Real op-amps can only approach this ideal: in addition to the practical limitations on slew rate, bandwidth, offset and so forth mentioned above, real op-amp parameters are subject to drift over time and with changes in temperature, input conditions, etc. Modern integrated FET or MOSFET op-amps approximate more closely the ideal op-amp than bipolar ICs where large signals must be handled at room temperature over a limited bandwidth; input impedance, in particular, is much higher, although the bipolar op-amps usually exhibit superior (i.e., lower) input offset drift and noise characteristics.
Where the limitations of real devices can be ignored, an op-amp can be viewed as a black box with gain; circuit function and parameters are determined by feedback, usually negative. IC op-amps as implemented in practice are moderately complex integrated circuits; see the internal circuitry for the relatively simple 741 op-amp below, for example.
Open-loop gain is defined as the amplification from input to output without any feedback applied. For most practical calculations, the open-loop gain is assumed to be infinite; in reality it is obviously not. Typical devices exhibit open-loop DC gain ranging from 100,000 to over 1 million; this is sufficiently large for circuit gain to be determined almost entirely by the amount of negative feedback used. Op-amps have performance limits that the designer must keep in mind and sometimes work around. In particular, instability is possible in a DC amplifier if AC aspects are neglected.
Other imperfections include:
- Finite gain — the effect is most pronounced when the overall design attempts to achieve gain close to the inherent gain of the op-amp.
- Finite input resistance — this puts an upper bound on the resistances in the feedback circuit. Some op-amps have circuitry to protect inputs from excessive voltage: this makes input parameters slightly worse. Some op-amps are available in protected (thus slightly degraded) and unprotected versions.
- Nonzero output resistance — important for low resistance loads. Except for very small voltage output, power considerations usually come into play first. (Output impedance is inversely proportional to the idle current in the output stage — very low idle current results in very high output impedance.)
- Input bias current — a small amount of current (typically ~10 nA for bipolar op-amps, or picoamperes for CMOS designs) flows into the inputs. This current is mismatched slightly between the inverting and non-inverting inputs (there is an input offset current). This effect is usually important only for very low power circuits.
- Input offset voltage — the voltage required across the op-amp's input terminals to drive the output voltage to zero. In the perfect amplifier, there would be no input offset voltage. However, it exists in actual op-amps because of imperfections in the differential amplifier that constitutes the input stage of the vast majority of these devices. Input offset voltage creates two problems: First, due to the amplifier's high voltage gain, it virtually assures that the amplifier output will go into saturation if it is operated without negative feedback, even when the input terminals are wired together. Second, in a closed loop, negative feedback configuration, the input offset voltage is amplified along with the signal and this may pose a problem if high precision DC amplification is required or if the input signal is very small.
- Common mode gain — A perfect operational amplifier amplifies only the voltage difference between its two inputs, completely rejecting all voltages that are common to both. However, the differential input stage of an operational amplifier is never perfect, leading to the amplification of these identical voltages to some degree. The standard measure of this defect is called the common-mode rejection ratio (denoted, CMRR). Minimization of common mode gain is usually important in non-inverting amplifiers (described below) that operate at high amplification.
- Temperature effects — all parameters change with temperature. Temperature drift of the input offset voltage is especially important.
The op-amp gain calculated at DC does not apply at higher frequencies. To a first approximation, the gain of a typical op-amp is inversely proportional to frequency. This means that an op-amp is characterized by its gain-bandwidth product. For example, an op-amp with a gain bandwidth product of 1 MHz would have a gain of 5 at 200 kHz, and a gain of 1 at 1 MHz. This low-pass characteristic is introduced deliberately, because it tends to stabilize the circuit by introducing a dominant pole. This is known as frequency compensation.
Typical low cost, general purpose op-amps exhibit a gain bandwidth product of a few megahertz. Specialty and high speed op-amps can achieve gain bandwidth products of hundreds of megahertz. For very high-frequency circuits, a completely different form of op-amp called the current-feedback operational amplifier is often used.
Other imperfections include:
- Finite bandwidth — all amplifiers have a finite bandwidth. This creates several problems for op amps. First, associated with the bandwidth limitation is a phase difference between the input signal and the amplifier output that can lead to oscillation in some feedback circuits. The internal frequency compensation used in some op amps to increase the gain or phase margin intentionally reduces the bandwidth even further to maintain output stability when using a wide variety of feedback networks. Second, reduced bandwidth results in lower amounts of feedback at higher frequencies, producing higher distortion, noise, and output impedance and also reduced output phase linearity as the frequency increases.
- Input capacitance — most important for high frequency operation because it further reduces the open loop bandwidth of the amplifier.
- Common mode gain — See DC imperfections, above.
- Saturation — output voltage is limited to a minimum and maximum value close to the power supply voltages. Saturation occurs when the output of the amplifier reaches this value and is usually due to:
- In the case of an op-amp using a bipolar power supply, a voltage gain that produces an output that is more positive or more negative than that maximum or minimum; or
- In the case of an op-amp using a single supply voltage, either a voltage gain that produces an output that is more positive than that maximum, or a signal so close to ground that the amplifier's gain is not sufficient to raise it above the lower threshold.
- Slewing — the amplifier's output voltage reaches its maximum rate of change. Measured as the slew rate, it is usually specified in volts per microsecond. When slewing occurs, further increases in the input signal have no effect on the rate of change of the output. Slewing is usually caused by internal capacitances in the amplifier, especially those used to implement its frequency compensation.
- Non-linear transfer function — The output voltage may not be accurately proportional to the difference between the input voltages. It is commonly called distortion when the input signal is a waveform. This effect will be very small in a practical circuit if substantial negative feedback is used.
Distortion in op-amps
Very often operational amplifiers are used for audio filters. The behavior of this type of operational amplifiers is important to get low distortion amplifiers and audio consoles for sound recording and reproduction. The evaluation of distortion is introduced using the Distortion Multiplication Factor (Kd).
- Limited output current — the output current must obviously be finite. In practice, most op-amps are designed to limit the output current so as not to exceed a specified level — around 25 mA for a type 741 IC op-amp — thus protecting the op-amp and associated circuitry from damage.
- Limited dissipated power — an opamp is a linear amplifier. It therefore dissipates some power as heat, proportional to the output current, and to the difference between the output voltage and the supply voltage. If the opamp dissipates too much power, then its temperature will increase above some safe limit. The opamp may enter thermal shutdown, or it may be destroyed.