Injection Locking
# Injection Locking: When One Oscillator Captures Another
Injection locking is synchronization by a periodic signal applied directly to an oscillator. Near its natural frequency, an oscillator can adopt the injected signal’s frequency while holding a constant phase difference. Its active circuit still supplies energy from DC power; the reference controls timing rather than powering the entire output.
## Follow the signal into the tank
An LC oscillator exchanges energy between an inductor and a capacitor. An active transistor core replenishes losses. Injecting a small periodic current changes the timing of that exchange. When the timing correction can cancel the frequency mismatch, phase stops drifting and the oscillator locks.
*Conceptual single-ended equivalent of an LC oscillator; practical differential circuits use topology-specific injection points. Waveforms show equal frequency with a nonzero, fixed phase offset.*
## Why a lock range exists
Let φ be oscillator phase minus injected-reference phase, and let Δω = ω₀ − ωinj be the free-running detuning. A common weak-injection phase model is dφ/dt = Δω − K sin φ, with K expressed in radians per second. A stable stationary phase is possible inside |Δω| < K. The ideal boundary is marginal; practical designs need margin for noise, drift and variation.
For a simple resonant oscillator under weak fundamental injection, a useful estimate is K ≈ [ω₀ / (2Q)] × (Iinj / Iosc). Current amplitudes must be defined consistently at the tank. Coupling efficiency and topology change the coefficient. This estimate is not a universal rule for ring oscillators, strong injection, multimode systems or harmonic locking.
*Conceptual capture map: horizontal position is detuning; vertical position is injected amplitude. The triangle illustrates the weak-injection scaling, not a measured operating envelope.*
Example: at f₀ = 5 GHz, Q = 10 and an effective injection-current ratio of 0.02, the model predicts a half-range of about 5 MHz, or a 10 MHz total locking span. At 3 MHz detuning the ideal stable phase offset is approximately arcsin(3/5) = 37°. Process, supply and temperature variation can move the natural frequency outside that span even when the reference stays constant.
## Locking, pulling and a PLL
| Behavior | What phase does | What the output does |
|---|---|---|
| Injection locking | Settles to a fixed offset | Runs at the injected frequency in fundamental locking |
| Injection pulling | Continues to slip | Frequency and phase are perturbed; beat-related sidebands can appear |
| Phase-locked loop (PLL) | Feedback regulates phase error | A detector, loop filter and tuning actuator steer the oscillator |
Injection locking acts through the oscillator’s dynamics. A PLL uses an explicit feedback loop. Designers can combine them: a slow tuning loop keeps the oscillator near the target, while injection supplies rapid timing correction. Harmonic and subharmonic injection can support frequency multiplication or division, but require their own capture analysis.
## What a chip designer must verify
Tune before relying on capture. Sweep the free-running frequency across process, supply voltage and temperature. Provide tuning coverage so the intended operating point stays safely inside the measured locking region.
Measure phase, not only the spectrum peak. A strong injected tone can be visible even when the oscillator has not synchronized. Check bounded relative phase, acquisition behavior and phase slips; sweep injection strength and detuning in both directions to identify topology-dependent hysteresis.
Treat the reference as part of the noise budget. Locking can suppress some oscillator phase noise within its effective synchronization bandwidth, while transferring reference noise. It does not make every offset cleaner. Evaluate output phase noise, spurs and jitter with the actual reference and injection network.
Control unintended capture. Intentional injection can help clock generation and synchronization; unwanted coupling from a power amplifier, clock or neighboring oscillator can pull or lock a sensitive oscillator. Isolation, supply filtering, differential layout and frequency planning reduce that risk. See also VCO pulling for the unwanted-coupling mechanism.
The design goal is reliable synchronization across the operating envelope: sufficient tuning and injection margin, acceptable reference-noise transfer, and verified acquisition without phase slips.
## References
- [B. Razavi, A Study of Injection Locking and Pulling in Oscillators, IEEE JSSC (2004)](https://doi.org/10.1109/JSSC.2004.831608).
- [T. Hiraoka et al., Injection Locking and Noise Reduction of Resonant Tunneling Diode Terahertz Oscillator](https://arxiv.org/abs/2101.04828), an experimental example of amplitude-dependent locking range in the small-signal regime.