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Combined frequency-resolved techniques are suitable to study electrochromic(EC) materials. We present an experimental setup for simultaneouselectrochemical and color impedance studies of EC systems in transmission modeand estimate its frequency-dependent uncertainty by measuring the backgroundnoise. We define the frequency-dependent variables that are relevant to thecombined measurement scheme, and a special emphasis is given to the complexoptical capacitance and the complex differential coloration efficiency, whichprovide the relation between the electrical and optical responses. Results of atest measurement on amorphous $\mathrm{WO}_3$ with LED light sources of peakwavelengths of $470$, $530$, and $810~\mathrm{nm}$ are shown and discussed. Inthis case, the amplitude of the complex differential coloration efficiencypresented a monotonous increase down to about $0.3~\mathrm{Hz}$ and was closeto a constant value for lower frequencies. We study the effect of theexcitation voltage amplitude on the linearity of the electrical and opticalresponses for the case of amorphous $\mathrm{WO}_3$ at$2.6~\mathrm{V}~\mathrm{vs.}~\mathrm{Li/Li}^+$, where a trade-off should bemade between the signal-to-noise ratio (SNR) of the optical signal and thelinearity of the system. For the studied case, it was possible to increase theupper accessible frequency of the combined techniques (defined in this work asthe upper threshold of the frequency region for which the SNR of the opticalsignal is greater than $5$) from $11.2~\mathrm{Hz}$ to $125.9~\mathrm{Hz}$while remaining in the linear regime with a tolerance of less than $5\%$.

Setup for simultaneous electrochemical and color impedance measurements of electrochromic films: theory, assessment, and test measurement