During the last 20 years, electronics has become primarily a digital domain. But even though modern mixed-signal ICs have replaced many traditional analog implementations, pure analog hardware continues to have its place in many systems.
A common example is the signal path in a typical control or instrumentation system. Here, the sensor signal generally requires some kind of conditioning before it can drive an Analog-to-Digital Converter (ADC). Nowadays the task of designing this analog circuit, usually based on an op-amp, is only a small part of the whole system design. This means that, more and more often, it will fall to engineers working primarily in the digital domain to perform this task. If the requirements of the analog section are demanding in terms of precision, this can present a tough challenge to the digital designer.
Precision signal path
In designing a precision signal path (which can be defined as a signal path with an input offset voltage [Vos] of less than 1mV), the overall strategy is to reach the required precision by controlling each individual source of error. These sources are the main components of the error budget equation (see Equation 1), which can be used when designing a signal-conditioning block.
Typical functions performed by the signal-conditioning block include amplification, level shifting, buffering and filtering. With the sensor already characterised and the ADC selected, it will be clear which of these must be implemented in order to match the sensor output to the ADC (see Figure 1). At this point the error limit is usually set in terms of the Least Significant Bit (LSB) of the ADC. Then, by considering the function's requirements and the maximum error allowed, the process of op-amp selection can start.
Single-supply op-amp selection
Selecting a single-supply op-amp that operates at the same power supply voltage (VDD) as the ADC can reduce part count and cost. When using a single-supply device, the first consideration is its behaviour under input common-mode voltages (VCM). Single-supply op-amps can manage input voltages close to one of the power-supply rails, either ground or VDD, but quite far from the opposite one, typically 1V. Alternatively, other single-supplied devices include the Rail-to-Rail Input (RRI) op-amps, which allow for input voltages close to both supply rails. However, the input stage structure of RRI op-amps means that their input offset voltage shows quite a big variation, sometimes even in polarity, as VCM swings from one rail to the other. In these kinds of op-amps the effect of common-mode voltages on input offset voltage must be considered. In most applications, the RRI feature is not absolutely essential; if this is the case, it is better to choose a single-supply op-amp that keeps VCM close to the appropriate rail.
In addition to considering the input voltage values, the output characteristics must be evaluated. To take advantage of the ADC's complete dynamic range, the op-amp output must match the ADC's Vref value. This frequently makes the use of rail-to-rail output op-amps mandatory.
Op-amp error budget
The major op-amp parameters that affect precision are:
Input offset voltage and drift (Vos, dVos/dT)
Common-Mode Rejection Ratio (CMRR)
Power-Supply Rejection Ratio (PSRR)
Open loop voltage gain (Avol)
Input bias current (IB)
(It is important to recognise that external components around the op-amp also affect circuit behaviour.)
To analyse the parameters above, equation 1 is used, with the output error given by Vin times the gain.
It is clear from Equation 1 that the output error can be controlled by managing separately each of the individual components of the error budget. This article will now examine each in turn.
Consider the well-known closed-loop gain expression:
where A0(w) is the open-loop gain and is the feedback factor (resistive in this case).
It can be noted that if A0(w) varies, then Acl will vary, and the output voltage will do as well. The A0(w) variation can come from frequency dependency or A(0) (DC-gain) variations.
Although in precision applications the signal frequency could be low, the amplifier bandwidth must be considered. The closed-loop bandwidth must be wide enough to avoid attenuating any frequency components. As most of the op-amps use dominant-pole compensation, the bode plot is the same as for a single-pole filter (-20dB/dec).
The frequency at A0(w) = 1 is specified in the datasheet – this is known as the Gain-Bandwidth Product (GBWP) and can be used to obtain the closed-loop bandwidth:
For example, an op-amp with a 6MHz GBWP, configured with a gain of 10, will have = 600kHz. At this frequency the error is 29.3%, which could be intolerable, so the maximum frequency of interest should be well bellow the -3dB point.
To achieve this, assuming an error target below half an LSB in an n-bit system, the signal's maximum frequency should be:
Once the required bandwidth is known, the influence of A0(0) must be considered. The first term of Equation 1 is due to the finite value of open-loop gain. In other words, to obtain a voltage at the output, an input voltage is needed. You should take into account that A0(0) varies if any of the following factors vary: output voltage, load impedance, VDD, and temperature. Usually, VDD and load impedance are fixed.
Even if an op-amp can be classed as having rail-to-rail output, the allowable output span and its load conditions must be taken into account. The gain reduction achieved by operating close to the rails also introduces a non-linearity, which cannot be zeroed out by calibration.
The specified minimum A0(0) value, at the system operating conditions, must be used to work out this error term.
If the output swing is limited to a safe value, and the op-amp was properly selected, the passive components around the device would dictate the gain error. In fact, in a simple inverting amplifier, if resistors with a tolerance of 1% are used, the maximum gain error will be 2%.
Input offset voltage (Vos)
The input offset voltage is usually one of the most significant error sources in precision op-amp circuits. Although it is a systematic error, and could be trimmed out, it is generally better to manage the offset voltage by selecting the proper device and its grade. This means that any manual adjustment or calibration routine code will be unnecessary.
The Vos can be considered as a voltage source at the op-amp input (see Figure 2), and its effect will appear at the output, multiplied by the noise gain. This parameter varies with temperature, and under large Delta Ts, this can result in significant error. This dependency is specified as dVos/dT, in ¼V/C.
The Vos parameter also depends on the elapsed time. It is specified in the datasheet as 'long-term drift', in ¼V/month. It is worth pointing out that its effect is not cumulative, but it obeys a 'drunkard's law', so its effect is proportional to the square root of the time interval.
Input bias current (IB+, IB-)
The input bias current flowing through the resistance viewed from the input creates an offset voltage, shown by terms 3 and 4 of equation 1. For the circuit shown in Figure 2 this is:
In this particular circuit, if R3 = R1//R2, the effect of both currents is cancelled out, and the remaining error source should be the offset current.
If it is not possible to implement this compensation, and the source resistance is high, the circuit can give rise to significant errors. In this case, the choice of op-amp is likely to be dictated by the need for low values of input bias current.
The assumption that the two input currents have the same direction is valid for the most frequently found architectures. For less common input structures, however, this is not the case. So if the source impedance is high, the relative direction of the input currents must be taken into account.
In the case of the LMP2011 high-precision op-amp from National Semiconductor, the input bias currents flow in opposite directions. Despite the value being so low as to be measured in picoAmps under most operating conditions, care must be taken if your application exhibits low VCM, or the device must operate at high temperature.
Common-Mode Rejection Ratio (CMRR)
The ideal op-amp only responds to differential voltages at the inputs; in reality, however, the op-amp will have a certain sensitivity to common-mode voltages, defined as (V+ + V-)/2. The CMRR could be defined as:
The influence of this error term will depend very much on the circuit's configuration. For example, for the typical inverting configuration with V+ = 0, there will be no error; on the other hand, in a buffer configuration (Acl = +1), the VCM could be high, though in this case the gain is low. In the case of an op-amp with a CMRR of 90dB, configured as a non-inverter, with a Delta VCM of 1V, this will cause an input error voltage of:
Delta VCM/CMRR = 32¼V.
If the Acl = +100, the output voltage would be 3.2mV.
Power-Supply Rejection Ratio (PSRR)
The PSRR parameter indicates how the output is modified when the power supply changes, and it is defined as:
At DC it has very little effect on total error, but the PSRR of op-amps is frequency-dependent, so decoupling is very important. A common solution is to use two capacitors, a 10-50¼F capacitor at the power supply for low frequencies, and a low-inductance capacitor of 0.1¼F for high frequencies, using short leads and PCB tracks.
The sections above have described the sources of error, the effect of which can be calculated with Equation 1. Apart from these sources, however, the effects of noise must also be considered. One of the noise sources found in amplifier circuits is the op-amp itself. In fact, the op-amp is the source for two types of noise: voltage noise and current noise. The main way to specify it is by using the noise spectral density.
Typically, there will be two spectral zones: white noise at medium frequencies, and '1/f' noise at low frequencies, as shown in Figure 4 for the LMP7715 low-noise amplifier from National Semiconductor. In precision applications, the low-frequency noise limits the attainable precision. The rms voltage in each zone can be calculated as:
where k is the input noise density at 1Hz
vnw is the noise density at medium frequencies
f2:f1, f4:f3 are frequency ranges inside each zone
The noise sources are specified in terms of referred-to input noise; this matches the noise model shown in Figure 3, which also shows the Johnson noise sources at the circuit resistors . The total noise at the output is therefore:
The noise gain (NG = 1 + R1/R2) in the formula above is the gain from the non-inverting input, and in the circuit shown is flat over the bandwidth of interest, because no reactive component is considered. The bandwidth used in the formula is a 'Noise power Bandwidth' (NBW), which assumes a brick-wall filter response. This means that a correction factor is needed for any other filter response. The factor 1.57 accounts for the noise under the skirt of the single-pole roll-off response (-6dB/oct).
Noise characteristics of National Semiconductor's LMP7715
Even though the 1/f noise characteristic is found in most op-amps, exceptions do exist. The LMP2011 from National Semiconductor is one of them. The LMP2011 op-amp – like the LMP7715, a 'PowerWise' product that is ideal for portable, low-power signal-path applications with low supply-voltage requirements – uses special techniques to continuously measure and correct the input offset voltage.
As a result, in addition to exhibiting excellent characteristics in relation to offset (0.8¼V, typ.), stability (0.015¼V/C) and ageing (0.006¼V/month), it has no 1/f region. In fact, the low-frequency noise spectrum is flat (35nV/Hz).
The effect of this can be shown in a comparison with other op-amps. If a traditional op-amp configured with Acl=100 has:
then applying the first part of equation (3) for the range 0.01Hz~1Hz:
To convert rms values to peak-to-peak, a factor of 6.6 is generally used:
so the noise at the output will be 0.13mVPP.
Repeating the calculation for the LMP2011, the output noise is 23¼VPP, a reduction by a factor of around 5.5.
In summary, then, managing the error budget in a precision signal chain entails a logical, step-by-step process of calculating and managing the errors introduced by a number of different phenomena present in the circuit. The patient and methodical use of the techniques and formulae described in this article will ensure the reliable operation of your design.
In addition, Future Electronics can supply on request an Error Budget Calculator for a range of high-precision op-amps from National Semiconductor. This is an extremely useful time-saving tool for the kind of applications discussed in this article.
Future Electronics (www.FutureElectronics.com) is a broadline distributor with operations and sales offices in all major regions of the world. Future Electronics is franchised to sell the LMP2011, the LMP7715 and any other component from National Semiconductor throughout Europe.