Obtain the time constant from a transfer function

[rusty009]

Hey, say I have a transfer function,

G(s) = s/(6.25+s)

How would I calculate the time constant for this transfer function? Also, if I wanted to sketch a bode plot for this transfer function, would I split it up into s* 1/(6.25+s) ?

Thanks in advance.

 

[berkeman]

Hey, say I have a transfer function,

G(s) = s/(6.25+s)

How would I calculate the time constant for this transfer function? Also, if I wanted to sketch a bode plot for this transfer function, would I split it up into s* 1/(6.25+s) ?

Thanks in advance.

Is this for school?

 

[oswaler]

To calculate the time constant for this transfer function, you would need to first rewrite it in the form of a first-order system. This can be done by factoring out the constant term, in this case 6.25, from the denominator:

G(s) = s/(6.25+s) = s/(6.25(1+s/6.25))

Now, we can see that the time constant is equal to the reciprocal of the coefficient of the s term in the denominator, which in this case is 6.25. So the time constant for this transfer function is 1/6.25 = 0.16 seconds.

For sketching a bode plot, you would need to break up the transfer function into its individual components. In this case, it would be s and 1/(6.25+s). The s term represents the gain, while the 1/(6.25+s) term represents the pole. You would plot the gain on the magnitude plot and the pole on the phase plot. The bode plot for this transfer function would have a straight line with a slope of +20dB/decade for the magnitude and a phase shift of -90 degrees for the phase.