# Transfer Function and loop transfer function

Discussion in 'Homework Help' started by Yasser979, Oct 12, 2013.

1. ### Yasser979 Thread Starter New Member

Oct 10, 2013
2
0
Dear All

I tried to solve this little thing in the class with my tutor and he shocked me when he said this is WRONG !!

The loop transfer function were right :
GL(s)= Gc(s) Gpwm(s) Gps(s) Kfb

and the transfer function i said ( which is wrong as he said !!)
H(s)= Gc(s) Gpwm(s) Gps(s) Kfb/1+ Gc(s) Gpwm(s) Gps(s) Kfb

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2. ### WBahn Moderator

Mar 31, 2012
18,085
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So (based on the response in your original post) if the marks A and B are the start and stop of the loop, then isn't the loop gain the gain from mark A to mark B?

What is the gain from mark A to mark B?

3. ### Yasser979 Thread Starter New Member

Oct 10, 2013
2
0
hi.
Again , the loop transfer function is solved correctly . from A to B ( as mentioned above )

but how about the TRANSFER FUNCTION

thanks

4. ### LvW Active Member

Jun 13, 2013
674
100
Yasser, the general expression for the closed-loop transfer of a system with (negative) feedback is:

H(s)=Forward transfer function/(1-LG). LG=Loop gain
In this context, please note that it is common to include the negative sign in the loop gain expression for LG,
that means: Loop gain has a minus sign (for negative feedback).|

That means, check again the numerator of your closed-loop function.

Last edited: Oct 13, 2013
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5. ### WBahn Moderator

Mar 31, 2012
18,085
4,917

Since you have the loop gain, i.e., Xb = Xa * LG, consider the following:

Q1) What is the output in terms of Xa?

Q2) What is the output in terms of the input and Xb?

Q3) What happens if you substitute the answer to Q2 into the answer to Q1?

6. ### LvW Active Member

Jun 13, 2013
674
100
Initiated by this thread, I like to stress again the definition of loop gain.
So - what means "loop gain"?
It is not surprising that this is the gain of the whole loop.
The definition of "gain" requires an input and an output. Thus the feedback loop must be opened at one point (preferably at the low-resistive output of an opamp). Then, a testsignal (ac) is applied at one node and the response is determined at the other node created by the opening (normal signal input grounded).

That is the method used for measurement as well as simulation of loop gain - and it is clear that the signal inversion, which is necessary for negative feedback, is INCLUDED in the output-to-input ratio.
This is important because for some systems with feedback the signal inversion does not take place "at the input" of the system (as in the classical feedback model shown in the first post). Rather, any other block may provide this signal inversion - and the feedback signal must be added with the input (and not substracted).

This definition corresponds with a stability limit (phase margin PM=0) in case the loop phase has a value of -360 deg at the loop gain magnitude cross-over frequency (gain magnitude 0 dB). Moreover, it also corresponds with the classic oscillation condition (Barkhausen, loop gain=1).
Note that for stable systems the loop gain (for dc) must always be negative.
This definition also avoids any confusion regarding determination of stability properties in the BODE diagram (phase threshold at -180 or at -360 deg ??).

Summary: For the system under discussion the loop gain is
LG= - Gc*Gpwm*Gps*Kfb.

Note: The consequences of the loop opening (dc bias point problems, load changes) sometimes require some special methods discussed elsewhere.

Last edited: Oct 14, 2013