# Linear regulators denoising

A simple trick to cancel the output noise of any voltage regulator

Many linear regulators show something like 50-500 µV of noise at their output. It’s origin is both external (e.g. the attenuated ripple transferred to the output due to finite ripple rejection of regulators) and internal (white and 1/f noises generated by the unfiltered noise reference and the error amplifier).

While ripple can be effectively attenuated by connecting a capacitance multiplier before the linear regulator, the internally generated noise is more difficult to filter without degrading the load regulation.

An interesting solution of this problem consists in the active noise cancellation of the output noise. This method requires only two circuital blocks: a voltage-controlled current sink, and a resistor.

### Active noise cancellation in linear regulators

The trick is very simple: a current sink is controlled in order to get a current $$i_L$$ that is proportional, in any moment, to the noise voltage $$v_n$$ at the regulator output. This noise-dependent current is drawn through a resistor, $$R_s$$, in series with the output, converting it in a corresponding voltage drop.

Now comes the good: if the transconductance of the voltage-dependent current sink is exactly equal to the series resistance $$R_s$$ (in other words if we set $$i_L(t) \equiv v_n(t)/R_s$$), the voltage drop on $$R_s$$ cancels, instant by instant, the noise voltage at the output.

From a theoretical point of view, the cancellation affects any AC voltage at the output of the regulator, including the noise voltage developed across the output impedance of the regulator due to AC load currents. While the DC output resistance of the circuit is now equal to $$R_s+R_o$$, the AC output impedance of the regulator is nulled and replaced by $$R_s$$, that can be kept small.

### Schematic of a regulator denoiser

A practical application is shown. The noise voltage is AC-coupled to the non-inverting input of a differential amplifier. A DC voltage of +35 mV is superimposed just to make sure that the circuits works only with positive voltages and currents; this voltage set the input dynamic of the circuit, and should be adjusted if greater amplitude of noise is expected. The difference amplifier drives a current sink ($$Q_3$$ e $$R_L$$) that is included in the negative feedback loop.

By choosing $$R_L\equiv R_s$$, the same voltage drop is developed on both resistors, cancelling the noise at the output. In this prototype, an attenuation of –20 dB is obtained without any adjustment.

The noise cancelling improves to –30 dB if $$R_L$$ is reduced to 0,9 Ω, because this compensates for the limited $$\beta$$ of transistors and open loop gain of the amplifier.

Spectral noise densities measured at the outputs show an impressive reduction, of approximatively –40 dB at medium frequencies for any tested regulator.

A series resistance of only 1 Ω is small enough to ensure a negligible 50 mV voltage drop at 50 mA of load current. This value should be reduced for higher currents, especially if significant AC load currents are expected.