Operational amplifier applications

s have several applications, optimised for use with negative feedback.
When positive feedback is required, a comparator is usually more appropriate; see Comparator applications for further information.

Practical considerations

In this article, a simplified schematic notation is used that ignores details such as device selection and power supply connections. Non-ideal properties are ignored.

Operational amplifiers parameter requirements

In order for a particular device to be used in an application, it must satisfy certain requirements. The operational amplifier must

have large open-loop signal gain, and
have input impedance large with respect to values present in the feedback network.

With these requirements satisfied, one can use the method of virtual ground to quickly and intuitively grasp the behavior of the op-amp circuits.

Component specification

Resistors used in practical solid-state op-amp circuits are typically in the kΩ range. Resistors much greater than 1 MΩ cause excessive thermal noise and make the circuit operation susceptible to significant errors due to bias or leakage currents.

Input bias currents and input offset

Practical operational amplifiers draw a small current from each of their inputs due to bias requirements or leakage.
These currents flow through the resistances connected to the inputs and produce small voltage drops across those resistances. Appropriate design of the feedback network can alleviate problems associated with input bias currents and common-mode gain, as explained below. The heuristic rule is to ensure that the impedance "looking out" of each input terminal is identical.
To the extent that the input bias currents do not match, there will be an effective input offset voltage present, which can lead to problems in circuit performance. Many commercial op-amp offerings provide a method for tuning the operational amplifier to balance the inputs. Alternatively, a tunable external voltage can be added to one of the inputs in order to balance out the offset effect. In cases where a design calls for one input to be short-circuited to ground, that short circuit can be replaced with a variable resistance that can be tuned to mitigate the offset problem.
Operational amplifiers using MOSFET-based input stages have input leakage currents that will be, in many designs, negligible.

Power supply effects

Although power supplies are not indicated in the operational amplifier designs below, they are nonetheless present and can be critical in operational amplifier circuit design.

Supply noise

Power supply imperfections may lead to noticeable deviations from ideal operational amplifier behavior. For example, operational amplifiers have a specified power supply rejection ratio that indicates how well the output can reject signals that appear on the power supply inputs. Power supply inputs are often noisy in large designs because the power supply is used by nearly every component in the design, and inductance effects prevent current from being instantaneously delivered to every component at once. As a consequence, when a component requires large injections of current, nearby components can experience sagging at their connection to the power supply. This problem can be mitigated with appropriate use of bypass capacitors connected across each power supply pin and ground. When bursts of current are required by a component, the component can bypass the power supply by receiving the current directly from the nearby capacitor.

Using power supply currents in the signal path

Additionally, current drawn into the operational amplifier from the power supply can be used as inputs to external circuitry that augment the capabilities of the operational amplifier. For example, an operational amplifier may not be fit for a particular high-gain application because its output would be required to generate signals outside of the safe range generated by the amplifier. In this case, an external push-pull amplifier can be controlled by the current into and out of the operational amplifier. Thus, the operational amplifier may itself operate within its factory specified bounds while still allowing the negative feedback path to include a large output signal well outside of those bounds.

Amplifiers

Differential amplifier (difference amplifier)

Amplifies the difference in voltage between its inputs.
The circuit shown computes the difference of two voltages, multiplied by some gain factor. The output voltage
Or, expressed as a function of the common-mode input V_com and difference input V_dif:
the output voltage is
In order for this circuit to produce a signal proportional to the voltage difference of the input terminals, the coefficient of the V_com term must be zero, or
With this constraint in place, the common-mode rejection ratio of this circuit is infinitely large, and the output
where the simple expression R_f / R₁ represents the closed-loop gain of the differential amplifier.
The special case when the closed-loop gain is unity is a differential follower, with

Inverting amplifier

An inverting amplifier is a special case of the differential amplifier in which that circuit's non-inverting input V₂ is grounded, and inverting input V₁ is identified with V_in above. The closed-loop gain is R_f / R_in, hence
The simplified circuit above is like the differential amplifier in the limit of R₂ and R_g very small. In this case, though, the circuit will be susceptible to input bias current drift because of the mismatch between R_f and R_in.
To intuitively see the gain equation above, calculate the current in R_in:
then recall that this same current must be passing through R_f, therefore :
A mechanical analogy is a seesaw, with the V₋ node as the fulcrum, at ground potential. V_in is at a length R_in from the fulcrum; V_out is at a length R_f. When V_in descends "below ground", the output V_out rises proportionately to balance the seesaw, and vice versa.
As the negative input of the op-amp acts as a virtual ground, the input impedance of this circuit is equal to R_in.

Non-inverting amplifier

A non-inverting amplifier is a special case of the differential amplifier in which that circuit's inverting input V₁ is grounded, and non-inverting input V₂ is identified with V_in above, with R₁ ≫ R₂.
Referring to the circuit immediately above,
To intuitively see this gain equation, use the virtual ground technique to calculate the current in resistor R₁:
then recall that this same current must be passing through R₂, therefore:
Unlike the inverting amplifier, a non-inverting amplifier cannot have a gain of less than 1.
A mechanical analogy is a class-2 lever, with one terminal of R₁ as the fulcrum, at ground potential. V_in is at a length R₁ from the fulcrum; V_out is at a length R₂ further along. When V_in ascends "above ground", the output V_out rises proportionately with the lever.
The input impedance of the simplified non-inverting amplifier is high:
where Z_dif is the op-amp's input impedance to differential signals, and A_OL is the open-loop voltage gain of the op-amp, and B is the feedback factor. In the case of the ideal op-amp, with A_OL infinite and Z_dif infinite, the input impedance is also infinite. In this case, though, the circuit will be susceptible to input bias current drift because of the mismatch between the impedances driving the V₊ and V₋ op-amp inputs.
The feedback loop similarly decreases the output impedance:
where Z_out is the output impedance with feedback, and Z_OL is the open-loop output impedance.

Voltage follower (unity buffer amplifier)

Used as a buffer amplifier to eliminate loading effects.
Due to the strong feedback and certain non-ideal characteristics of real operational amplifiers, this feedback system is prone to have poor stability margins. Consequently, the system may be unstable when connected to sufficiently capacitive loads. In these cases, a lag compensation network can be used to restore stability. The manufacturer data sheet for the operational amplifier may provide guidance for the selection of components in external compensation networks. Alternatively, another operational amplifier can be chosen that has more appropriate internal compensation.
The input and output impedance are affected by the feedback loop in the same way as the non-inverting amplifier, with B=1.

Summing amplifier

A summing amplifier produces the negative of the sum of several voltages:

When, and independent
When
Input impedance of the nth input is
Instrumentation amplifier

Combines very high input impedance, high common-mode rejection, low DC offset, and other properties used in making very accurate, low-noise measurements

Is made by adding a non-inverting buffer to each input of the differential amplifier to increase the input impedance.