# SIGNAL CHAIN BASICS (Part 28): Building (Electrical) Bridges

Many sensors that measure real-world phenomenon present their outputs in the form of a changing resistance: thermistors are temperature-sensitive resistors, strain gauges change resistance with applied force, etc. The system designer's challenge then is how to accurately measure resistance.

Figure 1. Simple voltage divider

Figure 1 shows you how to measure resistance using a voltage divider. VE is called the excitation voltage. The value of RG is given by:

Figure 1: Example of PC board EMI measurement

For most sensors, this circuit tends to produce very small changes in voltage, with a large offset voltage, if R1 and RG are approximately equal in value. These are very difficult to measure when the offset is unknown. The relationship is also non-linear. The large offset can be eliminated by adding a voltage divider and measuring the output differentially see Figure 2 .

Figure 1: Adding a second voltage divider and measuring differentially

The output voltage of this circuit is given by:

This assumes that, at rest, RG is roughly equal to R1 , and that all the R1 s are very closely matched. Bridge sensors are nearly always built this way. Note that the relationship remains non-linear.

Figure 3. Conventional way bridges are drawn

The circuit of Figure 3 is electrically identical to Figure 2. This is how bridge sensors are commonly drawn. Note that the bridges shown in Figures 2 and 3 are not really the same as the Wheatstone bridge you learned about in school.

The Wheatstone bridge, shown in Figure 4 , is a familiar circuit for measuring resistance very accurately. Invented in 1833 by Hunter Christie, the circuit was later studied by Charles Wheatstone, whose name became attached to the circuit thanks to his extensive analyses of it. Wheatstone also was the first to draw the circuit in the distinctive diamond style used ever since.

Figure 4. Wheatstone bridge

The principle of the Wheatstone bridge is this: If three resistances and the current in the cross branch are known, the fourth resistance can be calculated. The measurement can be made very precisely since zero current can be detected with extremely high accuracy using a sufficiently sensitive galvanometer. Thus, when the current is zero, the bridge is balanced and the fourth resistor is equal to the other three resistances — but only if they are all equal as shown in Figures 2 and 3.

Today, most people measure the voltage differential rather than the current, similar to what is shown in Figures 2 and 3.

Reference
–Ashton, M.P., “Bridge Measurement Systems,” 2006 Precision Analog Seminar, Texas Instruments.

Rick Downs is applications engineering manager for Texas Instruments' Precision Analog group, Tucson, Arizona. Over the past 23 years, Rick has held various positions in applications and marketing of analog semiconductors focused on audio, data acquisition, digital temperature sensors and battery management products.
Rick received his BSEE from the University of Arizona, and holds four patents. He has authored several articles and application notes on analog topics, and prepared and delivered several seminars on data acquisition. You can send your questions to Rick at .

Previous installments of this series:

• SIGNAL CHAIN BASICS (Part 27): Control EMI resulting from board-level clock distribution, click here
• SIGNAL CHAIN BASICS (Part 25): Designing the audio-signal chain for non-audio experts, Part 1, click here
• SIGNAL CHAIN BASICS (Part 24): Basic networking using the IEEE 802.15.4 PHY/MAC protocol, click here
• SIGNAL CHAIN BASICS (Part 22): Phantom microphone power–the ghost in the machine, click here
• SIGNAL CHAIN BASICS (Part 21): Understand and configure analog and digital grounds, click here
• SIGNAL CHAIN BASICS (Part 20): Understand the basics of op amps and speed, click here
• SIGNAL CHAIN BASICS (Part 19): Exploring and understanding linear voltage regulators, click here
• SIGNAL CHAIN BASICS (Part 18): The op amp as integrator, click here
• SIGNAL CHAIN BASICS (Part 16): Understanding the analog voltage comparator, click here
• SIGNAL CHAIN BASICS (Part 13): Putting the Bode plot to use, click here
• SIGNAL CHAIN BASICS (Part 12): The Bode plot, an essential ac-parameter display tool, click here
• SIGNAL CHAIN BASICS (Part 11): Introducing voltage- and power-conditioning circuits, click here
• SIGNAL CHAIN BASICS (Part 10): Exploring the Delta-Sigma Converter, click here
• SIGNAL CHAIN BASICS (Part 9): SAR Converter Operation Explored, click here
• SIGNAL CHAIN BASICS (Part 8): Flash- and Pipeline-Converter Operation Explored, click here
• SIGNAL CHAIN BASICS (Part 7): Op Amp Performance Specification–Bias Current, click here
• SIGNAL CHAIN BASICS (Part 6): Op Amp Input Voltage Offset, click here
• SIGNAL CHAIN BASICS (Part 5): Introduction to the Instrumentation Amplifier, click here
• SIGNAL CHAIN BASICS (Part 4): Introduction to analog/digital converter (ADC) types, click

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