Op-amp

An **operational amplifier** (often **op-amp** or **opamp**) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. Op-amps are among the most widely used electronic devices today.

The amplifier's differential inputs consist of a non-inverting input (+) with voltage *V*+ and an inverting input (–) with voltage *V*-. The op-amp amplifies the difference in voltage between the two, which is called the *differential input voltage*. The output voltage of the op-amp *V*out is given by the equation

V
out

=

A
OL

(

V

−

V
−

)
,

{\displaystyle V\_\text{out} = A\_\text{OL} (V\_+ - V\_-),}

where
*A*OL = open-loop gain of the amplifier.
The magnitude of *A*OL is typically very large (100,000 or more for integrated circuit op-amps), and therefore even a quite small difference between *V*+ and *V*- drives the amplifier output nearly to the supply voltage. Situations in which the output voltage is equal to or greater than the supply voltage are referred to as *saturation* of the amplifier. The magnitude of *A*OL is not well controlled by the manufacturing process, and so it is impractical to use an open-loop amplifier as a stand-alone differential amplifier.

## Feedback

The popularity of the op-amp as a building block in analog circuits is due to its versatility. By using negative feedback, the characteristics of an op-amp circuit, its gain, input and output impedance, bandwidth etc. are determined by external components and have little dependence on temperature coefficients or engineering tolerance in the op-amp itself.

High input impedance at the input terminals and low output impedance at the output terminal(s) are particularly useful features of an op-amp.

In the non-inverting amplifier on the right, the presence of negative feedback via the voltage divider *R*f, *R*g determines the *closed-loop gain* *A*CL = *V*out / *V*in. Equilibrium will be established when *V*out is just sufficient to "reach around and pull" the inverting input to the same voltage as *V*in. The voltage gain of the entire circuit is thus 1 + *R*f/*R*g. As a simple example, if *V*in = 1 V and Rf = *R*g, *V*out will be 2 V, exactly the amount required to keep *V*- at 1 V. Because of the feedback provided by the *R*f, *R*g network, this is a *closed-loop* circuit.

## Log amplifier

A **log amplifier** is an amplifier for which the output voltage *V*out is *K* times the natural log of the input voltage *V*in. This can be expressed as,

V
out

=
K
ln
⁡

(

V
in

V
ref

)

{\displaystyle V\_\text{out} = K \ln\left(\frac{V\_\text{in}}{V\_\text{ref}}\right)}

where
*V*ref = normalization constant in volts
*K* = scale factor.
The logarithm amplifier gives an output voltage which is proportional to the logarithm of applied input voltage.
To design a logarithm amplifier circuit, high performance op-amps like LM1458, LM771, LM714 are commonly used and a compensated logarithm amplifier may include more than one.

Logarithmic amplifiers are used in many ways, such as:

1. To perform mathematical operations like multiplication, division and exponentiation. Multiplication is also sometimes called mixing. This is similar to operation of a slide rule, and is used in analog computers, audio synthesis methods, and some measurement instruments (i.e. power as multiplication of current and voltage).
2. To calculate the dB value of a given quantity.
3. As a True RMS converter.
4. Extending dynamic range of other circuits, like automatic gain control of transmit power in RF circuits, or analog-to-digital converters.

The relationship between the input voltage

V
in

{\displaystyle V\_\text{in}}

 and the output voltage

V
out

{\displaystyle V\_\text{out}}

 is given by:

V

out

=
−

V
T

ln
⁡

(

V
in

I
S

R

)

{\displaystyle V\_{\text{out}} = -V\_\text{T} \ln \left(\frac{V\_\text{in}}{I\_\text{S} \, R} \right)}

where

I
S

{\displaystyle I\_\text{S}}

 = saturation current of the diode.

V
T

{\displaystyle V\_\text{T}}

 = thermal voltage of the diode.