What is the magnitude of this transfer function?
The magnitude of the transfer function is proportional to the product of the geometric distances on the s-plane from each zero to the point s divided by the product of the distances from each pole to the point.
How do you find the magnitude of a Bode plot?
The magnitude plot is having magnitude of 0 dB upto ω=1τ rad/sec. From ω=1τ rad/sec, it is having a slope of 20 dB/dec. In this case, the phase plot is having phase angle of 0 degrees up to ω=1τ rad/sec and from here, it is having phase angle of 900. This Bode plot is called the asymptotic Bode plot.
Why is the impulse response derivative of the step response?
Because the step response has a discontinuity in it (i.e., a step), and the impulse response is simply the derivative of the step response, this causes an impulse function as part of the impulse response.
How to plot magnitude and phase response by hand?
For a rough sketch, you can eyeball or measure the distance of the poles and zeros to a point on the unit circle, multiply/divide to get a magnitude, and sum/difference the angles from the poles and zeros to that point to get a phase. A protractor and ruler might be useful.
How is the output response related to the frequency response?
The frequency response H(jw) is a function that relates the output response to a sinusoidal input at frequency w. They are therefore, not surprisingly, related. In fact the frequency response of a system is simply its transfer function as evaluated by substituting s = jw.
How to calculate the impulse response of a system?
Calculating the impulse response of a system. The calculation of the impulse response of a system will proceed in two steps. First we find the unit step response (as described elsewhere), we then differentiate it. The only non-obvious step is that we must represent the unit step response in a functional form. Some examples will clarify.