- • plot the frequency response (amplitude and phase) using freqz • check zero and pole positions using zplane • determine zeros and poles using roots, or using [z,p,k]=tf2zp(b,a) • plot the impulse response using impz Exercise 13. Given the difference equation
- different magnitude and phase. The frequency response is defined as the magnitude and phase differences between the input and output sinusoids. Let us see how we can use the open-loop frequency response of a system to predict its behavior in closed -loop. To plot the frequency response, we create a vector of frequencies (varying between zero or ...
- Frequency response plots of linear systems are often displayed in the form of logarithmic plots, called Bode plots after the mathematician Hendrik W. Bode, where the horizontal axis represents frequency on a logarithmic scale (base 10) and the vertical axis represents either the amplitude or phase of the frequency response function.
- The pole-zero plot gives us a convenient way of visualizing the relationship between the Frequency domain and Z-domain. The frequency response H (e jw) is obtained from the transfer function H (z), by evaluating the transfer function at specific values of z = e jw.
- shows the frequency response of the Type−II compensation network. A zero−pole pair has been introduced to give a region of frequency where the gain is flat and no phase shift is introduced. The region with constant gain occurs between the break frequencies f1 and f2. This region must be used for loop gain crossover. The gain and break frequencies are
- For every pole or zero at zero frequency, the plot starts with the effect of that pole/zero on the slope. Zeros and poles at zero frequency are represented as : H (s)= As H (s)= A\frac {1} {s} which means that at frequency 1 rad/s, the magnitude must be equal to the DC magnitude A.

Scaling the time-domain response corresponds to frequency scaling its Laplace Transform. Therefore, as depicted in Fig. 2(b), time scaling by 1/P1 results in a translation of the system poles in the frequency domain so that the lowest frequency pole lies at s=-1 and the higher frequency pole is located at -ρ where: 1 2 P P ρ= (2) Note that in all cases, for frequencies << the pole frequency ‘b’, the response function assumes a constant value (i.e., the mid-band response). For TH(s), which is a first-order function, the frequency b becomes the -3db frequency for high frequency response, or the upper cut-off frequency. When there are several poles and zeros in the high

•The frequency response refers to the magnitude of the transfer function. •Bode’s approximation simplifies the plotting of the frequency response if pole and zero locations are known. •In general, we can associate a pole with each node in the signal path. •Bipolar and MOS devices possess various capacitances due to their physical ... • plot the frequency response (amplitude and phase) using freqz • check zero and pole positions using zplane • determine zeros and poles using roots, or using [z,p,k]=tf2zp(b,a) • plot the impulse response using impz Exercise 13. Given the difference equation

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