How do I calculate the 3 dB frequency from an oscilloscope reading using a logarithmic sweep? I made the mistake to use logarithmic instead of a linear sweep and now my data doesn't hold for the formula $$f(t)=f_{\text{start}}+(f_{\text{sweep}}/T_{\text{sweep}})⋅t$$ where \$f_{\text{start}}\$ is the starting frequency and \$f_{\text{sweep}}\$ is the starting frequency subtracted from the ending frequency.
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Well, the lineair sweep can be calculated from the logarithmic sweep using:
$$\left|\underline{\mathscr{H}}\left(\text{j}\omega\right)\right|_{\space\text{dB}}=20\log_{10}\left(\left|\underline{\mathscr{H}}\left(\text{j}\omega\right)\right|\right)\tag1$$
Taking the inverse gives:
$$\left|\underline{\mathscr{H}}\left(\text{j}\omega\right)\right|=10^{\frac{\left|\underline{\mathscr{H}}\left(\text{j}\omega\right)\right|_{\space\text{dB}}}{20}}\tag2$$
Jan Eerland
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