What Is an Active Inductor?

An active inductor is a circuit that emulates the behavior of a passive wound-coil inductor using transistors, resistors, and capacitors, without a physical winding. It presents an inductive impedance at its terminals by exploiting the gyrator principle: a gyrator circuit converts a capacitive load at one of its ports into an inductive impedance at the other. The resulting network stores energy in the electric fields of its capacitors while exhibiting the voltage-current phase relationship characteristic of an inductor. Active inductors are realized primarily in CMOS and other integrated circuit technologies, where the physical area of spiral inductors at frequencies below several gigahertz is prohibitively large.

The concept builds on Bernard Tellegen's formalization of the gyrator as a network element in 1948 and on subsequent transistor-based realizations developed as radio-frequency integrated circuit design matured in the 1990s and 2000s. They are a well-established tool in RFIC design, particularly for circuits requiring tunable inductive elements on chip.

Gyrator-Based Implementation

The standard active inductor circuit consists of two transconductors connected in a feedback loop, forming a gyrator. A capacitor attached to the internal node presents an equivalent inductance at the input terminals given by L = C / (Gm1 × Gm2), where Gm1 and Gm2 are the transconductances of the two amplifying stages. CMOS implementations use NMOS or PMOS transistors in common-source or common-gate configurations as the transconductors, with additional resistors or transistors included to set the loss and bias conditions. The equivalent inductance and the self-resonant frequency can be tuned by adjusting bias currents, which vary the transconductances. A review of CMOS active inductor design, including gyrator topologies and stability analysis, appears in Springer's Circuits, Systems, and Signal Processing.

Quality Factor and Tunability

The quality factor Q of an active inductor is determined by the ratio of the reactive component of the input impedance to its resistive component. Unlike passive spiral inductors, whose Q is set by conductor resistance and substrate losses, the Q of an active inductor depends on the bias conditions and can be significantly higher at targeted frequencies. Noise-canceling architectures use a feed-forward stage with degeneration to reduce the noise contribution of internal transistors, achieving Q values exceeding 400 in 90 nm CMOS processes while maintaining resonant frequencies in the low gigahertz range. Tunability is a key advantage: bias current adjustment shifts the inductive frequency range across a wide band, enabling reconfigurable RF front-end designs that would require switched passive inductor banks in conventional approaches. Published CMOS active inductor designs demonstrating these characteristics are surveyed in IntechOpen's chapter on CMOS active inductors and their applications.

RF and Microwave Circuit Applications

Active inductors are used in tunable band-pass filters, voltage-controlled oscillators (VCOs), low-noise amplifiers (LNAs), and impedance matching networks in RF integrated circuits. In a VCO, replacing the fixed-value spiral tank inductor with an active tunable inductor extends the oscillation frequency range. In LNAs, active inductors provide source degeneration inductive loading without consuming the area that a spiral would require at sub-gigahertz frequencies. Ku-band active inductors designed with multi-objective optimization have been demonstrated using SiGe BiCMOS processes, achieving inductive behavior at frequencies above 10 GHz, as documented in research from ScienceDirect on Ku-band active inductor design.

Applications

Active inductors have applications in a range of RF and integrated circuit contexts, including:

• Voltage-controlled oscillators in wireless transceiver chips where tunable tank circuits are required
• Low-noise amplifiers in Bluetooth, wireless LAN, and cellular receiver front-ends
• Tunable band-pass filters in software-defined radio platforms
• On-chip impedance matching networks replacing external surface-mount inductors
• Millimeter-wave and Ku-band circuits where conventional spiral inductors cannot meet size and performance targets