For signals near dc and measurements with narrow bandwidths, 1/f noise can become an accuracy bottleneck. Because the noise overlaps the wanted signal at low frequencies, narrowing a low-pass filter cannot fully separate them. A useful design approach first quantifies flicker and broadband contributions, then chooses chopping, synchronous detection, or ac excitation according to where the noise originates.
1 Defining low frequency noise by spectrum and observation time
The power spectral density of 1/f noise rises as frequency falls, approximately in inverse proportion to frequency. It is therefore also known as low frequency flicker noise. The phenomenon occurs beyond electronic devices, and its microscopic origins remain a subject of research. For circuit design, the key features are the rising low frequency region and its intersection with the broadband floor, called the 1/f corner frequency.
Figure 1 ADA4622-2 voltage noise density and its 1/f corner region
Corner frequencies vary among devices, so comparisons require a common bandwidth. Operational amplifiers often specify low frequency voltage noise as a peak-to-peak value from 0.1 Hz to 10 Hz. A test chain amplifies and band-limits the noise; the oscilloscope reading must then be divided by the actual gain of the complete measurement path to refer it back to the device.
The source describes a dual-supply arrangement with an ac-coupled active filter. AC coupling removes the effect of dc offset, while amplification makes device noise the dominant measured contribution. A 10 s observation corresponds to a low frequency scale of about 0.1 Hz. The source text uses a gain of 1000, but the gain labels in its test schematic are inconsistent with that description; a single multiplier should therefore not be applied indiscriminately to all original screenshots. The ADA4622-2 typical 0.1 Hz to 10 Hz specification is 0.75 μV p-p.
Figure 2 Original 0.1 Hz to 10 Hz noise waveform example at ±15 V supplies
2 Integrating flicker and broadband contributions separately
Flicker and broadband contributions can be calculated separately and combined as rms values. Passive components and current noise can also contain 1/f terms. Under the low resistance conditions discussed in the source, those contributions are small; the following analysis addresses voltage noise only.
If the corner exceeds 10 Hz, the 0.1 Hz to 10 Hz specification does not cover the entire flicker region. The integration range should be extended. The equation below uses noise density en,1Hz at 1 Hz, the corner frequency fh as the upper limit, and the reciprocal of total observation time as fl. Frequencies are entered in hertz; the 1 Hz normalization preserves dimensional consistency.
V1/f,rms = en,1Hz × √[(1 Hz) × ln(fh/fl)]
For the ADA4622-2, fh is approximately 60 Hz. A 10 s observation gives fl = 0.1 Hz, and en,1Hz is about 55 nV/√Hz. Integration gives 139 nV rms. Applying the source's factor of 6.6 gives an estimated 0.92 μV p-p, about 23% above the typical 0.1 Hz to 10 Hz value. This is a statistical amplitude estimate rather than a fixed waveform peak.
Broadband noise depends on density and noise equivalent bandwidth, NEBW. A practical filter passes noise beyond its nominal cutoff as its response rolls off. A single-pole Butterworth low-pass filter, or a simple RC low-pass filter, has an NEBW approximately 1.57 times its cutoff frequency.
VWB,rms = en × √NEBW
NEBW = 1.57 × fc
The ADA4622-2 broadband density at 1 kHz is approximately 12 nV/√Hz. An output RC filter with a 1 kHz cutoff therefore gives 475.5 nV rms of broadband noise.
VWB,rms = 12 nV/√Hz × √(1000 Hz × 1.57) ≈ 475.5 nV rms
Combining the uncorrelated terms by root sum of squares gives 495.4 nV rms, approximately 4% above the broadband contribution alone. Flicker noise is therefore not dominant at this bandwidth. Its relative contribution generally decreases when the effective bandwidth becomes sufficiently large compared with the corner frequency.
Vtotal,rms = √(V1/f,rms² + VWB,rms²) ≈ 495.4 nV rms
Whether a smaller source can be ignored depends on the allowed error. A source one fifth the amplitude of a larger source raises total rms noise by √(1 + 0.2²) − 1, or about 2%. The source text describes the magnitude as approximately 1%; an actual budget should use the root-sum-square relationship directly.
3 Moving amplifier noise out of baseband with chopping
Chopping modulates the input signal and synchronously demodulates it at the output. The signal returns to its original frequency, while input-stage offset and 1/f noise move to the chopping frequency. This reduces low frequency noise and initial offset, as well as offset variation with common mode and temperature, improving dc linearity and common-mode rejection. Amplifiers using this approach are commonly called zero-drift amplifiers.
Figure 3 Chopping and offset and ripple correction in the ADA4522
Switching has costs: output glitches, ripple, spectral spikes, and increased input bias current. The 55 V ADA4522 zero-drift family uses offset and ripple correction loops to reduce switching artifacts. Figure 4 provides a time-domain comparison.
Figure 4 Time-domain output noise and switching artifacts
Chopping is also used in instrumentation amplifiers and ADCs. Examples in the source include the rail-to-rail zero-drift AD8237, the low noise, low power 24-bit sigma-delta AD7124-4, and the ultralow noise 32-bit sigma-delta AD7177-2. Internal chopping addresses errors generated within the device; it does not automatically remove 1/f noise arriving from a sensor.
4 Choosing synchronous detection or ac excitation at the sensor
Square-wave modulation contains harmonics, and noise around those frequencies can be demodulated back to dc. A lock-in amplifier uses sinusoidal modulation and synchronous detection to recover small signals in substantial noise or interference. The surface-contamination example in Figure 5 modulates a light source, detects the optical signal, and demodulates it with the same sinusoidal reference.
Figure 5 Surface-contamination measurement using sinusoidal modulation and synchronous detection
Demodulation can occur in the analog domain or digitally after the ADC. The wanted output returns to dc while low frequency noise from the conditioning electronics moves to the modulation frequency. A very narrow low-pass filter, for example 0.01 Hz, then rejects out-of-band components. Reference accuracy and waveform quality are important. This method addresses the conditioning circuitry rather than directly removing the sensor's own 1/f noise.
For an excited bridge sensor, the excitation polarity can be alternated and the two measured phases subtracted. Ideally, the phases are VA + VOS and −VA + VOS; subtraction yields 2VA and cancels their common low frequency offset. The source uses this principle to discuss suppression of sensor low frequency noise, offset drift, and parasitic thermocouple errors. Cancellation relies on the relevant error remaining common to the two phases.
Figure 6 AC excitation of a bridge and subtraction of the two phases
A microcontroller and discrete switches can implement ac excitation. The 24-bit sigma-delta AD7195, which includes a PGA, provides drivers and synchronizes excitation with conversion to simplify control. Figure 7 retains the CN-0155 precision scale example.
Figure 7 AD7195 ac-excited precision scale circuit from CN-0155
5 Checking intermodulation between chopping clocks
Low noise specifications for individual devices do not guarantee a spur-free cascade. Chopping frequencies can mix to produce sum and difference components. In the source example, the ADA4522-2 at 800 kHz and the AD7177-2 at 250 kHz produce components at 1050 kHz and 550 kHz. The AD7177-2 digital filter has a maximum corner of 2.6 kHz, well below these components, providing the frequency separation needed to filter them in that example.
Two cascaded zero-drift amplifiers of the same type may have slightly different internal clocks. Their difference frequency can lie much closer to dc and enter the measurement band. The design should therefore check every chopping frequency, possible intermodulation products, and the following filter response. The high chopping frequency of the ADA4522 family is useful in this context, but does not remove the need for a system-level check.