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* Draw a smooth curve through those points using the straight lines as asymptotes (lines which the curve approaches).
Note that this correction method does not incorporate how to handle complex values of <math>x_n</math> or <math>y_n</math>. In the case of an [[irreducible polynomial]], the best way to correct the plot is to actually calculate the magnitude of the transfer function at the pole or zero corresponding to the irreducible polynomial, and put that dot over or under the line at that pole or zero.
=== Straight-line phase plot ===
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==Example==
To create a straight-line plot for a first-order (one-pole) low-pass filter, one considers the normalized form of the transfer function in terms of the [[angular frequency]]:
:<math>H_{\text{lp}}(\mathrm{j} \omega) = \frac{1}{1 + \mathrm{j} \frac{\omega}{\omega_\text{c}}}.</math>
The Bode plot is shown in Figure 1(b) above, and construction of the straight-line approximation is discussed next.
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where ''A''<sub>FB</sub> is the gain of the amplifier with feedback (the ''closed-loop gain''), ''β'' is the ''feedback factor'', and ''A''<sub>OL</sub> is the gain without feedback (the ''open-loop gain''). The gain ''A''<sub>OL</sub> is a complex function of frequency, with both magnitude and phase.<ref group="note">Ordinarily, as frequency increases, the magnitude of the gain drops, and the phase becomes more negative, although these are only trends and may be reversed in particular frequency ranges. Unusual gain behavior can render the concepts of gain and phase margin inapplicable. Then other methods such as the [[Nyquist plot]] have to be used to assess stability.</ref> Examination of this relation shows the possibility of infinite gain (interpreted as instability) if the product β''A''<sub>OL</sub> = −1 (that is, the magnitude of β''A''<sub>OL</sub> is unity and its phase is −180°, the so-called [[Barkhausen stability criterion]]). Bode plots are used to determine just how close an amplifier comes to satisfying this condition.
Key to this determination are two frequencies. The first, labeled here as ''f''<sub>180</sub>, is the frequency where the [[open-loop gain]] flips sign. The second, labeled here ''f''<sub>0 dB</sub>, is the frequency where the magnitude of the product |β''A''<sub>OL</sub>| = 1 = 0 dB. That is, frequency ''f''<sub>180</sub> is determined by the condition
:<math>\beta A_\text{OL}(f_{180}) = -|\beta A_\text{OL}(f_{180})| = -|\beta A_\text{OL}|_{180},</math>
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