# Significance of a zero of a transfer function on the positive real axis?

1. ## Significance of a zero of a transfer function on the positive real axis?

Consider the following transfer function (voltage out divided by voltage in) of a circuit:

(s-1)/(2s+1)

The question was posed in our engineering class, at what frequency does the gain equal zero? Zero here means for an input signal of a given frequency there is no signal at the output, ie. we are not talking about 0 dB.

I am of the opinion that there is no frequency for which the gain equals zero. The transfer function has a zero at s = 1, but that is not the same as saying the gain = 0 at that frequency.

What do you all think? Is my reasoning correct? And furthermore, what is the significance of a zero on the positive real axis here?

Thanks!!!

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2. ## Re: Significance of a zero of a transfer function on the positive real axis?

in this case, the significance is in making this a non-minimum phase system. Eg, the frequency magnitude response of (s+1)/(2s+1) is the same as (s-1)/(2s+1). But the phase shifts are different. the first case has a minimum phase shift, while the second case does not. This becomes very important for control systems.

There will be no real frequency with a gain of 0. the fourier transform is simply the imaginary axis of the laplace transform. (or the unit-circle of the z-transform for discrete samples). If you don't have any zeros on the axis due to the numerator, then you only need to check for zeros at inf. in this case, there are no zeros at inf, as the limit approaches 1/2.

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