Early operational amplifiers (op-amps) were used primarily to perform mathematical operations such as addition, subtraction, integration, and differentiation—thus the term operational. These early devices were constructed with vacuum tubes and worked with high voltages. Today’s op-amps are linear integrated circuits (IC s) that use relatively low dc supply voltages and are reliable and inexpensive.
The standard operational amplifier (op-amp) symbol is shown in Figure. It has two input terminals, the inverting (-) input and the noninverting (+) input, and one output terminal. Most op-amps operate with two dc supply voltages, one positive and the other negative, although some have a single dc supply. Usually these dc voltage terminals are left off the schematic symbol for simplicity but are understood to be there. Some typical op-amp IC packages. Op-amp symbols and packages are shown in above Figures:
The Ideal Op-Amp:
To illustrate what an op-amp is, let’s consider its ideal characteristics. A practical op-amp, of course, falls short of these ideal standards, but it is much easier to understand and analyze the device from an ideal point of view.
First, the ideal op-amp has infinite voltage gain and infinite bandwidth. Also, it has an infinite input impedance (open) so that it does not load the driving source. Finally, it has a zero output impedance. The input voltage, V in, appears between the two input terminals, and the output voltage is AvVin, as indicated by the internal voltage source symbol. The concept of infinite input impedance is a particularly valuable analysis tool for the various op-amp configurations.
Basic op-amp representations are shown in the above Figure:
The Practical Op-Amp:
Although integrated circuit (IC) op-amps approach parameter values that can be treated as ideal in many cases, the ideal device can never be made. Any device has limitations, and the IC op-amp is no exception. Op-amps have both voltage and current limitations. The peak-to-peak output voltage, for example, is usually limited to slightly less than the two supply voltages. Output current is also limited by internal restrictions such as power dissipation and component ratings.
Characteristics of a practical op-amp are very high voltage gain, very high input impedance, and very low output impedance. These are labeled in Figure. Another practical consideration is that there is always noise generated within the op-amp. Noise is an undesired signal that affects the quality of the desired signal. Today, circuit designers are using smaller voltages that require high accuracy, so low-noise components are in greater demand. All circuits generate noise; op-amps are no exception, but the amount can be minimized.
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Internal Block Diagram of an Op-Amp:
A typical op-amp is made up of three types of amplifier circuits: a differential amplifier, a voltage amplifier, and a push-pull amplifier. The differential amplifier is the input stage for the op-amp. It provides amplification of the difference voltage between the two inputs. The second stage is usually a class A amplifier that provides additional gain. Some op-amps may have more than one voltage amplifier stage. A push-pull class B amplifier is typically used for the output stage. The basic internal arrangement of an op-amp is shown in Figure:
The term differential comes from the amplifier’s ability to amplify the difference of two input signals applied to its inputs. Only the difference in the two signals is amplified; if there is no difference, the output is zero. The differential amplifier exhibits two modes of operation based on the type of input signals. These modes are differential and common, which are described in the next section. Since the differential amplifier is the input stage of the op-amp, the op-amp exhibits the same modes.
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Op-Amp Input Modes And Parameters:
In this section, important op-amp input modes and several parameters are defined. Also, several common IC op-amps are compared in terms of these parameters.
Input Signal Modes:
Recall that the input signal modes are determined by the differential amplifier input stage of the op-amp.
In the differential mode, either one signal is applied to an input with the other input grounded, or two opposite-polarity signals are applied to the inputs. When an op-amp is operated in the single-ended differential mode, one input is grounded and a signal voltage is applied to the other input, as shown in Figure. In the case where the signal voltage is applied to the inverting input as in part (a), an inverted, amplified signal voltage appears at the output. In the case where the signal is applied to the non-inverting input with the inverting input grounded, as in Figure, a noninverted, amplified signal voltage appears at the output. Single-ended differential modes is shown in Figure:
In the double-ended differential mode, two opposite-polarity (out-of-phase) signals are applied to the inputs, as shown in Figure. The amplified difference between the two inputs appears on the output. Equivalently, the double-ended differential mode can be represented by a single source connected between the two inputs, as shown in Figure:
In the common mode, two signal voltages of the same phase, frequency, and amplitude are applied to the two inputs, as shown in Figure. When equal input signals are applied to both inputs, they tend to cancel, resulting in a zero output voltage. Common-mode operation is shown in the above Figure:
This action is called common-mode rejection. Its importance lies in the situation where an unwanted signal appears commonly on both op-amp inputs. Common-mode rejection means that this unwanted signal will not appear on the output and distort the desired signal. Common-mode signals (noise) generally are the result of the pick-up of radiated energy on the input lines, from adjacent lines, the 60 Hz power line, or other sources.
Common-Mode Rejection Ratio:
Desired signals can appear on only one input or with opposite polarities on both input lines. These desired signals are amplified and appear on the output as previously discussed. Unwanted signals (noise) appearing with the same polarity on both input lines are essentially canceled by the op-amp and do not appear on the output. The measure of an amplifier’s ability to reject common-mode signals is a parameter called the CMRR (common-mode rejection ratio).
Ideally, an op-amp provides a very high gain for differential-mode signals and zero gain for common-mode signals. Practical op-amps, however, do exhibit a very small common-mode gain (usually much less than 1), while providing a high open-loop differential voltage gain (usually several thousand). The higher the open-loop gain with respect to the common-mode gain, the better the performance of the op-amp in terms of rejection of common-mode signals. This suggests that a good measure of the op-amp’s performance in rejecting unwanted common-mode signals is the ratio of the open-loop differential voltage gain, A ol , to the common-mode gain, Acm. This ratio is the common-mode rejection ratio, CMRR.
The higher the CMRR, the better. A very high value of CMRR means that the open-loop gain, A ol, is high and the common-mode gain, A cm, is low.
The CMRR is often expressed in decibels (dB) as:
The open-loop voltage gain, A ol, of an op-amp is the internal voltage gain of the device and represents the ratio of output voltage to input voltage when there are no external components. The open-loop voltage gain is set entirely by the internal design. Open-loop voltage gain can range up to 200,000 (106 dB) and is not a well-controlled parameter. Datasheets often refer to the open-loop voltage gain as the large-signal voltage gain.
A CMRR of 100,000, for example, means that the desired input signal (differential) is amplified 100,000 times more than the unwanted noise (common-mode). If the amplitudes of the differential input signal and the common-mode noise are equal, the desired signal will appear on the output 100,000 times greater in amplitude than the noise. Thus, the noise or interference has been essentially eliminated.
Maximum Output Voltage Swing (V O(p-p) :
With no input signal, the output of an op-amp is ideally 0 V. This is called the quiescent output voltage. When an input signal is applied, the ideal limits of the peak-to-peak output signal are ±V CC. In practice, however, this ideal can be approached but never reached. V O(p-p) varies with the load connected to the op-amp and increases directly with the load resistance. For example, the Fairchild KA741 datasheet shows a typical V O(p-p) of ±13 V for V CC = ±15 V when R L = 2 kΩ. V O(p-p) increases to ±14 V when R L = 10 kΩ.
Some op-amps do not use both positive and negative supply voltages. One example is when a single dc voltage source is used to power an op-amp that drives an analog-to-digital converter.In this case, the op-amp output is designed to operate between ground and a full-scale output that is near (or at) the positive supply voltage. Op-amps that operate on a single supply use the terminology V OH and VOL to specify the maximum and minimum output voltage. (Note that these are not the same as the digital definitions of VOL and V OH.) .
Input Offset Voltage:
The ideal op-amp produces zero volts out for zero volts in. In a practical op-amp, however, a small dc voltage, V OUT(error), appears at the output when no differential input voltage is applied. Its primary cause is a slight mismatch of the base-emitter voltages of the differential amplifier input stage of an op-amp.
As specified on an op-amp datasheet, the input offset voltage, V OS, is the differential dc voltage required between the inputs to force the output to zero volts. Typical values of input offset voltage are in the range of 2 mV or less. In the ideal case, it is 0 V.
The input offset voltage drift is a parameter related to VOS that specifies how much change occurs in the input offset voltage for each degree change in temperature. Typical values range anywhere from about 5 μV per degree Celsius to about 50 μV per degree Celsius. Usually, an op-amp with a higher nominal value of input offset voltage exhibits a higher drift.
Input Bias Current:
You have seen that the input terminals of a bipolar differential amplifier are the transistor bases and, therefore, the input currents are the base currents.
The input bias current is the dc current required by the inputs of the amplifier to properly operate the first stage. By definition, the input bias current is the average of both input currents and is calculated as follows:
The concept of input bias current is illustrated in Figure:
Two basic ways of specifying the input impedance of an op-amp are the differential and the common mode. The differential input impedance is the total resistance between the inverting and the noninverting inputs, as illustrated in Figure. Differential impedance is measured by determining the change in bias current for a given change in differential input voltage. The common-mode input impedance is the resistance change in differential input voltage. The common-mode input impedance is the resistance for a given change in common-mode input voltage. It is depicted in Figure:
Input Offset Current:
Ideally, the two input bias currents are equal, and thus their difference is zero. In a practical op-amp, however, the bias currents are not exactly equal.
The input offset current, I OS, is the difference of the input bias currents, expressed as an absolute value.
I OS | I1 I2 |
Actual magnitudes of offset current are usually at least an order of magnitude (ten times) less than the bias current. In many applications, the offset current can be neglected. However, high-gain, high-input impedance amplifiers should have as little I OS as possible because the difference in currents through large input resistances develops a substantial offset voltage, as shown in Figure:
The offset voltage developed by the input offset current is:
The error created by I OS is amplified by the gain Av of the op-amp and appears in the output as:
A change in offset current with temperature affects the error voltage. Values of temperature coefficient for the offset current in the range of 0.5 nA per degree Celsius are common.
The output impedance is the resistance viewed from the output terminal of the op-amp, as indicated in Figure:
The maximum rate of change of the output voltage in response to a step input voltage is the slew rate of an op-amp. The slew rate is dependent upon the high-frequency response of the amplifier stages within the op-amp.
Slew rate is measured with an op-amp connected as shown in Figure. This particular op-amp connection is a unity-gain, noninverting configuration. It gives a worst-case (slowest) slew rate. Recall that the high-frequency components of a voltage step are contained in the rising edge and that the upper critical frequency of an amplifier limits its response to a step input. For a step input, the slope on the output is inversely proportional to the upper critical frequency. Slope increases as upper critical frequency decreases.
A pulse is applied to the input and the resulting ideal output voltage is indicated in Figure. The width of the input pulse must be sufficient to allow the output to “slew” from its lower limit to its upper limit. A certain time interval, Δt, is required for the output voltage to go from its lower limit -V max to its upper limit +V max, once the input step is applied. The slew rate is expressed as:
where ΔV out = +V max – (-V max). The unit of slew rate is volts per microsecond (V/μs).
The internal amplifier stages that make up an op-amp have voltage gains limited by junction capacitances. Although the differential amplifiers used in op-amps are somewhat different from the basic amplifiers discussed earlier, the same principles apply. An op-amp has no internal coupling capacitors, however; therefore, the low-frequency response extends down to dc (0 Hz).
Noise has become a more important issue in new circuit designs because of the requirement to run at lower voltages and with greater accuracy than in the past. As little as two or three microvolts can create errors in analog-to-digital conversion. Many sensors produce only tiny voltages that can be masked by noise. As a result, unwanted noise from op-amps and components can degrade the performance of circuits.
Noise is defined as an unwanted signal that affects the quality of the desired signal. While interference from an external source (such as a nearby power line) qualifies as noise, for the purpose of op-amp specifications, interference is not included. Only noise generated within the op-amp is considered in the noise specification.
When the op-amp is added to a circuit, additional noise contributions are added from other circuit elements, such as the feedback resistors or any sensors. For example, all resistors generate thermal noise—even one sitting in the parts bin. The circuit designer must consider all sources within the circuit, but the concern here is the op-amp specification for noise, which only considers the op-amp.
There are two basic forms of noise. At low frequencies, noise is inversely proportional to the frequency; this is called 1/f noise or “pink noise”. Above a critical noise frequency, the noise becomes flat and is spread out equally across the frequency spectrum; this is called “white noise”. The power distribution of noise is measured in watts per hertz (W/Hz). Power is proportional to the square of the voltage, so noise voltage (density) is found by taking the square root of the noise power density, resulting in units of volts per square root hertz (V/1√¯Hz).
For operational amplifiers, the noise level is normally shown with units of n V/√¯Hz and is specified relative to the input at a specific frequency above the noise critical frequency. For example, a noise level graph for a very low-noise op-amp is shown in Figure; the specification for this op-amp will indicate that the input voltage noise density at 1 kHz is 1.1 n V/ √¯Hz. At low frequencies, the noise level is higher than this due to the 1/f noise contribution as you can see from the graph:
Comparison of Op-Amp Parameters:
a comparison of values showing selected parameters for some representative op-amps. As you can see from the table, there is a wide difference in certain specifications.
All designs involve certain compromises, so in order for designers to optimize one parameter, they must often sacrifice another parameter. Choosing an op-amp for a particular application depends on which parameters are important to optimize. Parameters depend on the conditions for which they are measured. For details on any of these specifications, consult the datasheet.
Most available op-amps have three important features: short-circuit protection, no latch-up, and input offset nulling. Short-circuit protection keeps the circuit from being damaged if the output becomes short, and the no latch-up feature prevents the op-amp from hanging up in one output state (high or low voltage level) under certain input conditions. Input offset nulling is achieved by an external potentiometer that sets the output voltage at precisely zero with zero input.
Negative feedback is one of the most useful concepts in electronics, particularly in op-amp applications. Negative feedback is the process whereby a portion of the output voltage of an amplifier is returned to the input with a phase angle that opposes (or subtracts from) the input signal.
Negative feedback is illustrated in Figure. The inverting (-) input effectively makes the feedback signal 180° out of phase with the input signal.
Why Use Negative Feedback?
As you can see in the Table, the inherent open-loop voltage gain of a typical op-amp is very high (usually greater than 100,000). Therefore, an extremely small input voltage drives the op-amp into its saturated output states. In fact, even the input offset voltage of the op-amp can drive it into saturation. For example, assume V IN 1 mV and Aol = 100,000. Then,
Since the output level of an op-amp can never reach 100 V, it is driven deep into saturation and the output is limited to its maximum output levels, as illustrated in Figure for both a positive and a negative input voltage of 1 mV.
The usefulness of an op-amp operated without negative feedback is generally limited to comparator applications. With negative feedback, the closed-loop voltage gain (A cl) can be reduced and controlled so that the op-amp can function as a:
linear amplifier. In addition to providing a controlled, stable voltage gain, negative feedback also provides for control of the input and output impedances and amplifier bandwidth. Table summarizes the general effects of negative feedback on op-amp performance.
Op-Amps With Negative Feedback:
An op-amp can be connected using negative feedback to stabilize the gain and increase
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