Op amp applications: sensing, comparators and data conversion

Lesson 8 analyzed the basic op amp circuits using the ideal model. This lesson applies them to the job op amps most often do: connecting the physical world to digital systems. A temperature, pressure, strain or current sensor produces a small voltage or current, often riding on a large common-mode voltage and surrounded by electrical noise. Op amp circuits amplify it accurately, convert it to a standard signal, compare it with a threshold, and present it to an analog-to-digital converter. Along the way we meet the limits of real op amps that matter most in DC measurement: offset, bias current and finite common-mode rejection.

Measuring differences: common-mode rejection

Many sensors produce a small difference between two voltages that both sit at a much larger common level. The strain gauge bridge of Lesson 3 gives 1.25 mV between two nodes that are both near 2.5 V; a current shunt in the high side of a 48 V supply gives a few millivolts between two nodes near 48 V. The amplifier must respond to the difference (the differential-mode voltage) and ignore the common level (the common-mode voltage):

The common-mode rejection ratio, \(CMRR = |A_{d}/A_{cm}|\), usually quoted in decibels as \(20\log_{10}CMRR\), measures how well it does so.

The single-op-amp difference amplifier of Lesson 8 rejects common-mode voltage only if its four resistors are perfectly matched. With resistor mismatch \(\varepsilon\) (as a fraction) and differential gain \(G\), the worst-case CMRR is approximately

The instrumentation amplifier

The instrumentation amplifier (in-amp) solves both problems of the simple difference amplifier: its input resistance is very high, so it does not load the bridge, and its CMRR is high, typically 90 dB to 120 dB. The classic three-op-amp design places two non-inverting amplifiers at the inputs, sharing a single gain resistor \(R_{G}\), followed by a difference amplifier:

A common-mode input moves both inverting inputs together, so no current flows through \(R_{G}\) and the first stage passes it with a gain of only 1, while the differential signal is amplified by \(1 + 2R_{1}/R_{G}\). Because the gain is applied before the difference stage, the overall CMRR improves roughly in proportion to the first-stage gain. Integrated in-amps contain laser-trimmed, matched resistors on one chip; the user sets the gain with a single external \(R_{G}\).

Offset voltage and bias current

Real op amps produce a small output even with both inputs grounded. This is modeled by an input offset voltage \(V_{OS}\), a small DC source in series with one input, typically 1 µV to 5 mV depending on the device, and input bias currents \(I_{B}\) flowing into each input, from picoamperes for CMOS and JFET inputs to hundreds of nanoamperes for some bipolar inputs. Both errors are amplified by the circuit's noise gain, \(1 + R_{f}/R_{1}\), regardless of whether the circuit is inverting or non-inverting:

Current loops: 4–20 mA

Industrial and building sensors, including the temperature, pressure, flow and humidity transmitters of data center cooling systems, commonly send their readings as a current between 4 mA and 20 mA rather than a voltage. A current signal is unaffected by the resistance of long wires, as long as the loop supply has enough voltage to drive it, and it is less susceptible to electrical noise. The "live zero" of 4 mA lets the receiver distinguish a reading of zero from a broken wire (0 mA), and lets two-wire transmitters power themselves from the loop.

Comparators and hysteresis

A comparator compares two voltages and switches its output between two levels depending on which is larger: a thermostat, an over-voltage detector, a zero-crossing detector. An op amp without feedback acts as a crude comparator, but dedicated comparator chips switch faster and have outputs designed to drive logic.

A comparator fed a slowly changing, noisy signal near its threshold will switch back and forth many times as noise crosses the threshold. Hysteresis fixes this by using positive feedback to create two thresholds: the output switches high at the upper threshold and back low only at the lower one. The circuit is called a Schmitt trigger.

Analog-to-digital conversion

An analog-to-digital converter (ADC) turns a voltage into a binary number. An \(n\)-bit ADC with a full-scale range \(V_{FS}\) divides it into \(2^{n}\) steps, each one least significant bit (LSB):

The conversion can never be more accurate than ±½ LSB, the quantization error. Real ADCs add offset, gain and linearity errors, and noise. Common architectures include successive-approximation (SAR) converters, which use an internal DAC like the R-2R ladder of Lesson 3 and a comparator to find each bit in turn; sigma-delta converters, which trade speed for very high resolution (24 bits) and suit slow sensors; and flash converters, which use a resistor string and \(2^{n} - 1\) comparators to convert in a single step at very high speed.

Measurement chains used for revenue metering in the US must meet ANSI C12 accuracy standards, and utility meters are regulated by state public utility commissions.