Frequency Domain Analysis lcs imp topic

Contents

• Closed loop frequency response, bode plots, stability and IQ op transfer function. 
• Frequency response specification relative stability, relation between time and frequency response for second order systems. A and N-circles, Log. 
• Magnitude versus phases angle plot. 
• Plot Nyquist criterion.

POINTS TO REMEMBER

• The magnitude and phase relationship between sinusoidal input and steady state output of a system is known as frequency response.
• The polar plot of a sinusoidal transfer function G (jw) is plot of the magnitude of G (jw) versus the phase angle of G (jw) on polar coordinates as ‘co’ varied from zero to infinity.
• The phase margin is that amount, of additional phase lag at the gain crossover frequency required to bring the system to the verge of instability. 
• The gain margin is the reciprocal of the magnitude l G(jw) l at the frequency at which the phase angle as _1800.
• The inverse polar plot at G (jw) is a graph of 1/G (jw) as a function of w.
• Bode plot is a graphical representation of the transfer function for determining the stability of control system.
• Bode plot is a combination of two plot - magnitude plot and phase plot.
• The transfer function having no poles and zeros in the right -half s-plane are called minimum phase transfer function. 
• System with minimum phase transfer function are called minimum phase systems. 
• The transfer function having poles and zeros in the right half s-plane are called non- minimum phase transfer functions systems with non-minimum phase transfer function. are called non-minimum phase system.
• In bode plot the relative stability of the system is determined from the gain margin and phase margin. .
• If gain cross frequency is less than phase cross over frequency then gain margin and phase margin both are positive and system is stable.
• If gain cross over frequency is greater than the phase crossover frequency than both gain margin and’phase margin are negative.
• It gain cross over frequency is equal to me phase cross over trequency me gain marg and phase margin are zero and system is marginally stable.
• The maximum value of magnitude is known as resonant peak.
• The magnitude of resonant peak gives the information about the relative stability of the system.
• The frequency at which magnitude has maximum value is known as resonant frequency.
• Bandwidth is defined a the range of frequencies in which the magnitude of closed loop does not drop —3 db. 

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