How I can plot the magnitude and phase response oh the function (2024)

FAQs

How do you find the magnitude and phase response? ›

A geometric way to obtain approximate magnitude and phase frequency responses is using the effects of zeros and poles on the frequency response of an LTI system. G ( s ) | s = j Ω 0 = K j Ω 0 − z j Ω 0 − p = K Z → ( Ω 0 ) P → ( Ω 0 ) .

It is customary to plot the magnitude of the frequency response function on the log scale as |G(jω)|dB=20log10|G(jω)|. The magnitude of the loop gain is given in dB as: |KGH(jω)|dB=20logK+∑mi=120log|1+jωzi|−(20n0)logω−∑n1i=120log|1+jωpi|−∑n2i=120log|1−ω2ω2n,i+j2ζiωωn,i|.

The two major components frequency and amplitude of a periodic signal define the Magnitude Spectrum of that signal. The frequency components of the periodic signal are plotted in the horizontal axis and amplitude component of the periodic signal is plotted in the vertical axis.

The magnitude describes the strength of each frequency in the signal. The phase describes the sine/cosine phase of each frequency. The phase can also be thought of as the relative proportion of sines and cosines in the signal (i.e., a phase of zero contains only cosines and a phase of 90 degrees contains only sines).

the magnitude plot is a straight line with a slope of 20 d B per decade, passing through the abscissa axis at ω = 1 rad/s, and the phase plot is a constant equal to 90 ∘ (Fig. 5.9): Figure 5.9. Bode plots of the monomial term j ω . | j ω | d B = 20 log 10 ω , 1 j ω = − 90 ∘ .

Thus, the formula to determine the magnitude of a vector (in two-dimensional space) v = (x, y) is: |v| =√(x² + y²). This formula is derived from the Pythagorean theorem. the formula to determine the magnitude of a vector (in three-dimensional space) V = (x, y, z) is: |V| = √(x² + y² + z²)

For the magnitude plot, mark the starting point on the graph and draw a straight line with the starting slope until you reach the frequency of a pole or zero. At this point, zeros change the slope by 20 dB/dec and poles change the slope by −20 dB/dec.

Draw a pair of axes and label them with 'Frequency' on the vertical axis ( y y y-axis) and 'Measurement' on the horizontal axis ( x x x-axis). Use a ruler to draw each bar with the correct height. Draw the heights of the bars depending on its frequency.

Frequency response plots provide insight into linear systems dynamics, such as frequency-dependent gains, resonances, and phase shifts. Frequency response plots also contain information about controller requirements and achievable bandwidths.

The magnitude is the square root of the sum of the squares of the real and imaginary parts. The phase is relative to the start of the time record or relative to a single-cycle cosine wave starting at the beginning of the time record.

What is the phase plot of a signal? ›

As defined earlier, a phase plot shows the difference in phase between the measured heterodyned beat signal and the superimposed reference signal as a function of time.

If the components of the vector are given instead, one can determine the magnitude of the vector using the Pythagorean theorem, expressed as: c 2 = a 2 + b 2 or A 2 = A x 2 + A y 2 where c/A is the hypotenuse/resultant vector, and a/A x and b/A y are the components.

A geometric way to obtain approximate magnitude and phase frequency responses is using the effects of zeros and poles on the frequency response of an LTI system. G ( s ) | s = j Ω 0 = K j Ω 0 − z j Ω 0 − p = K Z → ( Ω 0 ) P → ( Ω 0 ) .

Alternatively, the signal y(t) may be described by the magnitudes D_n and the phase angles φ_n: where the magnitude and the phase angle can be calculated from the Fourier coefficients as follows: φ_n = tan^-1 (B_n/A_n). The following interactive example shows you how to combine sines and cosines to form a signal y(t).

For phase response measurement we need to measure both the phase at the input and output of the filter and calculate the difference. We can do this with the DSP options. At the cut-of frequency we get a phase shift around 90degree.

Impedance in circuits

This is less mathematical and requires an appreciation that a sinusoidal curve can be constructed by a rotating vector arrow (seen in SHM), and a knowledge of Pythagoras. Here Z0​ is the magnitude of Z so Z0​=X2+Y2 ​ and ϕ is the phase of Z which has the value ϕ=arctan(XY​).

The response that the output signal reaches as time passes long is called the steady-state response. Interestingly, H ( ω ) , which represents the magnitude and phase at the steady-state response, can be derived: (1.59) ∫ 0 ∞ h ( t ) e − i ω t d t = H ( ω ) .