# Fundamental Physics/Electronics/Operational Amplifiers/Amplifier/DC amplifier

## DC amplifier[edit]

## Transformer Amplifier[edit]

### Non inverting Amplifier[edit]

With

- .

### Inverting Amplifier[edit]

With

- .

## Transistor Amplier[edit]

### Non inverting Amplifier[edit]

With

- .

### Inverting Amplifier[edit]

With

- .

## Operational Amplifier[edit]

We begin these examples with that of the differential amplifier, from which many of the other applications can be derived, including the inverting, non-inverting, and summing amplifier, the voltage follower, integrator, differentiator, and gyrator.

### Differential amplifier (difference amplifier)[edit]

*Main article: Differential amplifier*

Amplifies the difference in voltage between its inputs.

*The name "differential amplifier" must not be confused with the "differentiator," which is also shown on this page.*

*The "instrumentation amplifier," which is also shown on this page, is a modification of the differential amplifier that also provides high input impedance.*

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 (the common-mode gain) must be zero, or

With this constraint If you think of the left-hand side of the relation as the closed-loop gain of the inverting input, and the right-hand side as the gain of the non-inverting input, then matching these two quantities provides an output insensitive to the common-mode voltage of and .</ref> in place, the common-mode rejection ratio of this circuit is infinitely large, and the output

where the simple expression *R*_{f} / *R*_{1} 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[edit]

An inverting amplifier is a special case of the differential amplifier in which that circuit's non-inverting input *V*_{2} is grounded, and inverting input *V*_{1} 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 *R*_{2} 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 (because *V*_{−} = *V*_{+} = 0):

A mechanical analogy is a seesaw, with the *V*_{−} node (between *R*_{in} and *R*_{f}) 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*.

### Non-inverting amplifier[edit]

A non-inverting amplifier is a special case of the differential amplifier in which that circuit's inverting input *V*_{1} is grounded, and non-inverting input *V*_{2} is identified with *V*_{in} above, with *R*_{1} ≫ *R*_{2}.
Referring to the circuit immediately above,

- .

To intuitively see this gain equation, use the virtual ground technique to calculate the current in resistor *R*_{1}:

then recall that this same current must be passing through *R*_{2}, 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 *R*_{1} as the fulcrum, at ground potential. *V*_{in} is at a length *R*_{1} from the fulcrum; *V*_{out} is at a length *R*_{2} 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, of order *R*_{dif} × A_{OL} times the closed-loop gain, where *R*_{dif} is the op amp's input impedance to differential signals, and A_{OL} is the open-loop voltage gain of the op amp; in the case of the ideal op amp, with A_{OL} infinite and *R*_{dif} infinite, the input impedance is 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.

### Voltage follower (unity buffer amplifier)[edit]

Used as a buffer amplifier to eliminate loading effects (e.g., connecting a device with a high source impedance to a device with a low input impedance).

- (realistically, the differential input impedance of the op-amp itself, 1 MΩ to 1 TΩ)

Due to the strong (i.e., unity gain) 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 (e.g., connecting the load to the voltage follower through a resistor) 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.

### Summing amplifier[edit]

A summing amplifier sums several (weighted) voltages:

- When , and independent

- When

- Output is inverted
- Input impedance of the
input is ( is a virtual ground)*n*th

#### Instrumentation amplifier[edit]

*Main article: 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.