Active Ripple Cancellation

• Active ripple cancellation is a disturbance-suppression method that synthesizes a compensating signal with matched amplitude and opposite phase to cancel unwanted ripple.
• It is applied across domains such as low-dropout regulators, RF self-interference, radio astronomy, and converter ripple management, utilizing delay alignment and adaptive control.
• The method employs online adaptation and architectural diversity to address trade-offs like oscillator phase noise and stability issues while ensuring effective performance.

Active ripple cancellation is a disturbance-suppression principle in which an unwanted component is estimated or measured, a compensating replica with matched amplitude and opposite phase is synthesized, and that replica is injected so that the undesired component is reduced by superposition. In the cited literature, this principle appears explicitly in low-dropout regulators and implicitly or analogously in RF self-interference cancellation, radio-astronomy interference excision, RIS-assisted electromagnetic-interference suppression, simultaneous transmit-receive radios, converter dc-link ripple management, and active acoustics. Across these settings, the recurring elements are disturbance-path modeling, delay or phase alignment, and minimization of the residual rather than reliance on passive attenuation alone (Zhang et al., 28 Jul 2025, Huusari et al., 2015, Kiayani et al., 2017, Nigra et al., 2010, Khaleel et al., 2023, Deakin et al., 20 Dec 2025, Mishaly et al., 3 Feb 2025).

1. Core operating principle

A canonical formulation appears in wideband RF self-interference cancellation, where the disturbance observed at the receiver input is modeled as

$y(t)=h(t)\ast x(t)+n(t),$

with $x(t)$ taken from the power-amplifier output, $h(t)$ the effective multipath coupling channel, and $n(t)$ noise. The canceller synthesizes an RF anti-copy

$z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$

using delayed replicas and complex weights, so that the post-cancellation residual becomes

$e(t)=y(t)-z(t).$

This formulation makes explicit that active cancellation is an approximation problem: the compensating waveform must match the disturbance after propagation through the relevant physical path, including practical transmit-chain impairments (Huusari et al., 2015).

In LDO design, the same principle is formulated through supply-ripple feedthrough terms rather than a multipath convolution. The two-stage PSRR model separates bandgap, error-amplifier, and power-stage contributions: $$V_1 = \mathrm{PSRR}_{EA}V_{dd} + (V_{an} - \mathrm{PSRR}_{bg}V_{dd})A_1,$$

$$V_{an} = \mathrm{PSRR}_{pow}V_{dd} + (V_{ad} - V_1)A_2,$$

and yields

$$\mathrm{PSRR}_{LDO} = \mathrm{PSRR}_{bg} + \frac{A_2\mathrm{PSRR}_{EA} + \mathrm{PSRR}_{pow}}{1 + BA_1A_2}.$$

Here, active ripple cancellation is implemented by arranging the error-amplifier and power-path ripple terms so that they cancel or are strongly reduced at the regulated output (Zhang et al., 28 Jul 2025).

A broader converter-oriented formulation represents ripple directly as a bilinear $2\omega$ power phasor,

$x(t)$0

with dc-link ripple power

$x(t)$1

This does not necessarily imply injection of an explicit anti-signal at a summing node; instead, ripple can be cancelled at the system level by choosing operating points whose per-terminal contributions offset each other (Deakin et al., 20 Dec 2025). This suggests that active ripple cancellation spans both local compensating-waveform synthesis and global operating-point design.

2. Architectural realizations

The most explicit architectural taxonomy in the cited literature is the classification of full-duplex active cancellation by how the cancelling signal is computed and where it is injected (Sahai et al., 2012).

Architecture	Cancelling signal computed	Injected
Pre-mixer canceller	Before upconversion in baseband	At RF
Post-mixer canceller	After upconversion, directly at carrier frequency	At RF
Baseband analog canceller	Entirely in analog baseband	At analog baseband
Digital cancellation	After conversion to digital samples	After ADC

Within that taxonomy, several concrete realizations appear. The wideband self-adaptive RF canceller for in-band full-duplex radios is a direct-conversion transceiver front end with either a shared antenna with circulator/hybrid isolation or a dual-antenna configuration with passive antenna separation. Its canceller sits in front of the LNA, uses two fixed-delay branches, vector modulators for continuous amplitude/phase tuning, an LNA in the cancellation path, a Wilkinson combiner for RF summation/subtraction, and a directional coupler for adaptation feedback. The use of vector modulators reduces the number of required delay lines relative to amplitude-only schemes (Huusari et al., 2015).

A related but more nonlinear architecture uses an auxiliary transmitter chain. There, the cancellation waveform is digitally generated in baseband by a nonlinear filter driven by the known transmit data, upconverted by the auxiliary transmitter, and injected at the LNA input via a directional coupler. The disturbance model is explicitly parallel-Hammerstein, so the cancellation signal reproduces PA nonlinearity and memory, not merely the linear leakage component (Kiayani et al., 2017).

In radio astronomy, active cancellation is implemented as a turn-key insertable module in the telescope IF path before backend processing. The architecture includes IF input, down-conversion or frequency shifting, a programmable digital delay line, a multi-channel GPS receiver, an interferer model, an adaptive filter or canceller, subtraction from the telescope path, and a blanking control signal for intervals when cancellation is temporarily unreliable (Nigra et al., 2010).

In RIS-assisted communications, the architecture is neither RF front-end subtraction nor adaptive IF excision. Instead, the RIS uses the first time slot to obtain an EMI-contaminated observation and later time slots to produce destructive combining through the phase relation

$x(t)$2

so that $x(t)$3. The cancellation mechanism is therefore time-domain destructive combining implemented through passive beamforming control (Khaleel et al., 2023).

The LDO realization is yet another architectural form. The regulator uses a bandgap reference with bias and startup, a dual-stage error amplifier, a pass device, a feedback divider, an adaptive fast feedback branch, compensation capacitor $x(t)$4, and output capacitor $x(t)$5. Active ripple cancellation is applied along both the power path and the error amplifier’s supply path, so that the principal supply-noise coupling mechanisms are directly attacked rather than only filtered at the output (Zhang et al., 28 Jul 2025).

3. Adaptation, estimation, and self-healing

A defining feature of many active ripple-cancellation systems is online adjustment of the compensating signal. In the wideband RF canceller, this is realized by a fully analog LMS-like loop that minimizes the instantaneous residual power at the canceller output. With IQ-demodulated feedback, the update is written as

$x(t)$6

with separate $x(t)$7 and $x(t)$8 control updates for the vector modulators. Because the loop is implemented in analog hardware, it continuously tracks time-varying reflections and does not require ADC/DAC-heavy adaptation or preamble-based retraining (Huusari et al., 2015).

The nonlinear RF canceller adopts a closed-loop decorrelation rule. Its adaptive filter is built on orthogonalized nonlinear basis functions,

$x(t)$9

and its block update is

$h(t)$0

The purpose is to drive the residual leakage toward decorrelation from the nonlinear basis set while learning in the presence of a nonlinear PA with memory, finite passive isolation, and even a nonlinear RX LNA. The closed-loop structure is important because reduction of leakage at the LNA input progressively reduces LNA distortion during subsequent learning iterations (Kiayani et al., 2017).

In the Arecibo GPS L3 concept, adaptation is inseparable from signal-state detection. The subsystem detects whether L3 is in its unmodulated mode or high-rate data-modulated mode by comparing a 1 ms coherent integration with an incoherent sum over 121 sequential $h(t)$1 coherent sums. When the signal is known well enough, cancellation proceeds; when the modulation changes too quickly or demodulation is unreliable, the system can issue a blanking signal. The mitigation logic is therefore adaptive both in filter estimation and in mode-dependent policy selection (Nigra et al., 2010).

Deep active speech cancellation replaces LMS-style coefficient adjustment with learned sequence modeling. The reference is decomposed into multiple frequency bands, each band is encoded and processed by a Mamba-based masking network, masked latent representations are concatenated, and a decoder synthesizes the canceling waveform. Training combines a residual-based ANC loss with a Near Optimal Anti-Signal objective,

$h(t)$2

$h(t)$3

This formulation makes the supervisory target depend on the secondary path, not just the raw waveform, which is consistent with the physical cancellation objective (Mishaly et al., 3 Feb 2025).

4. Limiting mechanisms and design trade-offs

A central result in full-duplex radio is that residual self-interference is not limited primarily by channel-estimation error but by oscillator phase noise. With phase noise, the residual after analog cancellation contains terms that do not vanish with better channel estimation and may become uncorrelated with the self-interference waveform, which limits the effectiveness of subsequent digital cancellation. In pre-mixer architectures with independent oscillators, cancellation is fundamentally bounded by phase-noise variance; with matched oscillators, common phase noise partially cancels and performance improves (Sahai et al., 2012).

Wideband operation introduces a different trade-off. In the self-adaptive RF canceller, a single tap is insufficient for a frequency-selective self-interference channel, especially at 100 MHz-class bandwidths. Multiple delayed branches are needed, yet the two-branch demonstrator is already not fully optimized for $h(t)$4 MHz operation. The paper explicitly notes that wider bandwidths are harder because more taps would ideally be needed (Huusari et al., 2015).

Architectures that suppress interference by altering a beamforming or control configuration generally incur performance trade-offs elsewhere. In the RIS case, the $h(t)$5-shift relation that removes EMI in later slots sacrifices the usual passive beamforming gain; the method is advantageous when EMI is comparable to or larger than the desired reflected signal, but the benchmark beamforming strategy can be better when EMI is weak and AWGN dominates (Khaleel et al., 2023).

Mode-changing interferers create another limit. In the GPS L3 case, single-bit demodulation during modulated intervals may make the SNR too poor for effective cancellation, so temporary blanking becomes part of the design. This is not a failure of the active-cancellation concept but a recognition that an inaccurate reference can be worse than a brief interruption (Nigra et al., 2010).

In regulators, ripple cancellation interacts with loop stability. The dual-stage amplifier, extra gain, and active ripple-cancellation paths improve PSRR, but the same additions increase the risk of stability issues and necessitate on-chip frequency compensation. The adaptive fast feedback branch is introduced to preserve transient speed without destabilizing the regulator (Zhang et al., 28 Jul 2025).

Converter ripple mitigation reveals a further trade-off: zero-sequence and negative-sequence current injections do not affect the dc link in the same way. For a four-wire converter, $h(t)$6 yields no negative-sequence current and no $h(t)$7 ripple but maximum neutral current, whereas $h(t)$8 yields zero neutral current but maximum $h(t)$9 ripple. Constraining only ripple or only neutral current is therefore insufficient (Deakin et al., 20 Dec 2025).

5. Representative domains and reported performance

The breadth of active ripple-cancellation practice is illustrated by the following implementations and reported outcomes.

Domain	Mechanism	Reported outcome
Wide-input LDO	Active ripple cancellation along the power path and the error amplifier’s supply	$n(t)$0 dB low-frequency PSRR; $n(t)$1 V droop and $n(t)$2 recovery for a $n(t)$3 load step (Zhang et al., 28 Jul 2025)
Wideband full-duplex RF	Two delay branches, vector modulators, PA-output reference, analog LMS adaptation	Around $n(t)$4 dB total cancellation at $n(t)$5 MHz and $n(t)$6 dB at $n(t)$7 MHz in the shared-antenna setup; close to $n(t)$8 dB at $n(t)$9 MHz in the dual-antenna setup (Huusari et al., 2015)
Nonlinear RF leakage suppression	Auxiliary transmitter chain and closed-loop nonlinear decorrelation learning	Up to about $z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$0 dB suppression at the LNA input; total passive + active isolation exceeding $z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$1 dB in the IBFD example (Kiayani et al., 2017)
Radio astronomy GPS L3 excision	Receiver-assisted reference reconstruction, programmable delay alignment, adaptive cancellation, blanking fallback	Simulated spectrometer result with no apparent residual RFI for noise plus a single GPS L3 interferer at $z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$2 dB-Hz and $z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$3 ms integration (Nigra et al., 2010)
RIS-assisted EMI suppression	First-slot EMI sampling and later-slot $z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$4-phase inversion	For $z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$5, the benchmark outage probability equals $z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$6 for all tested $z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$7, while the proposed method has much lower outage probability (Khaleel et al., 2023)
Active acoustics	Multi-band Mamba masking with NOAS supervision	Up to $z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$8 dB improvement in ANC and $z(t)=\sum_{n=1}^{N} w_n x(t-T_n),$9 dB in ASC (Mishaly et al., 3 Feb 2025)
Multi-terminal converter operation	Opposing sequence injections that cancel net dc-link ripple	Total motor derating reduced from $e(t)=y(t)-z(t).$0 kW to $e(t)=y(t)-z(t).$1 kW, with dc-link ripple about $e(t)=y(t)-z(t).$2 W in the reported SOP solution (Deakin et al., 20 Dec 2025)

The LDO case is the clearest example in conventional power-management terminology. The regulator explicitly couples ripple to the pass-transistor gate or control node and to the error-amplifier supply so that the resulting feedthrough terms oppose the input ripple. The paper states that if the gate and source of the PMOS experience supply noise of the same magnitude, the common-source and common-gate gain paths produce output noise contributions of opposite phase, enabling cancellation at the amplifier output node (Zhang et al., 28 Jul 2025).

In RF systems, the strongest reported outcomes come from architectures that model the actual transmit leakage rather than an idealized reference. The self-adaptive canceller samples the PA output, which includes practical impairments, while the nonlinear auxiliary-transmitter design explicitly reproduces PA memory and intermodulation through odd-order basis functions. Both approaches address the physical disturbance path before the receiver front end is overloaded (Huusari et al., 2015, Kiayani et al., 2017).

6. Broader interpretation and recurrent misconceptions

A common misconception is that active ripple cancellation is merely an adjunct to passive filtering. The cited work instead shows several distinct roles: direct cancellation of supply ripple in an LDO, RF anti-copy synthesis for self-interference suppression, adaptive excision of structured satellite interference from a telescope IF chain, time-slot-based EMI cancellation through RIS phase inversion, and dc-link ripple minimization through converter operating-point coordination (Zhang et al., 28 Jul 2025, Huusari et al., 2015, Nigra et al., 2010, Khaleel et al., 2023, Deakin et al., 20 Dec 2025).

A second misconception is that accurate channel estimation alone is sufficient. In full-duplex radio, the phase-noise analysis shows that residual interference can persist even with perfect self-interference channel knowledge, because the dominant impairment is differential oscillator phase noise rather than estimation error. This is one reason measured cancellation floors saturate far above thermal noise in practical systems (Sahai et al., 2012).

A third misconception is that active cancellation is necessarily digital. The surveyed realizations include fully analog LMS-like adaptation, auxiliary-RF injection, analog baseband cancellation, IF-path adaptive excision, FPGA-centered receiver-assisted processing, and learned neural waveform synthesis. The distinguishing property is not the implementation substrate but the synthesis of a compensating disturbance-aware signal or operating condition (Huusari et al., 2015, Kiayani et al., 2017, Nigra et al., 2010, Mishaly et al., 3 Feb 2025).

A plausible implication is that the most robust active ripple-cancellation schemes are those that model both the disturbance-generation path and the cancellation-actuation path. This implication is consistent with the repeated emphasis on PA-output referencing, programmable delay alignment, secondary-path-aware objectives, phase-noise-aware modeling, and bilinear dc-link ripple constraints. In that sense, active ripple cancellation is less a single circuit technique than a general design doctrine: cancellation quality depends on how faithfully the compensating mechanism reproduces the disturbance after all relevant plant dynamics, impairments, and constraints are included.