Equivalent Circuit of the Bolometer Detector

A small-signal dynamic equivalent circuit is established for the output voltage of a dc-biased bolometer (barretter) detector. The circuit consists of a voltage generator /spl upsi//sub g/, whose output is an undistorted replica of the incident RF-power modulation envelope, followed by a series resistor R/sub 1/ of dynamic origin, a shunt capacitor C that represents heat storage in the bolometer wire, and a series resistor R/sub 0/ equal to the dc resistance, usually 200 ohms. The resistance R/sub 1/ is independent of signal level, and is typically about 220 ohms for an 8.75-mA bolometer and about 120 ohms for a 4.5-mA bolometer. At a modulation frequency f/sub m/ near 0 Hz, the equivalent audio source impedance of the bolometer is R/sub 1/ +R/sub 0/. The common belief that the source impedance is R/sub 0/ in the weak-signal case is, therefore, refuted. Formulas are derived giving v/sub g/ / /P/sub RF/ and R/sub 1/ as functions of basic, easily determined bolometer parameters. The time constant for open-circuit load is /spl tau//sub oc/= R/sub 1/C, where /spl tau//sub oc/ is determined best by measurement, since catalog values of /spl tau//sub oc/ often are seriously in error. The capacitance is C=/spl tau//sub oc/ / /R/sub 1/. With one type of bolometer /spl tau//sub oc/ measures about 110 /spl mu/s, while various catalogs state values of 250 to 350 /spl mu/s. The equivalent circuit is confirmed quantitatively by measurements of output voltage and source impedance versus modulation frequency.