Dummy question regarding closed loop and open loop bandwidth

[CAMALEAO]

Hi everyone.

I have tried myself to understand these two concepts but it is turning out to be very confusing.

I have read several stuff, but still don't get.
Also adding to this we have the 3dB point, which some people call it bandwidth. Geez!

Can you share the way you interpret these two concepts?

 

[KlausST]

Hi,

I assume you are talking about amplifiers.

Bandwidth.
The bandwidth is defined as a frequency range with (I call it) "useful" gain.

Now what is "useful"?
It is defined with the -3dB limit.

Now you may ask: Why -3dB?

There are several explanations:
* graphical: take chart of a first order low pass filter. There is a horizontal line....becoming a line with constant fall rate.
Extend both lines and find the cross point. It is the -3dB frequency.
* power: the -3dB point is where the power is half. Now imagine a loudspeaker crossover. Ther is a low pass and a high pass filter.
At crossover frequency the high pass filterd signal delivers 50% of power and the low pass filtered signal delivers 50% of power..adding to exactely 100% of power.

Now look at an open loop diagram of an amplifier. Maybe it has 110dB at DC...take -3dB and get 107dB as the limit.
Maybe it is at 20Hz. This is the bandwidth limit.

Now let's say you have a feedbacked amplifier with gain of 30.
Now subtract 3dB and get 27dB...
Find the frequency where the gain is 27dB...maybe it is at 200.000Hz.

Is this what you wanted to know?

Klaus

 

[CAMALEAO]

Thank you, Klauss. It sounds good to me and that's my view also.

But, some of the conversations that I have had with other people and some other comments I read around the web, made me realise that people might not know what they are talking about. Or they are mixing up concepts. But maybe that I could be wrong.

Now let me ask you this.

I think that you came across with this: Suppose in a multi-loop circuit, you might have heard people saying that the inner loop has to be faster than the outer loop, etc. Or in other words they might say that the inner loop has to have higher bandwidth.

Based on this I ask a person, what was in this the bandwidth that he was referring to, and he saying the UGB.

Can you comment on this example? The inner loop has to be faster, meaning has to have the higher bandwidth? What's your view?

Regards

 

[KlausST]

Hi,

I agree that you will find a lot of incorrect informations in the internet. --> Try to find reliable informations. Universities, application notes ...

I agree that - to ensure stability - the inner loop needs a higher bandwidth than the outer loop.
Mainly stability depends on phase shift (and gain). Expect a 45° phase shift at the -3dB limit.

About "UGB": Please post a schematic we can discuss about.

My recommendation: If possible - avoid multi-loops.

Klaus

 

[CAMALEAO]

Hi Klauss, I see your point.

Regarding your comment:

"Mainly stability depends on phase shift (and gain). Expect a 45° phase shift at the -3dB limit."

I didn't understand, what you mean? Shouldn't be 45deg at 0dB?

Basically, what I meant about the UGB was that someone told me that to check the stability of the multiloop, the inner loop has to be stable and it's bandwidth should be higher and to check that you should look at the UGB frequency, that is, where the gain crosses the 0dB point. So basically he was implying that the UGB is the indicator of the bandwidth.

 

[KlausST]

Hi,

Shouldn't be 45deg at 0dB?

Why?

UGB: At the frequency where the gain is 0dB (= UGB) you have to look at the phase shift to check about stability.
180° and more is not stable. Up to ...120° is considered as stable. The difference to 180° is called the "phase margin".
Thus you should look for a phase margin >60°.

Klaus

 

[CataM]

Basically, what I meant about the UGB was that someone told me that to check the stability of the multiloop, the inner loop has to be stable and it's bandwidth should be higher and to check that you should look at the UGB frequency, that is, where the gain crosses the 0dB point. So basically he was implying that the UGB is the indicator of the bandwidth.

We check the closed loop stability by looking at the loop gain's phase and gain margins, in other words, if the loop gain has any positive phase margin (even by 1º) and gain margin > 1, the closed loop is stable.

Phase margin impacts the damping of the system and the crossover frequency impacts the fastness of the system (closed loop, obviously).

 

[CAMALEAO]

Thanks for you reply.

The crossover frequency impacts the fastness? What about the 3d point? What do you make of it? Shouldn't this be defining the fastness? Isn't fastness of the circuit characterised by the 3db point? Because in closed loop you have also the 3db point.

Can you elaborate more please?

 

[FvM]

The crossover frequency impacts the fastness? What about the 3d point?

I feel that some terms are used too vaguely in this thread.

Phase and gain margin and crossover frequency are parameters of the loop gain of a feedback system. It's only identical with the open loop gain of an amplifier for a feedback factor of -1, on in other words a closed loop gain of +1. Unfortunately feedback factor wasn't mentioned explicitly in this thread, it's only implied in post #2.

"3 dB point" can be read as synonym for the closed loop bandwidth of a feedback system with intentionally flat gain characteristic respectively frequency independent feedback factor, e.g. said -1. It's related to the loop unity gain bandwidth (or cross over frequency), but not the same. For a system with sufficient phase margin, both frequencies are close together. The smaller the phase margin, the higher the gain peaking at the crossover frequency, resulting in an increase of closed loop bandwidth.

We check the closed loop stability by looking at the loop gain's phase and gain margins, in other words, if the loop gain has any positive phase margin (even by 1º) and gain margin > 1, the closed loop is stable.

Phase margin impacts the damping of the system and the crossover frequency impacts the fastness of the system (closed loop, obviously).

The loop gain can have multiple crossover frequencies, in this case the simplified (Barkhausen) stability criterion isn't applicable. You have to evaluate the full Nyquist stability criterion.

Suggestion, review previous Edaboard threads about feedback system calculation, particularly contributions of senior expert LvW.

 

[CataM]

The loop gain can have multiple crossover frequencies, in this case the simplified (Barkhausen) stability criterion isn't applicable. You have to evaluate the full Nyquist stability criterion.

The full Nyquist stability criterion must be applied for nonminimum phase systems in order to determine the stability. I am not saying Nyquist can't be applied to any system, it can be, because is the general approach. However, the Bode diagram approach (Barkhausen criterion) can be applied for more than one crossover frequency systems, by checking the phase margin at the highest crossover.

See page 466 and 467 (bottom) of Ogata: **broken link removed**

It is also important to point out that conditionally stable systems will have two or
more phase crossover frequencies, and some higher-order systems with complicated
numerator dynamics may also have two or more gain crossover frequencies, as shown
in Figure 7–68. For stable systems having two or more gain crossover frequencies, the
phase margin is measured at the highest gain crossover frequency

- - - Updated - - -

I did not want to get into those details because the OP would get even more confused.

 

[FvM]

However, the Bode diagram approach (Barkhausen criterion) can be applied for more than one crossover frequency systems, by checking the phase margin at the highest crossover.

I'm not sure about a general criterion for stability of a minimal phase system, looking only at the highest crossover frequency seems arbitrary to me.

But I agree that the thread primarily addresses amplifiers with simple gain-phase curve that can be analyzed according to Barkhausen criterion.