As we have seen in the earlier discussions, the open-loop gain of an operational amplifier (Op-amp) can be extremely high, about 1,000,000 or more. This very high gain makes the operational amplifier very unstable, and a very small input signal, even if they are in μV, is enough to cause the output voltage to rise to uncontrollable extents where they saturate, and we completely lose control over the output. Therefore we are going to study about feed-backs and inverting amplifier as a solution to the above related problems.

## Saturation

Before learning about the inverting amplifier we need to know about feed-backs and what is meant by saturation. The output voltage of an op-amp is limited to a minimum and maximum value, which is Almost equal to the supplied power voltage.

The connection from the output to the input via external wiring is known as feedback connection. There are generally two types of feedback: positive feedback and negative feedback.

**Negative feedback and inverting operational amplifier configuration**

If the feedback is connected to the inverting amplifier input terminal (negative) of the op-amp, using a suitable resistor called feedback resistor, then the feedback is known as negative feedback. And, if the feedback connection is made between the output and the non-inverting (positive) terminal of the op-amp through a suitable feedback resistor, then it is known as positive feedback. In most applications of the op-amp the negative feedback is most widely used.

The negative feedback results in a different value of voltage in the inverting input (-ve), resulting in a new signal rather than the actual input signal as the inverting terminal voltage will be the summation of the voltages and the negative feedback voltage coming from the output terminal. Therefore to separate the actual input signal from the inverting terminal input signal an Input Resistor, R_{1} is being used.

If we contemplate an ideal equivalent circuit, the closed-loop voltage gain is

Specifically, if output voltage is V_{O}, at that moment

The gain A will be infinity; the voltage V_{1} idyllically turn out to be equal to V_{2}. This is signified as a virtual short circuit condition. A virtually short circuit shows that whether the voltage is at one and only of the input terminals will automatically act at the other input terminal due to infinite or practically very high gain. The non-inverting terminal 2 is grounded, thus V_{2}= 0 and V_{1} = 0. Hence, terminal 1 is being virtually ground, that means it actually representing zero volt even without being grounded.

**Inverting Amplifier Configuration and Working**

Current i_{1} through R_{1} can be given as:

This current i1 cannot go into op-amp, since an ideal inverting amplifier has infinite input resistance and hence draws zero current. Therefore, I! will pass through the R2 resistor and will go towards the terminal no. 3.

Applying ohm’s law, we can determine V_{o }as:

V_{o} = V_{1} – i_{1}R_{2}

= 0 –

Therefore, the closed-loop voltage gain is:

As we observed that the –ve is accompanying with the closed-loop gain term, hence this configuration of the op-amp is recognized as the inverting configuration.

Due to the virtual ground concept, the input resistance is defined as R_{i }= V_{i}/i_{1 }= R_{1}

The equation for the output voltage (V_{o}) implies that the circuit works in a linear way for a constant amplifier gain A_{v} as V_{o} = V_{i} x A_{v}. This property is very useful for converting a small magnitude signal to a much larger voltage signal. And as there are no capacitors in the inverting operational amplifier circuit, hence, the input and the output voltages, as well as the currents in the resistors, can be DC signals, and therefore the op-amp will be able to amplify DC signals too.

**Application of inverting amplifier**

**What is Transresistance amplifier ?**

**Transresistance amplifier or current-to-voltage converter**

A very useful application of an inverting operational amplifier is that of a Trans-impedance amplifier or current to voltage converter. A Trans-resistance or a trans-impedance op-amp is employed as a current-to-voltage converter circuitry. These are comprehensively utilized in circuit designing as it’s good to convert a very small current generated by a circuitry or sensor to sufficiently high proportionate output voltage.

Consider the circuit in the figure. The input resistance R_{i} at virtual node is R_{i }= V_{1}/i_{1} = 0 as studied before.

The current i_{1} is essentially equal to I_{s} and so,

i_{2 }= i_{1 }= I_{s}

And, V_{o }= -i_{2}R_{f} = -I_{s}R_{f}

The o/p voltage is directly proportionate to signal current, and the feedback resistance R_{f} is equivalent to the ratio of the output voltage to current in input terminal.

We will be learning about the non-inverting amplifier in the upcoming section.

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