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July 29, 2019

Every electrical engineer knows how to determine the electrical power P dissipated by a resistor. You measure the voltage E across the resistor and the current I flowing through it, then use the formula, P = EI. You can take a shortcut in the measurement by using the formula, E = IR, to create the alternative power formulas, P = I2R and P = E2/R.

Power dissipation in a resistor

Power dissipation in a resistor.

The important variables are the resistance (R, ohms), the voltage (E, volts), and the current (I, amperes).

Since the voltage, current, and resistance are related by the formula, E=IR, there are alternative expressions for the power, as shown.

(Click for larger image.)

These simple expressions serve electrical engineers quite well in their usual tasks of circuit design, but power comes in many guises in the physical world. Power is measured in watts in homage to James Watt (1736-1819) of steam engine fame, but the general form of power is kg·m2/s3, which makes more sense when written (kg·m2/s2)/sec, since power is work done per unit of time, and work is in units kg·m2/s2. Power can be expressed in other forms, as detailed below.

P = U/t U = energy and t = time
P = F·v F = force and v = velocity
P = T·ω T = torque and ω = angular velocity

While the calculation of the electrical power dissipated in a DC circuit is easily realized through use of a voltmeter and an ammeter, the general problem of measuring power, itself, as with some sort of power meter, takes more effort. Interestingly, effort is defined as the amount of work involved in achieving something, and work is a component of power. Radiant power, such as the power captured from the Sun, is difficult to measure. Radiant power, often called the radiant flux, is the energy emitted, reflected, transmitted or received, per unit time.

If you're a physicist faced with such a measurement, the idea of a black body immediately comes to mind. A black body absorbs incident electromagnetic radiation at all wavelengths, and its temperature will rise according to the heat capacity of the material from which it's made. This means that a temperature measurement becomes a power measurement. The most common device used to measure radiant power is the bolometer, a device that captures incident electromagnetic radiation to heat a material, much like a black body, so that radiant power can be measured by measuring temperature.

The bolometer, the name of which derived from the Greek words, βολη (ray) and μετρον (meter), was invented by American astronomer, Samuel Pierpont Langley (1834-1906), in 1878, and it was published shortly thereafter.[1] Langley's bolometer consisted of two platinum resistance thermometers coated with soot so that they would act as black bodies. One of these resistors was exposed to a radiant source, while the other was shielded, and the resistance difference between these two was detected by a Wheatstone bridge to indicate the received power.

Wheatstone bridge circuit

Wheatstone bridge circuit.

This circuit is named after English scientist, Charles Wheatstone (1802-1875), who popularized an original 1833 concept by English polymath, Samuel Hunter Christie (1784-1865). Wheatstone was also the inventor of the Playfair symmetric key cipher

In this circuit, the resistor pairs, R1/R3 and R2/R4 act as voltage dividers. When R1=R2 and R3=R4, the voltage at the galvanometer G is zero.

Large voltages E and a sensitive galvanometer enable measurement of a very small change in any resistor. Sensitive measurement of radiant power is possible when R1 and R2 are the radiated and shielded resistors of a bolometer.

(Created using Inkscape. Click for larger image.)

The bolometer was an advance over thermopiles, series-connected arrays of thermocouples, that were used for the same purpose. Using his sensitive bolometer, Langley discovered new atomic and molecular absorption lines in the infrared, and he made a temperature measurement of the Moon. In 1896, Swedish physicist and chemist, Svante Arrhenius (1859-1927), used the lunar measurements of Langley and others to calculate the extent that carbon dioxide and water trap infrared radiation on Earth.

Langley invented the bolometer to detect visible and infrared light, but nearly coincident with his invention were the discovery of X-rays by Wilhelm Röntgen in 1895, and radioactivity by Henri Becquerel in 1896. A bolometer will also act as a detector for these radiations if they are absorbed in the resistive elements, since they will also cause heating. Since bolometers are slow to thermally equilibrate with the environment, they will effectively integratee such radiation for increased sensitivity.

Samuel Pierpont Langley (1834-1906)

Samuel Pierpont Langley (1834-1906), circa 1895.

In his paper describing the bolometer, Langley writes, "I have entered into these preliminary remarks as an explanation of the necessity for such an instrument as that which I have called the Bolometer (βολη μετρον)... Impelled by the pressure of this actual necessity, I therefore tried to invent something more sensitive than the thermopile, which should be at the same time equally accurate, - which should, I mean, be essentially a "meter" and not a mere indicator of the presence of feeble radiation."[1]

Langley was the first director of the Allegheny Observatory (Pittsburgh, Pennsylvania), where he established a time distribution system essential to government and the railroads.

Langley was also an aviation pioneer for whom Langley Field, Newport News, Virginia, was named.

(Wikimedia Commons image from the Smithsonian Institution Archives, Record Unit 95, Box 15, Folder 8, modified for artistic effect.)

While platinum was the best bolometer material during Langley's time, there are better materials available today. Vanadium pentoxide (V2O5) has a high temperature coefficient of resistance up to -3%/°C.[2] Also, sensitivity is enhanced when bolometers are cooled to cryogenic temperatures. Microbolometers, generally created as arrays of vanadium oxide devices, are used in infrared digital cameras. Bolometers are also used as microwave detectors with the resistive element of the proper impedance terminating a stripline waveguide.

Far above the Wi-Fi bands at 2.4 and 5 gigahertz (GHz) are the terahertz (THz) frequencies. A terahertz is a thousand times larger than a gigahertz; and, since semiconductor devices have difficulty operating even below 100 GHz, you can imagine the problems involved getting circuit elements to work at a terahertz. Frequencies around a terahertz exist in a so-called "terahertz gap" between those considered to be radio frequencies and light. Visible light exists in the 425-775 terahertz frequency band.

The terahertz spectrum has been relatively underutilized, since it's difficult to generate terahertz radiation and also difficult making detectors at those frequencies. Since terahertz radiation will penetrate thin material layers, it's useful for non-destructive sensing, and also for devices such as full-body scanners. An ideal detector of terahertz radiation would have high sensitivity, a rapid response time, and it would be operable at room temperature.

A team of scientists and engineers from the University of Tokyo (Tokyo, Japan), the Tokyo University of Agriculture and Technology (Tokyo, Japan), and Chung-Ang University (Seoul, Korea) has just advanced terahertz detector technology by developing a bolometer for terahertz radiation.[3-4] Their bolometer is a thermomechanical device that's applicable to terahertz imagers.[4]

Doubly-clamped MEMS resonator bolometer

Doubly-clamped MEMS resonator bolometer.

Heating of the resonant beam by terahertz radiation changes its resonant frequency, which is easily detected.

(University of Tokyo image, simplified)

The bolometer is a doubly-clamped microelectromechanical beam resonator that's made from gallium arsenide using standard MEMS processing techniques.[3] Heating by terahertz radiation expands the beam very slightly, and this changes its resonant frequency.[4] Says corresponding author of the paper describing this work, Kazuhiko Hirakawa,
"Using our doubly clamped microelectromechanical beam made of gallium arsenide, we could effectively sense THz radiation at room temperature... This structure is particularly effective as it can detect THz radiation very quickly, typically 100 times faster than other conventional room-temperature thermal THz sensors."[4]

The temperature sensitivity, expressed as a noise-equivalent temperature difference, is about 1 μK/√Hz.[3] The device is a hundred times faster than other uncooled terahertz thermal sensors in a bandwidth of several kilohertz, which is more than enough for imaging.[3] The detection level is a noise-equivalent power of about 90 pW/√Hz.[3]


  1. S. P. Langley, "The Bolometer and Radiant Energy". Proceedings of the American Academy of Arts and Sciences, vol. 16 (May, 1880 - June, 1881), pp. 342-358, DOI: 10.2307/25138616.
  2. Mohamed Abdel-Rahman, Muhammad Zia, and Mohammad Alduraibi, "Temperature-Dependent Resistive Properties of Vanadium Pentoxide/Vanadium Multi-Layer Thin Films for Microbolometer & Antenna-Coupled Microbolometer Applications," Sensors, vol. 19, Article no. 1320, March 16, 2019, doi:10.3390/s19061320 (Open Access PDF file).
  3. Ya Zhang, Suguru Hosono, Naomi Nagai, Sang-Hun Song, and Kazuhiko Hirakawa,, "Fast and sensitive bolometric terahertz detection at room temperature through thermomechanical transduction," Journal of Applied Physics, vol. 125, no. 15 (March 28, 2019), Article no. 151602, https://doi.org/10.1063/1.5045256.
  4. Balancing the beam: thermomechanical micromachine detects terahertz radiation, University of Tokyo Press Release, May 7, 2019.

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