What Are Active Inductors?

Active inductors are integrated circuit structures that replicate the inductive impedance of a wound coil using transistors and capacitors rather than a physical winding. They present a voltage-current relationship with the 90-degree phase lead characteristic of an inductor across a designed frequency range, achieved by applying the gyrator principle: a pair of transconductor stages connected in feedback converts a capacitive loading into an equivalent inductive impedance at the input terminals. Active inductors are used primarily in radio-frequency (RF) and microwave integrated circuits, where passive spiral inductors consume prohibitive silicon area at frequencies below the low gigahertz range and cannot be tuned after fabrication.

Active inductors are a mature topic in RFIC design, drawing on analog circuit theory, feedback analysis, and the physics of short-channel MOSFET devices. Their design involves trade-offs among inductance magnitude, self-resonant frequency, quality factor, noise, power consumption, and layout area in standard CMOS or BiCMOS processes.

Gyrator Circuit Design

The gyrator, formalized by Tellegen in 1948, is the conceptual basis for all active inductors. A gyrator is a two-port network characterized by the property that a load impedance Z at one port appears as the dual impedance 1/Z at the other. Connecting a capacitor C to one port yields an inductance L = C / (Gm1 × Gm2) at the other, where Gm1 and Gm2 are the transconductances of the two amplifying stages forming the gyrator. Real gyrator realizations introduce finite input and output resistances that cause the equivalent inductor to have an associated series resistance and a finite quality factor Q. Noise-canceling circuit architectures reduce the dominant noise contribution from the input transistor by introducing a feed-forward path, enabling Q values above 400 in 90 nm CMOS. The design space for these circuits, including stability conditions, self-resonant frequency, and Q optimization, is surveyed in the Springer review of CMOS active inductors.

MOSFET Implementation

MOSFET transistors are the dominant active device in practical active inductor circuits. Common configurations use NMOS transistors in common-source or common-gate stages as the two transconductors, with cascode variants added to improve output resistance and extend the self-resonant frequency. The inductance and the resonant frequency are tuned by adjusting gate bias voltages or drain bias currents, which shift the transconductances without changing device geometry. PMOS transistors may replace NMOS devices when the circuit topology benefits from a complementary supply rail. BiCMOS processes substitute bipolar junction transistors for one or both transconductors to exploit the higher transconductance per unit area and lower noise of bipolar devices at millimeter-wave frequencies. IntechOpen's chapter on CMOS active inductors and their applications details NMOS, PMOS, and complementary MOSFET topologies with performance comparisons across CMOS technology nodes.

Performance Characteristics and Trade-offs

The principal performance figures for active inductors are the inductance value, the quality factor at the operating frequency, the self-resonant frequency, the inductance tuning range, noise figure contribution, and DC power consumption. Passive spiral inductors in standard CMOS achieve Q values of 5 to 20 at a few gigahertz; active inductors can significantly exceed this at targeted frequencies, though they consume power and contribute noise from their transistors. A noise-canceling CMOS active inductor reported in the International Journal of Microwave Science and Technology achieved 80 percent noise reduction relative to a baseline design, with a maximum resonant frequency of 3.8 GHz and Q exceeding 400 in 90 nm CMOS, illustrating the level of performance achievable with optimized architectures.

Applications

Active inductors have applications across RF and integrated circuit design, including:

• Voltage-controlled oscillators in Bluetooth, WiFi, and cellular transceiver chips requiring wide tuning range
• Low-noise amplifiers where inductive source degeneration improves input match without area penalty
• On-chip tunable band-pass filters for software-defined radio and cognitive radio front-ends
• Ku-band and millimeter-wave circuits where spiral inductors are physically impractical
• Active balun and impedance matching networks in highly integrated RF system-on-chip designs