Measuring 2 nV/√Hz noise and 120 dB supply rejection in linear regulators; the Quest for Quiet, part 2
Part 1 of this article is here.
Component choice is important
Choosing the right components for any circuit is important, but when it comes to ultralow noise measurement, it becomes even more so. The most critical point in the noise amplifier is the input stage; once you get beyond this first stage many of the difficulties drop away. The RC filter used for DC blocking directly at the input must be carefully considered.
The resistor is not one where there is much to debate; a metal film resistor is used to ensure low 1/f noise as compared to thin film resistors. The capacitor is another matter entirely that must be reviewed. In AN124, an expensive wet slug tantalum was used to provide low 1/f noise after being hand-selected for low leakage. When operating as low as 0.1 Hz, these characteristics are more important. With a 10 Hz low frequency band stop for broadband noise, lower cost capacitors provide acceptable performance. Large multilayer ceramic capacitors are a poor choice as they are piezoelectric in nature; any mechanical vibration injects signal into the circuit that quickly exceeds the measured noise levels. Additionally, the voltage coefficient causes a change in the corner frequency based on the regulator output voltage, an undesirable characteristic. Tantalum and aluminium electrolytic capacitors are not costly and do not show voltage coefficients or mechanical sensitivity. More expensive capacitors such as polyethylene-terephthalate film were considered, but low availability, high cost, and lack of performance gain ruled them out.
Even with these possible choices, capacitors do show noise characteristics that must be considered. Large multilayer ceramic capacitors show low noise operation but have already been ruled out due to their mechanical vibration sensitivity. Tantalum and aluminium electrolytic capacitors show higher levels of noise (see Sikula, et al. in References for further reading). Standard tantalum capacitors were finally chosen for their reasonable cost, good characteristics with bias voltage, and lack of response to physical vibrations. Multiple capacitors are paralleled to get the voltage rating and net capacitance needed, while lowering the contributed noise.
The blocking/filtering between first stage gain blocks and the second stage gain block was also chosen to be tantalum for similar reasons. Even though the gain from the first stage amplified the noise, ceramics were found to generate signal from piezoelectric response beyond desired levels.
Almost any capacitor is suitable for the final output blocking/filtering networks, ceramic capacitors are chosen. The amplified noise is now large enough in relation to piezoelectric response from the capacitors, and the lack of DC offset means that capacitors are close to their expected values. Capacitors for compensation in the first gain stage and also the ones used in the Butterworth filters are C0G, NPO, or polyethylene-terephthalate as these dielectrics show little to no piezoelectric effect or DC bias shifts.
Powering the circuit itself is one last important decision. Battery power from alkaline cells was chosen to provide the quietest source for all stages and prevent possible ground loops in equipment from corrupting measurements. One must remember that all circuits used here do not have infinite supply rejection capabilities and any noise on supplies can make it through to the outputs and potentially affect measurement results. Take this into careful consideration before choosing to supply power from any line-based supply.
Practical circuit limitations
The amplifier has practical limitations that cannot be ignored. Given the 80 dB of gain provided by the circuit, a signal on the input of 100 µVP-P will show as 1 VP-P on the output. Running from ±4.5V supplies dictates an output signal is less than ±3.5V in amplitude. Thus, the input cannot see more than ±350 µV total amplitude or signal fidelity cannot be guaranteed. Expecting a worst-case crest factor of 10 for Gaussian noise, only 70 µVRMS maximum is measurable with this circuit.
From here, making sure the tantalum capacitors are properly biased is also important. For the input blocking capacitor, the transistors are operating almost at ground potential, so a positive output voltage regulator requires that the positive side of the capacitor be connected to the regulator output. Contrarily, the capacitor is reversed when measuring a negative output voltage. For the DC blocking and filtering between the first and second stages, the negative side of the capacitor should be connected to the first stage. Base current of the transistors pulls their bases slightly negative through the 499Ω resistor, and this slightly negative voltage is amplified further through the gain of 25 in the first stage, requiring this orientation.
Calibration, Verification, and Measurement
Once the circuit is built, the gain needs to be verified as well as the input-referred noise. To calibrate gain, 60 dB attenuation is used to bring the signal from a function generator down to a level that avoids running the amplifier output against the rails. With 100 mVP-P at a midrange frequency of 1 kHz from the function generator into the attenuator, the potentiometer in the final gain stage is adjusted to give 1 VP-P at the output. Adjusting the frequency up and down from 10 Hz to 1 MHz gives indication that the gain is flat across the desired bandwidth.
Figure 3. Gain of circuit in figure 1. filter responses show steep roll-off at desired corner frequencies
Verification of gain and frequency response is done with a network analyser. The reference signal is fed through the 60 dB attenuator into the input of the amplifier. The three separate outputs are connected as the test point, and sweeps across frequency are made. Figure 3 shows the gain as a function of frequency for each of the three outputs, highlighting the excellent flatness and appropriate corner frequencies.
To verify input-referred noise, short the input of the amplifier to ground and measure the noise at the output. Measurements are taken directly with an RMS voltmeter or oscilloscope; noise spectral density is viewed with a spectrum analyser. Measured noise spectral density of the wideband output (shown in Figure 4) has 1/f noise with a corner at 200 Hz, and white noise characteristics of 5 µV/√Hz from 200 Hz to 1 MHz. Dividing this down by the gain of 80 dB indicates input-referred noise is 500 pV/√Hz, slightly above the target. Even with the 1/f component, this calculates to 0.15 µVRMS over the 10 Hz to 100 kHz bandwidth, low enough to allow measurement of 1 µVRMS over the same bandwidth with confidence. The measurements correlate well with the peak-to-peak noise measured on an oscilloscope as shown in Figure 5.
Figure 4. Noise spectral density of amplifier with input shorted shows 1/f component. Dividing by 80dB circuit gain yields input referred noise
Figure 5. Peak-to-peak amplifier noise with input shorted (100kHz Range) correlates to noise spectral density
next… still not simple…
Measurements are still not a simple task
Several subtle effects cropped up during the design and testing of this circuit that showcased the difficulty in measuring ultralow noise levels. Shorting the input to ground and connecting the output to an oscilloscope reveals much that cannot be seen with an RMS voltmeter or spectrum analyser. Large signal excursions when using ceramic capacitors for the input filter and second stage filtering showcased their piezoelectric nature from simple finger taps on the bench. This made the case for the switch to solid tantalum capacitors.
What was also apparent was that the noise levels for measurement were so small that extraordinary measures were required to ensure solid results. Placing the amplifier board in front of an older oscilloscope showed a regular 20 kHz signal (likely a switching regulator inside the oscilloscope) that was larger in amplitude than the input referred noise. Placing it close to a benchtop multimeter resulted in a large 60 Hz signal. Figure 6 shows just how sensitive the amplifier is when placed just a few inches in front of the powered oscilloscope. In both cases, moving the board away from the equipment or changing the orientation of the board would change the amplitude of the signal and turning the equipment off would remove the signal. A few loops of wire around the end of a pencil were connected to a function generator to operate as a small antenna at various frequencies. Not surprisingly, some areas of the board showed circuit loops that were magnetically coupling with the inductors and transformers inside the bench equipment. Some layout improvements were made to help minimise loops, but it was immediately obvious that external shielding would be required.
Figure 6. Signal shown with input shorted and close to oscilloscope highlights sensitivity to magnetic fields
Shielded box construction
Figures 7 and 8 show the internal construction of the shielded box used to house the noise amplifier board. The amplifier board is housed together with six D cell alkaline batteries inside a box constructed from 0.050 in. (1.27 mm) thick Mu Metal to give good shielding against low frequency magnetic fields. This is then placed ½-in. inside a box made from 2oz. copper clad, chosen to give good shielding against higher frequencies. These are lastly placed ½ in. inside a steel can (a repurposed cookie tin that gives some initial shielding from magnetic fields. The ½-in. air gaps between boxes help with attenuation of fields. For a discussion on materials useful for low frequency magnetic field shielding, please see Appendix A, Materials for Magnetic Shielding.
Figure 7. Shielded box construction uses mu metal inside copper inside steel tin to attenuate fields
Figure 8. Details of shielded box construction. Note only input coax shield is connected to metal can to prevent ground loops
There are a few worthwhile items to note about the construction of this box. The internal amplifier board uses coaxial cable to go from the board out to the input and output BNC connectors. However, one must watch connections for the shield of the coaxial cables; only the input shield is connected to the ground plane of the board and the outermost steel can. Input and output BNC shields connect to the steel can, while coaxial cable shields tie to the board ground on both sides. If the output shield connections were to be connected to the steel can as well, a ground loop is formed that can pick up stray fields. Each layer of the shielding box electrically connects to the one outside it via metal screws and standoffs with the amplifier board isolated by solder mask. These provide connections between each box without connecting to the ground plane of the amplifier board internally and creating possible loops. Last, the steel can itself is given added attention: the inside and outside edges of the can and lid were sanded to remove the decorative paint and clear protective layers to ensure good electrical contact between the lid and can.
It is worth noting that even with all of the attention paid to shielding the circuit, line frequency fields are strong enough to make their way into the noise plot shown in Figure 4. Fortunately, the shielding is enough to minimise signals created by these fields. Even so, one should be fully aware of the potential for fields to interact with this circuit when making measurements.
Part 3 of this article will continue by moving on from the extensive preparatory work, to making actual measurements of Regulator Output Noise.
Todd Owen and Amit Patel are Senior IC Design Engineers at Linear Technology Corporation.