VOLTAGE REFERENCES generate wideband noise spectrums. For most semiconductor devices, this spectrum usually has a wideband “white noise” component with relatively constant power density versus frequency, and a “pink noise” or “1/f noise” component that grows with the inverse of frequency.1,2 The pink noise component rises up from the relatively flat white noise level at a point somewhere between a few hundred hertz and a kilohertz, and it increases 3 dB per octave (approximately 10 dB per decade) in the direction of decreasing frequency.
The frequency at which the 1/f noise 3-dB/ octave slope projection intersects the white noise theoretical flat line projection is commonly referred to as the 1/f corner frequency. It typically occurs at a few hundred hertz for bipolar technologies and around 1 kHz for CMOS technologies.
The difference between white and pink noise spectra, indicated by the different slopes (zero for white noise and 3 dB/octave for pink), is that the white noise can be described as having constant energy/bandwidth. As an example, for white noise, the same frequency slot (say, 1 kHz) will have the same energy at 100 kHz than at 1 MHz. For pink noise, the same frequency-relative slot (decade, octave) will maintain constant energy through the whole range considered.
Both the 1/f corner frequency and the white noise level depend heavily on the type and quality of the manufacturing process.
The problems with pink noise appear mostly in the measurement and control applications requiring the highest grade of accuracy and precision. Examples of such applications include calibration sources, high-end digital voltmeters, and the generation of ultra-precision magnetic fields.
In all of these applications, inherent noise above the 1/f corner (and sometimes well below it) is filtered out by the long time constants derived from the acquisition time or from the measurement integration time. It could also be filtered out due to the slow time response of the controlled elements (magnets).
However, measurement is, by definition, the comparison with a standard or reference, and controlling a physical quantity implies that it needs to be measured first. The uncertainty caused in the results of a measurement by the reference’s noise appears directly (plus any other added in the process) as uncertainty in the measurement result. As such, the absolute limit to the quality of any measurement or control is the quality of the reference used.
It’s for the applications mentioned above where the 1/f noise components of references collide with the measurement quality—both in the bandwidth of interest and with the level of uncertainty required. That’s where the reduction of those components can be of interest.
The higher-frequency components of a voltagereference noise spectrum are easily removed by inserting a passive or active low-pass filter (normally an RC filter) without affecting the reference-voltage accuracy or temperature uncertainty. For the low-frequency components (those below 10 Hz), it’s difficult to create a filter that can suppress several decades of frequency below 10 Hz while maintaining the original quality of the reference, which is the dc-output accuracy.
In all cases, the problem is the long time constant (RC product) necessary to obtain a low corner frequency for the low-pass filter. A large resistor value must be placed in the dc path of the reference, and a large capacitor value placed in shunt with the output side of the resistor.
High-value resistors introduce voltage-drop uncertainties that are unacceptably large, even for the very small leakage current circulating through the shunt capacitor. This current, though very low for capacitors built with the best dielectrics, is measurable for the high-value capacitors in question.
If you use active filters, almost any value of bias current from the amplifiers can cause the same problem, and the noise-current component of that bias current adds a considerable amount of voltage noise when it circulates through the high resistance seen from the inputs. And yet, the lowest-noise amplifiers are almost always designed with bipolar technology, which has an appreciable input bias current (in the nanoampere region).
In Figure 1, the circuit filters the low-frequency components of the noise spectrum of a voltage reference without introducing significant dc-offset voltage errors. The filter approximates a one-pole transfer function with corner frequency at 10 MHz and produces a 22-dB reduction in total integrated noise voltage from 0.1 to 10 Hz.
The Filter Circuit
The circuit shown in Figure 1 is a bootstrapped filter. Amplifier A1, a high-precision chopper-stabilized CMOS type, is configured as an inverting single-pole high-pass filter with gain of 100 at mid-band (set by the ratio of R2/R3, as C1 approaches a short to common). It also has a gain of unity at dc (because R2 and R1 are connected to the same dc potential).
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The position of the high-pass filter’s corner pole is defined by the product R1C1 = 0.0053 Hz. The A1 output’s amplified and phase-inverted voltage-reference noise is applied through C2 to a cancellation divider consisting of R4 and R5, with a dividing ratio equal to the A1 ac gain. The cancellation point is at the non-inverting input of A2. This circuit scheme begins to work at frequencies above the corner defined by the time-constant C2(R5 + R4), which is about 0.016 Hz.
The cancellation scheme allows the use of a second capacitor (C2), which significantly reduces the dc influence of any drop across the resistor of the first RC filter (R1) by breaking the dc path. The drop across R1 is caused by the leakage current through C1 and appears amplified at the output of A1.
The gain/attenuation factor of 100 used for the cancellation lets you insert a large-valued resistor of 1 MO (R5) to determine the time constant of the second RC product (R5C2). As a result, this time constant is determined by a resistor that’s not in series with the dc “signal” path. The cancellation-divider resistor in series with that path (R4) is only 10 kO, which is small enough to make drops due to C2 leakage currents negligible.
The second chopper-stabilized amplifier (A2) buffers the load from the divider impedance seen from A2’s non-inverting input. For frequencies below the corner defined as 1/2p\\[C2(R5 + R4)\\], that impedance approaches a maximum of 10 kO at dc.
The dc-insertion offset is 0.35 µV at room temperature, and the total change from –30°C to 80°C is 0.150 µV (Fig. 2). At dc, the temperature-dependent uncertainty added by the filter per °C is two to three orders of magnitude lower than the temperature coefficient of available bandgap and buried-Zener voltage references.
The filter’s frequency response is taken with a white noise source whose power spectral density (PSD) is flat at an approximate level of 5 µV/vHz and with no 1/f components down to a few millihertz (Fig. 3). This source level is defined as 0 dB. The lower curve is the output in dB of the second amplifier (A2), referred to the noise applied at the filter input.
Figure 4 shows the circuit response to a 4-V source suddenly connected at the input. Settling time to the ppm level requires several minutes, which is consistent with the behavior of ultraprecision circuits. Experimental results observed for several Maxim references are presented as the obtained noise reduction plotted against the datasheet noise value for each one (Fig. 5). Also shown are the noise-reduction values obtained by computer simulation, when the filter simulation is fed with datasheet noise values for each reference. Agreement with the experimental data is reasonable.
The dc uncertainty sources include voltage drops across the resistor in the signal path, caused by capacitor leakage and amplifier bias currents, and changes in the amplifier offset voltages. This design handles capacitor leakage by choosing the best capacitor type available.
Similarly, the selection of CMOS amplifiers minimizes the influence of amplifier input current on the dc uncertainties and on the noise induced by input current. CMOS chopper-stabilized amplifiers almost eliminate offset-voltage drift and its change with temperature, as well as the 1/f noise components otherwise introduced by the op amps.
Included among ac uncertainty sources are noise introduced by the amplifiers themselves, and the mismatch of amplifier gain with the resistor ratio of the cancelling divider. The filter’s output-referred noise is approximately twice the input-referred noise of a single operational amplifier of the type used.
The critical capacitors C1 and C2, polypropylene- film-dielectric types made by Cornell Dubilier (type 935C1W10K), are specified to have a minimum RC time constant of 30,000 seconds. For a 10-µF capacitance, that value yields a worst-case leakage resistance of 3000 MO.
The two op amps (MAX4238) are CMOS chopper- stabilized devices, a requirement imposed by the need for zero bias current. For this application, the essential chopper-stabilized-amplifier parameters include a noise spectrum free of the 1/f component, an extremely low voltage offset and voltage-offset temperature coefficient, and low wideband noise.
Because A1 and A2 are chopper-stabilized amplifiers, the circuit output contains switching noise at the chopper frequency, distributed from 10 kHz to 15 kHz. These high-frequency components are far removed from the frequencies of interest (<10 Hz). They can be easily filtered if the need arises and are negligible for most applications that require the stability of the reference types discussed here. All resistors are 1% metal-film, low-noise types.
The accurate measurement of low-frequency noise requires care and specialized test fixtures. Because the noise being measured is often lower than the noise floor of available test equipment (the low-frequency noise floor in particular), several low-frequency amplifiers were developed to boost the signals to measurable levels. Lowfrequency noise measurements are usually specified for a specific signal bandwidth, such as the industry-standard band from 0.1 Hz to 10 Hz.
The noise source used for the frequencyresponse curves also included a MAX4238, amplifying its own noise, in a configuration using low-value resistors. Figure 6 shows the schematic for this noise source.3 The source works based on the principle that the 1/f internal noise components of a chopper stabilized op amp are aliased out to an out-of-interest, much higher frequency region. The noise spectrum at the output of the source is used to test the filter performance (Fig. 7).
All voltages (including noise) were measured with a high-end 8.5-digit DMM (HP3458A). For each noise test, multiple 4096-point measurements were taken over a 10-second interval (i.e., a sampling rate of 409.6Hz). The FFT of each 4096-point measurement series was computed and then divided by the sample rate to obtain a value normalized to a 1-Hz bandwidth. These values were averaged to reduce the uncertainty of data points in the resulting plot.
1. Motchenbacher, C.D. & Connelly, J.A., Low-Noise Electronic System Design, John Wiley & Sons, 1993
2. Pallas-Areny, Ramon & Webster, John G., Sensors and Signal Conditioning, John Wiley & Sons, 1991
3. Saab, A.H., Randall, R., “White Noise Generator with no Flicker Noise Component,” EDN, March 20, 2008