The Designer's Guide Community
Forum
Welcome, Guest. Please Login or Register. Please follow the Forum guidelines.
Sep 29th, 2024, 2:16am
Pages: 1 2 
Send Topic Print
constant gm bias goes unstable after modification (Read 18237 times)
trond
Senior Member
****
Offline



Posts: 168
Glasgow, Scotland
constant gm bias goes unstable after modification
Nov 03rd, 2008, 6:17am
 
Hello All,

I have a constant gm bias circuit as shown in the picture below. The left circuit is pretty much standard even though it uses cascode current mirrors. I found that the red transistors M7 and M1 always slipped into triode region no matter what I tried. In order to solve this I added a "beta-helper" (not sure how to call them) into each diode connected transistor as shown in the right had circuit. Now all transistors remain in saturation over all corners and mismatch and process. Everything seemed fine but the stability was effected. I included a bode plot of a stability analysis as well for each circuit.

Can anyone help me understand where the peaking in the gain comes from. I know it is due to the added transistor, but I fail to see how they would have such an effect.
The peaking, since it makes the gain go >1, makes the bias circuit unstable.

Thanks,
Back to top
 

const_gm_bias.jpg
View Profile   IP Logged
HdrChopper
Community Fellow
*****
Offline



Posts: 493

Re: constant gm bias goes unstable after modification
Reply #1 - Nov 3rd, 2008, 3:10pm
 
Hi Trond,

I'm not totally sure how you worked out the circuit with the beta helpers to get all transistors work in saturation. From my viewpoint you still need on each branch at least 2 VTH + 2 VDSATS, which hadrly fits into 1.2v.
Nevertheless, a significant difference between both circuits is the high impedance node seen at the beta helper gate node, while in the original circuit such impedance was 1/gm.
In the beta helper circuit I envision such high impedance will bring a non-dominant pole down to the low frequencies in combination with the gate capacitance now hanging from that node.
Hope this helps

Tosei
Back to top
 
 

Keep it simple
View Profile   IP Logged
nobody
Community Member
***
Offline



Posts: 75

Re: constant gm bias goes unstable after modification
Reply #2 - Nov 3rd, 2008, 6:39pm
 
Hello, Tosei

I was wondering if it is true that the impedance seen in the gate(or beta helper) is high because I though of the adder mos as a gain stage like a source follower or common source amplifier. Then the impedence will be 1/(A*gm), which A represents the gain of added mos like gm*ro for C.S and gm/(gm+gmb) for S.F.

The original CKT for me is much like high swing CKT. If you look that way, then you have to bias Vg2=Vd1=Vov+Vt2, Vg1=2Vov+Vt1 to make sure M1 in saturation. Be careful of body effect on M2. Any comments are appreciated.
Back to top
 
 
View Profile   IP Logged
HdrChopper
Community Fellow
*****
Offline



Posts: 493

Re: constant gm bias goes unstable after modification
Reply #3 - Nov 4th, 2008, 2:58pm
 
Hi nobody,

The beta helper is in fact a source follower stage. Therefore it introduces positive feedback from gate to source, such feedback having a gain < 1.

However, I do not see why the impedance on the gate node would be 1/(A*gm). In any case I would expect it to be 1/(A*ro), with A < 1 and ro the output impedance of the cascode.

I do not see how the beta helper could work as a common source amplifier, since there is zero load at the drain and therefore the gain is 0 under this configuration + the drain is not an output for the beta helper stage.

As for the original CKT I agree is a High swing cascode and M1 will be in saturation, but according to Trond his problem is the pass transistors not being in saturation rather than the othe ones.

Regards
Tosei

Back to top
 
 

Keep it simple
View Profile   IP Logged
raja.cedt
Senior Fellow
******
Offline



Posts: 1516
Germany
Re: constant gm bias goes unstable after modification
Reply #4 - Nov 4th, 2008, 9:12pm
 
hi,
   i didn't understand how the second circuit has high impedance node(still M7 node is high impedance with 1/gm impedence) and where is +ve feedback in the circuit?

Thank you.
Back to top
 
 
View Profile WWW raja.sekhar86   IP Logged
nobody
Community Member
***
Offline



Posts: 75

Re: constant gm bias goes unstable after modification
Reply #5 - Nov 4th, 2008, 9:52pm
 
Hi, Tosei

Here is how I derive the impedace.
Add a test current It and a test voltage Vt @ gate of the source follower, which is also drain of M7. Then the gate voltage of M8 is A*Vt where A represents the gain of source follower. KCL @ gate of the source follower. A*Vt*gm8=It . Therefore, Rt=1/(A*gm8).

You are right about the gain of the source follower, which is supposed to lower than 1.
As the common source amplifier, I am confused about the righ handed side beta helper because the arrow seems to be wrong for me.
I am not sure about what problem came up in Trond's CKT and I would guess it is probably due to a doublet on the current mirror.
Back to top
 
 
View Profile   IP Logged
raja.cedt
Senior Fellow
******
Offline



Posts: 1516
Germany
Re: constant gm bias goes unstable after modification
Reply #6 - Nov 4th, 2008, 10:29pm
 
hi trond,
              i have some questions regarding your circuit. 1.why you want keep cascode transistors? May be u want to get high PSRR from suppl and good mirroring,if u r working with short channel devices..but same things you can achieve by using op amp inside the loop with out putting cascodes.
2.you can keep m7 and m1 in saturation by adjusting its bias rather than adding one CD stage.I guess stability problems are coming because -ve feedback loops around high swing cascode.Here inside the loop one high impedance,one low impedance  nodes are there,probably they may move to complex plane.
Back to top
 
 
View Profile WWW raja.sekhar86   IP Logged
trond
Senior Member
****
Offline



Posts: 168
Glasgow, Scotland
Re: constant gm bias goes unstable after modification
Reply #7 - Nov 5th, 2008, 7:44am
 
Thank you all for your feedback so far.

rja.cedt

1) I decided to use cascoded current mirrors as the transistor output impedence was the major limitation in obtaining a "constant" gm (even with an ideal resistor).
2) Agreed, I could try adjusting the bias separately and maybe removing one cascode. So far I have mainly considered to circuit shown though. Essentially there is some information in Johns/Martin "Analog Integrated Circuit Design" book on page 259. This seemed a good starting point.

Nobody
1) The arrow of the beta helper in the picture is indeed wrong. The circuit's correct though.
2) I verified that the impedance seen at the gate of the beta helper is pretty much the same as without it. As Nobody pointed out already, due to the SF stage the impedance only slightly increases. The gain of the SF was determined to be ~ -1dB in simulation.

So why are we seeing a peaking in the OPEN loop TF? Is it because a SF as a negative input resistance at high frequenies of -gm/(CgsCLw^2)? Is it because a SF can have an inductive output impedance?


Cheers,
Back to top
 
 
View Profile   IP Logged
HdrChopper
Community Fellow
*****
Offline



Posts: 493

Re: constant gm bias goes unstable after modification
Reply #8 - Nov 5th, 2008, 6:35pm
 
Hi Trond / nobody,

I was certainly wrong about the impedance of the gate node corresponding to the beta helper. I also checked it and it is just slightly larger than 1/gm for lower frequencies. So nobody was correct about it.
However I noticed that at very high frequencies it behaves as an inductive output impedance. This is something you Trond suggested in your last post and might explain this behavior. Try to increase the size of your beta helper device to see if stability imroves.

Also another question: did you check the transient step response by applying a small perturbation to the loop and looking to the loop current ? I wonder how well the stability analysis matches the transient response for this circuit.

Tosei
Back to top
 
 

Keep it simple
View Profile   IP Logged
raja.cedt
Senior Fellow
******
Offline



Posts: 1516
Germany
Re: constant gm bias goes unstable after modification
Reply #9 - Nov 5th, 2008, 10:04pm
 
hi THE CHOPPER,
                               as you said in your earlier post, by increasing  the size of beta helper we can reduce inductance at the source,i tried i did not get any improvement(i guess the reason is  -ve resistance at the gate of beta helper is also increasing). But i think   problem is coming because  of  the poles at the  source of M8 is moving to complex plane due to -ve feedback around the loop.
          But i have one basic question regarding stability,how to know which loop is causing problem(because in our problem we have around 2 -ve feedback,1 +ve feedback).is there any way to figure out this problem

Thank you.
                       
Back to top
 
 
View Profile WWW raja.sekhar86   IP Logged
buddypoor
Community Fellow
*****
Offline



Posts: 529
Bremen, Germany
Re: constant gm bias goes unstable after modification
Reply #10 - Nov 6th, 2008, 2:39am
 
raja.cedt wrote on Nov 5th, 2008, 10:04pm:
................................
          But i have one basic question regarding stability,how to know which loop is causing problem(because in our problem we have around 2 -ve feedback,1 +ve feedback).is there any way to figure out this problem



Hi raja.cedt
I do not know much about your circuit (and the beta-helper stuff), but your last question touches control theory.
And from this I know, that it is a basic problem to know which loop causes problems if the whole system contains more than one feedback loop. Normally, one can say that the SLOWEST loop determines to a great extent the system behaviour - that means it is the "dominating" loop. But in some cases this does not help because it is not always possible to discriminate between "local" and "over all" loops.
More than that, opening one loop can sometimes make the system unstable.
In summary, as far as I know there is no general rule in control theory which allows us to find the most critical loop in a multi-loop structure.
Regards    
Back to top
 
 

LvW (buddypoor: In memory of the great late Buddy Rich)
View Profile   IP Logged
raja.cedt
Senior Fellow
******
Offline



Posts: 1516
Germany
Re: constant gm bias goes unstable after modification
Reply #11 - Nov 6th, 2008, 2:57am
 
hi buddypoor,
                    Thanks for your answer,if you consider the above beta helper circuit, there everybody is raising different issues for oscillations  like 1.inductance of the source follower  output,-ve resistance from the source,complex poles in the -ve feedback loop .....Finally which one is the dominant   culprit. Intuitively what i feel is  if inductance and -ve resistance are belonged to  same node then u can expect   ringing(i  am saying this one from a well known example of ource follower driving another source follower).so kindly please tell  sme why oscillations are coming here.
Thank you.

               
               
               
             
               
             
           
Back to top
 
 
View Profile WWW raja.sekhar86   IP Logged
Prabhu
Junior Member
**
Offline



Posts: 23

Re: constant gm bias goes unstable after modification
Reply #12 - Nov 6th, 2008, 3:42am
 
Trond,

This is a typical replica bias problem.
First check stabilty for each of the SF loops separately (imitating the loading conditions properly when the whole circuit is active). Typically you will identify the problem here. Compensate these local loops first satisfactorily and then check for the whole circuit.

Regards,
Prabhu
Back to top
 
 
View Profile   IP Logged
Tlaloc
Community Member
***
Offline



Posts: 81
Dallas, TX
Re: constant gm bias goes unstable after modification
Reply #13 - Nov 6th, 2008, 8:33am
 
buddypoor wrote on Nov 6th, 2008, 2:39am:
More than that, opening one loop can sometimes make the system unstable.
In summary, as far as I know there is no general rule in control theory which allows us to find the most critical loop in a multi-loop structure.

I was under the impression that even though the stability of each loop is a necessary if not sufficient condition of total stability, in practical circuits, if each loop by itself is stable, it tends to make the overall system stable.

With that in mind, the solution for Trond would be to run three different stb analysis (if using spectre) for the three loops.  From there, he could stabilize each one sufficiently.  I believe that is the same solution that the previous post by Prabhu put forth.
Back to top
 
 
View Profile   IP Logged
buddypoor
Community Fellow
*****
Offline



Posts: 529
Bremen, Germany
Re: constant gm bias goes unstable after modification
Reply #14 - Nov 6th, 2008, 2:08pm
 
Tlaloc wrote on Nov 6th, 2008, 8:33am:
I was under the impression that even though the stability of each loop is a necessary if not sufficient condition of total stability, in practical circuits, if each loop by itself is stable, it tends to make the overall system stable.
With that in mind, the solution for Trond would be to run three different stb analysis (if using spectre) for the three loops.  From there, he could stabilize each one sufficiently.  I believe that is the same solution that the previous post by Prabhu put forth.


Hi Tlaloc,
I like to remind you on the Nyquist stability criterion in its most general form. This criterion allows us to prove the stability of a closed loop system also in case that the open loop is unstable (i. e. it has poles with a positive real part).  There are a lot of examples that closing one specific loop can stabilize another loop which is unstable.
Regards
Back to top
 
 

LvW (buddypoor: In memory of the great late Buddy Rich)
View Profile   IP Logged
Pages: 1 2 
Send Topic Print
Copyright 2002-2024 Designer’s Guide Consulting, Inc. Designer’s Guide® is a registered trademark of Designer’s Guide Consulting, Inc. All rights reserved. Send comments or questions to editor@designers-guide.org. Consider submitting a paper or model.