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Precision Electronics Part 3: difference & instrumentation amplifiers In this third article in this series, we will further develop our precision current measuring circuit. We will consider how to sense the current if the shunt was in the positive line instead of referenced to circuit ground. By Andrew Levido Y ou will recall that previously, we sensed a 0 to 1A current using a 100mW resistor, one side of which was connected to circuit ground. We amplified the resulting voltage by a factor of around 25 to get a ground-­ referenced signal of about 2.5V fullscale, which we could apply to an analog-­to-digital converter (ADC) to make the measurement. We are assuming there is a microcontroller in the circuit that can trim out much of the fixed offset and gain error, leaving us with a trimmed precision of around ±0.04% at 25°C with about ±0.075% additional error over the 0–50°C operating temperature range. We deemed this overall precision of just over 0.1% ‘good enough’ for our purposes. In practice, we often want to sense the current in the positive leg of the circuit, as shown in Fig.1. The reason is that it is possible (sometimes even unavoidable) that the grounds of both the source and the load are connected to a common potential, such as mains Earth. If this were to happen with the original circuit, the sense resistor would be shorted out, so measuring the current would be impossible. Moving the shunt resistor to the positive line solves that problem but introduces another. One terminal of the resistor is sitting at the load’s positive supply voltage (up to 20V in our example), while the other is up to 100mV higher, depending on the current through it. We are interested in amplifying only the difference in voltage between these two points, not the much larger voltage on which it is floating. We also want the resulting amplified signal to be referenced to circuit ground so it’s within the ADC’s range, and so we don’t need to use a differential ADC to measure it. Fig.1: to measure current with a sense resistor in the positive line, we need to extract the relatively small differential signal from the larger common-mode signal. Fig.2: to achieve what we need in Fig.1, the “Signal Conditioning” box needs to amplify Vdm with a high gain (Gdm) but minimise the contribution of Vcm, meaning Gcm should be kept low. 42 Silicon Chip Differential and common mode signals In cases like this where we have two sense terminals, we refer to the voltage between them as the differential-mode voltage (Vdm) and the voltage at the terminals with respect to ground as the common-mode voltage (Vcm). This is shown diagrammatically in Fig.2. The differential voltage of interest (Vdm) is ‘riding on’ the common-mode voltage (Vcm) that we want to ignore. For ground-referenced signals, the common-mode voltage is zero (in an ideal world, anyway). The output of the generalised conditioning circuit block will be a voltage that is the sum of the differential-­ mode input (Vdm) multiplied by a differential-­ mode gain (Gdm), along Australia's electronics magazine with the common-mode input (Vcm) multiplied by the common-mode gain (Gcm). We usually want Gcm to be zero (or as close to it as we can practically get) so that the unwanted common-­ mode voltage is rejected. We describe the degree to which a circuit like this rejects common mode signals as the common-mode rejection ratio (CMRR). This is the ratio of the differential-mode gain to the common-­ mode gain (Gdm ÷ Gcm) and is usually expressed in decibels, calculated as 20log10(Gdm ÷ Gcm). You have probably guessed by now that any hope of perfectly rejecting common-mode signals (ie, achieving an infinite CMRR) is just a pipe dream. The harsh reality of electronics design means we always have to put up with something less than perfection. Difference amplifiers One of the most common ways to amplify a small differential signal riding on a large common-mode voltage is to use a difference amplifier like that shown in Fig.3. Two pairs of matched resistors (R1a = R1b & R2a = R2b) and an op amp form an amplifier with some very interesting characteristics. This general form of difference amplifier (with separate sense and reference terminals) is a very flexible Fig.3: the classic difference amplifier using an op amp and four resistors is a very useful and flexible circuit. Usually, the value of R1a is the same as R1b and R2a the same as R2b. siliconchip.com.au circuit that can be used to implement a wide variety of functions, as shown in Fig.4. All those circuits use a difference amplifier with unity gain (R1a = R1b = R2a = R2b). The terms “difference amplifier” and “differential amplifier” are often used interchangeably. I am using the former term to describe any amplifier in which the output is proportional to the difference between the input voltages. Some sources use “differential amplifier” as the general term and “difference amplifier” to describe the specific configuration where the differential-­mode gain is equal to one (eg, siliconchip.au/link/ac1h). To add to the confusion, the terms “differential amplifier” and “fully differential amplifier” are both used to describe op amps with complimentary positive and negative outputs. These are specialised devices are normally used to drive high-speed twisted pairs or differential input ADCs Getting back to the device itself, connecting the sense terminal of a difference amplifier to the output and the reference terminal to ground produces the familiar configuration illustrated in Fig.5. This has a differential-mode gain of Gdm = R2 ÷ R1 (where R1 = R1a = R1b and R2 = R2a = R2b). The common-mode gain of the difference amplifier would be zero if the op amp was ideal and the resistor matching was perfect. If you build a difference amp with a typical op amp with an open loop gain of 100,000 and 1% resistors, the CMRR would be in the region of 34dB. This means you would see about 1/50th of the common-mode voltage at the output. That would equate to 400mV in our example, almost half of the differential-mode signal we are interested in! We can do better with matched resistors. For example, using the ACASA range of resistor arrays we used last time (matched to within 0.05%), we would have a CMRR in the order of 60dB. That still means we would see a common-mode voltage of up to 20mV at the output, which is clearly not good enough for our application. You can buy integrated difference amplifiers with on-board lasertrimmed resistors that have CMRR values in the 80-100dB range at modest cost. If we used one of these, say with a CMRR of 90dB, the common-­ mode voltage at the output would be just 632µV. That is pretty good, but it still represents a 0.025% error, which will have to be added to the other errors. There is a bigger problem, however. Off-the-shelf difference amplifiers are typically only available with gains up to about 10, with most having a gain of just one or two (we will see why a little later). Another limitation of difference amplifiers is their relatively low input impedance, typically in the range of 10-500kW. That is not much of a problem with a very low impedance source such as our 100mW shunt, but it becomes more of a concern as the source impedance rises. You can see from Fig.5 that any source impedance will be in series with the difference amplifier’s input resistors R1a and R1b, potentially impacting both the gain and CMRR. A good rule of thumb is to make sure the source impedance is lower than the input impedance of the difference amplifier by the same order of magnitude as the CMRR. So, for a difference amplifier with a 90dB CMRR and 10kW input resistors, the source impedance should be less than 316mW. Any higher than that and the CMRR will be adversely impacted. Fig.5: this configuration delivers a ground-referenced voltage proportional to the difference between the input voltages; Vout = (R2 ÷ R1) × (Vin+ – Vin–). In fact, the data sheets generally specify CMRR with an input source impedance of 0W. That is obviously a totally unrealistic scenario – yet another reason to be wary of data sheet claims. You might think that the CMRR would be maintained if you had equal source impedances on each input, since both input resistors would be increased by the same amount, but no such luck. The manufacturer’s laser-trimming matches the R1/R2 ratios in each divider, not necessarily their absolute values, which may be a bit different. Adding the same source resistance to both inputs will likely unbalance the ratios, making the CMRR worse. By now you might be asking why we should even bother with difference amplifiers if they have all these limitations. Apart from the flexibility we have already seen, and their role in instrumentation amplifiers that we will discuss soon, the difference amplifier excels in the area of input common-mode voltage range. With the right resistor values, the common-mode voltage can extend well beyond the op amp’s power supply rails. Off-the-shelf devices are readily available with common mode input ranges better than ±100V. I have built discrete difference amps with Fig.4: eight possible ways to use the Fig.3 circuit to achieve different gains, level-shift signals and even sum/average voltages. siliconchip.com.au Australia's electronics magazine January 2025  43 Table 1: error budget for Fig.8 using an INA821 At Nominal 25°C Abs. Error Error Nominal Value Shunt Resistor: RESI PCSR2512 (0.5%, 15ppm/˚C) 100mW Differential Voltage due to I × Rshunt 100mV 0.5mV InAmp: INA821 (Vos ±35µv, 5µV/˚C) 0mV 0.035mV InAmp Input Voltage total (Line 2 + Line 3) 100mV 0.535mV 0.54% 0.1625mV 0.163% InAmp Gain Resistor Rg: RN73C2A (0.1%, 10ppm/˚C) 2kW 2W 0.10% 0.5W 0.025% InAmp Gain (Line 5 × Line 6) 25.7 0.0296 0.12% 0.0289 0.113% Vout DM (Line 4 × Line 7) 2.57V 0.0167V 0.65% 0.0071V 0.275% Vout CM (20V, 120db, ±1.5db over 0-50˚C) 0V 0.02mV Vout (Line 8 + Line 9) 2.57V 0.0167V Instrumentation amplifiers One obvious solution to the difference amplifier’s input impedance problem is to add a pair of unity-gain input buffers in front of the input resistors, as shown in Fig.6. This solves the input impedance problem (at the expense of common mode voltage range), but does nothing to help us reach higher gains or achieve better CMRR. The classic three-op-amp instrumentation amplifier (or ‘inamp’) shown in Fig.7 is a neat solution to the problem. The two input op amps now work to maintain the differential-­ mode voltage across resistor Rg. With this understanding, it is pretty easy to show that this input stage has a differential mode gain of Gdm = 1 + 2 × (R3 ÷ Rg) and a common mode gain of Gcm = 1. We can see that with the right choice of resistor values, this input stage can improve the overall circuit’s differential gain but, given it has a common-­ mode gain of one, it may not be as obvious how this front-end can improve the overall CMRR. Consider a situation where we want an overall differential gain of 100 and the highest possible CMRR. Imagine the difference amplifier has a differential gain of 1 and a CMRR of 80dB. The input stage will have a differential gain of 100 and a common-mode gain of 1, giving a CMRR of 40dB. The second stage adds 80dB of additional CMRR for a total circuit CMRR of 120dB. The instrumentation amp is effectively a gain stage with a CMRR equal to the gain, followed by a common-­mode rejection stage with a differential gain Fig.7: the classic threeop amp instrumentation amplifier consists of a high impedance gain stage made up of two op amps followed by a difference amplifier. This can provide both higher gain and improved CMRR compared to difference amplifier alone. Silicon Chip 0.50% Australia's electronics magazine Rel. Error 0.038% 0.0375mV 0.038% 0.125mV 0.02% Fig.6: this circuit fixes the low input impedance exhibited by difference amplifiers but it limits the input voltage range and does not add gain. 44 Abs. Error 0.50% InAmp Gain Error (0.015% ±35ppm/˚C) common mode voltages up to ±300V without problems (but a lot of care). Rel. Error 0-50°C (Nominal ±25°C) 0.088% 0.0038mV 0.65% 0.0071V 0.275% of unity or thereabouts. You can now see why lots of the difference amps on the market favour CMRR over gain – they are intended for use in instrumentation amplifier applications. Another nice feature of the instrumentation amp is that the gain can be set by changing just one resistor, Rg. This means practical devices can have precision-trimmed matched resistors R1a/b, R2a/b and R3a/b, leaving the user to provide Rg externally to set the gain. You can even switch in different resistors to change the gain or use a potentiometer to trim it. A typical example of an off-theshelf instrumentation amplifier is the INA821 from Texas Instruments (TI). The data sheets show it has a CMRR of 112dB for Gdm = 10 and 132dB for Gdm = 100. This suggests they are getting 92dB of CMRR from the difference amp stage (and 20dB or 40dB from the input stage). The input impedance is 100GW, which should be high enough for pretty much any source impedance. The cost of the INA821 is about $8.60 in single quantities, which is much cheaper than anything you could build yourself, given the very tight-tolerance resistor matching required. Let’s go through the process of designing the circuit of Fig.8 to compare with the ground-referenced circuit we built last time. We will build up the error budget shown in Table 1 as we go. Fig.9 shows the internal configuration of the INA821. We need a gain of around 25, so we will choose Rg to be 2kW, giving a gain of 25.7. The tolerance of this resistor is not critical since we’ll trim the gain, but we do care about its tempco. For this reason, I chose the RN73C2A2K0BTD from TE siliconchip.com.au Table 2: error budget for Fig.8 using an LT1167A instead At Nominal 25°C Abs. Error Error Nominal Value Shunt Resistor: RESI PCSR2512 (0.5%, 15ppm/˚C) 100mW Differential Voltage due to I × Rshunt 100mV 0.5mV InAmp: LT1167A (Vos ±40µv, 0.2µV/˚C) 0mV 0.04mV InAmp Input Voltage total (Line 2 + Line 3) 100mV 0.54mV 0.54% 0.0425mV 0.043% InAmp Gain Resistor Rg: RN73C2A (0.1%, 10ppm/˚C) 2kW 2W 0.10% 0.5W 0.025% InAmp Gain (Line 5 × Line 6) 25.7 0.0308 0.12% 0.0129 0.050% Vout DM (Line 4 × Line 7) 2.57V 0.017V 0.66% 0.0024V 0.093% Vout CM (20V, 106db over 0-50˚C) 0V 0.1002mV Vout (Line 8 + Line 9) 2.57V 0.0171V Fig.8: an off-the shelf instrumentation amplifier (‘inamp’) can provide the necessary gain (about 25) with around 120dB of common-mode rejection. siliconchip.com.au Abs. Error 0.50% InAmp Gain Error (0.02% ±10ppm/˚C) Connectivity. It has a tolerance of 0.1% and a tempco of ±10ppm/°C. The INA821’s input common mode voltage range extends to within 2V of either supply rail, so we need a power supply of 22V or more on the positive side and -2V or more on the negative side. I am going to assume we have a +24V DC supply available, since this would be the sort of input the power supply’s series pass stage would need. I have already used ±5V power rails in my previous experiments, so I will power the instrumentation amplifier from +24V and –5V rails. The INA821 has a maximum power supply voltage of 36V, so this should be fine, with a total of 29V applied (24V + 5V). It is worth noting that it is quite OK to power op amps asymmetrically like this, as long as you understand that the input common mode range and output swing will likewise be asymmetrical. We can now complete the error budget table (Table 1). The first 8 lines of the table are similar to the previous examples, arriving at a cumulative error of 0.65% with an additional Rel. Error 0-50°C (Nominal ±25°C) 0.50% 0.038% 0.0375mV 0.038% 0.005mV 0.02% 0.275% error over the 0°C to 50°C temperature range. Unlike the previous circuit, we now need to add the error due to the common-mode signal making its way through to the output. With a gain of 25.7, we can estimate the CMRR to be 120dB based on 92dB for the difference amp stage plus 20log10(25.7) = 28dB for the input stage. With a common-mode voltage of 20V, we will therefore see 20µV at the output. That’s insignificant compared to the 16mV of error due to the differential-­mode stage. The change in CMRR with temperature is a bit harder to estimate. TI provides graphs that show the temperature variation of CMRR for five sample devices at gains of one and ten. From these, I have taken a value ±1.5dB over 0°C to 50°C. It is a bit of a guesstimation, but it does not matter since the overall level of common-mode feedthrough is so low as to make this figure irrelevant. The net result is shown therefore shown at the bottom of Table 1. The worst-case untrimmed error at 25°C is ±0.65%, just a little worse than the ±0.55% error for the ground-­ referenced circuit. In both cases, most of this error is the 0.5% shunt resistor tolerance. Rel. Error 0.025% 0V 0.66% 0.0024V 0.093% Unfortunately, the circuit’s performance over the temperature range is not great. We are seeing ±0.275% error, with two major contributors: the instrumentation amplifier’s input offset voltage drift and its gain drift. The LTC2057-based circuit was much better at 0.075%, as we would expect from an auto-zero op amp. Doing better – but at a price I wanted to see if we could improve on this, so I looked for a ‘better’ instrumentation amp. The LT1167A fits the bill. Its input offset voltage at 25°C is similar to the INA821, but its offset drift is 25 times better at 0.2µV/°C. Its gain drift with temperature is also better at ±10ppm°/C, compared with the ±35ppm/°C. Table 2 shows the error budget for this version of the circuit. As an aside, it’s a good idea to create these error budget tables in a program like Excel or LibreOffice Calc. I set up the formulas so that I can easily try new parts and have the whole table recalculate automatically. Compared to the INA821, the new circuit shows a similar error at nominal temperature of ±0.66%, but an error over the temperature range three times better at 0.093%. So, we should use this device, right? Well, the LT1167A costs $30 each in one-off Fig.9: the INA821 has six laser-trimmed precision resistors and three op amps. The user must provide an external resistor (Rg) to set the overall gain. Australia's electronics magazine January 2025  45 Fig.10: the measured untrimmed data for the INA821based circuit shows about 0.3% gain error; most of this is due to the shunt resistor tolerance. quantities, so we would want to be certain there was no alternative. It should however come as no surprise that precision components that are at the very extremes of performance will be costly. The manufacturers know full well that if there are no or few alternatives, you will have to pay up. Test results I spared no expense and tested both devices. I built the circuits and measured the input current vs output voltage characteristics with both zero and the full common-mode voltage of 20V. The results for VCM = 20V are shown in Tables 3 and 4, and plotted in Figs.10 & 11. For the INA821, the untrimmed errors range from 0.01% at zero current to around 0.33% at 1A. The results were a little better with zero common mode voltage. As expected, this is better than our error budget’s 0.65% worst-case estimate. The errors increase steadily with the magnitude Fig.11: the untrimmed data for the LT1167A-based circuit shows the same 0.3% gain error as Fig.10 but has more offset error. It should perform better over the temperature range. of current, suggesting a gain error is the main contributor. The graphed results and line of best fit shows this to be the case. The offset correction we need to apply is very low (around 250µV) and the gain error is about 0.3% (the measured gain is about 0.3% higher than we expect). Again, the shunt resistor with its 0.5% tolerance is likely to be the culprit. After correcting the results, we get a trimmed error of ±0.03%, very comparable with the ground-referenced circuit. However, our concern with the INA821 circuit is its performance over temperature. The measured CMRR of this circuit was 106dB – not as good as the estimates of 120dB, but nevertheless acceptable. It’s actually a bit difficult to measure CMRR, since things like op amp input offset voltage can also change over the common-mode range, and it’s impossible to isolate the causes with a simple output voltage measurement. The LT1167A circuit has worse Table 5: theoretical improvement to Table 1 with dynamic zero trim untrimmed accuracy, peaking at almost 0.47%, but again the graphs show it to be almost all gain error. After trimming, the error is reduced to ±0.025%, very similar to the INA821. The temperature coefficient is better, of course. Another solution Rather than commit to a $30 chip, I want to introduce another trick we can use to improve precision in this type of situation. So far, we have applied fixed offset and gain corrections to minimise the static errors in the circuit. In practice, this would be done for each sample in software, based on some one-off calibration performed at a standard temperature when we initially set up the instrument (and maybe when we periodically re-calibrated it). Another approach might be to try to obtain the corrections in real-time at the ambient operating temperature. High-end instruments, like the 6½ digit multimeters that I used to obtain At Nominal 25°C Abs. Error Rel. Error 0-50°C (Nominal ±25°C) Error Nominal Value Shunt Resistor: RESI PCSR2512 (0.5%, 15ppm/˚C) 100mW Abs. Error Differential Voltage due to I × Rshunt 100mV 0.5mV InAmp: INA821 (Vos ±35µv, 5µV/˚C) – zero trimmed 0mV 0.035mV InAmp Input Voltage total (Line 2 + Line 3) 100mV 0.535mV 0.54% 0.0375mV 0.038% InAmpGain Resistor Rg: RN73C2A (0.1%, 10ppm/˚C) 2kW 2W 0.10% 0.5W 0.025% 0.50% InAmp Gain Error (0.015% ±35ppm/˚C) 0.50% Rel. Error 0.038% 0.0375mV 0.038% 0mV 0.02% 0.088% InAmp Gain (Line 5 × Line 6) 25.7 0.0296 0.12% 0.0289 0.113% Vout DM (Line 4 × Line 7) 2.57V 0.0167V 0.65% 0.0039V 0.150% Vout CM (20V, 120db, ±1.5db over 0-50˚C) 0V 0.02mV Vout (Line 8 + Line 9) 2.57V 0.0167V 46 Silicon Chip Australia's electronics magazine 0.0038mV 0.65% 0.0039V 0.150% siliconchip.com.au Measured Data I (mA) Fig.12: we can improve the temperature-dependent error of the circuit by adding switches to dynamically measure the offset, like an auto-zero op amp. the results shown here, effectively perform a zero and full-scale calibration every 20ms measurement cycle. Any temperature drift is calibrated out more-or-less in real-time. We are not aiming for anything near that level of precision, but a simpler version can be a useful technique. It is pretty difficult to do a full-scale calibration of our test circuit, as we would need a precision 1A current source, but we could do a zero calibration fairly easily. This won’t let us trim out gain drift due to temperature but would let us calibrate out temperature-dependent offset errors in real-time – a bit like auto-zero op amps do. Let’s take a look at this approach using the INA821 example. Looking at the error budget table, we can see in line 3 that we have a possible ±125µV drift in offset voltage over the temperature range. If we could calibrate that out, as shown in Table 5, we would almost halve the temperature error from ±0.275% to ±0.15%. Fig.12 shows one way we could achieve this in practice. Normally, S1 would be closed and S2 open so that we could take current measurements as before. Opening S1 and closing S2 shorts the inputs of the instrumentation amplifier so that we can use the ADC to read the circuit’s offset voltage. We would still need a fixed gain correction as before, but we can use the zero-scale reading to create a dynamic offset correction that will eliminate some of the temperature drift error. Extending the range Let’s regroup and consider what we have achieved so far. siliconchip.com.au Untrimmed Error Vout (mV) Absolute (mV) Trimmed Error Relative Absolute (mV) Relative 0.000 0.233 0.23 0.01% 0.48 0.019% 99.726 256.654 0.36 0.01% -0.19 -0.007% 199.824 514.948 1.40 0.05% 0.05 0.002% 299.980 772.739 1.79 0.07% -0.36 -0.014% 400.008 1031.164 3.14 0.12% 0.19 0.008% 499.980 1289.040 4.09 0.16% 0.34 0.013% 600.007 1546.980 4.96 0.19% 0.41 0.016% 699.965 1804.750 5.84 0.23% 0.49 0.019% 800.024 2062.770 6.71 0.26% 0.56 0.022% 899.971 2320.490 7.56 0.29% 0.61 0.024% 999.866 2578.110 8.45 0.33% 0.70 0.027% Table 3 – untrimmed measured results from the INA821 circuit shown in Fig.8. Measured Data Untrimmed Error Trimmed Error I (mA) Vout (mV) Absolute (mV) Relative Absolute (mV) Relative 0.000 1.614 1.61 0.06% 0.46 0.018% 99.759 258.745 2.37 0.09% 0.14 0.005% 199.898 517.182 3.44 0.13% 0.14 0.005% 299.829 775.181 4.62 0.18% 0.24 0.009% 400.044 1033.716 5.60 0.22% 0.15 0.006% 500.013 1291.840 6.81 0.26% 0.28 0.011% 600.390 1549.970 6.97 0.27% -0.64 -0.025% 700.009 1807.980 8.96 0.35% 0.28 0.011% 800.060 2066.110 9.96 0.39% 0.20 0.008% 899.975 2323.980 11.04 0.43% 0.21 0.008% 999.872 2581.780 12.11 0.47% 0.20 0.008% Table 4 – untrimmed measured results from the INA821 circuit shown in Fig.8 when replaced with an LT1167A. We have shown that with the shunt in the positive supply, we can probably achieve a trimmed accuracy of around 0.03% at 25°C with an additional 0.15% error over the 0–50°C temperature range if we use the INA821 instrumentation amplifier and dynamic offset correction. Let’s call this 0.2% of total error. This suggests we will have an overall resolution of ±2mA in our 1A current (ignoring ADC precision for now). That is not good enough to measure the microamp resolution we would like to achieve. I hope it is clear by now that we are not going to get the required three orders of magnitude improvement in precision just by improving the signal conditioning circuit. Even if we could, we will run into ADC quantisation limits, which we will cover in a later article. Australia's electronics magazine The current circuit needs an ADC with at least 10 effective bits of resolution – three more orders of magnitude would require over 33 bits of effective resolution, which is pushing the limits of what is possible! There is another way. We could pretty easily scale the range of the circuit by using a different shunt resistor. For example, using a 10W resistor would give a range of 0 to 10mA with ±20µA resolution, while a 1kW resistor would yield a range of 100µA fullscale with ±200nA resolution. That will require some additional circuitry to switch the ranges. This, and the dynamic offset zeroing, will require us to add some switching elements to our signal path, which will themselves introduce some imprecision. We will look more deeply into signal switching in the next instalment of this series. SC January 2025  47