# marginally stable system

Thread Starter

#### sch_987

Joined Oct 27, 2011
2
Hello Friends,

My homework is that I have to create marginally stable system with the help of Op-amp.

Can some tell me the circuit of it?
how to find Transfer function of it.
how to find I/p and o/p of the system.
how to plot the poles and zeros of the system.

All friends are welcome express their knowledge.

Thanks,
Schneider...

#### steveb

Joined Jul 3, 2008
2,436
marginally stable systems are systems that have poles on the jw axis. That is, some of the poles have a real part of zero, and there are no zeros in the right half of the complex frequency plane. The simplest example is an integrator which can be made from an opamp circuit.

• sch_987
Thread Starter

#### sch_987

Joined Oct 27, 2011
2
marginally stable systems are systems that have poles on the jw axis. That is, some of the poles have a real part of zero, and there are no zeros in the right half of the complex frequency plane. The simplest example is an integrator which can be made from an opamp circuit.
Thanks for your help..

But can you help me more ,,,,,

What will be the transfer function of that integrator circuit and how to calculate poles and zeros?
i/p and o/p of the system.
what will be the compensation circuit to make it stable or unstable?

#### bountyhunter

Joined Sep 7, 2009
2,512
Actually, in reference to op amps or other closed loop gain blocks using negative feedback for stability:

The "phase shift" of the signal around the feedback loop determines if it is stable, unstable, or marginally stable.

If negative feedback is used, it starts at -180 which means it is 180 degrees out of phase with the source signal. As phase shift occurs, the phase margin decreases. Phase margin is defined as how many degrees phase you are away from a total shift of 180 degrees around the freedback loop which equates to postive feedback which is UNSTABLE.

In most amplifiers: a phase margin of about 45 degrees is ideal and very stable. A phase margin of 0 degrees is unstable. Values considered marginal are in between, usually any phase margin less than 10 degres is dangerously marginal.

If you actually build an amplifier loop and set it up with 5 - 10 degrees of phase margin, you will see a lot of ringing on the output voltage when the load suddenly changes.

Stability, phase margin, and it's effects are covered in articles I had published:

http://www.national.com/an/AN/AN-1148.pdf

http://www.national.com/an/AN/AN-1733.pdf

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