the following cases: no capacitor, 0.1µF 50V (C0805C104J5RAC7800), and 100µF 10V (C3216X5R1A107M160AC).
Figure 12. V_{OUT}(T) –V_{OUT} (25°C): output voltage temperature drift of the MAX6126 for three cases of capacitors on NR pin.
Figures 13, 14, and 15 illustrate the noise performance of the MAX9632 used as a preamplifier in this application note. This data should show readers why choosing a verylownoise amplifier is of prime importance to an application.
Figure 13. The 0.1Hz to 10Hz noise performance of the MAX9632 (see MAX9632 data sheet).
Figure 14. Inputvoltage noise density performance of the MAX9632 (see MAX9632 data sheet).
Figure 15. Inputcurrent noise density performance of the MAX9632 (see MAX9632 data sheet).
This method measures noise of a highprecision, lownoise voltage references using two identical voltage references and a differential amplifier. Using a highpass filter eliminates expensive components otherwise needed.
A similar version of this App Note appeared in ECN Magazine on August 21, 2015.
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MAX6126  超高精度、超低噪声、串联型电压基准  免费样品 
MAX9632  36V、高精度、低噪声宽带放大器 
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© Oct 24, 2016, Maxim Integrated Products, Inc. 
APP 6206: Oct 24, 2016
应用笔记6206, AN6206, AN 6206, APP6206, Appnote6206, Appnote 6206 