Characterization of operational amplifiers#
Operational amplifiers are often specified with the aid of a collection of parameters and plots. In this section, we will define the most commonly used parameters and list some frequently used plots. The reader is invited to download some data sheets of operational amplifiers and study them to better understand the specification of these components.
Commonly used terms#
As mentioned earlier, operational amplifiers are almost always used as controllers in feedback circuits. Hence, they are amplifiers and should be specified as such, as was discussed in Chapter Modeling and specification of amplifiers. However, in common design practice , parameter names can be somewhat confusing. This is because the specification of operational amplifiers is very much connected to the design of negative-feedback (voltage) amplifiers. In data sheets of operational amplifiers , one often finds the terms \emph{closed-loop }gain and\ \emph{open-loop }gain. In this book, we try to avoid these terms. We speak rather of the gain of the operational amplifier, the gain of a negative feedback amplifier and the loop gain of a negative feedback amplifier. These terms have a well-defined meaning in the asymptotic gain model , that will be used for the design and analysis of negative feedback circuits (see Chapter Modeling of negative feedback circuits).
The popular term \emph{open-loop }gain in data sheets refers to the gain of the operational amplifier. It is a property of the operational amplifier itself and it does not need a feedback loop for its existence, nor for its definition. This also holds for the term \emph{open-loop }output impedance. It is simply the output impedance of the operational amplifier itself.
The term \emph{closed-loop }gain in data sheets refers to the gain of a feedback amplifier equipped with the operational amplifier. Hence, it is a property of the circuit with the operational amplifier, rather than a property of the operational amplifier itself. This is also the case for the term \emph{closed-loop }output impedance.
In Chapter Modeling of negative feedback circuits, we will discuss the analysis of circuits with feedback. We will then relate the gain of the negative feedback amplifier to its ideal gain as it is defined in Chapter Design of feedback amplifier configurations, and to the gain of the operational amplifier.
Terminal voltages and currents#
name |
symbol |
definition |
common-mode input voltage |
\(V_{cm}\) |
\(\frac{1}{2}\left( V_{i+}+V_{i-}\right) \) |
differential-mode input voltage |
\(V_{dm}\) |
\(V_{i+}-V_{i-} \) |
bias current |
\(I_{BIAS}\) |
\(I_{i+};~I_{i-}\) |
common-mode input current |
\(I_{cm}\) |
\(I_{i+}+I_{i-}\) |
differential-mode input current |
\(I_{dm}\) |
\(\frac{1}{2}\left( I_{i+}-I_{i-}\right) \) |
output voltage |
\(V_{out}\) |
\(V_{out}\) |
output current |
\(I_{out}\) |
\(I_{out}\) |
supply current (no load) |
\(I_{supply}\) |
\(\frac{1}{2}\left( I_{P}-I_{N}\right) \) |
Fig. 274 shows the definitions of the terminal voltages and currents of the operational amplifier. Their general names and definitions are given in the Table 20. These names and definitions will be used throughout this chapter.
In the following sections, we will discuss parameters that describe the:
Static nonlinear behavior of operational amplifiers (section Static nonlinear behavior)
Small-signal dynamic behavior and noise behavior of operational amplifiers (section Noise and small-signal dynamic behavior)
Large-signal dynamic behavior of operational amplifiers (section Large-signal dynamic behavior).
Static nonlinear behavior#
The parameters that characterize the static nonlinear behavior (also large-signal instantaneous behavior) are given in Table 21.
name |
symbol |
definition |
{\small maximum positive }\(V_{cm}\) |
\(V_{cm+}\) |
\(V_{cm}<V_{cm+}\)\ for operation within specifications |
{\small maximum negative }\(V_{cm}\) |
\(V_{cm-}\) |
\(V_{cm}>V_{cm-}\)\ for operation within specifications |
offset voltage |
\(V_{off}\) |
{\small standard deviation of the differential-mode input voltage for }\(V_{out}=0\) |
offset voltage drift |
\(dV_{off}/dT\) |
{\small change of }\(V_{off} \)\ with temperature |
bias current drift |
\(dI_{BIAS}/dT\) |
{\small change of }\(I_{BIAS} \)\ with temperature |
offset current |
\(I_{off}\) |
{\small standard deviation of the differential-mode input current for }\(V_{out}=0\) |
offset current drift |
\(dI_{off}/dT\) |
{\small change of }\(I_{off} \)\ with temperature |
quiescent supply current (no load) |
\(I_{Q}\) |
\(\left( I_{+} -I_{-}\right) /2\) |
{\small maximum positive }\(V_{out}\)\ (no load) |
\(V_{out+}\) |
{\small positive clipping value of }\(V_{out}\) |
{\small maximum negative }\(V_{out}\)\ (no load) |
\(V_{out-}\) |
{\small negative clipping value of }\(V_{out}\) |
maximum output source current |
\(I_{out+}\) |
{\small maximum positive value of }\(I_{out}\) |
maximum output sink current |
\(I_{out-}\) |
{\small maximum negative value of }\(I_{out}\) |
In many cases, manufacturers of operational amplifiers add graphs to these lists of parameters. These graphs show:
Temperature dependencies (i.e., bias current versus temperature or versus the common-mode input voltage)
Transfer characteristics (i.e., offset voltage versus the common-mode input voltage)
Statistical information (i.e., histogram of the offset voltage).
There are three effects that cause limitation of the low-frequency (static) signal handling capability of operational amplifiers: limitation of the common-mode input voltage range , limitation of the output current and limitation of the output voltage of the operational amplifier. The latter two are related to each other.
Limitation of the common-mode input voltage range of the operational amplifier:
The common-mode input voltage range of operational amplifiers is usually smaller than the total supply voltage \(V_{P}-V_{N}\). Only operational amplifiers with rail-to-rail inputs have a common-mode input voltage range equal to or (slightly) larger than the total power supply voltage. When driven beyond these limits, some operational amplifiers show\emph{ phase reversal} , an effect that may result in a response, as has been shown in Fig. 56.
Limitation of the low-frequency output current and voltage handling capability:
The maximum current that an operational amplifier can source or sink, depending on the load voltage. A typical plot of the voltage and current drive capability is shown in Fig. 275.
Noise and small-signal dynamic behavior#
The small-signal voltage transfer of the operational amplifier is usually characterized with the aid of Bode plots of the gain and a small-signal step response of an application. Amplitude and phase characteristics of the operational amplifier’s voltage transfer are indispensable for the design of stable negative feedback applications.
Modern rail-to-rail output operational amplifiers do not have a negligibly small output impedance. Bode plots of the output impedance of a feedback circuit with the operational amplifier are sometimes provided and may be used to estimate this impedance. In many applications, knowledge of this output impedance is indispensable for the design of the high-frequency stability of a circuit. Unfortunately, in many cases, the output impedance of an operational amplifier is not or incompletely specified.
name |
symbol |
definition |
common-mode input impedance (complex) |
\(Z_{cm}\) |
\(dV_{cm}/dI_{cm}\) |
differential-mode input impedance (complex) |
\(Z_{dm}\) |
\(dV_{dm}/dI_{dm}\) |
voltage gain |
\(A_{dm}\) |
\(dV_{out}/dV _{dm}\) |
output impedance |
\(Z_{out}\) |
\(-dV_{out}/dI_{out}\) |
gain-bandwidth product |
\(GB\) |
unity-gain frequency |
spectral density of input noise voltage |
\(S_{V_{inoise}}\) |
in series with input |
spectral density of input noise current |
\(S_{I_{inoise}}\) |
parallel with input |
common mode rejection ratio |
\(CMRR\) |
\(\left.dV_{icm}/dV_{idm}\right\vert _{V_{out}=0}\) |
positive power supply rejection ratio |
\(PSRR+\) |
\(\left.dV_{p}/dV_{idm}\right\vert _{V_{out}=0}\) |
negative power supply rejection ratio |
\(PSRR-\) |
\(\left.dV_{n}/dV_{idm}\right\vert _{V_{out}=0}\) |
Plots of the frequency-dependent spectral densities of the equivalent input voltage and current noise sources are almost always provided.
The parameters that describe the small-signal dynamic behavior and the stationary noise behavior of the operational amplifier are listed in Table 22.
Large-signal dynamic behavior#
name |
symbol |
definition |
positive slew rate |
\(SR^{+}\) |
{\small maximum positive rate of change of }\(V_{out}\) |
negative slew rate |
\(SR^{-}\) |
{\small maximum negative rate of change of }\(V_{out}\) |
full-power bandwidth |
\(f_{fp}\) |
maximum frequency for sine wave with |
{\small amplitude }\(\left( V_{out+}-V_{out-}\right) /2\) |
||
harmonic distortion |
\(THD\) |
{\small see definition in Chapter Modeling and specification of amplifiers} |
intermodulation distortion |
\(IM\) |
{\small see definition in Chapter Modeling and specification of amplifiers} |
differential gain |
{\small see definition in Chapter Modeling and specification of amplifiers} |
|
differential phase |
{\small see definition in Chapter Modeling and specification of amplifiers} |
Parameters that describe the large-signal dynamic behavior of operational amplifiers are listed in Table 23. Aside from these parameters, graphs of pulse responses in typical applications are often provided.