1. Introduction
The world is analog. With the invention of the transistor, electronics engineers gained competence in the digital processing of analog signals. However, in all signal processing systems, designers have to receive, amplify or attenuate, or process the analog signals using varieties of analog techniques. The operational amplifier (opamp) is one of most commonly used analog components for such tasks.
Bob Widlar, working at Fairchild, designed the first successful opamp back in 1965. The first commercial monolithic device was uA709. The developments that continued from this experience provided several successful opamps, such as the uA741 and the LM301. With advancements in semiconductor manufacturing technologies, many advanced opamps entered the market. Today opamps are available in a wide variety of technologies, specifications, prices, and package styles from a multitude of vendors. When a circuit requires an opamp, the designer is confronted with a bewildering number of devices from which to choose. These varieties may be identified as basic voltage feedback, current feedback, micro-power, video, and chopper stabilized types.
This section provides a designer's viewpoint on the use of opamps, identifying their characteristics and limitations in a practical sense and discussing the use of different kinds. Many excellent references (Horowitz and Hill, 1996; Analog Devices, 1987, 1990, 1992, 1995; Dostal, 1993) support this section with more detailed fundamentals.
2. Introduction to Amplifiers
There are four general classes of amplifiers, characterized by transfer characteristics expressed in volts per volt, amperes per ampere, volts per ampere, and amperes per volt. These four cases are illustrated in FIG. 1.
These basic amplifiers are the building blocks required to synthesize larger electronic systems. Although some simple electronic devices are voltage amplifiers (the triode vacuum tube), current amplifiers (the bipolar transistor), and transconductance amplifiers (the field effect transistor), presently no electronic devices demonstrate the intrinsic characteristics of a transimpedance amplifier.
Hence transimpedance amplifiers must be synthesized from voltage, current, or transconductance amplifiers. Characteristics of the ideal amplifiers are shown in Table 1 and the amplifier equivalent circuits are shown in FIG. 2.
FIG. 1 Types of amplifiers: (a) Voltage amplifier, (b) Current amplifier,
(c) Trans-impedance amplifier, (d) Transconductance amplifier
TABLE 1 Ideal Amplifier Characteristics
Voltage Current Transconductance Transimpedance
FIG. 2 Amplifier equivalent circuits" (a) Voltage amplifier, (b)
Current amplifier, (c) Transconductance amplifier, (d) Transimpedance amplifier
3. Basic Operational Amplifier
The ideal opamp has differential inputs, an infinite input impedance, a single-ended output, and infinite gain at all frequencies. The ideal opamp always must be considered as a four-terminal device, the fourth terminal being the return path for the output current. In most designs, it’s assumed that the amplifier is deal and that no current flows into the input terminals, there is no input offset voltage, and no power is required for its operation. FIG. 3 shows the ideal opamp.
3.1 The Real Operational Amplifier
FIG. 4 depicts a real opamp based on a voltage amplifier. Let us briefly
discuss the input imperfections and output obstacles.
FIG. 3 The ideal opamp
3.1.1 Input Imperfections
The actual characteristics of real opamps are considerably more complicated. Each input contains a DC current source (In, the bias current), and a DC voltage source (Vos, the offset voltage) in series with the inputs. The amplifier has differential and common mode input impedances (Zin(DIFF) and Zin (CM), respectively), which usually are complex and consist of a resistor and a capacitor n parallel.
Also, there are three uncorrelated noise sources: two current sources (IN) and a voltage source (VN) that appear differentially. Finally, the amplifier has gain with regard to common mode signals, which the ideal amplifier does not have, and so its common mode rejection ratio (CMRR) needs to be specified.
FIG. 4 A practical opamp
FIG. 5 A simplified real opamp showing a single-ended output and differential
input
3.1.2 Output Stage
The output side of the model also is not ideal. There is an output impedance (Ro) in series with the voltage sources. The gain (A, infinite in the ideal model)
is both finite and a function of frequency in a real amplifier, which also has a finite slew rate (the rate of rise of output voltage per microsecond) and listed output voltage and current capabilities.
3.1.3 Differential to Single-Ended Conversion
One fundamental requirement of a simple opamp is that an applied signal, which is fully differential at the input, must be converted to a single-ended output; that is, with respect to the often neglected fourth terminal. To see how this can lead to difficulties, look at FIG. 5. The signal flow illustrated by FIG. 5 is used in several popular integrated circuit families, such as the 101, 741, 748, 503, and other integrated circuit amplifiers.
The circuit first transforms a differential input voltage into a differential current. This input stage function is represented by PNP transistors in FIG. 5.
The current then is converted from differential to single-ended form by a current mirror connected to the negative supply rail. The output from the current mirror drives a voltage amplifier and power output stage, which is connected as an integrator. The integrator controls the open-loop frequency response, and its capacitor may be added externally, as in the 101, or self-contained, as in the 741. Most descriptions of this simplified model don’t emphasize that the integrator has a differential input, of course. It’s biased positive by a couple of base-emitter voltages, but the noninverting integrator input is referred to the negative supply.
It should be apparent that most of the voltage difference between the amplifier output and the negative supply appears across the compensation capacitor.
If the negative supply voltage is changed abruptly, the integrator amplifier will force the output to follow the change. When the entire amplifier is in a closed-loop configuration the resulting error signal at its input will tend to restore the output, but the recovery will be limited by the slew rate of the amplifier. As a result, an amplifier of this type may have outstanding low-frequency power supply rejection, but the negative supply rejection is fundamentally limited at high frequencies. Since the feedback signal to the input causes restoration of the output, the negative supply rejection will approach 0 for signals at frequencies above the closed-loop bandwidth. This means that high-speed, high-level circuits can "talk" to low-level circuits through the common impedance of the negative supply line. This phenomenon demands some special consideration in decoupling and grounding; details are discussed in Brokraw (Analog Devices, AN-202).
3.2 Amplifier Specifications
3.2.1 Offset Voltage
Offset voltage (Vos) is defined as the voltage that must be applied to the input to cause the output to be 0. Offset voltage is the result of a mismatch in the base-emitter voltages of the differential input transistors (the gate-source voltage mismatch in FET-input amplifiers) and is indistinguishable from a DC input signal. This offset can be trimmed to 0 with a potentiometer, which adjusts the balance of the operating currents in the input stage until Vsel and VBE 2 (or VGS 1 and VGS2) are equal. Even if the offset voltage is trimmed to 0 at one particular temperature, it will vary with the temperature. When a bipolar transistor opamp is trimmed for minimum offset, it’s trimmed for minimum temperature drift, but this is not the case for FET-input opamps.
3.2.2 Input Bias Current
Another DC parameter of opamps is input bias current (18). If an opamp uses bipolar transistors in its input stage, a base current must be supplied from somewhere to bias them into their active operating region. Since Kirchhoff's law tells us that current must flow in circles, this current also must return to its origin through a DC path. Therefore, operational amplifiers cannot be used with input signal sources that are not referred to the same power source as the amplifier itself. Although FETs don’t require a base current, they nevertheless have a leakage current from their gate junction diode, which results in an input bias current. In many applications, the errors due to bias currents actually are less than the errors caused by the mismatch of the bias currents on the two inputs.
This difference between the bias currents, called the input offset current, usually is specified along with the bias current.
Like the input offset voltage, bias currents also vary with temperature. In an amplifier with a bipolar input stage, the bias current decreases with increasing temperature because the transistors' /3 increases, and since their emitter current remains constant, the base current decreases. In FET input amplifiers, the bias current is the gate leakage current of an FET, which is the leakage current of a reverse-biased junction diode. Such leakage currents double for every 10°C rise in junction temperature.
An ideal opamp has no current going into its input terminals; real opamps approach this by reducing bias currents to femtoamp levels. As a category, one can consider low bias current opamps as those-with less than 1 nA bias currents.
3.2.3 Open-Loop Voltage Gain
Another opamp parameter that distinguishes a real amplifier from an ideal amplifier is the open-loop gain. The open-loop gain of an ideal opamp is assumed to be infinite. The same assumption occasionally is made of real amplifiers, with unfortunate results. Opamps generally have around 20 V of output swing and gains of over 1 million--the input therefore would need to be on the order of 1 uV, and it’s very hard to handle such signals without unacceptable errors due to thermoelectric potentials. Special circuits are necessary to measure the open-loop voltage gain.
3.2.4 Frequency Response
Most operational amplifiers have a very simple frequency response. The gain is constant at DC and very low frequencies, then has a single-pole roll-off, falling at 6 dB/octave (-20 dB/decade). It’s obvious that, throughout the region where this single-pole frequency response applies, the product of gain and frequency is a constant, known as the gain-bandwidth product of the amplifier, and a measure of its high-frequency performance. In the majority of opamps, this single-pole response continues past the point where the gain has dropped to unity (such amplifiers are known as internally compensated or unity gain stable amplifiers). Some amplifiers have a more complex response, and at a gain of something less than 10, a second pole appears. These amplifiers are not stable at low-closed loop gains but generally have better high-frequency performance than the internally compensated types. Opamps are considered wideband fast settling if their bandwidth is greater than 5 MHz, they slew at more than 10 V/us, and they settle to 0.1% in 1 ps or less.
3.2.5 Slew Rate
The slew rate of an amplifier is the rate at which the output voltage can change when high drive is applied to the input. When the circuit is used to measure slew rate, the input signal is a fast square wave of sufficient amplitude to drive the output of the device under test (DUT) to saturation. An oscilloscope is used to observe the slew rate of the DUT output. See FIG. 6 for slew rate and settling time.
FIG. 6 Amplifier settling time and slew rate
3.2.6 Common Mode Rejection Ratio
The ideal operational amplifier has only differential gain and is insensitive to the absolute voltage on the inputs. A real amplifier has several nonideal characteristics associated with input levels. First of all, the range of input voltage is limited. Few IC opamps will operate when the voltages on the input terminals are outside the supply voltages. The second, and perhaps more subtle, characteristic is the common mode rejection ratio. The CMRR is the ratio of a change in common mode voltage to the change in differential input voltage that would produce the same change in output. It often is convenient to specify this parameter in decibels.
3.2.7 Settling Time
Settling time is an important opamp specification, especially when the amplifier must handle rapidly changing signals. In applications such as multiplexers, sample/hold amplifiers, and amplifiers used with A/D and D/A converters, the amplifier settling time often determines the maximum data rate for a specified accuracy.
Settling time is the time that elapses between the application of a step input to the time at which the amplifier output enters, and remains within, a specified error band symmetrical to the final output value.
Settling time is determined by both linear and nonlinear characteristics of the amplifier. It varies with the input signal level and is greatly affected by impedances external to the amplifier. For these reasons, extrapolation of settling times from one set of operating conditions to another becomes virtually impossible. Settling time cannot be predicted from open-loop specifications, such as slew rate or small signal and bandwidth, as it’s a closed-loop parameter. The best way to know how fast an amplifier will settle in a particular application is to measure it.
3.2.8 Noise
In addition to noise present on the input signal, opamp circuits have noise due to external interference and the inherent noise of the circuit itself. Interference noise originates from sources not related to the actual circuit; such noises include ground and power supply noise, stray electromagnetic pickup, contact arcing in switches and relays, and transients due to switching in reactive circuits. Even mechanical vibration can create noise in high-impedance amplifier circuits, either by piezoelectric pickup due to the use of piezoelectric plastic material in cables or circuit boards or by capacitance variation as the circuit vibrates. External interference often can be eliminated, once the interfering source is identified and appropriate action taken. The inherent noise of the opamp circuit itself cannot be totally eliminated, since it’s caused by components within the circuit. The best that can be accomplished is to minimize the noise in a specific bandwidth of interest. Four types of noise are commonly encountered in operational amplifiers: popcorn noise, flicker noise, shot noise, and Johnson noise. Popcorn noise is well understood and of less importance in modern components. Flicker noise is the dominant noise at low frequencies. It has a power spectral density inversely proportional to frequency (hence the term 1/f noise). The noise voltage spectral density therefore is inversely proportional to the square root of frequency. In modern opamps, it’s rarely significant above 50 Hz.
Thermal excitation of the electrons in conductors causes random movement of charge. In a resistor, this random current causes a noise voltage, known as Johnson noise, whose amplitude is given by the formula
EN(rms) = ~/4KTRB (2.1)
where
K = Boltzman's constant (1.38 x 10 -23 J/°K); T = temperature (K); R = resistance (Ohms, fa); B = bandwidth (Hertz). At room temperature (25°C), this may be simplified to EN (rms) ~ (2.2)
or e~ ~ 4v/-R (3)
where:
EN = total noise (g V rms); R = resistance (k ~); B = bandwidth (kHz); en = spectral density (nV/vCH-z).
Johnson noise is a fundamental property of resistance and important in designing low-noise circuitry. It could be reduced only by reducing the temperature, the resistance, or the working bandwidth. As a reference point, it’s useful to remember that at room temperature a 1 kfa resistor has 4 nV/~H-~ of white noise. This is equivalent to 128 nV rms noise in a 1 kHz bandwidth.
Shot, or Schottky, noise is caused by the statistical variations in the rate of electron flow; these manifest themselves as a noise current in semiconductors, where the current consists of a flow of electrons or holes. Shot noise IN is given by the formula
IN --5.7 x 10-4vqjB (4)
Where:
IN = noise current (picoamps rms); l j = junction current (picoamps); B = bandwidth of interest.
above: Eqns 5, 6, and 7.
FIG. 7 Opamp noise model
Shot noise is important only when the operational bandwidth is large or the noise current is an appreciable factor of the total current.
FIG. 7 shows a generalized noise model applicable to all opamps, including current feedback types. In addition to the input noise currents and voltages, the Johnson thermal noise voltages associated with the three resistors are included.
Equation (7) is given for calculating the effective integrated output noise voltage in a given bandwidth. The appropriate values for Is-, Is+, and VN are taken from the current and voltage noise spectral densities given on the data sheet. Usually the noninverting input noise current IN+ is neglected because the noninverting input almost always is grounded, bypassed, or driven from a low-impedance source. In making noise performance comparisons among opamps, it often is useful to convert the output noise voltage (VoN) tO an effective integrated input noise voltage (VIN). This is accomplished easily by dividing the integrated output noise voltage by the noise gain; that is,
1 4-RFB/RFF.
As applied to FIG. 7, the gain of stage is ...
...where VON = effective integrated output noise; VIN = effective integrated input noise;
FIG. 8 Equivalent input noise for the AD9617. (Analog Devices Inc.)
FIG. 8 shows the noise current and voltage spectral density for a practical opamp such as AD9617 from Analog Devices.
Both the noise current and noise voltage are a function of frequency but flatten out above 1 kHz, where the 1/f current noise no longer is significant. To determine the effective noise over a bandwidth where the curves are not flat, the designer must determine the areas under the respective curves for the bandwidth of interest.
FIG. 9 shows a plot of the effective integrated output noise for the AD844 current feedback opamp from Analog Devices. Note that, at low closed-loop gains, the predominant noise source is the input current noise that flows through the feedback resistor (1000 f2). For closed-loop gains greater than 15, however, the effects of the "gained-up" input voltage noise begin to dominate the output noise.
Low-noise opamps can be considered those with less than 15-20 nV/~-z.
In the most recent low-noise devices, typical noise voltages of 2-4 nV/~-H-~ and noise currents of 2-4 nA/~/-H-~ are common.
3.2.9 Linearity and Distortion
An ideal amplifier produces an exact scaled replica of its input signal at its output. To do this, the slope of its transfer characteristic must be constant.
Altering the shape of the input signal between the input and the output is referred to as distorting it. Distortion is the result of processing a signal in a nonlinear system. A remarkable property of feedback amplifiers is their ability to improve linearity through the use of feedback. The actual mechanism by which this is accomplished is not obvious but may be approached by using a combination of analytical and graphic techniques.
The effect of adding feedback to improve linearity may be treated mathematically. These methods of analysis become increasingly more important as the total harmonic distortion (THD) in an amplifier is used as a criterion for selecting it.
It’s clear from FIG. 10(a) that feedback improves linearity. As per FIG. 10(b),
It’s apparent from equation (2.10) that increasing the product GH reduces the sensitivity of the overall amplifier to a variation of G and hence reduces nonlinearity. It’s difficult to discern the presence of distortion on a sinusoidal waveform visually by using an oscilloscope; our eyeballs just are not calibrated to detect slightly distorted sinusoids (it sometimes is less difficult to perceive distortion on noncurvy waveforms such as pulses and square, triangular, and sawtooth waves). The most effective means of measuring distortion is to use a spectrum analyzer and measure the harmonically related components resulting from the nonlinear characteristics of an amplifier.
FIG. 9 Equivalent integrated output noise vs. gain for the AD844. (Analog
Devices Inc.)
FIG. 10 Feedback and nonlinearity: (a) Feedback improving linearity,
(b) Nonlinearity gain sensitivity
The most common form of distortion is "limiting" or "clipping," which occurs when the required output voltage from an amplifier is larger than the maximum voltage the amplifier actually can provide (the output is said to exceed the amplifier's "headroom" or to "limit"). Symmetrical clipping introduces high levels of odd harmonics into a waveform, asymmetrical clipping introduces even harmonics as well. The cures are to either reduce the gain of the amplifier or increase its supply voltages.
Although clipping may be considered a gross form of nonlinearity, the term normally is reserved for phenomena that cause the central part of the amplifier transfer characteristic to deviate from a straight line. Consider a 12-bit system with a full-scale range of 10 V. Specifying the system to be linear to 12 bits implies that the maximum deviation from the ideal transfer curve is 1 LSB (2.44 mV).
The two most common types of nonlinearity are square law and logarithmic.
Square law nonlinearity occurs when there is a quadratic term in the transfer characteristic of the amplifier and can be produced by a field effect transistor with a resistive load. Logarithmic nonlinearity is produced by a logarithmic (inverse exponential) term in the transfer characteristic and can be caused by bipolar transistors and diodes. A rigorous treatment of opamp characteristics and specifications is given by Analog Devices (1987, 1990).