# Amplifiers

An amplifier is an integral part of any signal conditioning circuit. There are different configurations of amplifiers depending on the type of the requirement, one should select the proper configuration. An amplifier is used to increase the amplitude of a signal waveform, without changing other parameters such as frequency or wave shape.

## Inverting and Non-inverting Amplifiers

Inverting and Non-inverting Amplifiers are single-ended amplifiers, with one terminal of the input, is grounded. From the schematics of these two popular amplifiers, shown in the below figure

The voltage gain for the inverting amplifier is

\frac { e_0 }{ e_1 } =-\frac { R_2 }{ R_1 }

while the voltage gain for the non-inverting amplifier is:

\frac { e_0 }{ e_1 } =1+\frac { R_2 }{ R_1 }

Both the two amplifiers are capable of delivering any desired voltage gain, provided the phase inversion in the first case is not a problem. But looking carefully into the circuits, one can easily understand, that, the input impedance of the inverting amplifier is finite and is approximately R_1, while a non-inverting amplifier has an infinite input impedance. The second amplifier will perform better, if we want that, the amplifier should not load the sensor.

## Differential Amplifier

Differential amplifiers are useful for the cases, where both the input terminals are floating. These amplifiers find wide applications in instrumentation. A typical differential amplifier with a single opamp configuration is shown in figure

By applying superposition theorem, one can easily obtain the contribution of each input and add them algebraically to obtain the output voltage as:

e_0=\frac { R_4 }{ R_3+R_4 } \left( 1+\frac { R_2 }{ R_1 } \right) e_2-\frac { R_2 }{ R_1 } e_1

If we select

\frac { R_4 }{ R_3 } =\frac { R_2 }{ R_1 }

then, the output voltage becomes:

e_0=\frac { R_2 }{ R_1 } \left( e_2-e_1 \right)

Differential amplifier with single op.amp. the configuration also suffers from the limitation of finite input impedance.

Performance of an amplifier judge by using these parameters

• Offset and drift
• Input impedance
• Gain and bandwidth
• Common mode rejection ratio (CMRR)

CMRR is a very important parameter for instrumentation circuit applications and it is desirable to use amplifiers of high CMRR when connected to instrumentation circuits.

The CMRR is defined as:

CMRR = 20\log _{ 10 }{ \frac { A_d }{ A_e } }

where A_d is the differential mode gain and A_e is the common-mode gain of the amplifier.

## Instrumentation Amplifier

We need to amplify a small differential voltage a few hundred times in instrumentation applications. A single-stage differential amplifier is not capable of performing this job efficiently, because of several reasons.

First of all, the input impedance is finite; moreover, the achievable gain in this single-stage amplifier is also limited due to gain-bandwidth product limitation as well as limitations due to the offset current of the op. amp.

A three op. amp. Instrumentation amplifier, shown in the figure below given is an ideal choice for achieving the objective.

The major properties are

• High differential gain (adjustable up to 1000)
• Infinite input impedance
• Large CMRR (80 dB or more)
• Moderate bandwidth

It is apparent that, no current will be drown by the input stage of the op. amps. Thus the second property mentioned above is achieved.

Looking at the input stage, the same current I will flow through the resistances R_1 and R_2. Using the properties of ideal op. amp., we can have:

I=\frac { e_1-e_{i1} }{ R_1 } =\frac { e_{i1}-e_{i2} }{ R_2 } =\frac { e_{i2}-e_2 }{ R_1 }

e_1=e_{i1}+\frac { R_1 }{ R_2 } \left( e_{i1}-e_{i2} \right)

e_1=e_{i2}-\frac { R_1 }{ R_2 } \left( e_{i1}-e_{i2} \right)

Therefore,

e_1-e_2=(1+\frac { 2R_1 }{ R_2 } )\left( e_{i1}-e_{i2} \right)

The second stage of the instrumentation amplifier is a simple differential amplifier the overall gain is

e_0=\frac { R_4 }{ R_3 } \left( e_2-e_1 \right) =\frac { R_4 }{ R_3 } (1+\frac { 2R_1 }{ R_2 } )(e_{i2}-e_{i1})

Thus by varying R_2 very large gain can be achieved, but the relationship is inverse. Since three op. amps. are responsible for achieving this gain, the bandwidth does not suffer.