**Operational Amplifier**

**Operational Amplifier** – a direct current amplifier characterized by very high gain coefficient. It is mainly used for amplifying the voltage or power from its input, and put “processed”, amplified signal to its output. It** **usually** **operates in a closed feedback loop configuration. Operational amplifiers have **high voltage gain**, **very high input resistance** and **very low output resistance (for ideal op-amp, input resistance value should be close to infinity and output resistance close to zero).** The first used Operational Amplifiers were used to perform mathematical operations such as additions, subtractions or integrations (hence the name “operational”).

**Operational Amplifier – Construction**

**The input with the “-“ sign is called the inverting input (shifts phase of the input signal 180 degrees towards output)**, and the input with the “+” sign is a non-inverting input. To allow the occurrence of positive and negative voltages on the input as well as the output, it is crucial to supply it from external power supply with positive and negative voltage through “x” and “y” terminals.

**Operational Amplifier – Tasks for students**

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**Operational Amplifier – Feedback and principle of operation**

There is basically no difference between a regular amplifier and an operational amplifier – both are used to amplify voltage or power. However, the mode of operation of an ordinary amplifier depends on its internal structure, operational amplifier’s operation modes are mainly dependent on external feedback circuits. For this purpose, operational amplifiers have constant current feedback between amplifier stages and rest potential on input/output terminals equal to zero.

Negative voltage “V-” was applied to the inverting input of the amplifier and positive voltage “V+” to the non-inverting input. The signal that occurs between the inputs is named as differential voltage “V_{D}” expressed as the substraction of “V–” and “V+” signals. There is also a differential input resistance “R_{D}” between the inputs of the amplifier. **The output voltage** “**V _{OUT}” is comparable to the V_{D }voltage**. K

_{uo}(A

_{vo}) coefficient is a designation of voltage gain of the open loop amplifier.

**Operational Amplifier – Feedback**

The basic amplifier system with feedback is shown in Figure 3. A part of the output voltage is fed back to the input. **If the feedback voltage is subtracted from the input voltage, then we are talking about negative feedback, if it is added – positive feedback.** In further considerations, we will only deal with negative feedback. From the aforementioned analysis the relationship occurs as follows:

In order to explain how the circuit from Fig. 3. operate let us assume, that the output voltage “V_{out}” changes from zero to a certain positive value of the input voltage “V_{in}“. At first, the output voltage “V_{out}” (and therefore the voltage “βV_{out}“) still equals zero. At the input of the amplifier there will be voltage “V_{D }= V_{in}“, because this voltage is amplified with a large positive amplification coefficient “A_{vd}“. Therefore, the output voltage “V_{out}” rapidly increases in the positive direction and with it also “βV_{out}“. This reduces the “V_{D}” voltage. The fact of counteracting the changes of the input voltage by changes in the output voltage is characteristic to the negative feedback. It can be inferred from this that a stable final state will be established. It will be achieved when the output voltage rises enough to meet the following condition:

In the simplest case, the feedback circuit consists of a voltage divider. The system then works as a linear amplifier and its amplification depends only on the divider. If the RC system is used in the feedback system, we will create an **active filter**. One can

also use non-linear components in the feedback, such as diodes or transistors and in this way obtain e.g. log amplifier.

**Operational Amplifier – Ideal component parameters**

During designing and analysing systems based on operational amplifiers, it should be nearly always assumed that the amplifier is ideal, which means that it has the following characteristics:

- Infinitely high gain in open loop (k
_{uo}(A_{vo}) -> ∞), - Infinitely high input impedance,
- Output impedance is zero,
- Infinitely wide frequency response,
- Output voltage equals zero for the same input voltages,
- Zero input current (current is not drawn from the external circuits),
- Infinitely high allowable output current,
- No interference of their own,
- Its parameters do not depend on temperature.

**Operational Amplifier – Real component parameters**

In reality, operational amplifiers are described by the following parameters:

- Open-loop gain coefficient reaches very high but finite values,
- Input impedance has high value, but finite,
- Output impedance of several dozens,
- Upper frequency limit of several dozens of MHz,
- There is an input current of low rate of 10-4 to 10-15 A,
- They produce self-interference,
- Parameters of the amplifier are dependent from temperature and they change with time of use of the system.

**Operational Amplifier – Basic operation systems and applications**

Operational amplifiers are used in systems such as:

- Inverting and non-inverting amplifiers,
- Audio/video frequency pre-amplifiers,
- Summing and differential amplifiers,
- Integrators,
- Voltage followers,
- “Current to Voltage” converters,
- Phase shifters.

Operational amplifiers are currently the most used components in all kinds of analog circuits, one can even say that they are the foundation of the analogue electronics. Below you can find more of the most popular applications of the operational amplifier:

- In analogue electronic circuits, where they are responsible for performing mathematical operations,
- In logarithmic amplifiers,
- In active filters,
- In some generators,
- In linear detectors and peak detectors,
- In sampling circuits with memory.

**Source:** A. Filipkowski: “Układy elektroniczne analogowe i cyfrowe”, WNT, Warszawa 2006

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