Some ideal operational amplifier (often op-amp or opamp) configurations assume that the feedback resistors exhibit perfect matching. In practice, resistor nonidealities can affect various circuit parameters such as common mode rejection ratio (CMRR), harmonic distortion, and stability.
An op-amp is a DC-coupled high-gain electronic voltage amplification device with a differential input and, usually, a single-ended output. In this configuration, an op-amp produces an output potential (relative to circuit ground) that is typically dozens of thousands of times larger than the potential difference between its input terminals.
The actual performance of precision amplifiers and analog-to-digital converters (ADCs) is often difficult to achieve since datasheet specifications assume ideal components. Carefully matched resistor networks enable precision matching orders of magnitude better than unmatched discrete components, ensuring datasheet specifications are met for precision integrated circuits (ICs).
In the design of monolithic ICs for power solutions, we routinely exploit the ability to accurately match internal components. Input transistors of op-amps, for example, are accurately matched to provide low offset voltage. If we had to make our own op-amps with discrete transistors, we would have offset voltages of 30 mV or more. This ability to accurately match components includes on-chip resistors.
Inverting Operational Amplifier Configuration
Integrated differential amplifiers make use of precise on-chip resistor matching and laser trimming. The excellent common-mode rejection of these integrated devices relies on the accurate matching and temperature tracking of a carefully designed integrated circuit.
A significant tracking gain is achieved by using chips that have been diced in pairs (1:1 ratio) and put in a hermetic network package. The ultimate gain can be accomplished by using ultra-high-precision resistors featuring temperature coefficient of resistance (TCR) of 0.05 ppm/o C on the hot or cold side, and with two adjacent chips displaying a track within 0.1 ppm/o C. To get the best tracking it is necessary to use resistors featuring very low absolute TCR (known as ultra-high-precision resistors), which also helps avoid complications due to temperature gradients.
Matched resistors are critical to the performance of a large class of differential circuits. Any mismatch between these ratios will contribute to a common mode error. The CMRR is an important metric in these circuits, as it indicates how much of the unwanted common mode signal will appear in the output. The CMRR due to the resistors in these circuits can be calculated using the following formula:
CMRR=1/2(G+1)/ Δ R/R (whereas G = gain [amplification coefficient], and R = resistance [ohms])
Differential amplifiers’ usage of high-matched precision resistors is critical in precise medical equipment such as electronic scanned microscopes, blood cells count equipment, and internal body diagnostics probes.
The Wheatstone bridge (or resistance bridge) circuit can be used in a number of applications, and today, with modern op-amps, we can use the Wheatstone bridge circuit to interface various transducers and sensors to these amplifier circuits. The Wheatstone bridge has many uses in electronic circuits other than comparing an unknown resistance with a known resistance. The Wheatstone bridge circuit is nothing more than two simple series-parallel arrangements of resistances connected between a voltage supply terminal and ground-producing zero voltage difference between the two parallel branches when balanced.
A Wheatstone bridge circuit has two input terminals and two output terminals consisting of four resistors configured in a diamond-like arrangement as shown. This is typical of how the Wheatstone bridge is drawn. When used with op-amps, the Wheatstone bridge circuit can be used to measure and amplify small changes in resistance. The usage of ultra-high-precision resistors grounds the bridge balance much more precisely in comparison to when regular thin film resistors are used. All four resistors are active, so their matching and stability are very imperative for bridge balance.
Wheatstone Bridge Differential Amplifier
Well-balanced Wheatstone bridge differential amplifiers are used in smart-grid power circuitry measurement for power stations. They are also used in solar energy converters, where the efficiency of the converter directly relies on the balance of the resistive bridge using highly stable resistors.
Precision and low-noise op-amps are often used to condition the signal coming from a sensor (e.g., temperature, pressure, light) before it enters an ADC. In such a role, two particular op-amp specifications are crucial for good system resolution: the input offset voltage and the input voltage noise. The low offset and noise specifications of ultra-high-precision resistors make the devices ideal for sensor interfaces and transmitters.
Summing Op Amp Equation:
High-precision resistors, for reference, are also preferable for inputs of digital-to-analog converters (DACs). Digital signals passing via high-precision matched resistors make less noise and distortion for output analog signals. The Bulk Metal Foil technology noise level is -40 dB, making this resistive technology an ideal solution in high-end audio ADC/DAC circuits as references and gain resistors. Low-noise op-amps are also critical in avionics, military, and space (AMS) RFI equipment, including gyroscopes, GPS chipset control amplifiers, and antenna direction control units.
Kai Karstensen is the managing director of Powertron GmbH, a VPG Foil Resistors brand. Previously, he served as managing director of Aktiv-Electronics.