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.
Filter Performance
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.
Uncertainty Sources
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 Components
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.
Methods
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.
References:
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