CHAPTER 2

Instrumentation Amplifiers and Parameter Errors

2-0 INTRODUCTION

This chapter is concerned with the devices and circuits that comprise the electronic amplifiers of linear systems utilized in instrumentation applications. This development begins with the temperature limitations of semiconductor devices, which is then extended to differential amplifiers and an analysis of their parameters for understanding operational amplifiers from the perspective of their internal stages. This includes gain–bandwidth–phase stability relationships and interactions in multiple amplifier systems. An understanding of the capabilities and limitations of operational amplifiers is a prerequisite to understanding instrumentation amplifiers.

An instrumentation amplifier usually is the first electronic device encountered in a signal acquisition system, and in large part it is responsible for the ultimate data accuracy attainable. Present instrumentation amplifiers are shown to possess sufficient linearity, common-mode rejection ratio (CMRR), low noise, and precision for total errors in the microvolt range. Five categories of instrumentation amplifier applications are described with representative contemporary devices and parameters provided for each. These parameters are then utilized to compare amplifier circuits for implementations ranging from low input voltage error to wide bandwidth applications.

2-1 DEVICE TEMPERATURE CHARACTERISTICS

The elemental semiconductor device in electronic circuits is the pn junction; among its forms are diodes and bipolar and FET transistors. The availability of free carriers that result in current flow in a semiconductor is a direct function of the applied thermal energy. At room temperature, taken as 20°C (293°K above absolute zero), there is abundant energy to liberate the valence electrons of a semiconductor. These carriers are then free to drift under the influence of an applied potential. The magnitude of this current flow is essentially a function of the thermal energy instead of the applied voltage and accounts for the negative temperature coefficient exhibited by semiconductor devices (increasing current with increasing temperature).

The primary variation associated with reverse-biased pn junctions is the change in reverse saturation current Is with temperature. Is is determined by device geometry and doping with a variation of 7% per degree centrigrade both in silicon and germanium, doubling with every 10°C rise. This behavior is shown by Figure 2-1 and Equation (2-1). Forward-biased pn junctions exhibit a decreasing junction potential, having an expected value of −2.0 mV per degree centigrade rise, as defined by Equation (2-2). The dV/dT temperature variation is shown to be the difference between the forward-junction potential V and the temperature of Is. This relationship is the source of the voltage offset drift with temperature exhibited by semiconductor devices. The volt-equivalent of temperature is an empirical model in both equations, defined as VT = (273°K + T°C)/11,600, having an expected value of 25 mV at room temperature.

(2-1)

(2-2)

2-2 DIFFERENTIAL AMPLIFIERS

The first electronic circuit encountered by a sensor signal in a data acquisition system typically is the differential input stage of an instrumentation amplifier. The balanced bipolar differential amplifier of Figure 2-2(a) is an important circuit used in many linear applications. Operation with symmetrical plus minus power supplies as shown results in the input base terminals being at 0 V under quiescent conditions. Due to the interaction that occurs in this emitter-coupled circuit, the algebraic difference signal applied across the input terminals is the effective drive signal, whereas equally applied input signals are cancelled by the symmetry of the circuit. With reference to a single-ended output Vo2, amplifier Q1 may be considered an emitter follower with the constant-current source an emitter load impedance in the megohm range. This results in a noninverting voltage gain for Q1 very close to unity (0.99999), that is, emitter coupled to the common-emitter amplifer Q2, where Q2 provides the differential voltage gain Avdiff by Equation (2-3).

Differential amplifier volt-ampere transfer curves are defined by Figure 2-2(b), where the abscissa represents normalized differential input voltage (V1 − V2)/VT. The transfer characteristics are shown to be linear about the operating point corresponding to an input-voltage swing of approximately 50 mV (± 1 VT unit). The maximum slope of the curves occurs at the operating point of Io/2, and defines the effective transconductance of the circuit as ΔIc/Δ(V1 − V2)/VT. The value of this slope is determined by the total current Io of Equation (2-4). Differential input impedances Rdiff and Rcm are defined by Equations (2-5) and (2-6). The effective voltage gain cancellation between the noninverting and inverting inputs is represented by the common-mode gain Avcm of Equation (2-7). The ratio of differential gain to common-mode gain also provides a dimensionless figure of merit for differential amplifiers as the common-mode rejection ratio (CMRR). This is expressed by Equation (2-8), having a typical value of 105.

(2-3)

(2-4)

(2-5)

(2-6)

(2-7)

(2-8)

The performance of operational and instrumentation amplifiers is largely determined by the errors associated with their input stages. It is convention to express these errors as voltage and current offset values, including their variation with temperature with respect to the input terminals, so that various amplifiers may be compared on the same basis. In this manner, factors such as the choice of gain and the amplification of the error values do not result in confusion concerning their true magnitude. It is also notable that the symmetry provided by the differential amplifier circuit primarily serves to offer excellent dc stability and the minimization of input errors in comparison with those of nondifferential amplifiers.

The base-emitter voltages of a group of the same type of bipolar transistors at the same collector current are typically only within 20 mV. Operation of a differential pair with a constant-current emitter sink as shown in Figure 2-2(a), however, provides a Vbe match of Vos of about 1 mV. Equation (2-9) defines this input offset voltage and its dependence on the mismatch in reverse saturation current Is between the differential pair. This mismatch is a consequence of variations in doping and geometry of the devices during their manufacture. Offset adjustment is frequently provided by the introduction of an external trimpot RVos in the emitter circuit shown in Figure 2-4. That permits the incremental addition and subtraction of emitter voltage to drop to 0 Vos without disturbing the emitter current Io.

Of greater concern is the offset voltage drift with temperature dVos/dT. This input error results from mistracking of Vbe1 and Vbe2, described by Equation (2-10), and is difficult to compensate. However, the differential circuit reduces dVos/dT to 2μV/°C from the −2mV/°C for a single device of Equation (2-2), for an improvement factor of 1/1000. By way of comparison, JFET differential circuit Vos is larger and on the order of 10 mV, and dVos/dT typically 5μV/°C. Minimization of these errors is achieved by matching the device pinch-off voltage parameter. Bipolar input bias-current offset and offset-current drift are described by Equations (2-11) and (2-12), and have their genesis in a mismatch in current gain (hfe1 ≠ hfe2). JFET devices intrinsically offer lower input bias currents and offset-current errors in differential circuits, which is advantageous for the amplification of current-type sensor signals. However, the rate of increase of JFET bias current with temperature is exponential, as illustrated in Figure 2-3, and results in values that exceed bipolar input bias currents at temperatures beyond 100°C, thereby limiting the utility of JFET differential amplifiers above this temperature.

(2-9)

(2-10)

(2-11)

(2-12)

2-3 OPERATIONAL AMPLIFIERS

Most operational amplifiers are of similar design, as described by Figure 2-4, and consist of a differential-input stage cascaded with a high-gain interstage followed by a power-output stage. Operational amplifiers are characterized by very high gain at dc and a uniform rolloff in this gain with frequency. This enables these devices to accept feedback from arbitrary networks with high stability and simultaneous dc and ac amplification. Consequently, such networks can accurately impart their characteristics to electronic systems with negligible degradation. The earliest integrated-circuit amplifier was offered in 1963 by Texas...