EC-8.3 Bridges and Instrumentation Amplifiers

What this is and why it exists

Most quantities worth measuring arrive as a very small change sitting on top of a large steady value. A strain gauge changes its resistance by a fraction of a per cent. A thermocouple produces tens of microvolts on top of whatever the wiring picked up.

Reading that directly wastes almost all of an instrument's range on the part you already knew.

The bridge is the classical answer to that problem and it is still the right one. Nearly every load cell, pressure sensor and strain installation in service is wired as one, which is reason enough to understand it properly.

The vocabulary

• Wheatstone bridge — four resistances in two dividers, with the reading taken between their midpoints.
• Balance — the condition in which the bridge output is zero, set by a ratio of resistances.
• Gauge factor — how much a strain gauge's relative resistance change compares with the strain applied.
• Common-mode voltage — the voltage shared by both inputs of a difference measurement.
• Common-mode rejection — how much of that shared voltage the amplifier removes.
• Instrumentation amplifier — a three-amplifier arrangement with high input impedance and gain set by one resistor.
• Loading — the error caused by the measuring circuit drawing current from the source.

The mental model

A bridge turns a measurement of a large quantity into a measurement of a small difference. Two voltage dividers are driven from the same supply. If the two dividers have the same ratio, their midpoints sit at the same voltage and the difference between them is zero.

Now change one resistance slightly. The output is no longer zero, and it is proportional to the change rather than to the whole resistance. An instrument that could never resolve one part in ten thousand of the total can easily resolve the difference.

The balance condition is the second gift. At balance the result depends on a ratio of known resistances and not on the accuracy of the meter at all. A meter that only has to tell zero from not-zero can be a very simple one. This is why bridge methods gave accurate results long before accurate meters existed.

Driving the same arrangement with a sinusoid extends it to reactive components. Now balance requires the magnitude and the phase both to match, which needs two adjustments instead of one. In exchange, the bridge returns inductance or capacitance together with the loss that comes with it.

The strain gauge is the standard application. A gauge bonded to a surface stretches with it and its resistance changes by a fraction of a per cent. Putting the gauge into one arm of a bridge gives an output proportional to the strain and nothing else.

Temperature is the reason the arrangement gets more elaborate. A gauge also changes resistance with temperature, and that change can swamp the strain. Putting a second, unstrained gauge in the adjacent arm makes both change together with temperature, so the bridge stays balanced and only the strain shows. Using four active gauges raises the output further and cancels more.

Now the amplifier, because a bridge output of a few millivolts still has to be read. The obvious answer is a difference amplifier built from one operational amplifier and four resistors. It has two problems and both matter.

The two inputs are loaded unequally, because one sees a resistor to the input and the other sees a divider. And its rejection of the common-mode voltage depends entirely on those four resistors matching. A mismatch of one per cent leaves a large fraction of the shared voltage in the output.

The instrumentation amplifier fixes both. Two buffer stages sit in front of the difference stage. Each input then sees an amplifier input rather than a resistor, and the impedance is enormous. The gain of that first stage is set by a single resistor, and the matching that matters is inside the part, done at manufacture.

The figure to look for is common-mode rejection, quoted in decibels. It says how much of the voltage shared by both inputs survives to the output. For a bridge sitting halfway up its supply, that shared voltage is large and the signal is tiny. The rejection figure is what decides whether the measurement works.

Loading is the last idea and it applies to everything in this module. Any measuring circuit draws some current from what it measures, and that current shifts the reading. The rule is that the input impedance must be far larger than the source impedance. How far depends on the accuracy you want. A factor of a hundred costs you about one per cent, and a factor of ten thousand costs one part in ten thousand.

What you should now be able to explain or do

• Explain why a bridge measures a small change better than a direct reading of the whole quantity.
• State the balance condition of a Wheatstone bridge and say why balance methods beat meter accuracy.
• Design a strain gauge bridge that cancels the effect of temperature.
• Say what a single-amplifier difference stage does badly and what an instrumentation amplifier fixes.
• Read a common-mode rejection figure and say what it means for a bridge measurement.
• Choose an input impedance from the accuracy you need and the source impedance you have.

Check yourself