How can you create a negative impedance and what’s it good for?

Negative impedance can be created using active circuits like negative impedance converters (NICs), and it’s useful for canceling out unwanted inductance in circuits, improving power system compensation, and enabling wider bandwidths in applications like audio systems, communication, and metamaterials.

NICS can improve the bandwidth and efficiency of electrically small antennas, including those that comprise metasurfaces, by compensating for the antenna’s inductive characteristics. NICs can be integrated into metamaterial structures to create active metamaterials.

Metasurfaces are being used in 5G technology to enhance signal propagation, coverage, and efficiency, especially in electrically complex urban environments. Metasurfaces with integrated NICs can act as intelligent reflecting surfaces (IRS) or frequency selective surfaces (FSS), manipulating electromagnetic waves to improve signal direction, strength, and bandwidth.

Overcoming Foster’s Reactance Theorem

An NIC is an active electronic circuit that synthesizes a negative resistance, capacitance, or inductance by inverting the voltage-current relationship of a passive impedance. An active circuit is used to overcome the limitations imposed by Foster’s Reactance Theorem.

Foster’s theorem requires that the reactance of a passive, lossless, two-terminal network, like a capacitor or inductor, must always monotonically increase or decrease with frequency. Therefore, to obey Foster’s theorem, a passive circuit can only have reactance that always increases with frequency, like an inductor, or always decreases with frequency, like a capacitor.

That can place limitations on the operation of passive impedance matching networks. For example, in the case of antennas, impedance matching can only be achieved at a limited number of discrete frequencies.

An NIC is an active circuit that manipulates impedance, making it appear negative from an external perspective. It injects energy into circuits in contrast with a conventional impedance that consumes energy.

As a result, NICs can overcome the limitations of passive matching networks by adding or subtracting excessive varying voltage or current in series to the voltage or current drop across an equivalent positive impedance.

An NIC works by reversing, or inverting, the voltage polarity or current direction with a phase shift of 180°. The negative of any impedance can be produced with an NIC, including negative resistance, negative capacitance, and negative inductance. There are two types of NICs, voltage inversion (VNIC) and current inversion (INIC).

A typical VNIC implemented with an op-amp terminates on an electrical ground and is not practical in real applications. An INIC will typically be used in parallel with a source and can support practical applications (Figure 1).

Figure 1. Op-amp based INIC examples. (Image: Wikipedia)

Negative aspects of NICs

NICs are often better suited for low-frequency applications like audio systems due to the challenges related to stability at higher frequencies. In addition, they can have a complex input impedance, and the negative impedance they produce isn’t ideal, reducing overall efficiency.

The combination of active components and positive feedback used in NICs requires careful design, especially at higher frequencies. Otherwise, it can lead to instability and oscillation. In addition, parasitics like the capacitances of transistors are more pronounced at higher frequencies, increasing the challenge of maintaining stability.

Figure 2. A non-Foster element (-L) can be used to overcome the Chu Limit in small piezoelectric speakers. (Image: National Academy of Sciences)

The sensitivity of NICs to parasitics makes PCB layout a critical consideration. At audio frequencies, common op-amps can be used to create stable high-Q filters.

Overcoming the Acoustic Chu Limit

The Acoustic Chu Limit describes the fundamental limitations on the bandwidth and radiation efficiency of small acoustic radiators like piezoelectric transducers or speakers. It states that the bandwidth performance is inversely proportional to the volume of the transducer normalized to the emitted wavelength.

As a result, smaller speakers like those used in compact devices have a narrower bandwidth and lower radiation efficiency. When connected to a non-Foster element like a negative inductor or NIC, small speakers can overcome the Chu Limit (Figure 2).

Summary

NICs can be used to manipulate impedance, making it appear to be negative. A NIC can produce the effects of negative resistance, negative capacitance, and negative inductance. The requirement for positive feedback in NICs and the resulting stability issues are a significant challenge when using NICs with devices like metamaterials, antennas, and small piezoelectric speakers.