Question

The octave frequency range is specified by
1. \(\frac{{{\omega _2}}}{{{\omega _1}}} = 2\)
2. \(\frac{{{\omega _2}}}{{{\omega _1}}} = 8\)
3. \(\frac{{{\omega _2}}}{{{\omega _1}}} = 10\)
4. \(\frac{{{\omega _2}}}{{{\omega _1}}} = 5\)

Answer 1

Correct Answer - Option 1 : \(\frac{{{\omega _2}}}{{{\omega _1}}} = 2\)

An octave is a logarithmic unit for ratios between frequencies, with one octave corresponding to a doubling of frequency i.e. the upper band frequency is twice the lower band frequency.

\(\frac{{{\omega _2}}}{{{\omega _1}}} = 2\)

The frequency range of the decade is, \(\frac{{{\omega _2}}}{{{\omega _1}}} = 10\)

Important Points:

In Bode plot,

• The initial slope for each pole at origin is -20 dB/decade or -6 dB/octave.
• The initial slope for each zero at origin is +20 dB/decade or +6 dB/octave.
• The initial slope is zero if there are no poles or zeros at the origin.