“Noise” can have different meanings. It could be the common phenomenon of, say, a buzz in an audio system. Other times it may refer to something less acoustic, perhaps a limit on the precision of measurements. As an example of the way the latter has become more problematic for designers, consider the analog portion of one channel in an industrial control or automotive system.
As IC and sensor supply voltages keep shrinking, that kind of noise has become increasingly troublesome. Employing ±22-V operating voltages used to be common, but now we see ±1.5 or even ±0.9 V. At the same time, applications need greater precision and accuracy. Many apps have moved from 8 bits to 12 and higher. These trends make measurements of microvolts challenging.
For example, for a 14-bit system, when full-scale was 5 V, the least significant bit (LSB) represented 305 µV. Now, for a realworld signal of 30 mV full-scale, at 12 bits (don’t even think about 14), half an LSB is 3.5 µV. In that kind of situation, if there were just 1 µV of input-referred error or noise from the amplifier, the measurement would be invalid.
If you want to know all of the fundamentals about signal-conditioning amplifiers, including their noise performance, you can’t go wrong with Analog Devices’ Op Amp Applications Handbook (2006), edited by Walt Jung. It can be downloaded as a .pdf file at http://www.analog.com/library/analogDialogue/archives/39-05/op_amp_applications_handbook.html.
Much of what follows is distilled from that, with further input from ADI’s Reza Moghimi. Moghimi also has a pair of webinars on intrinsic and extrinsic noise that can be accessed at www.analog.com/webinar/noise-optimization1and2.
All ICs contain inherent noise sources. In amplifiers, they can be modeled as zeroimpedance voltage generators in series with the input (en) and infinite-impedance current sources in parallel with the input (in). (The lower-case convention for potential and current indicates noise spectral density that’s a quantity that varies across frequencies. Upper-case indicates instantaneous values at specific frequencies.)
The noise from these intrinsic sources has different characteristics, depending on how it arises. Some of the terminology is fanciful. There’s white and pink noise, popcorn noise, shot noise, avalanche noise, and thermal noise. (While those are the most common designations, alternative terms will often be encountered.)
Other characteristics also are derived from noise. For instance, an amplifier’s noise figure (expressed in dB) is the amount by which the amplifier’s noise exceeds the noise of a perfect amplifier in the same environment. It’s generally only used in communications work.
Critically, the noise floor of the systems and a limiting factor for system resolution is the white or broadband noise. Observed in the frequency domain, it’s the flat part of the circuit’s noise spectrum. In expressing it, bandwidth must be specified. If F is frequency:
That is, it can be approximated as simply en times the square root of the upper frequency limit.
Distinguished from white noise, pink noise (also called flicker, or 1/f noise) occurs below a certain value called the corner frequency (FC). In that lower region, it increases inversely with frequency at 3 dB/octave (Fig. 1). (Actually, there’s no hard corner. The transition occurs gradually. Corner frequency is determined by extending the straight-line portions of white and pink noise and noting where they cross.)
Pink noise only occurs under conditions where current is flowing. It’s a manifestation of charge carriers being captured and released randomly. In bipolar transistors, that’s due to contamination and imperfect surface conditions at the base-emitter junction. In CMOS devices, it’s primarily associated with extra electron energy states at the boundary between silicon and silicon dioxide.
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In general, voltage or current noise spectral density in the 1/f region is:
where k is the level of the “white” current or voltage noise level, and FC is the 1/f corner frequency. A good low-frequency, low-noise amplifier will have corner frequencies below 10 Hz. JFET devices and general-purpose op amps have values up to 100 Hz. Very fast amplifiers may achieve their high speed at the cost of a high FC, but that’s not much of a concern in a wideband application.
To obtain a value for rms noise, the noise spectral density can be integrated over the bandwidth of interest. In the pink-noise region, the rms noise from F1 to FC would be represetned by Equation 6, where en is the voltage noise spectral density of the white noise, F1 is the lowest frequency of interest in the pink-noise region, and FC is the corner frequency. Note that the corner frequency for a voltage noise needn’t be the same as the corner frequency for current noise.
Voltage noise is expressed in nV/vHz, and current noise may be expressed in terms of µA/vHz. One characteristic of 1/f noise is that the power content in each decade is constant. Keep in mind that white noise has equal energy per frequency. Its rms value is set by F2. Pink noise has equal energy per octave, and its rms value is set by the ratio of F2 to F1.
In the white-noise area above FC, the rms noise is given by:
Combining the last two equations, the total rms noise from Fl to F2 would be represented by Equation 8. At higher frequencies, the term in the above equation containing the natural logarithm becomes insignificant, and the expression reduces to:
Shot (Schottky) noise is a component of white noise. It occurs whenever a current passes through PN junctions. Barrier crossings are random events, and the total current is the sum of those random elementary current pulses. The expression for shot noise is:
where q is the charge on an electron (1.6 × 10-19 C), Ib is the bias current, and ?F is the bandwidth in Hz. If Ib is expressed in picoamperes, it simplifies to:
Then, of course, there’s thermal, or Johnson noise, from the thermal agitation of electrons in the gain-setting resistors, and:
where k is Boltzmann’s constant (1.374 × 10-23J/K), T is Kelvin temperature, R is resistance in ohms, and ?F is bandwidth in hertz. (For convenience, 4kT = 1.65 × 10-20 W/Hz.) The less the resistance, the less the thermal noise. Halving the resistance decreases the noise by 3 dB because R is under the radical sign.
Popcorn or “burst” noise is rarely encountered these days because parts are screened for it in the fab. It represents step-function voltage changes at the output of an amplifier caused by random current-gain transitions in bipolar transistors, which then cause variations in input offset. If it happens at all, it’s at low frequencies, so it’s part of 1/f noise.
Avalanche noise is also rare. It’s encountered in PN junctions operated in reverse breakdown modes. It occurs when electrons acquire enough kinetic energy under the influence of the strong electric field to create additional electron-hole pairs by colliding with the atoms in the crystal lattice. If that happens to spill over into an avalanche effect, random noise spikes may be observed.
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It’s highly unusual to encounter only one source of intrinsic noise. If those sources are uncorrelated, they can be combined as the square root of the sum of the squares:
Thus, the total effect from two noise sources with the same energy is a 3-dB increase in total noise energy. More importantly, any noise voltage more than three or five times greater than any of the others will dominate, and the others may be neglected.
Today, it’s not so strange for a nearby cell phone to interfere with a process-control system. It does so by introducing RF interference into the signal condition amplifiers between a sensor and the analog-to-digital converter (ADC) that digitizes the signal from that sensor.
In fact, that’s the real-world example in National Semiconductor application note AN-1698 (A Specification for EMI Hardened Operational Amplifiers, www.national.com/an/AN/AN-1698.pdf). The company proposes a standard method for a new kind of “rejection-ratio” amplifier spec, “EMIRR,” or electromagnetic-interference rejection ratio.
The appnote shows a signal chain and a scope measurement that demonstrates the effects on the same circuit built using generic op amps and the company’s “EMIhardened” op amps (Fig. 2). The RF signal at the op-amp input is –20 dBVP at 900 MHz, and the op-amp voltage gain is 101.
With the standard op amp, when the phone is called, the input-referred offset voltage shifts about 0.32 mV, so the output voltage is shifted by 32 mV. With the hardened amp, the output shift is about 1 mV. For a 10-bit ADC with a 5-V input range, the difference in the ability to resolve a change in sensor voltage is 7 bits of ambiguity versus 0.2 bits.
The point of NSC’s appnote is to define how to measure the EMI hardness of an amplifier in a reasonable and standard way. But first, it’s necessary to understand the path the RF from the cell phone takes to get into the amplifier. That is, is the interference radiated or conducted? The cell phone is radiating, but even at 900 MHz, there’s not much inside the IC package that has the capture area to pick up much RF energy. The elements in the external circuit pick up the radio waves and conduct them into the package.
When determining actual numbers for EMIRR, treating the interference as conducted requires more steps in the test procedure. It’s necessary to apply signals separately to input, output, and power pins. But it also simplifies the test setup, as there’s no need for a screen room and antennas.
Once the interfering signal gets inside the package, pass-band noise problems arise when it encounters nonlinear circuit elements. “The highest nonlinearity is obtained for signals with a frequency that falls outside the band of the op-amp circuit, i.e., for frequencies at which the overall feedback is virtually zero,” according to the appnote.
“This nonlinearity results in the detection of the so-called out-of-band signals. The obtained effect is that the amplitude modulation of the out-of-band signal is downconverted into the baseband. This baseband can easily overlap with the band of the op-amp circuit,” the appnote continues. “The practical effect is that the amplifier offset voltage varies in step with the keying of the digital signal on whatever stage in the transmitter chain is being modulated.”
The engineers at NSC have defined the EMI rejection ratio as represented by Equation 14, where VRF_PEAK is the amplitude of the applied unmodulated RF signal (V) and ?VOS is the resulting input-referred offset voltage shift (V). For reasons too complicated even for the appnote, there’s a quadratic relation between the resulting offset voltage shift and the RF signal level (Fig 3).
The appnote recommends a standard test condition of 100 mVP (–20 dBVP), but notes that it might be necessary to use larger signals for measurements on amps with very good EMIRR. For those cases, it provides an algorithm for normalizing measurements under different RF signal levels.
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You need to take care with the test setup (e.g., proper termination at the point at which the signal is applied), and the measurement procedures themselves will be different for different pins. Since the noninverting input pin and the supply pins are tested with the amp set for unity gain, the input-referred output shift will be the same as the measured output shift.
On the other hand, some voltage gain is necessary when coupling the test signal to the inverting input and the output. This requires accounting for that gain in the calculations of EMIRR. Figure 4 shows typical results.
BUZZ AND HUM
There’s the kind of noise we’ve been talking about, the noise that makes it impossible to achieve all of the precision that’s theoretically attainable with an analog-to-digital converter (ADC). Then there’s noisy noise—the hum in the speaker, accompanied by related pops and clicks, that drive you crazy during quiet musical passages.
When I spoke with Audio Precision founder Bruce Hofer and mentioned common- mode rejection ratio (CMRR), he called my attention to the Audio Engineering Society’s (AES) pragmatic and outspoken expert on audio buzz (and, by extension, CMRR), Jensen Transformers’ president, Bill Whitlock. Hofer then provided me with a copy of Whitlock’s paper from the June 1995 issue of the Journal of the AES, “Balanced Lines in Audio Systems: Fact, Fiction, and Transformers.”
Hofer said he tends to agree with Whitlock. In fact, Hofer recently modified some of Audio Precision’s manuals to reflect what Whitlock says. Hofer also supports efforts to modify the IEC specification for audio testing to better reflect an understanding of what Whitlock and others have been saying.
Since the subject is common mode, Hofer is talking about differential signals and differential amplifiers. The idea, as it was explained to me many years ago when I was an undergraduate summer intern at a local TV station, was that by using shielded twisted pair, any stray fields that got through the shield affected both wires in the pair equally. Meanwhile, the amplifiers responded only to differences in potential between the wires.
It was also standard operating procedure at the TV station to connect the cable grounds at only one end to avoid ground loops. Those approaches were pretty successful. I worked in Master Control on the 83rd floor of the Empire State Building, and there were fields from our transmitter and a number of others in close proximity, yet none of the fields floating around got coupled into the audio.
Empirically, those techniques work. But Hofer said that in terms of measurement, it’s misguided to do what we’ve always done: looking at CMRR performance (and circuit design) from the standpoint of system response to in-phase balanced signals on the wires in the twisted pair. You need to focus on the differences in impedance at the driver and receiver ends of the cable, because they cause imbalances in the signals on the cables. If you’re really going to measure real-world rejection of “commonmode” signals, your test practices must take those impedance-match imbalances and their effects into account.
BY THE BLOCK
When it comes to grounding only the end of the shield on twisted pair, Audio Precision’s Audio Measurement Handbook is less prescriptive than my old TV-station mentors, some of whom had been working there long enough to have done the sound effects for The Shadow. In the section under “Balanced Devices,” it observes that most commercial cable assemblies will have the shield connected to chassis ground at both ends.
This is optimum from a standpoint of rejection of high frequency and RF interference. Theoretically, power mains-related hum problems due to ground loops will be minimized if the cable shield doesn’t connect to both the device under test (DUT) and the test equipment.
But it opines that “with balanced devices and test equipment, ground loops should not be a problem.” Still, it acknowledges that “in case of severe problems, breaking all cable shield connects between the DUT and test instrument and then making a separate large-conductor ground connection between the chassis of the DUT and the audio test set may be optimum.”
On the other hand, the handbook is all for breaking the shield in unbalanced connections, saying, “The cable from DUT output to audio analyzer should have its shield connected to chassis ground only at the audio analyzer input end.”
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Whitlock is a treat to read. “More often than not, the reduction or elimination of system hum and buzz is the result of a long series of experiments that stop when someone says, ‘I can live with that,’” he says in the 1995 AES paper. “In an audio system, delivering an audio signal voltage from the output of device A to the input of device B may sound simple, but doing so without adding hum, buzz, clicks, and pops coupled from the ac power line is not easy.”
More seriously, he’s good at presenting noise problems heuristically and step by step. In the paper, he later defines “audio system” as two or more physically separated devices that are connected by audio cables, with at least two devices that are ac-powered. Almost inevitably, one device exhibits a noisy voltage with respect to ground in another device.
That’s because “inside each device, small but significant alternating currents flow from the power line through interwinding capacitances of the power transformer and the capacitors in the RFI filter to the chassis.” Relative to an external reference point, such as the safety ground on the ac outlet, both chassis carry an ac voltage.
If the devices have three-wire power cords, the currents go to ground through the green safety ground wire. But since the green wire isn’t a perfect conductor, the chassis aren’t quite at ground potential. It’s not rocket science, but it’s something that’s easy to forget on the way to “I can live with that.”
The coupling capacitance and the wire resistance and inductance effectively form a high-pass filter, says Whitlock. So, “the resulting chassis voltage will generally be a rich mixture of high-frequency power line distortion components, commonly known as buzz.”
That particular paper is available from the Audio Engineering Society at www.aes.org/e-lib/browse.cfm?elib=7944. The 1.2-Mbyte pdf costs $5 for members of the AES and $20 for non-members. Other Whitlock reading material is available for free on the Web.