Instrumentation Amplifier: Design Rules and Process Limits

An instrumentation amplifier is chosen for its common mode rejection and its stable gain, and it is often blamed for noise that comes from somewhere else. Splitting the noise into the contributions of the amplifier, the source impedance and the gain setting network is what turns a frustrating measurement into a design calculation.

Where the Noise Comes From

The amplifier contributes a voltage noise in series with the input and a current noise that flows in the source impedance and produces a voltage. Which of the two dominates depends on the resistance the amplifier sees.

A source of ten kiloohms produces a thermal noise of about thirteen nanovolts per root hertz at room temperature, which is comparable with the voltage noise of a good amplifier. The resistor noise is not optional, and it sets a floor for any design with a high impedance source.

The gain setting network and the feedback resistors also contribute, but they are internal to the part and are included in the datasheet noise figure. The external source impedance is the part the designer controls.

Voltage Noise and Current Noise

Voltage noise is quoted as a spectral density at a specified frequency. At low frequencies the value is higher because of the flicker component, and the graph in the datasheet slopes down until it flattens at a corner frequency of a few tens of hertz.

Current noise is quoted the same way and becomes important when the source impedance is high. A part with two picocamps per root hertz into a hundred kiloohm source produces two hundred nanovolts per root hertz, which is far more than the voltage noise of almost any amplifier.

Choosing between a bipolar and a field effect input is therefore a decision about the source impedance. The bipolar part has a lower voltage noise, the field effect part has a much lower current noise, and the crossover is usually in the tens of kiloohms.

Source Impedance and Thermal Noise

The thermal noise of a resistor is proportional to the square root of its resistance and to the square root of the temperature. Cooling a sensor can reduce its noise, and that is one reason some measurements are made at low temperature.

Where the source is a bridge or a sensor with a low resistance, the resistor noise is small and the amplifier voltage noise dominates. Where the source is a high resistance, the two trade places and the current noise becomes the limit.

Adding a resistor in the input path to protect the amplifier is common and it adds noise. A hundred ohms in series with each input adds about one and a quarter nanovolts per root hertz, which is small but should be counted rather than forgotten.

gain bandwidth and Noise Bandwidth

gain bandwidth is the product of the closed loop gain and the bandwidth over which the amplifier holds it. Selecting a gain that uses the available bandwidth leaves no margin, and selecting too high a gain reduces the bandwidth below what the measurement needs.

The noise that matters is the noise over the bandwidth of the measurement, not the noise density at the input. A wide band front end collects more noise, and narrowing the bandwidth to what the signal needs improves the signal to noise ratio without changing the amplifier.

A first order filter reduces the noise bandwidth by a factor of about one and a half compared with its corner frequency, while a second order filter reduces it further. The improvement from the filter is often worth more than a change of amplifier.

common mode rejection and Its Limits

common mode rejection is specified at direct current and falls with frequency. At the mains frequency the value is still high, and at the switching frequency of a nearby converter it may be thirty or forty decibels lower.

The rejection also depends on the matching of the source impedances. A difference of one percent between the two source resistances destroys the rejection of a common mode signal, which is why the two input paths must be identical in resistance and in layout.

The rejection is often the reason a part is chosen in the first place, and it is worth measuring in the application rather than trusting the datasheet figure. Applying a common mode signal at the frequency of interest and measuring the output is a two minute test.

Building the Noise Budget

A noise budget adds the contributions in power rather than in voltage. Each source contributes a density in nanovolts per root hertz, the squares are added, and the square root of the sum gives the total density at the input.

The total input noise is then multiplied by the gain to give the output noise, unless the later stages add their own contribution. Where a second stage has a comparable noise, its contribution referred to the input is divided by the gain of the first stage, which is why the first stage sets the performance.

The result is compared with the smallest signal that has to be resolved. If the amplifier noise is a small fraction of the signal, the design is done; if it is comparable, the source impedance or the bandwidth has to change, because another amplifier will not fix a thermal noise problem.

Layout, Guarding and Thermocouples

Guard the input traces with a track at the common mode potential, or at least keep them equal in length and close together. The two inputs see the same noise, and the rejection of the following stage depends on that symmetry being preserved on the board.

Keep the amplifier away from heat sources, because a thermal gradient across the input pins produces a thermocouple voltage of a few microvolts per degree. The effect is comparable with the offset drift of the part and appears as a slow drift that is difficult to explain.

Keep digital lines away from the input network. A clock trace passing close to the gain setting resistor couples into it, and the coupling is amplified by the full gain of the stage. The wider layout discipline for a precision node is covered in our guide to mixed signal board design.

Verification and Common Faults

Measure the noise with the input shorted to the common mode voltage and with the source connected. The difference between the two measurements is the contribution of the source, and it separates an amplifier problem from a source problem.

Measure the noise over the bandwidth of interest with a filter, not with a wideband instrument. A wideband measurement includes noise that the system will never see and leads to a design that is quieter than necessary.

Check the rejection by applying a common mode signal and looking for the output. A rejection that is far worse than the datasheet value points to unequal source impedances or to a layout asymmetry. The release checks that keep such a board consistent are collected in our PCB design release checklist, and the assembly points are listed in judging PCB quality.

FAQ

Why is my instrumentation amplifier so noisy? Check the source impedance. A high resistance converts the current noise of the amplifier into a voltage that may exceed the thermal noise of the resistor.

Does a higher gain reduce the noise? It reduces the contribution of later stages, but the input noise is amplified with the signal. Narrowing the bandwidth is usually the better move.

Why is my common mode rejection worse than specified? Unequal source resistances and asymmetric layout destroy the matching. Measure the two input paths and make them identical.