Every experienced amplifier designer has, at some point, encountered a circuit that looks perfect on paper and terrifying on the oscilloscope. The Bode plot promises stability. The simulated phase margin sits at a comfortable 60 degrees. The soldered board screams at a frequency nobody invited. When the post-mortem investigation begins, the culprit is rarely a miscalculated component. More often, it is a single PCB trace: the one that carries the feedback signal from the wrong side of the output filter.
That trace is the Kelvin point of the feedback chain. Its placement is not a layout detail. It is a topological decision that fundamentally reshapes the open-loop transfer function and determines whether the amplifier converges to a stable operating point or decides, unprompted, to become an oscillator.
What a Kelvin Point Actually Is
The term originates with Lord Kelvin's four-terminal sensing technique, in which the current-carrying path and the voltage-sensing path are physically separated so that the impedance of the conductors carrying current cannot corrupt the voltage measurement. A pair of sense connections made immediately adjacent to the target impedance carries virtually no current, so the voltage drop in the sense leads is negligible and the measurement reflects only the quantity of interest.
In an amplifier feedback chain, the Kelvin point is the precise node from which the feedback signal is lifted. Move that point by five millimeters, and the impedance between the old node and the new one becomes part of the feedback path. At audio frequencies, that impedance is negligible. Above a few hundred kilohertz, it is not. A short PCB trace carries nanohenries of parasitic inductance. A nanohenry at one megahertz presents an inductive reactance of over six milliohms. This sounds inconsequential until one considers that the current flowing through it during a reactive load transient can run into tens of amperes, generating voltage spikes that the feedback network interprets as legitimate signal and dutifully attempts to correct.
The Output Filter as a Phase-Generating Machine
The output filter in any power amplifier is an LC network with a transfer function, poles, and a phase lag that deepens steeply around the filter's resonant frequency. A second-order LC low-pass filter contributes up to 180 degrees of phase shift above its corner frequency, and a high-Q filter reaches close to that 180-degree limit in an almost discontinuous transition near resonance. This is not a problem that can be compensated by tweaking gain. It is a structural feature of the filter's transfer function.
What the designer can control is whether this phase shift is inside the feedback loop or outside it. That choice is made entirely by the placement of the Kelvin point.
Pre-Filter Feedback: Simplicity at a Price
When the feedback sense point sits before the output filter, the filter is outside the feedback loop. The loop transfer function does not include the filter poles, and phase margin is easier to achieve because the open-loop phase never has to contend with the filter's 180-degree asymptote.
The tradeoff is significant. Because the filter is not inside the loop, the amplifier cannot correct for any nonlinearity or load-dependent frequency-response variation the filter introduces. In Class D amplifiers, the filter's resonant behavior depends on the effective load impedance. Pre-filter feedback for driving an inductive transducer will always result in some high-frequency peaking unless a custom RC damper is used. The filter, operating open-loop relative to the feedback, produces a frequency response that rises before it falls and shifts with every different speaker load connected to the terminals.
For a pre-filter scheme, the Kelvin point is relatively forgiving. A few millimeters of trace between the switching node and the sense pad represents a modest parasitic inductance, and the absence of filter poles from the loop transfer function means the overall phase budget is generous enough to accommodate modest layout imprecision.
Post-Filter Feedback: Full Correction, Dangerous Edges
Closing the feedback loop after the output filter changes everything. The error amplifier now compares the actual voltage at the output terminal to the reference. Any deviation from load modulation, output stage nonlinearity, filter resonance, or supply rejection is visible to the corrective mechanism and reduced by the loop gain. Load-invariant frequency response and substantially lower distortion both become achievable.
The problem is that the loop now encompasses the filter poles. The second-order filter contributes 180 degrees of phase shift. The amplifier's own internal poles contribute additional phase shift. Propagation delays in the modulator, driver stage, and PCB traces add more. The total accumulated phase at the unity-gain crossover frequency must stay well clear of 180 degrees. Post-filter NFB schemes require a maximum load resistance for proper phase margin to avoid the phase approaching 180 degrees at too low a frequency. In the presence of negative feedback, a zero or negative phase margin at a frequency where the loop gain exceeds unity guarantees instability.
What makes the Kelvin point critical is that five millimeters of copper trace between "just before the filter output capacitor" and "just after the filter output capacitor" represents two fundamentally different transfer functions. One includes only the trace inductance of the wiring to the sense pad. The other includes the full LC filter transfer function with its phase-rotating poles. The phase budget is not infinite. The difference between those two sense locations can be the difference between a phase margin of 55 degrees and one of 15 degrees at the critical crossover frequency.
The Mechanics of Phase Destruction
Consider a typical Class D amplifier output filter: a 10-microhenry inductor in series with a 1-microfarad capacitor, designed for a nominal 8-ohm load. The resonant frequency sits near 50 kilohertz. The amplifier's unity-gain crossover is likely designed for 50 to 150 kilohertz, precisely the frequency range where the filter's phase transition is most aggressive.
If the Kelvin point is taken from the junction of the inductor and capacitor rather than from the output terminal, the feedback network has sampled the voltage at the midpoint of a reactive divider whose impedance ratio changes sharply near resonance. The feedback signal is not the output voltage. It is the output voltage plus the voltage developed across the inductor by the load current, high-pass filtered in a way that emphasizes exactly the frequency range where the phase budget is already thin.
A resistor in series with the filter capacitor, paralleled by another cap with a fraction of the filter cap value, yields a slower phase lag in the resonant region, simplifying the feedback design of post-filter topologies. This approach softens the phase cliff near resonance but cannot substitute for picking the sense node correctly in the first place. Taking the Kelvin point from the wrong side of even a short ferrite bead, often used to suppress RF, introduces an unintentional pole-zero pair that subtracts from the phase margin without any corresponding benefit.
Distributed Inductance, Ground Plane Currents, and What 5 Millimeters Actually Costs
A common instinct when post-filter feedback exhibits peaking is to add a Zobel network, the RC damper that provides a resistive path preventing load impedance from rising unboundedly with frequency. Without the Zobel, gain starts to increase at high frequencies exactly when it should be decreasing to ensure it falls below unity before phase shift reaches 180 degrees. The Zobel helps, but it cannot move the Kelvin point. If the sense node sits on a portion of the circuit that already sees a phase-shifted version of the true output voltage, the Zobel damps the filter resonance as seen by the load but does not change what the feedback network is sampling. This residual phase error is decisive in high-feedback-gain designs.
The reason five millimeters matters is traceable to conductor inductance. A standard PCB trace of 1-millimeter width over a ground plane carries approximately 1 nanohenry per millimeter. Five millimeters introduces roughly 5 nanohenries of series inductance between the sense pad and the true output node. At 500 kilohertz, this presents an inductive reactance of about 15 milliohms. Against an 8-ohm load that is negligible. Against the milliohm-range output impedance of a deeply feedback-corrected amplifier, the inductance represents a meaningful fraction of the open-loop output impedance. The feedback network sees the sum of the true output voltage and a frequency-dependent inductive voltage developed by the load current, a term that grows with frequency and steals phase margin at exactly the frequencies where it is most needed.
Ground plane currents compound this. Asymmetric inductance in sense traces creates common-mode to differential-mode conversion of fast transients. If the feedback signal's ground reference passes through copper shared with the high-current output stage return, large transient currents develop voltages that appear as noise on the feedback signal. The amplifier faithfully tries to reject this noise, creating corrective currents that become their own source of instability. Separating the sense ground from the power ground, and returning both to a single Kelvin node at the output capacitor, eliminates the mechanism entirely. This is the four-terminal Kelvin principle applied directly to the feedback chain.
The Correct Approach and What It Demands
Placing the Kelvin point correctly for a post-filter design means connecting the feedback sense trace directly to the output terminal, after the series output inductor, after any RF-suppression bead or Thiele network wiring, and at the same node that connects to the load. The sense trace should carry no load current, should take a separate routing path back to the feedback divider, and its ground return should connect to the ground side of the output capacitor by a dedicated trace, not to the power stage ground.
The phase margin recovered by this discipline is not marginal. In amplifiers with high feedback depth and post-filter sensing, moving the Kelvin point from an intermediate node to the true output terminal can recover 20 to 40 degrees of phase margin at the crossover frequency. A design that was oscillating at 15 degrees phase margin can reach the 45 to 60 degree target range that experienced designers regard as the minimum for reliable operation across component tolerances, temperature variation, and the full range of real-world loads.
The feedback chain is not a passive routing detail. It is an active participant in the loop transfer function. Every nanohenry, every shared ground trace, and every carelessly placed via in the feedback path is a circuit element that contributes phase shift. The Kelvin point is the precise location where the amplifier decides what the truth is, and that decision, made in copper, determines whether the circuit amplifies or oscillates. Five millimeters is not a rounding error. In a post-filter feedback amplifier, it can be the difference between a finished product and a persistent, expensive mystery.
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