Inverting Amplifier

OBJECTIVE:

To measure the gain and verify the inverted output waveform from inverting amplifier circuit design.

THEORY :

An inverting-amplifier circuit is built by grounding the positive input of the operational amplifier and connecting resistors R1 and R2, called the feedback networks, between the inverting input and the signal source and amplifier output node, respectively. With assumption that reverse-transfer parameter is negligibly small, open-circuit voltage gain Av, input resistance Zin and output resistance Zo can be calculated.


Figure 1: Inverting Amplifier configuration of an op-amp

Inverting Amplifier Voltage Gain

To find A_va single loop from the figure1 is being considered and hence the below equation,



Applying KCL at the inverting input to the amplifier yields a relationship between i₁and i_f , i₁ = i_- + i_f where i_- i.e. the current at the inverting input must be zero thus, i₁ = i_f. Hence the above equation becomes,



where i₁ = v_in / R₁ , Hence after adding the value of i1 in the above equation the voltage gain is given by:



The voltage gain is negative, indicative of an inverting amplifier with a 180� phase shift between dc or sinusoidal input and output signals. In addition, the gain can be greater than or equal to 1 if R₂>R₁, but it can also be less than 1 for R₁ < R₂

The output of this amplifier will invert the waveform like positive magnitude wave will show amplified negative magnitude and vice versa, for example sine wave as input will look like a amplified cosine wave. The positive pulse will generate negative pulse and so on. The ideal operational amplifier adjusts its output to whatever voltage is necessary to force the differential input voltage to zero. However, although the inverting input represents a virtual ground, it is not connected directly to ground.

Input and Output Resistance of Inverting Amplifier

The input resistance of the overall amplifier Z_in is equal to the input resistance R₁. As the op-amp is supposed to be ideal the output resistance of the inverting amplifier is equal to zero. The input & output impedances of an inverting amplifier are







where, A_ol = open-loop voltage gain of op-amp Z_o= internal output impedance of op-amp (without feedback) beta= attenuation of the feedback circuit


The output impedance of both the non-inverting and inverting amplifier configurations is very low; in fact, it is almost zero in practical cases. Because of this near zero output impedance, any load impedance connected to the op-amp output can vary greatly and not change the output voltage at all.