Hi everyone, need some guidance regarding example on drawing Bode diagram.
Example:
For the system H(s) draw the Bode diagram and transfer function. Mark characteristic points on the drawings.
H(s)= (1000*s)/(1+10*s)
Now, I'm fairly familiar with this kind of examples, but I struggle with this one.
I'm not sure how to get to the point where the form is reduced enough so I can draw plot.

 

Given that s is a complex number, you form the the magnitude and phase, then you plot them.

 

Given that s is a complex number, you form the magnitude and phase, then you plot them.

Expounding upon Dave's response, here is a step-by-step procedure:

Step 1. Replace s by jw into the H(s) transfer function.

H(jw) = [1000jw/(1+10jw)]

Step 2. Mulitply H(jw) by a factor that will eliminate the imaginary number j from the denominator without changing the magnitude of the transfer function. The appropriate factor is the complex conjugate of the denominator divided by itself.

H(jw) = [(1000jw/(1+10jw)]*[(1-10jw)/(1-10jw)] = (10000w^2+1000jw)/(1+100w^2)

Step 3. Find the equation for the magnitude by multiplying the result of step 2 by its complex conjugate and then taking the square root.

sqrt([(10000w^2+1000jw)/(1+100w^2)]*[(10000w^2-1000jw)/(1+100w^2)]) = (10000w^2+ 1000w)/(1+100w^2)

Step 4. Substitute various values for w into the result of Step 3 and plot the results to yield the magnitude plot. See attached file for plot.

Step 5 Take the real and imaginary parts of the result of Step 2 and calculate the phase using the following formula:

Phase = atan2(y,x) where y is the imaginary part and x is the real part.

x = 10000w^2/(1+100w^2)

y = 1000w/(1+100w^2)

Substitute various values for w into the phase equation. Plot the results. See attached file for plot. Note that at w=0 both the real and imaginary parts of the transfer function are zero. Therefore, the phase at w=0 is undefined.