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, micropower, 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) Transimpedance 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 singleended output, and infinite gain at all frequencies. The ideal
opamp always must be considered as a fourterminal 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 singleended 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 SingleEnded 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 singleended
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 singleended 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 openloop frequency
response, and its capacitor may be added externally, as in the 101, or
selfcontained, 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 baseemitter 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 closedloop 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 lowfrequency 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 closedloop
bandwidth. This means that highspeed, highlevel circuits can "talk" to
lowlevel 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, AN202).
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 baseemitter voltages of the differential input transistors
(the gatesource voltage mismatch in FETinput 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 FETinput 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 reversebiased 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 thosewith less than 1 nA bias
currents.
3.2.3 OpenLoop Voltage Gain
Another opamp parameter that distinguishes a real amplifier from an ideal
amplifier is the openloop gain. The openloop 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 millionthe 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 openloop 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 singlepole
rolloff, falling at 6 dB/octave (20 dB/decade). It’s obvious that, throughout
the region where this singlepole frequency response applies, the product
of gain and frequency is a constant, known as the gainbandwidth product
of the amplifier, and a measure of its highfrequency performance. In the
majority of opamps, this singlepole 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 lowclosed loop gains but generally
have better highfrequency 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 openloop
specifications, such as slew rate or small signal and bandwidth, as it’s
a closedloop 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 highimpedance
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/vCHz).
Johnson noise is a fundamental property of resistance and important in
designing lownoise 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 104vqjB (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 lowimpedance 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 4RFB/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 closedloop
gains, the predominant noise source is the input current noise that flows
through the feedback resistor (1000 f2). For closedloop gains greater
than 15, however, the effects of the "gainedup" input voltage
noise begin to dominate the output noise.
Lownoise opamps can be considered those with less than 1520 nV/~z.
In the most recent lownoise devices, typical noise voltages of 24 nV/~H~
and noise currents of 24 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 12bit system with a fullscale 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).
cont. to part 2 >>
