Volts to Microvolts

From a Volt-Level Spec to a Microvolt Error Term

Converting volts to microvolts is the first arithmetic in most low-noise design reviews. Rails, full-scale ranges and datasheet decibel figures all arrive in volts, but an error budget is added up in microvolts at the amplifier input. Once every term sits in µV, a noise floor, an offset drift and a supply-rejection residue become directly comparable.

Conversion factor: 1 V = 1 000 000 µV, so µV = V × 10⁶. Worked example: 100 mV of rail ripple is 0.1 × 1 000 000 = 100 000 µV; an amplifier with 80 dB of PSRR divides that by 10^80/20 = 10 000, leaving 10 µV of input-referred error.

Why the Two Scales Live Side by Side

Where the volts come from

Rails, regulator ripple, full-scale ranges and common-mode levels — the disturbance side of the budget, always quoted in volts.

Where the microvolts land

Every term is referred back to the amplifier input, ahead of the gain stage, so a 0.8 µV noise floor and a 25 µV offset weigh against each other on one scale.

The decibel middleman

PSRR and CMRR are ratios in dB: divide the disturbance by 10^dB/20. 80 dB is ÷10 000, 100 dB is ÷100 000, 120 dB is ÷1 000 000.

Why µV beats percent

50 µV on a 1 V full scale is 50 ppm, or 0.005 %. As a percentage it looks like nothing; in microvolts it stays visible next to every other term.

Working a Datasheet Figure Through the Converter

The workflow is one datasheet line or scope measurement at a time, landing in the budget sheet as a microvolt number.

Type the volt-level figure

Put the rail ripple, full-scale range or common-mode voltage into the Volts field (it starts at 1). Both fields are editable and the other side updates live as you type. Comma or dot both work as the decimal separator and spaces are ignored, so 0,1 and 0.1 each read as 100 000 µV.

Read the microvolt term

Results carry up to 8 decimals with thousands grouped by a space, and switch to scientific notation below 10⁻⁶ — the region where nanovolt terms live, so a sub-microvolt figure never rounds away to zero.

Copy the bare number into the budget

The copy button on each field takes the number alone — no unit, no grouping spaces — as does Ctrl + C inside a field. It pastes straight into the cell that will later be squared for the root-sum-square total.

Retarget either side

Both dropdowns are searchable and carry all twelve units — GV, MV, kV, V, dV, cV, mV, µV, nV, pV plus the CGS abvolt and statvolt. Point the output at nanovolts when a noise-density term is naturally in nV.

Going Back the Other Way

To return a budget total to volts, divide by a million: V = µV ÷ 1 000 000, so a 29.8 µV root-sum-square total is 0.0000298 V. The swap button (↔) reverses the direction in place, letting you check a µV figure against the rail it came from without retyping.

Noise Floors and Error Budgets, Restated in Microvolts

Below is a realistic precision front end — 1 V full scale, 10 kHz measurement bandwidth, a 40 °C temperature swing and 100 mV of ripple on the rail — with each volt-level or decibel spec restated as the input-referred error it contributes.

Spec as the datasheet writes it	Arithmetic	Input-referred error	Share of 1 V full scale
Voltage noise density 8 nV/√Hz, 10 kHz bandwidth	8 nV × √10 000 = 800 nV	0.8 µV RMS	0.8 ppm
Input offset voltage 25 µV max	already a µV figure	25 µV	25 ppm
Offset drift 0.2 µV/°C, ΔT = 40 °C	0.2 × 40	8 µV	8 ppm
PSRR 80 dB against 100 mV rail ripple	0.1 V ÷ 10^80/20 = 0.1 ÷ 10 000	10 µV	10 ppm
CMRR 100 dB against 1 V common-mode	1 V ÷ 10^100/20 = 1 ÷ 100 000	10 µV	10 ppm
Untrimmed gain error 1 % of 1 V full scale	0.01 × 1 V = 10 mV	10 000 µV dominant	10 000 ppm

The first five rows are the terms a low-noise design can genuinely trade against each other. In root-sum-square they give √(0.8² + 25² + 8² + 10² + 10²) = √889.64 ≈ 29.8 µV; added arithmetically they give 53.8 µV. Against a 50 µV budget the same circuit passes on RSS and fails on worst case — which is why the summation rule has to be agreed before the numbers are argued over.

Check the scale first: the 1 % gain error in the last row is 10 000 µV — two hundred times the whole 50 µV budget. While a term that large is still in the sheet, amplifier selection changes nothing; it has to be trimmed, calibrated or ratio-cancelled out first.

What the Converter Does for a Budget Sheet

Spec in, error term out

Both fields stay live, so you can also work backwards — type the allowed µV on the right and read the rail ripple it permits.

Sub-microvolt terms keep their digits

Eight decimals plus automatic scientific notation below 10⁻⁶, so a noise floor in the hundreds of nanovolts stays readable instead of collapsing to 0.00.

Numbers that paste clean

Copy returns the bare value with no unit or grouping spaces, so a pasted cell stays numeric and can be squared and summed without cleanup.

Twelve units on both sides

Searchable dropdowns from gigavolt to picovolt, plus abvolt and statvolt, so an integrated-noise figure in nV and a rail spec in V reconcile on one page.

Error Budget Questions Designers Ask

How many microvolts does 80 dB of PSRR leave from 100 mV of supply ripple?

Ten. A rejection ratio in decibels becomes a plain divisor as 10^dB/20, so 80 dB is a factor of 10 000: 100 mV = 100 000 µV, divided by 10 000, leaves 10 µV of input-referred error.

The catch is that PSRR is frequency-dependent and the headline number is a DC or low-frequency value. Rejection rolls off with open-loop gain and can fall to 20–30 dB in the tens-to-hundreds of kilohertz. At 30 dB the same ripple leaves 0.1 ÷ 31.6 ≈ 3.2 mV — over three thousand microvolts. Read PSRR at the frequency your switching regulator actually produces.

How do I turn nV/√Hz noise density into a microvolt figure over my bandwidth?

Multiply the density by the square root of the bandwidth, because broadband noise adds in power rather than amplitude: 8 nV/√Hz over a 10 kHz brick-wall bandwidth gives 8 × √10 000 = 800 nV = 0.8 µV RMS.

Two corrections matter. A single-pole roll-off has an equivalent noise bandwidth of 1.57 × f_-3dB, so behind a real 10 kHz pole the same amplifier sees √15 700 ≈ 125 and gives about 1.0 µV RMS. For peak-to-peak, the usual convention is roughly 6.6 × RMS — 0.8 µV RMS becomes about 5.3 µV p-p. Low-frequency 1/f noise below the corner is budgeted separately, normally as µV p-p over 0.1–10 Hz.

What does 100 dB of CMRR mean in microvolts for my common-mode voltage?

Divide the common-mode voltage by 10^dB/20. At 100 dB the divisor is 100 000, so 1 V of common-mode leaves 10 µV at the input and 5 V leaves 50 µV; a 120 dB part divides by a million, dropping the same 1 V to 1 µV.

Like PSRR, CMRR degrades with frequency, so the DC figure flatters the design. The disturbance that usually matters is mains pickup at 50 or 60 Hz, where the spec is still near its DC value — anything higher should be read off the CMRR-versus-frequency curve. In an instrumentation amplifier the rejection also depends on source-impedance balance between the inputs, so mismatched sensor leads can add microvolts that no amplifier can recover.

Does a microvolt-level error matter when the signal is measured in volts?

Only relative to the accuracy class you promised. As a ratio, 1 µV on a 1 V full scale is 1 ppm, or 0.0001 %, and the span from 1 V down to 1 µV is 20 × log₁₀(10⁶) = 120 dB of dynamic range.

A 1 % industrial channel can ignore microvolts outright — a 10 000 µV gain error swamps them. A 0.01 % (100 ppm) instrument cannot: 100 ppm of 1 V is 100 µV, and a 30 µV budget already eats a third of it. Convert both the spec and the error to the same unit before judging; a term that looks negligible as a percentage often looks alarming in microvolts, and that is the honest view.

Should I add my microvolt error terms straight up or use root-sum-square?

Both, for different purposes. Independent random terms — broadband noise, thermal noise, a part-to-part offset drawn from a distribution — combine in power, so the correct total is the root-sum-square: ≈ 29.8 µV for the table above. Systematic terms that always push the same way — gain error, a known thermal gradient, an uncalibrated reference tolerance — add linearly.

Common practice is to RSS the random terms, add the systematic ones on top of that result, and quote the plain worst-case sum (53.8 µV here) alongside as the guaranteed-never-exceeded number. Reporting only the RSS figure without saying so is the easiest way to make a marginal design look comfortable, because RSS is dominated by the largest term and quietly discounts everything smaller.