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Inverting Operational Amplifier

Inverting Operational Amplifier

The Inverting Operational Amplifier configuration is one of the simplest and most commonly used op-amp topologies

The inverting operational amplifier is basically a constant or fixed-gain amplifier producing a negative output voltage as its gain is always negative.

We saw in the last tutorial that the Open Loop Gain, ( AVO ) of an operational amplifier can be very high, as much as 1,000,000 (120dB) or more.

However, this very high gain is of no real use to us as it makes the amplifier both unstable and hard to control as the smallest of input signals, just a few micro-volts, (μV) would be enough to cause the output voltage to saturate and swing towards one or the other of the voltage supply rails losing complete control of the output.

As the open loop DC gain of an operational amplifier is extremely high we can therefore afford to lose some of this high gain by connecting a suitable resistor across the amplifier from the output terminal back to the inverting input terminal to both reduce and control the overall gain of the amplifier. This then produces and effect known commonly as Negative Feedback, and thus produces a very stable Operational Amplifier based system.

Negative Feedback is the process of “feeding back” a fraction of the output signal back to the input, but to make the feedback negative, we must feed it back to the negative or “inverting input” terminal of the op-amp using an external Feedback Resistor called . This feedback connection between the output and the inverting input terminal forces the differential input voltage towards zero.

This effect produces a closed loop circuit to the amplifier resulting in the gain of the amplifier now being called its Closed-loop Gain. Then a closed-loop inverting amplifier uses negative feedback to accurately control the overall gain of the amplifier, but at a cost in the reduction of the amplifiers gain.

This negative feedback results in the inverting input terminal having a different signal on it than the actual input voltage as it will be the sum of the input voltage plus the negative feedback voltage giving it the label or term of a Summing Point. We must therefore separate the real input signal from the inverting input by using an Input Resistor, Rin.

As we are not using the positive non-inverting input this is connected to a common ground or zero voltage terminal as shown below, but the effect of this closed loop feedback circuit results in the voltage potential at the inverting input being equal to that at the non-inverting input producing a Virtual Earth summing point because it will be at the same potential as the grounded reference input. In other words, the op-amp becomes a “differential amplifier”.

Inverting Operational Amplifier Configuration

inverting operational amplifier

In this Inverting Amplifier circuit the operational amplifier is connected with feedback to produce a closed loop operation. When dealing with operational amplifiers there are two very important rules to remember about inverting amplifiers, these are: “No current flows into the input terminal” and that “V1 always equals V2”. However, in real world op-amp circuits both of these rules are slightly broken.

This is because the junction of the input and feedback signal ( X ) is at the same potential as the positive ( + ) input which is at zero volts or ground then, the junction is a “Virtual Earth”. Because of this virtual earth node the input resistance of the amplifier is equal to the value of the input resistor, Rin and the closed loop gain of the inverting amplifier can be set by the ratio of the two external resistors.

We said above that there are two very important rules to remember about Inverting Amplifiers or any operational amplifier for that matter and these are.

  • No Current Flows into the Input Terminals
  • The Differential Input Voltage is Zero as V1 = V2 = 0 (Virtual Earth)

Then by using these two rules we can derive the equation for calculating the closed-loop gain of an inverting amplifier, using first principles.

Current ( i ) flows through the resistor network as shown.

resistor feedback circuit

inverting op-amp gain formula

Then, the Closed-Loop Voltage Gain of an Inverting Amplifier is given as.

inverting operational amplifier gain equation

and this can be transposed to give Vout as:

inverting operational amplifier gain

op-amp linear output

Linear Output

The negative sign in the equation indicates an inversion of the output signal with respect to the input as it is 180o out of phase. This is due to the feedback being negative in value.

The equation for the output voltage Vout also shows that the circuit is linear in nature for a fixed amplifier gain as Vout = Vin x Gain. This property can be very useful for converting a smaller sensor signal to a much larger voltage.

Another useful application of an inverting amplifier is that of a “transresistance amplifier” circuit. A Transresistance Amplifier also known as a “transimpedance amplifier”, is basically a current-to-voltage converter (Current “in” and Voltage “out”). They can be used in low-power applications to convert a very small current generated by a photo-diode or photo-detecting device etc, into a usable output voltage which is proportional to the input current as shown.

Transresistance Amplifier Circuit

trans-resistance operational amplifier

The simple light-activated circuit above, converts a current generated by the photo-diode into a voltage. The feedback resistor sets the operating voltage point at the inverting input and controls the amount of output. The output voltage is given as Vout = Is x Rƒ. Therefore, the output voltage is proportional to the amount of input current generated by the photo-diode.

Inverting Operational Amplifier Example No1

Find the closed loop gain of the following inverting amplifier circuit.

inverting op-amp circuit

Using the previously found formula for the gain of the circuit

inverting op-amp gain

we can now substitute the values of the resistors in the circuit as follows,

Rin = 10kΩ  and  Rƒ = 100kΩ

and the gain of the circuit is calculated as: -Rƒ/Rin = 100k/10k = -10

Therefore, the closed loop gain of the inverting amplifier circuit above is given -10 or 20dB (20log(10)).

Inverting Operational Amplifier Example No2

The gain of the original circuit is to be increased to 40 (32dB), find the new values of the resistors required.

Assuming that the input resistor is to remain at the same value of 10KΩ, then by re-arranging the closed loop voltage gain formula we can find the new value required for the feedback resistor .

   Gain = Rƒ/Rin

therefore,   Rƒ = Gain x Rin

  Rƒ = 40 x 10,000

  Rƒ = 400,000 or 400KΩ

The new values of resistors required for the circuit to have a gain of 40 would be:

 Rin = 10KΩ  and  Rƒ = 400KΩ

The formula could also be rearranged to give a new value of Rin, keeping the same value of .

One final point to note about the Inverting Amplifier configuration for an operational amplifier, if the two resistors are of equal value, Rin = Rƒ  then the gain of the amplifier will be -1 producing a complementary form of the input voltage at its output as Vout = -Vin. This type of inverting amplifier configuration is generally called a Unity Gain Inverter of simply an Inverting Buffer.

In the next tutorial about Operational Amplifiers, we will analyse the complement of the Inverting Amplifier operational amplifier circuit called the Non-inverting Amplifier that produces an output signal which is “in-phase” with the input.

166 Comments

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  • Bharti

    Want… to active in any…. Typ… Of conversion…. Related to study

  • Mac Shadow

    This is so good, very understandable

  • Ankush

    Very nice article……need more such articles on various topics in the future.

  • asfak

    super

  • Manish

    This is very helpful persuing Hons physics

  • Yuri Edward Sianski

    Gave a non power to scifi

  • Tegyih Martin Tawiah

    How to determine the output voltage of inverting amplifier with an input of +0.4

    • Faraday

      Multiply your the value for your close loop gain by 0.4 that’s your input voltage.
      Divide your answer by 1000 to convert it to volt.

  • عمرعبدالعزيزحسن سعيد

    Well done post💞💚

  • Sonu Sonkar

    No coment

  • Chamaunga Alex

    It’s good staff

  • ally

    What the heck? this works!! I have to take a class about op-amps!

  • Max

    I’m a bit confused by this –
    “This is because the junction of the input and feedback signal ( X ) is at the same potential as the positive ( + ) input which is at zero volts or ground …”

    To me, this is a mix of cause and effect. The part behind “because” is a result of the assumption, or belief or as the desired behaviour, that “V1 always equals V2”, not the reason for it.

  • Max

    Looks like good content. One question about “Negative Feedback is the process of “feeding back” a fraction of the output signal back to the input, but to make the feedback negative, we must feed it back to the negative or “inverting input” terminal of the op-amp using an external Feedback Resistor called Rƒ.” —

    Is it really the case that negative feedback is called negative because and only because the feedback is hooked up with the (-) terminal of the op-amp?

    Thanks.

    • Wayne Storr

      As stated in the tutorial. Feedback is the process of taking some small fraction of the output signal and “feeding” it back to the input via some sub-circuit, thus producing a circuit response that differs substantially from the circuits natural response in the absence of feedback. There are two types of feedback: Positive (or regenerative) feedback where the setpoint and output values are “added”, and Negative (or degenerative) feedback where the setpoint and output values are “subtracted”. Generally, negative feedback systems are more stable than positive feedback systems. This concept is explored here.

      • Max

        Thanks Wayne for your explanation. I’m aware of the “feeding” back which is physically hooking or wiring up the output pin in some way back to the input terminals. No difficulty in understanding this.

        Also understand the existence of positive and negative feedbacks and that negative is more stable and that positive feedback is most of the time harmful. No difficulty in understanding this as well.

        My question is specifically that in calling a feedback negative whether it’s because output is physically connected to the inverting (-) terminal. Asking this because, apart from this physical topology, it’s not obvious to me whether the feedback SIGNAL is negative or positive.

        My apologies for my dumb newbie question.

        • Wayne Storr

          The “feedback” signal is neither negative or positive, as it is a representation of the output signal. It is how the circuit is configured which dictates whether it becomes negative or positive. For an inverting amplifier configuration, we require the high open-loop gain to be reduced and controlled, thus the output is fed back to the inverting input via a suitable feedback (degeneration) shunt resistor. The configuration of the external feedback resistor connected to the inverting input results in negative feedback. Thus the circuit is configured in such a way as to produce the negative feedback action and not as a consequence of connecting the resistor to the inverting input.

  • Hari

    Good explanation

  • Harsha

    Can we design and use an inverting amplifier with gain less than 1?
    Is there any practical issue?

    • Wayne Storr

      Inverting operational amplifier attenuation is possible with the correct op-amp as many op-amps are unstable at gains of less than unity (1). A non-inverting attenuator can be performed using a voltage divider network and an op-amp configured as a non-inverting buffer.

  • Sefineh Tesfa

    Good explanation. However, I think it is better to include more than two examples for clearity rather than only one example per each topics.
    Thank you

  • Sevan Massihi Shabronian

    Hello!
    Can someone please explain this part “Because of this virtual earth node the input resistance of the amplifier is equal to the value of the input resistor, Rin” and what does “Input resistance of op amp” exactly mean?
    Thank you in advance.

    • Wayne Storr

      Every electrical/electronic circuit has an input resistance and an output resistance when viewed by an external source. Please read the tutorial about Input Impedance for more information

  • chnadn jige

    calculate the output of the inverting amplifier having input in=0.5v, r1=1k and rf=10k

  • musabbir hossain

    not too good