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I have a question on a the units of a first order system's time constant.

If i have a first order system the basic transfer function will be:

K/(tau*s+1)

where K is the Gain, and tau is the system's time constant.

tau's units, according to what i've learned, are [sec].

but aren't the s plane's units in [rad/sec] (s=jw+sigma)?

That means that tau should be given in [sec/rad] to match the "1"-'s units in the transfer function.

I know that rad can be considered "unitless" but when dealing with actual numbers it matters if the system's time constant is 1 [sec] or 1[sec/rad]= 2*pi [sec].

My question is specifically about the units of tau in the transfer function,

not when it is used in the decay rate of e (e^(-t/tau)), there it has to be sec.

I'll appreciate a clarification.

Thanks

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# First Order System's Time Constant

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