LT1468CDD

Vol 53 No 3, July 2019 Can You Really Get ppm Accuracies from Op Amps? Barry Harvey The next category is older classic op amp designs, such as OP-07, that may have high gain, CMRR, and PSRR, and good offsets and noise, but that cannot achieve better than –100 dBc distortion, especially into a 1 kΩ or heavier load. Then there are the cheap amplifiers, new or old, that cannot best –100 dBc when loaded more heavily than 10 kΩ. There is the audio amplifier class of op amps. They are fairly cheap, and their distortions can be very good. However, they are not designed for and do not offer good offsets nor good 1/f noise. They also cannot deliver distortion beyond perhaps 10 kHz. There are op amps meant to support MHz signals linearly. These are usually bipolar throughout and have large input bias currents and 1/f noise. This   //    //    //    //  Figure 1 shows a simplified op amp block diagram with ac and dc error sources added. The topology is a single-pole amplifier with an input gm that drives a gain node that is buffered as the output. While there are many op amp topologies, the error sources shown apply to them all. +IN VCMR CCOMPP Vsp Visit analog.com lCMRR–VSM lCMRR+VSM INOISE– INOISE+ –IN Let’s discuss the types of amplifiers we reject as not highly linear. The least linearity is found in so-called video or line driver amplifiers. These are wideband amplifiers with terrible dc accuracies: offsets in the several millivolts and bias currents in the 1 µA to 50 µA range, and usually with poor 1/f noise. Expected accuracies are 0.3% to 0.1% at dc, although the ac distortion can be from –55 dBc to –90 dBc (2000 ppm to 30 ppm linearity). //  Op Amp Error Sources + VNOISE Non-ppm Amplifier Types   Then we have the modern general-purpose amplifiers. They typically have a 1 mV offset and microvolts of 1/f noise. They support –100 dBc distortion but usually not when heavily loaded. – CCOMPM In this article we will use the rough equivalency of 1 ppm nonlinearity in the transfer function as –120 dBc distortion in harmonic distortion. Current feedback amplifiers also cannot support deep linearity nor even modest accuracy, no matter how wideband nor huge their slew rates may be. Their input stage has a mess of error sources, and they do not have much gain nor input nor supply rejections. Current feedback amplifiers also have a thermal drift that extends fine settling times greatly. lCMRR–VSP Accuracy is about numbers: how closely a system works to intended numerical value. Precision is about the depth of the numerical value in terms of digits. In this article we will use accuracy as a term that includes all limitations to system measurements, such as noise, offset, gain error, and nonlinearity. Many op amps have some error terms at ppm levels, but none have all the errors at the ppm level. For instance, chopper amplifiers can provide ppm-level offset voltages, dc linearity, and low frequency noise, but they have problematic input bias currents and linearity at frequency. Bipolar amplifiers can provide low wideband noise and good linearity, but their input currents can still cause in-circuit errors (we will hence use the term application for in-circuit). MOS amplifiers have excellent bias currents but are generally deficient in the low frequency noise and linearity areas. application space sees more like –80 dBc to –100 dBc performance, and ppm performance is not practical with these op amps. lCMRR+VSP Industrial and medical design continually push to improve product accuracy and speed. The analog integrated circuit industry has generally kept up with speed requirements, but it is falling behind on accuracy demands. There is a march toward 1 ppm accurate systems, especially now that 1 ppm linear ADCs are becoming common. This article presents op amp accuracy limitations and how to choose the few op amps that have a chance of 1 ppm accuracy. We will also discuss a few application improvements to existing op amp limitations. R1 Gain Node Av~+1 OUT R2 Vsm Figure 1. Simplified op amp and sources of error. Input Noises We have an input noise voltage VNOISE with wideband and 1/f spectral content. You can’t measure a signal accurately if the noise is of similar magnitude or more than a system LSB. For example, if we had a 6 nV/√Hz wideband noise and a 100 kHz system bandwidth, we would have 1.9 µV rms noise at the input. We could filter this noise down: for instance, dropping bandwidth to 1 kHz drops the noise to 0.19 µV rms, or about 1 µV p-p (peakto-peak). Low-pass filtering in the frequency domain drops noise magnitude, as would averaging the output of an ADC over time. However, 1/f noise cannot be practically filtered or averaged away because it is so slow. 1/f noise is usually characterized by peak-to-peak voltage noise generated in the 0.1 Hz to 10 Hz spectrum. Most op amps have between 1 µV p-p and 6 µV p-p low frequency noise and are thus not suitable for dc-accurate ppm levels, especially if providing gain. Figure 2 shows the current and voltage noise of a good high accuracy amplifier, the LT1468. VS = ±15 V TA = 25°C AV = 101 RS = 100 k for in in 100 10 1 en 10 0.1 Input Current Noise (pA/√Hz) Input Voltage Noise (nV/√Hz) 1k with the input signal’s common-mode level is ICMRR, which is the input bias current and its variation with supplies. The broken lines suggest that the bias currents are variable with voltage and also may not be linear. There are four ICMRRs because both inputs can have independent bias currents and level dependencies, and because each input is varied by both supplies independently. The circuit effect of the ICMRRs (which sum to form bias current) is to multiply against application circuit resistances to add to overall circuit offset. Figure 4 shows the bias currents of an LT1468 vs. VCM (the ICMR specification). The slope as shown by the added line is ~8 nA/V, which would be 8 µV/V with a 1 kμΩ applications resistor, or a low ppm error. The deviation from straight line is about 15 nA, which in a 1 kΩ application environment creates 15 µV error over a 26 V span, or a 0.6 ppm nonlinearity. 80 1 1 10 100 1k Frequency (Hz) 0.01 100k 10k Figure 2. LT1468 input voltage and current noise. At the inputs in Figure 1, we also have bias current noise sources INOISE+ and INOISE–. They contain both wideband and 1/f spectral content. INOISE multiplies against application resistors to become more input voltage noise. Generally, the two current noises are uncorrelated and do not cancel with equal input resistors but add in rms fashion. Quite often INOISE times application resistors exceeds VNOISE in the 1/f region. Input Common-Mode Rejection and Offset Errors The next error source is VCMRR. This embodies the common-mode rejection ratio specification where an offset voltage changes in response to the input’s level relative to both supply rails (the so-called common-mode voltage, VCM). The symbol used indicates supply interaction at the arrows, and the segmented line through it suggests it’s variable but might not be linear. The major effect of CMRR on signals is that the linear part is indistinguishable from a gain error. The nonlinear part will be a distortion. Figure 3 shows the CMRR of an LT6018. The added line intersects extreme points of the CMRR curve just before the curve diverges into overload. The slope of the line gives a CMRR = 133 dB. The CMRR curve diverges from a perfect line by only about 0.5 µV per 30 V span—a very successfully sub-ppm input. Other amplifiers can have much more curvature. 4 Input Offset Voltage (µV) 3 2 1 40 20 IB– 0 I B+ –20 –40 –60 –80 –15 –10 –5 0 5 Input Common-Mode Voltage (V) 10 15 Figure 4. LT1468 input bias current vs. VCM. Input Stage Distortion Figure 1 shows the input stage, which is generally a transconductor made from a differential pair of transistors. The top of Figure 5 shows the collector, or drain currents, of various differential amplifier types vs. differential input voltage. We simulate a simple bipolar pair, a translinear circuit that we will call clever bipolar, a subthreshold (that is, very large) MOS differential pair, a bipolar pair with emitter resistors (degenerated in Figure 5), and a smaller MOS pair operating out of the subthreshold region and into its square-law regime. All differential amplifiers are simulated with a 100 μA tail current. At dc, the open-loop voltage gain of the op amp is ~gm (R1||R2), assuming the output buffer gain is about unity. R1 and R2 represent the output impedances of various transistors in the signal path, each connected to a supply rail or other. This is the basis of limited gain in an op amp. R1 and R2 are not guaranteed to be linear; they are a cause of unloaded distortion or nonlinearity. Aside from linearity, we need gains approaching or exceeding one million for ppm gain accuracies. 0 –1 –2 –3 –4 –10 –5 0 5 Input Common-Mode Voltage (V) 10 15 Figure 3. LT6018 input offset voltage vs. VCM. Offset voltage (VOS) will be lumped into CMRR here. Chopper amplifiers have sub-10 µV input offsets, and that’s close to a single-ppm error, relative to typical signals of 2 V p-p to 10 V p-p. Even the best ADCs generally have as much as 100 µV offset. So, the onus of offset is not so much on the op amps; the system will have to auto-zero itself, anyway. Associated 2 VS = ±15 V TA = 25°C Not a lot of information is obvious until we display transconductance vs. VIN, as shown at the bottom of Figure 5. Transconductance (gm) is the derivative of output current with respect to the input voltage, as generated using the LTspice® simulator. The syntax has d() to be mathematically equal to d()/d(VINP). The non-flatness of gm is the basic distortion mechanism of op amps at frequency. 5 –5 –15 Input Bias Current (nA) 60 // Analog Dialogue 53-07, July 2019 Observing the standard bipolar curve, we see it has the greatest transconductance of the group, but that transconductance fades quickly as the input moves from zero volts. This is concerning—a basic requirement for linearity is constant gain or gm. On the other hand, who cares that the amplifier voltage gain is so high that the differential input would only move microvolts as the output moves volts? Time to introduce CCOMP. CCOMP (the parallel of CCOMPP and CCOMPM) absorbs most of the gm’s output current over frequency. It sets the gain bandwidth product (GBW) of the 100 Ix(i19:C) Ix(i15:D) Ix(i18:C) Ix(i23:C) Ix(i13:C) + Ix(i10:C) Ix(i24:C) Ix(i11:C) + Ix(i12:C) Ix(i16:D) Ix(i17:D) Ix(i14:D) 90 80 70 µA 60 Differential Amplifier ID or IC vs. VIN 50 40 30 20 10 0 4.0 Standard Bipolar Clever Bipolar Subthreshold MOS Degenerated Bipolar Square-Law MOS Differential Amplifier Transconductance vs. VIN 3.6 3.2 2.8 d(Ix(i19:C) – Ix(i18:C)) d(Ix(i14:D) – Ix(i15:D)) d(Ix(i13:C) + Ix(i10:C) – Ix(i11:C) – Ix(i12:C)) d(Ix(i24:D) – Ix(i23:C)) d(Ix(i16:D) – Ix(i17:D)) mΩ-1 2.4 2.0 1.6 1.2 0.8 0.4 0.0 –200 –160 –120 –80 –40 0 40 VINP × 2 mV 80 120 160 –200 Figure 5. Various differential amplifiers’ output current and transconductance vs. input voltage. amplifier. GBW establishes that, at a frequency f, the amplifier will have an open-loop gain of GBW/f. If the amplifier is outputting 1 V p-p at f = GBW/10 with a closed-loop gain of +1, then we have 100 mV p-p between the inputs. That’s ±50 mV from balance. Note that the standard bipolar curve shown in Figure 5 has lost about half its gain at ±50 mV, guaranteeing massive distortion. However, the clever bipolar only lost 13% of its gain, the subthreshold MOS lost 26%, the degenerated bipolar lost 12%, and the square-law MOS lost 15%. Figure 6 shows the distortion vs. amplitude for the input stage. This will appear (times the noise gain) at the output of the application circuit. You may get more output distortion than this, but not less. Input Voltage Distortion (%) Consider a unity-gain buffer with a bipolar input. For an output of VOUT peakto-peak volts, the input differential signal would be fSIGNAL × VOUT GBW (1) We estimate that 100 10 Excluding the clever bipolar stage, the differential amps show that the distortion is proportional to the square of the input. In a unity-gain application, the output distortion contribution is equal to the input distortion. This is the dominant distortion source for most op amps. %Distortion INPUT = 0.3% × Standard Bipolar Clever Bipolar Subthreshold MOS Degenerated Bipolar Square-Law MOS VIN p-p 10 mV 2 (2) And 1 %Distortion OUTPUT = GNOISE × %Distortion INPUT = 0.3% × VOUT, p-p × f SIGNAL 10 mV × GBW 2 (3) 0.1 where GNOISE is the noise gain of the application. 0.01 10 100 VIN p-p (mV) Figure 6. Total harmonic distortion of the input stage vs. differential input voltage. A 1 ppm nonlinearity is like –120 dBc harmonic distortion, and that’s 0.0001%. Given an amplifier with a bipolar input stage, a 15 MHz GBW, and outputting 5 V p-p as a buffer, Equation 2 tells us that the maximum frequency for that linearity is just 548 Hz. This assumes the amplifier is at Visit analogdialogue.com // 3 least that linear at lower frequencies. Of course, when the amplifier provides gain, the noise gain increases and the –120 dBc frequency drops. The subthreshold MOS input stage supports –120 dBc up to 866 Hz, squarelaw MOS up to 1342 Hz, and degenerated bipolar up to 1500 Hz. Clever bipolar does not follow the distortion prediction and one must get estimates from the data sheet. Output Stage Distortions The last item in Figure 1 is the output stage, which is considered a buffer for this discussion. A typical output stage transfer function is shown in Figure 7. We can use the simpler formula %Distortion OUTPUT = K × GNOISE × VOUT, p-p × f SIGNAL GBW 2 5 VOUT, Unloaded VOUT, Light Load VOUT, Heavy Load 4 3 2 (4) 1 –5 –4 –3 –2 –1 0 0 1 2 3 4 5 –1 where K is found from the distortion curves of an op amp’s data sheet. As a side-note, there are many op amps with rail-to-rail input stages. Most get this ability from two separate input stages that have a hand-off from one to the other over the input common-mode range. This hand-off generates changes in offset voltage, and potentially bias current, noise, and even bandwidth. It also essentially causes a switching transient at the output. These amplifiers cannot be used for low distortion if the signal ever traverses the crossover region. An inverting application may work, however. We haven’t discussed slew-enhanced amplifiers yet. These designs do not run out of current with large differential inputs. Unfortunately, small differential inputs still cause variations in gm of similar magnitude to the inputs discussed, and low distortion still demands a large loop gain at frequency. Since we are looking for ppm-level distortion, we will not operate the amplifier anywhere near its slew rate limit, so, oddly enough slew rate is not an important parameter for ppm linearity at frequency, just GBW. We’ve discussed open-loop gain as modeled by a single-pole compensation design. Not all op amps are compensated that way. Generally, open-loop gain is taken from the data sheet curve, and GBW/(GNOISE × fSIGNAL) in the equation is that open-loop gain at frequency. Gain Node Errors The next items in Figure 1 to discuss are R1 and R2. These resistors, along with the input gm, give the amplifier its open-loop dc gain of gm × (R1||R2). These resistors have been drawn with the variable and nonlinear strikethrough in the schematic. Nonlinearities of these resistors embody the amplifier’s unloaded distortions. Further, R1 injects influence from the positive supply such that the dc positive power supply rejection ratio (PSRR+) and is approximately equal to gm × R1. Similarly, R2 is responsible for PSRR–. Note how PSRR is almost equivalent to open-loop gain in magnitude. CCOMPP and CCOMPM have an analogous injection of supply signals to R1 and R2; they set PSRR+ and PSRR– over frequency. It is possible that an amplifier with modest gain (