Advanced Techniques

The Gyrator

Real inductors are heavy, expensive, and magnetically noisy. A gyrator uses a capacitor and an active element to simulate an inductor — same impedance behavior, zero magnetic pickup, adjustable Q.

Theory

Why Simulate an Inductor?

Real inductors are impractical at audio frequencies — gyrators solve this

Real inductors at audio frequencies are large, heavy, and lossy. A 10H inductor for a tone stack can weigh over a kilogram and picks up magnetic interference from transformers and mains wiring. The gyrator offers an elegant alternative.

A gyrator uses a capacitor combined with a gain element (op-amp, transistor, or tube) to present an inductive impedance at its input. It "rotates" the capacitor's impedance by 90°, transforming 1/jωC into jωL.

Z_in = jω × R² × C = jωL_eq

The equivalent inductance is given by:

L_eq = R² × C

With a 100kΩ resistor and a 100nF capacitor, you get L_eq = (100k)² × 100n = 1000H — an impossibly large value for a real inductor, yet trivially achieved with a gyrator.

Real inductor 10H>1 kg
Gyrator 10H~2 g

Ref: Horowitz & Hill, "The Art of Electronics" 3rd Ed. §2.4.1 — Impedance transformation via gyration

Interactive Calculator

Gyrator Designer

Set R and C to compute the equivalent inductance

The gyrator converts capacitance to inductance: L_eq = R² × C. Adjust the sliders below.

L_eq = R² × C
R100kΩ
C100nF
C_load100pF
L_eq1.0 kH
Resonance503Hz
Q factor3162.3
Loss R1.0kΩ
Quick reference
100kΩ + 100nF → 1000H
47kΩ + 47nF → 103.8H
10kΩ + 1µF → 100H
4.7kΩ + 10nF → 0.22H
Circuit Design

Tube Gyrator Circuit

Using a triode to simulate inductance

A triode (like one half of a 12AX7) can serve as the active element in a gyrator. The plate load is a capacitor instead of a resistor. The cathode resistor sets the bias. The circuit presents an inductive impedance at the input.

L_eq = R_k × R_p × C_p

Where R_k is the cathode resistor, R_p is the plate resistance (r_p of the tube), and C_p is the plate capacitor. The tube’s gain converts the capacitive impedance at the plate into an inductive impedance looking into the circuit.

Typical values: R_k = 1.5kΩ, r_p = 62.5kΩ (12AX7), C_p = 100nF gives L_eq ≈ 9.4H — perfect for a mid-frequency tone stack inductor replacement.

Applications

Where Gyrators Shine

Four key applications in tube audio

Tone Stacks

Replace heavy inductors in Fender/Marshall mid-scoop EQ circuits. A gyrator gives identical frequency response in a fraction of the space.

Active EQ

Parametric and graphic EQ circuits using gyrators for each band. Adjustable center frequency, Q, and gain.

RIAA Phono

RIAA equalization with gyrator-simulated inductance. Avoids large, expensive inductors while maintaining accuracy.

PSU Filtering

Electronic choke: a gyrator in the power supply filter replaces a heavy iron choke, providing superior ripple rejection.

Reference

Real Inductor vs Gyrator

ParameterReal InductorGyrator
SizeLarge (>100cm³)Tiny (<1cm³)
Weight0.5–2 kg< 5 g
Magnetic pickupYes (shielding needed)None
Q factorFixed by constructionAdjustable via R
Cost$10–$50+$1–$5
Frequency rangeWide (DC to RF)Audio (20Hz–20kHz)
Power requiredNoYes (B+ supply)
Quiz de synthèse

Testez vos connaissances

Question 1 / 5

What does a gyrator circuit simulate?

References

  1. Paul Horowitz & Winfield Hill, The Art of Electronics, 3rd ed., Cambridge University Press, 2015. ISBN 978-0521809269Canonical reference for analog design — covers tubes in Ch. 2.4 & Ch. 3.