Using this circuit and matlab info answer the following questions... For questio

Question

Using this circuit and matlab info answer the following questions...

For question 1...

impulse(G)

step(G)

pzmap(G)

bode(G)

1. Why does the unit step response of the circuit given in the first part of this settle out at 1 and not at 0? Justify and briefly explain your answer based on the transfer function derived in the first circuit. (Hint: it has to do with the DC gain of the circuit and in circuit terms with the impedance of capacitor and inductor at DC.) What kind of a filter does this circuit represent (bandpass, bandstop, low pass, high pass)?

2. Why does the unit step response of the 2nd circuit given go to zero rather than unity? Briefly explain and justify your answer.

3. What kind of filter (bandpass, bandstop, low pass, high pass) does the 2nd circuit shown represent? Briefly justify your answer.

4. Why does swapping the arms of the filter change the type of filter that is realized?

5. What is the numerical value of impedance of an ideal inductor at DC and as frequency approaches infinity?

6. What is the numerical value of impedance of an ideal capacitor at DC and as frequency approaches infinity?

7. Why does the pole zero map shown above have only two zeroes, while the transfer function has four zeroes? (Hint: use the roots command of MATLAB to find out.)

Explanation / Answer

1. The question implies why is there an offset i.e. mathematically equal to (steady state response) minus (response without any input). For offset find steady state response for s = 0 and initial response for s tending to infinity.

One can check for type of filter using transfer fns by putting s tending to zero it will check for DC values with low frquency if fn is zero its not low pass and for high frequency or infinite s if fn is zero then its not Highpass.

Other approximate way to check high and lowpass filter using circuit is given below:-

At very high frequency capacitor will act as short circuit and inductor as infinite impedance so Vout = Vin.

At low frequency vice versa happens circuit does not form loop.

So it seems more like a high pass.

PS:- for band pass circuit does not work for both low and high frequencies while in case of band stop it works for both low and high frequencies. In All pass circuit works in all condition

2. in second circuit voltage accross part 1 of circuit is output this output is zero as we increase frequency to very high value say infinite as capacitor gets short circuited to ground, so response bacomes zero.

3.Bandpass (as does not work for both very low or very high frequecies but will work at some middle frequencies).

4. swapping the parts of circuit changed the transfer fn and the type of differently behaving set of elements across which we voltage was measured LCR series LR parallel with C.

5. Infinite

6. Zero

7. other two zeroes are at two ends of real axis in zero map.

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