Now, let’s analyze this circuit. The aim is to find out the relationship between output voltage vo and vi or the gain of the amplifier.
For an ideal Op Amp, we should consider the virtual ground concept. That is, the non-inverting terminal is tied to the ground. It is physically connected to the ground. However, the inverting terminal is at the virtual ground but not physically connected to the ground. We consider this because of the infinite open loop gain of the Opamp.
Similarly, for an ideal Op Amp we should consider the input resistance of the Op Amp is infinite. No current flows through the input terminals of the Opamp. Hence the input current i1 = if. No current flows through inside the Opamp.
Apply KCL at the node 1.
This is the required closed-loop gain. It simply depends on the external resistors. The minus sign shows the signal inversion at the output.
Inverting Amplifier With Compensating Resistor R:
There is another way of implementing an inverting amplifier, it is given below. In this configuration, there is a resistor known as a compensating resistor. This resistor is commonly denoted as RC. For inverting configuration, this compensating resistor is equal to:
Given:
Rin = 1kOhm
R = 1kOhm
Rf = 10kOhm
Calculate the gain.
There is no effect of a compensation resistor on the gain.
Inverting Amplifiers With Load Resistor:
Given:
Rin = 1kOhm
R = 1kOhm
Rf = 10kOhm
Calculate the gain.
Inverting Amplifier Another Configuration:
Given:
Rin = 1kOhm
R = 1kOhm
Rf = 10kOhm
Calculate the gain.
Don’t get confused with the extra resistor. Start your analysis with the same method. Apply KCL at node A.
So, there is no change in the value of gain.
Frequently Asked Questions:
What are the advantages of inverting amplifiers?
It has less input impedance, because of the feedback resistor. In comparison with the open loop configuration, the input signal directly applied to the inverting terminal has much greater input resistance than the closed loop inverting configuration. The input resistance only depends on the external resistors.
What are the disadvantages of inverting amplifiers?
Its input resistor is the biggest disadvantage as well. If an application calls for a higher input impedance, both Rin and Rf have to be greater enough. For example, to minimize signal source loading, greater values of resistors are required. However, larger values of input resistors increase offset errors which arise due to amplifier bias current.
Why is it called an inverting configuration?
The output signal is out of phase. The amplifier reverses the phase angle of the output and hence input and output are 180° out of phase with each other.
What is the purpose of a feedback resistor?
It determines the gain or amplification factor of the amplifier. The higher the value of the feedback resistor (Rf) as compared to the input resistor (Rin), the higher the gain of the inverting amplifier.
What are the applications of inverting amplifiers?
It is commonly used in precision scaling applications, audio processing, active filters, voltage-controlled oscillators, and instrumentation amplifiers for sensor interfacing.
What is the transfer function of inverting amplifiers?
The transfer function (Vout/Vin) of an inverting amplifier is given by the formula:
What is the maximum output of an inverting amplifier?
The maximum output voltage is limited by the power supply of the Opamp. If the external supply is ± 12V, the Opamp will saturate after this voltage. Similarly, if the supply voltage is ± 15V, the output voltage swing is limited by the power supply voltage.
Conclusion:
I have analyzed all four circuits, and they are quite similar to each other. I try to make sure that I have cleared up all the concepts in every possible way.