The Quest for Quiet: Measuring 2nV/√Hz Noise and 120dB Supply Rejection in Linear Regulators, Part 1

Todd Owen and Amit Patel, Senior IC Design Engineers, Linear Technology Corporation -January 10, 2016


Editor’s note: We will publish this application note in two parts; here is Part 1.


Introduction


A quiet, well regulated supply is important for optimum performance in a number of circuit applications. Voltage controlled oscillators (VCOs) and precision voltage controlled crystal oscillators (VCXOs) respond to small changes in their supply very quickly. Phase-locked loops (PLLs) require a stable supply, as signal on the supply translates directly to phase noise in the output. RF amplifiers require quiet supplies, as they lack the ability to reject supply variations, and regulator variation will appear as unwanted side bands and lower the signal-to-noise ratio.


Low noise amplifiers and analog-to-digital converters (ADCs) do not have infinite supply rejection and the cleaner the regulator output is, the higher their performance. These are just a few applications where linear regulators are required to provide quiet power supply rails, but how does one ensure that the regulator performs as specified?


Once fully built, one can determine if the supply has low enough noise for the application. Oscillator phase noise is measured and compared against results achieved with a known good supply, ADCs are checked to ensure they are getting the maximum number of bits. These are tricky, time consuming measurements and it would be better to make sure the noise levels are low enough for your needs without expensive trials.


In addition to noise, one must also consider the supply rejection capabilities of the linear regulator. Poor rejection from a linear regulator will bring switching regulator residue or other unwanted signals through, corrupting the hard work done to ensure a clean supply. Extremely low noise from the regulator is worthless if poor supply rejection brings enough signal through to swamp noise levels.


MEASURING OUTPUT VOLTAGE NOISE


Being Quiet is Nothing New


The subject of noise has been broached before. Linear Technology Application Note 83, “Performance Verification of Low Noise, Low Dropout Regulators,” published in March of 2000, describes in detail a method for measuring output voltage noise of regulators down as low as 4µVRMS with confidence. The amplifier circuit and filters in the Application Note gave 60dB of gain across a 10Hz to 100kHz bandwidth. This is a good starting point to determine confidence in measurement of noise levels.


New linear regulators such as the LT3042 are now in production with much lower output voltage noise levels. While the family of regulators released around the publication of Application Note 83 operate with approximately 20µVRMS noise in the 10Hz to 100kHz band, the LT3042 is now available with noise levels as low as 0.8µVRMS across the same frequency band. Reviewing the circuit from Application Note 83 shows an input referred noise floor of 0.5µVRMS, which provides less than 1% error when measuring noise levels as low as 4µVRMS. With output noise levels of 0.8µVRMS, this noise floor is now unacceptable; the regulator itself operates at noise levels only slightly above the measurement circuit. This translates to almost 20% error, making the measurement circuit too significant a factor to be able to measure signals with confidence.


Measuring less than 1µVRMS noise is not a trivial task. Working backward from a 10Hz to 100kHz measurement band, this equates to a noise spectral density of 3.16nV/√Hz (assuming white noise). This is equivalent to the Johnson noise of a 625Ω resistor! Measuring noise at these levels within 5% requires that instrumentation have an input referred noise of 1nV/√Hz; measuring within 1% requires input referred noise of 450pV/√Hz.


What Measurement to Make?


We now have an idea of the noise floor required by instrumentation, but there is a question as to what frequency range is critical and what instrument is to be used to measure the resultant noise. To measure noise spectral density, the regulator output can simply be fed through low noise gain stages1 and then fed into a spectrum analyzer, blocking out unwanted frequencies from measurement. If peak-to-peak or RMS noise is desired, then band stops are warranted on the low noise gain stages to ensure that only signal in the desired bandwidth is measured.


A commonly used broadband noise measurement frequency range is 10Hz to 100kHz. This encompasses the audio frequency band and ensures minimal side bands for baseband data transmitted over RF. Low noise regulators used in phase-locked loops and high accuracy instrumentation require higher frequency measurements (up to 1MHz and beyond), so we should not limit ourselves to only the 100kHz range. Ideally, band stops would be absolute brick-wall filters at the desired frequency, but the realities of circuit design prevent us from achieving this.


Higher order Butterworth filters are selected to maintain maximum flatness in the range of the frequencies of interest as well as their ability to give a better brick-wall approximation. The order of the filter is determined by the error introduced by their equivalent noise bandwidth (ENB): a second-order low pass Butterworth has an ENB of 1.11fH, too high of an error. Fourth-order filters drop the ENB to 1.026fH, which gives error levels of approximately 1.3%. Higher order filters would add unnecessary complexity and cost while accomplishing minimal improvement in performance.


Fourth-order filter error is coupled with errors introduced by the input referred noise, indicating that a measurement within 5% requires that input referred noise of the amplifier be targeted to contribute no more than 1% maximum error.


Circuit gain must be considered as well. If the gain is too low, noise of the measurement device will sum in and corrupt measurements the same as input noise of the amplifier. At the same time, instrumentation may not be sensitive enough to provide reliable results. For RMS noise measurements, an HP3400A RMS voltmeter has a bottom range of 1mV, so 60dB is an absolute minimum gain. Based on the noise floor of spectrum analyzers currently commercially available (and available from the secondary market), it was decided that 80dB would work best.


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