Question about AGC circuit

[kooller]

Hi everyone,
How should I analyses the loop stability of the AGC system, and make sure the designed system is absolutely stable, as the AGC circuit is a nonlinear system.

 

[flatulent]

you will have to do the analysis at a variety of input signal levels. Determine the loop gain and poles and zeros at each of these and make sure no poles are in the right half plane or near the imaginary axis.

You should have a potentiometer in the circuit so that users can make adjustments. Many years ago I owned a short wave receiver that had these problems at a certain input signal level. I turned down the AGC gain and all was well.

 

[kooller]

To find the poles and zeros of the system, it must find the system transfer function,but the AGC is a nonlinear system, then how should i model this system?

you will have to do the analysis at a variety of input signal levels. Determine the loop gain and poles and zeros at each of these and make sure no poles are in the right half plane or near the imaginary axis.

You should have a potentiometer in the circuit so that users can make adjustments. Many years ago I owned a short wave receiver that had these problems at a certain input signal level. I turned down the AGC gain and all was well.

 

[LvW]

To find the poles and zeros of the system, it must find the system transfer function,but the AGC is a nonlinear system, then how should i model this system?

Yes, you are right. Before doing a stability analysis you have to linearize the system. But this procedure, of course, depends on the kind of non-linearity in your AGC circuit.
However, I assume that you are using an amplifier which is controlled in a anti-logarithmic fashion based on the e-function - that means "linear in dB" . Is this correct ?

In this case, it is rather simple to linearize the loop by taking the log (basis e) of the whole system. In addition, it is convenient to convert to the log (basis 10) and then to dB. As a result, your input and output signals all are in dBV.

I have done this procedure with the aim to simulate the behaviour of the linear model of the AGC loop and to adjust the parameters (controller, filter,...).
After comparison with the nonlinear loop (simulation) there was a very good agreement between both models. It can be shown that it is allowed to design the loop components based on the linear model - and that there is a good matching of both models within a limited range of ± 1.6 dB for the input range.
Regards and good luck.

PS: I remember that there was a "critical" point - but I don´t remember the details at the moment. Perhaps I give notice somewhat later.

 

[kooller]

LvW,
Thank you for your reply,and should I consider the poles and zeros of the vga when I model it. That is, will this affect the stability of the AGC.

And I also don't know how to model the peak detector and the comparator, which are both nonlinear components.

Can you suggest me some paper about the stability analyses of the AGC system?

Thank you!

To find the poles and zeros of the system, it must find the system transfer function,but the AGC is a nonlinear system, then how should i model this system?

Yes, you are right. Before doing a stability analysis you have to linearize the system. But this procedure, of course, depends on the kind of non-linearity in your AGC circuit.
However, I assume that you are using an amplifier which is controlled in a anti-logarithmic fashion based on the e-function - that means "linear in dB" . Is this correct ?

In this case, it is rather simple to linearize the loop by taking the log (basis e) of the whole system. In addition, it is convenient to convert to the log (basis 10) and then to dB. As a result, your input and output signals all are in dBV.

I have done this procedure with the aim to simulate the behaviour of the linear model of the AGC loop and to adjust the parameters (controller, filter,...).
After comparison with the nonlinear loop (simulation) there was a very good agreement between both models. It can be shown that it is allowed to design the loop components based on the linear model - and that there is a good matching of both models within a limited range of ± 1.6 dB for the input range.
Regards and good luck.

PS: I remember that there was a "critical" point - but I don´t remember the details at the moment. Perhaps I give notice somewhat later.

 

[vfone]

http://www.eecg.toronto.edu/~kphang/papers/2001/martin_AGC.pdf

 

[LvW]

Yes, the above mentioned paper is a very good one.
Another paper is attached.

To your question:
1.) Normally, poles and zeros of the AGC amplifier itself are far outside the active range of the loop (which normally has a rather large time constant). So you should not take them into consideration.
2.) Regarding the peak detector, I think the most important part is the lowpass/integrator associated with it.
3.) Where is a comparator ?

 

[LvW]

Can you suggest me some paper about the stability analyses of the AGC system?

Hi kooler,

here are further two papers which I consider as appropriate and very interesting:

1.) **broken link removed**
2.) see attachement

Regards

Just one additional remark:
Flatulent wrote: you will have to do the analysis at a variety of input signal levels
I think, this is not necessary because the advantage of an amplifier controlled with an e-function shape is that the loop transfer function is NOT dependent on the signal level.

 

[kooller]

Thank you for your reply,
I have read the first paper you uploaded, but this paper focus on the settling time of the AGC, and I also don't know how to make the AGC stable.

From the first paper you uploaded it seem to be that the AGC will be stable if an exponent VGA is used , and the time constant of the loop filter is much larger than the peak detect time. Is this right?

Yes, the above mentioned paper is a very good one.
Another paper is attached.

To your question:
1.) Normally, poles and zeros of the AGC amplifier itself are far outside the active range of the loop (which normally has a rather large time constant). So you should not take them into consideration.
2.) Regarding the peak detector, I think the most important part is the lowpass/integrator associated with it.
3.) Where is a comparator ?

 

[LvW]

......................................
From the first paper you uploaded it seem to be that the AGC will be stable if an exponent VGA is used , and the time constant of the loop filter is much larger than the peak detect time. Is this right?

No, the characteristic of the VGA is chosen because the loop behaviour should be independent on the mean power of the incoming signal. Stability is another issue.

In general, is it correct that your aim is to find the AGC loop transfer function in order to design the several loop components - especially the controller ?
In this case, you should be aware of two basic facts:
1.) It is not a servo loop (with the aim to follow a leading parameter), but instead it is a "disturbance control action". (I hope, this is the correct expression).
2.) As the loop shall not FOLLOW the input signal but supress its long term variations (below a specific frequency), your linear loop model input is only this signal variation. Therfore, the second "subtractor block" within the loop for comparing the actual level with any reference does NOT appaer in this loop (because the reference is assumed to be constant and has no influence on loop stability.).

 

[kooller]

My AGC is consist of VGA(exponent function), peak detector, comparator (to make the peak of output signal be equal to Vref), LPF. So which parameter will affect the stability of the AGC loop, It seems to be that only the dynamic of VGA, the time to detect the peak of the output signal, time constant of LPF will affect the loop stability, Is this right?

Thanks!

......................................
From the first paper you uploaded it seem to be that the AGC will be stable if an exponent VGA is used , and the time constant of the loop filter is much larger than the peak detect time. Is this right?

No, the characteristic of the VGA is chosen because the loop behaviour should be independent on the mean power of the incoming signal. Stability is another issue.

In general, is it correct that your aim is to find the AGC loop transfer function in order to design the several loop components - especially the controller ?
In this case, you should be aware of two basic facts:
1.) It is not a servo loop (with the aim to follow a leading parameter), but instead it is a "disturbance control action". (I hope, this is the correct expression).
2.) As the loop shall not FOLLOW the input signal but supress its long term variations (below a specific frequency), your linear loop model input is only this signal variation. Therfore, the second "subtractor block" within the loop for comparing the actual level with any reference does NOT appaer in this loop (because the reference is assumed to be constant and has no influence on loop stability.).

 

[LvW]

My AGC is consist of VGA(exponent function), peak detector, comparator (to make the peak of output signal be equal to Vref), LPF. So which parameter will affect the stability of the AGC loop, It seems to be that only the dynamic of VGA, the time to detect the peak of the output signal, time constant of LPF will affect the loop stability, Is this right?

1.) Comparator: I assume that this "comparator" is purely a subtractor which creates an error signal which simply consists of the difference between output peak and reference. Is this the case ? Or does your comparator has any gain ?

2.) The above listing of parameters which affect the loop behaviour is not complete as of course the various constants (gain and the constants associated with log conversion) have to be considered. Moreover, I am sure that also the reference voltage value appears in the transfer function as part of any constant.

 

[kooller]

Yes, if the LPF is a integrator(1/st), then the the comparator can be a purely subtractor(how to design this subtractor?). But if the LPF is not a integrator, such as 1/(1+st), then the comparator should have relative large gain.

I have analysed the loop, and found it only has one left pole(because of the LPF) for the transfunction from input to output, if I don't care the poles and zeros of the VGA. This meas the AGC will be absolutely stable, but from the simulation it seems to be that the gain of VGA will affect the stability of the AGC.

My AGC is consist of VGA(exponent function), peak detector, comparator (to make the peak of output signal be equal to Vref), LPF. So which parameter will affect the stability of the AGC loop, It seems to be that only the dynamic of VGA, the time to detect the peak of the output signal, time constant of LPF will affect the loop stability, Is this right?

1.) Comparator: I assume that this "comparator" is purely a subtractor which creates an error signal which simply consists of the difference between output peak and reference. Is this the case ? Or does your comparator has any gain ?

2.) The above listing of parameters which affect the loop behaviour is not complete as of course the various constants (gain and the constants associated with log conversion) have to be considered. Moreover, I am sure that also the reference voltage value appears in the transfer function as part of any constant.

 

[LvW]

I have analysed the loop, and found it only has one left pole(because of the LPF) for the transfunction from input to output, if I don't care the poles and zeros of the VGA. This meas the AGC will be absolutely stable, but from the simulation it seems to be that the gain of VGA will affect the stability of the AGC.

Do you take the frequency behaviour of the detector into account ?

If you have linearized the loop by taking the log and if you investigate the loop behaviour for signal variations, the gain of the VGA is not part of the loop. Thus, it can have no influence on stability.