The Art of Electronics / Edition 3

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Chapter 7: Precision Circuits and Low-Noise Techniques

In the preceding chapters we have dealt with many aspects of analog circuit design, including the circuit properties of passive devices, transistors, FETs, and op-amps, the subject of feedback, and numerous applications of these devices and circuit methods. In all our discussions, however, we have not yet addressed the question of the best that can be done, for example, in minimizing amplifier errors (nonlinearities, drifts, etc.) and in amplifying weak signals with minimum degradation by amplifier "noise." In many applications these are the most important issues, and they form an important part of the art of electronics. In this chapter, therefore, we will look at methods of precision circuit design and the issue of noise in amplifiers. With the exception of the introduction to noise in Section 7.11, this chapter can be skipped over in a first reading. This material is not essential for an understanding of later chapters.

Precision Op-Amp Design Techniques

In the field of measurement and control there is often a need for circuits of high precision. Control circuits should be accurate, stable with time and temperature, and predictable. The usefulness of measuring instruments likewise depends on their accuracy and stability. In almost all electronic subspecialties we always have the desire to do things more accurately -- you might call it the joy of perfection. Even if you don't always actually need the highest precision, you can still delight in the joy of fully understanding what's going on.

7.01: Precision versus dynamic range

It is easy to get confused between the concepts ofprecision and dynamic range, especially since some of the same techniques are used to achieve both. Perhaps the difference can best be clarified by some examples: A 5-digit multimeter has high precision; voltage measurements are accurate to 0.01% or better. Such a device also has wide dynamic range; it can measure millivolts and volts on the same scale. A precision decade amplifier (one with selectable gains of 1, 10, and 100, say) and a precision voltage reference may have plenty of precision, but not necessarily much dynamic range. An example of a device with wide dynamic range but only moderate accuracy might be a 6-decade logarithmic amplifier (log amp) built with carefully trimmed op-amps but with components of only 5% accuracy; even with accurate components a log amp might have limited accuracy because of lack of log conformity (at the extremes of current) of the transistor junction used for the conversion. Another example of a wide-dynamic-range instrument (greater than 10,000:1 range of input currents) with only moderate accuracy (1%) is the coulomb meter described in Section 9.26. It was originally designed to keep track of the total charge put through an electrochemical cell, a quantity that needs to be known only to approximately 5% but that may be the cumulative result of a current that varies over a wide range. It is a general characteristic of wide-dynamic-range design that input offsets must be carefully trimmed in order to maintain good proportionality for signal levels near zero; this is also necessary in precision design, but, in addition, precise components, stable references, and careful attention to every possible source of error must be used to keep the sum total of all errors within the so-called error budget.

7.02: Error budget

A few words on error budgets. There is a tendency for the beginner to fall into the trap of thinking that a few strategically placed precision components will result in a device with precision performance. On rare occasions this will be true. But even a circuit peppered with 0.01% resistors and expensive op-amps won't perform to expectations if somewhere in the circuit there is an input offset current multiplied by a source resistance that gives a voltage error of 10mV, say. With almost any circuit there will be errors arising all over the place, and it is essential to tally them up, if for no other reason than to locate problem areas where better devices or a circuit change might be needed. Such an error budget results in rational design, in many cases revealing where an inexpensive component will suffice, and eventually permitting a careful estimate of performance.

7.03: Example circuit: precision amplifier with automatic null offset

In order to motivate the discussion of precision circuits, we have designed an extremely precise decade amplifier with automatic offset. This gadget lets you "freeze" the value of the input signal, amplifying any subsequent changes from that level by gains of exactly 10, 100, or 1000. This might come in particularly handy in an experiment in which you wish to measure a small change in some quantity (e.g., light transmission or radiofrequency absorption) as some condition of the experiment is varied. It is ordinarily difficult to get accurate measurements of small changes in a large dc signal, owing to drifts and instabilities in the amplifier. In such a situation a circuit of extreme precision and stability is required. We will describe the design choices and errors of this particular circuit in the framework of precision design in general, thus rendering painless what could otherwise become a tedious exercise. A note at the outset: Digital techniques offer an attractive alternative to the purely analog circuitry used here. Look forward to exciting revelations in chapters to come!

Circuit descriptionThe basic circuit is a follower (U₁) driving an inverting amplifier of selectable gain (U₂), the latter offsettable by a signal applied to its noninverting input. Q₁ and Q₂ are FETs, used in this application as simple analog switches; Q₃ - Q₅ generate suitable levels, from a logic-level input, to activate the switches. Q₁ through Q₅ and their associated circuitry could all be replaced by a relay, or even a switch, if desired, For now, just think of it as a simple SPST switch.

When the logic input is HIGH ("autozero"), the switch is closed, and U₃ charges the analog "memory" capacitor (C₁) as necessary to maintain zero output. No attempt is made to follow rapidly changing signals, since in the sort of application for which this was designed the signals are essentially dc, and some averaging is a desirable feature. When the switch is opened, the voltage on the capacitor remains stable, resulting in an output signal proportional to the wanderings of the input thereafter.

There are a few additional features that should be described before going on to explain in detail the principles of precision design as applied here: (a) U₄ participates in a first-order leakage-current compensation scheme, whereby the tendency of C₁ to discharge slowly through its own leakage (100,000M, minimum, corresponding to a time constant of 2 weeks!) is compensated by a small charging current through R₁₅ proportional to the voltage across C₁. (b) Instead of a single FET switch, two are used in series in a "guarded leakage-cancellation" arrangement. The small leakage current through Q₂, when switched OFF, flows to ground through R₂₃, keeping all terminals of Q₁ within millivolts of ground. Without any appreciable voltage drops, Q₁ hasn't any appreciable leakage! (See Section 4.15 and Fig. 4.50 for similar circuit tricks.) (c) The offsetting voltage generated at the output of U₃ is attenuated by R₁₁ - R₁₄, according to the gain setting. This is done to avoid problems with dynamic range and accuracy in U₃, since drifts or errors in the offset holding circuitry are not amplified by U₂ (more on this later).

7.04: A precision-design error budget

For each category of circuit error and design strategy we will devote a few paragraphs to a general discussion, followed by illustrations from the preceding circuit. Circuit errors can be divided into the categories of (a) errors in the external network components, (b) op-amp (or amplifier) errors associated with the input circuitry, and (c) op-amp errors associated with the output circuitry. Examples of the three are resistor tolerances, input offset voltage, and errors due to finite slew rate, respectively.

Let's start by setting out our error budget. It is based on a desire to keep input errors down to the 10µV level, output drift (from capacitor "droop") below 1mV in 10 minutes, and gain accuracy in the neighborhood of 0.01%. As with any budget, the individual items are arrived at by a process of trade-offs, based on what can be done with available technology. In a sense the budget represents the end result of the design, rather than the starting point. However, it will aid our discussion to have it now.

Error budget (worst-case values)

1. Buffer amplifier (U₁)
    Voltage errors referred to input:
Temperature               1.2µV/4°C
Time                           1.0µV/month
Power supply              0.3µV/100mV change
Bias current x R_S        2.0µV/1k of R_S
Load-current heating   0.3µV @ full scale (10V)

2. Gain amplifier (U₂)
    Voltage errors referred to input:
Temperature                     1.2µV/4°C
Time                                 1.0µV/month
Power supply                    0.3µV/100mV change
Bias offset current drift      1.6µV/4°C/lk
Load-current heating         0.3µV @ full scale (R_L = 10k)

3. Hold amplifier (U₃)
    Voltage errors referred to output:
U₃ offset tempco                   60µV/4°C
Power supply                        10µV/100mV change
Capacitor droop                    100µV/min
    (see current error budget)
Charge transfer                      10µV

Current errors applied to C₁ (needed for preceding voltage error budget):
Capacitor leakage
    Maximum (uncompensated)         (100pA)
    Typical (compensated)                 l0pA
U₃ input current                               0.2pA
U₃ & U₄ offset voltage across R₁₅   1.0pA
FET switch OFF leakage                 0.5pA
Printed-circuit-board leakage           5.0pA

The various items in the budget will make sense as we discuss the choices faced in this particular design. We will organize by the categories of circuit errors listed earlier: network components, amplifier input errors, and amplifier output errors. ...