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The observed large variation in the abundance of deuterium (D) in the interstellar medium (ISM) suggests that a significant fraction of D may be depleted into polycyclic aromatic hydrocarbons (PAHs). Signatures of deuteration of PAHs are expected to appear most clearly through C-D stretching modes at 4.4--4.7 micron, whose strengths in emission spectra relative to those of C-H stretching modes at 3.3--3.5 micron provide the relative abundance of D to hydrogen (H) in PAHs once we have accurate relative band strengths of both stretching modes. We report experimental results of the band strength of C-D stretching modes relative to C-H. We employ a laboratory analogue of interstellar carbonaceous dust, Quenched Carbonaceous Composite (QCC), and synthesize deuterated QCC (D-QCC) by replacing the starting gas of CH$_4$ of QCC by mixtures of CH$_4$ and CD$_4$ with various ratios. Infrared spectra of D-QCC are taken to estimate the relative band strengths of the stretching modes, while the D/H ratios in the D-QCC samples are measured with a nano-scale secondary ion mass spectrometer (NanoSIMS). We obtain that the relative strength of aromatic and aliphatic C-D to C-H stretches is 0.56 +/- 0.04 and 0.38 +/- 0.01 per D/H, respectively. The ratio for the aromatic stretches is in good agreement with the results of theoretical calculations, while that of aliphatic stretches is smaller than that of aromatic. The present results do not significantly change the D/H ratios in the interstellar PAHs previously estimated from observed spectra.