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 υ_g, whose output is an undistorted replica of the incident RF-power modulation envelope, followed by a series resistor R₁ of dynamic origin, a shunt capacitor C that represents heat storage in the bolometer wire, and a series resistor R₀ equal to the dc resistance, usually 200 ohms. The resistance R₁ 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_m near 0 Hz, the equivalent audio source impedance of the bolometer is R₁ +R₀. The common belief that the source impedance is R₀ in the weak-signal case is, therefore, refuted. Formulas are derived giving v_g / /P_RF and R₁ as functions of basic, easily determined bolometer parameters. The time constant for open-circuit load is τ_oc= R₁C, where τ_oc is determined best by measurement, since catalog values of τ_oc often are seriously in error. The capacitance is C=τ_oc / /R₁. With one type of bolometer τ_oc measures about 110 μs, while various catalogs state values of 250 to 350 μs. The equivalent circuit is confirmed quantitatively by measurements of output voltage and source impedance versus modulation frequency.