Negative impedance converter

Circuit design of a NIC using an operational amplifier .

A negative impedance converter , in English as Negative Impedance Converter abbreviated NIC refers to is a form of impedance converter having an electrically negative resistance is. With this electronic circuit it is possible to convert the always positive resistance value of an electrical resistance component into a negative resistance value.

A negative resistance represents a reversal of the relationship between the electrical voltage U and the electrical current I flowing through the constant resistance R , known as Ohm's law :

${\displaystyle U=R\cdot I}$

A negative impedance converter, as shown in the adjacent circuit diagram, implements the following relationship at its connection terminals for the external voltage source V _s , with R ₃ equal to R ₂ :

${\displaystyle V_{s}=-I_{s}\cdot R_{1}}$

This means that the higher the voltage, the greater the current that flows into the external voltage source V _s . In other words, electrical power flows into the voltage source.

The voltage source is connected to the negative resistance R _in

${\displaystyle R_{\text{in}}=-R_{3}\cdot {\frac {R_{1}}{R_{2}}}}$

burdened. As mentioned, this outputs power to the voltage source and can therefore in principle only be implemented with active electronic circuits, which for example consist of operational amplifiers .

Since the above equation also applies to AC voltage , the resistor R ₁ in the converter can also be replaced by a complex impedance Z , consisting of coils or capacitors . In this configuration, the NIC is the basis of the gyrator , a circuit that can be used to convert any impedance into its dual impedance, for example an electrical capacitance into an inductance .

The practical benefit lies in the fact that electrical capacitances in the form of capacitors can be produced much more easily and cost-effectively than is the case with inductances in the form of coils. The negative impedance converter therefore plays an important role in the implementation of analog electrical filters without coils.

Compensation of the undesired internal resistance

Another application of this circuit is to be able to compensate unavoidable but undesirable internal resistances of real sources. The figure on the right shows a real power source with an undesirable internal resistance R _s , outlined in red. By externally connecting a negative resistance R _{s of} equal magnitude in parallel, an ideal current source with the ideal internal resistance of infinitely high value (∞ Ω) can be implemented from the point of view of the consumer Z _L.

literature

• Reinhold Paul: Electrical engineering basic textbook Volume 2: Networks . 3. Edition. Springer, 1996, ISBN 978-3-540-55866-8 .
• Ulrich Tietze, Christoph Schenk: Semiconductor circuit technology . 12th edition. Springer, Berlin 2002, ISBN 3-540-42849-6 .