= Constant-temperature hot-wire anemometer
A <constant-temperature hot-wire anemometer> is a <hot-wire anemometer> whose electrical feedback adjusts wire heating to keep a chosen wire resistance approximately constant. The resistance acts as a <temperature> indicator; increasing flow cooling calls for increased electrical <power>. The primary manufacturer's arrangement places the wire in a <Wheatstone bridge> controlled by a servo amplifier.<Measurement Principles of CTA by Dantec Dynamics>[CTA principles]{ref}
A simple resistance-temperature calibration illustrates the setpoint. If the cold resistance at fluid <temperature> $T_a$ is $R_a$, approximate
$$
R_w=R_a[1+\alpha_R(T_w-T_a)],\qquad
T_w-T_a=\frac{R_w/R_a-1}{\alpha_R}.
$$
For stipulated $R_a=5\,\Omega$, $R_w=7.5\,\Omega$ and $\alpha_R=0.004\,\mathrm{K^{-1}}$, the overtemperature is $125\,\mathrm K$. At ambient $20\,{}^{\circ}\mathrm C$, that corresponds to wire <temperature> $145\,{}^{\circ}\mathrm C$ in this linear model. These parameters are illustrative, not universal tungsten specifications. A fixed resistance setpoint and a fixed overtemperature require different adjustments when ambient <temperature> changes.
At steady state, the heating balances convective, support-conduction and radiative losses. The observed bridge output must be calibrated against known flow with the same probe, fluid and operating conditions. A bridge output squared may follow an empirical relation $E^2=A+BU^n$ over a limited range, but circuit ratios and losses matter before identifying that output with wire <power>. The manufacturer's technical account separately treats <velocity>, directional and <temperature> calibration.<Measurement Principles of CTA by Dantec Dynamics>[Velocity sensitivity, Directional sensitivity and Temperature sensitivity]{ref}
<Finite-bandwidth thermal feedback in hot-wire anemometry> can be explored with an original local model. Let a <temperature> perturbation satisfy
$$
C_w\,\delta\dot T=\delta P-K\delta T-F\delta U,
$$
where $C_w>0$ is wire <heat capacity>, $K>0$ a linearized thermal-loss coefficient and $F>0$ the incremental cooling per <speed> change. An ideal proportional <power> controller applies $\delta P=-K_c\delta T$, with $K_c>0$. Hence
$$
\boxed{\frac{\delta P(s)}{\delta U(s)}=\frac{K_cF}{C_ws+K+K_c},\qquad
\tau_{\rm closed}=\frac{C_w}{K+K_c}.}
$$
A cooling perturbation first lowers <temperature>, causing the controller to raise <power>. Finite feedback gain leaves a residual <temperature> perturbation and gives DC <power> sensitivity $FK_c/(K+K_c)$.
For $C_w=10^{-8}\,\mathrm{J/K}$, $K=10^{-4}\,\mathrm{W/K}$ and $K_c=9\times10^{-4}\,\mathrm{W/K}$, the model's thermal time constant changes from $100$ to $10\,\mathrm{\mu s}$ and its half-power <frequency> from about $1.59$ to $15.9\,\mathrm{kHz}$. The closed-loop DC response is $0.9F$. This calculation assumes an instantaneous controller; real amplifier and cable dynamics can add phase lag and limit usable gain.
A proposed characterization calibrates the steady <speed> response, then applies a small electrical test perturbation and examines settling and ringing while measuring ambient <temperature>. Check the response over the intended flow range and verify that the measuring electronics do not clip. The primary practical guide describes the feedback bridge as part of the complete measuring chain.<How to measure turbulence with hot-wire anemometers - a practical guide by Finn E. Jørgensen>[§15.5, printed p. 51]{ref} A fast electrical response alone does not establish spatial resolution or uniquely determine the direction of a reversing flow.
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