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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