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TANGEDCO AE EE 2015 Official Paper

Option 1 : Introduces phase angle of \(\frac{{ - \omega {\tau _d} \times 180^\circ }}{\pi }\) in phase plot

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

Bode plot:

- A Bode plot is a graph of the magnitude (in dB) or phase of the transfer function versus frequency.
- It can be used for both continuous-time and a discrete-time system but not directly a function of gain.

Consider a transfer function G(s) without any dead time.

Magnitude = |G(jω)|

Phase angle = ∠G(jω)

Now, consider a transfer function with dead time.

\(TF = G\left( s \right){e^{ - \omega {\tau _d}}}\)

Magnitude: |G(jω)|

Phase angle \( = \angle G\left( {j\omega } \right) - \frac{{\omega {\tau _d} \times 180^\circ }}{\pi }\)

The magnitude is the same in both cases but the phase angle is delayed by \(\frac{{ - \omega {\tau _d} \times 180^\circ }}{\pi }\)

Therefore, **the magnitude plot is not affected but introduces a phase angle of** \(\frac{{ - \omega {\tau _d} \times 180^\circ }}{\pi }\) in **the phase plot.**