Negative impedance converter

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The negative impedance converter (NIC) is a configuration of an operational amplifier which acts as a negative load. This is achieved by introducing a phase shift of 180° (inversion) between the voltage and the current for any signal generator. The basic circuit of an NIC and its analysis is shown below.

1 Basic circuit and analysis
2 Application
3 See also
4 External links

[edit] Basic circuit and analysis

If the operational amplifier is ideal, the inverting and non-inverting inputs have the same voltage, so the current $I 2$ is simply given by:

$I_2 = \frac{V_s}{R_1}$

Then, considering the voltage from one ground to the other one, it is possible to write:

$(R_1 + R_2) I_2 + R_3 \cdot I_s - V_s = 0$

Replacing the previous relationship and rearranging we get:

$V_s = - I_s \cdot R_3 \frac{R_1}{R_2}$

from which we get the input resistance:

$\frac{V_s}{I_s} = R_{in} = - R_3 \frac{R_1}{R_2}$

[edit] Application

Main article: Negative resistance

By using an NIC as a negative resistor, it is possible to let a real generator behave (almost) like an ideal generator, i.e. the magnitude of the current or of the voltage generated does not depend on the load.

An example is shown in the following picture:

The current generator and the resistor within the dotted line is the Norton representation of a circuit comprising a real generator and $R s$ is its internal resistance. If an NIC is placed in parallel to that internal resistance, and the NIC has the same magnitude but inverted resistance value, there will be $R s$ and $- R s$ in parallel, thus the equivalent resistance is:

$R||(-R) = \frac{R^2}{(R - R)} \to \infty$

so the real generator will now behave like an ideal one, and the generator's entire current will go to the load $Z L$ , whatever the value of $Z L$ and $R s$ .