# Homework Help: Can anyone solve this Nyquist plot problem?

1. Oct 10, 2012

### rudra

1. Problem is given in the following link:
http://s11.postimage.org/mrns0fu37/Problem.jpg

2. Relevant equations

In my opinion open loop transfer function is given stable. So poles on RHS for open loop t.f. will be 0. But nyquist plot rotates (0,0) point by -360 . So thare will be one RHS open loop zero.

Correct me if I am wrong.

Last edited by a moderator: Oct 10, 2012
2. Oct 11, 2012

### Staff: Mentor

Hi rudra, http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

It does look stable, and has no poles—is that what you are saying?

I have forgotten a lot about Nyquist plots but if there were a zero in the open loop transfer function, then surely the plot would go though (0,0)?

Last edited by a moderator: May 6, 2017
3. Oct 11, 2012

### rudra

In my opinion open loop t.f. should have a R.H.S. zero. But I think that's the wrong answer. Because when I searched the answer keys for the problem. Every website or book gives option (c) i.e. G(s) is the impedance of passive network. But none of the book or websites explain the answer neither can I.

4. Oct 12, 2012

### Staff: Mentor

Last edited: Oct 12, 2012
5. Oct 12, 2012

### uart

No it can't be the impedance of a passive network, because it has a negative real component for some values of frequency. A passive network can't have a negative resistance, so I think that your answer (b) is correct. Even by process of elimination, I think the only answer that is possible is "b".

Process of elimination.
(a) Allpass filter has constant gain, therefore constant radius (from origin) of Nyquist plot. So cannot be this.
(c) Cannot be impedance of passive network because it has a negative resistance at some frequencies.
(d) Cannot be marginally stable, as a pole on the $jw$ axis would result in asymptotes (to infinity) at some points on the Nyquist plot.

Last edited: Oct 12, 2012
6. Oct 12, 2012

### Staff: Mentor

It depends on what you expect from an allpass network. I contend that it is an allpass network—across the entire spectrum it has a uniform gain of unity, with a ripple ±6 dB.

7. Oct 12, 2012

### rudra

At last someone gave some answer. Thank you uart for the help.