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Design >> Analog Design >> Biasing circuit for telescopic amplifier
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Message started by steven on Jan 18^th, 2006, 10:12pm

Title: Biasing circuit for telescopic amplifier
Post by steven on Jan 18^th, 2006, 10:12pm

Hello,

I have a question on biasing circuit for telescopic amp. Hope I can get some references and comments on my doubts. Taking a conventional telescopic amplifier, ie., the half circuit contains 2 PMOS and 2 NMOS, the bottom has a current source NMOS at the common gate of the two paths, there are 4 biasing voltages. These voltages are for the top PMOS pair, second PMOS pair, stacked NMOS pair, and the bottom NMOS. Also assuming that these biasing voltages can use idea voltage sources, that is, no using biasing networks. Given these freedom, what is the best way to design these voltages? Further assume the biasing voltages set all input/output common mode voltages at the middle of their ranges.

I was thinking like this: since the key is to make the transistors at saturation, so with Vdssat=0.2 for all devices I should be able to set the biasing voltages. However, it seems that it is not as easy as I thought since some transistors will be easily out of saturation if a little change in the input common mode voltage or some variation in mismatching. Am I thinking this problem in a wrong way? I mean the biasing circuit should be dynamic rather than making the above fixed biasing voltages assumption.

Anyhow, references are well appreciated.

Title: Re: Biasing circuit for telescopic amplifier
Post by uncle_ezra on Jan 19^th, 2006, 1:19am

Hi,

Why don't you want to have a biasing network? I highly recommend you design a biasing network so that it will make your life easier. A biasing network will help track process, voltage and temperature variation and hence change the voltage bias accordingly. Also is the architecture differential or single-ended? If differential you need a CMFB network.

Hope this helps!

Title: Re: Biasing circuit for telescopic amplifier
Post by steven on Jan 19^th, 2006, 9:08am

Hi Ezra,

Maybe I didn't express my point well: in design, we always can set the overdrive voltage or Vgs by biasing current and transistor size. However, Vds is controlled by factors external to the transistor, which needs some thoughts in picking the drain voltage Vd(assume the source voltage Vs has been set by the condition Vgs>Vth). Even though Vds>Vov=Vgs-Vth is met, I think there are still many options can be done and also changing Vd sometimes will change the transistor state too. In the telescopic amplifier example, excluding the biasing circuit, I was thinking a best way to bias the stacked transistors using independant voltage sources. That was my question.

Yes, I know biasing circuit is easier and I have found some references later on. But I want to check if my thoughts are wrong or not.

Thanks.

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Jan 25^th, 2006, 2:44pm

Hi Steven, the fact is that Vds will change as circuit voltages wiggle. That's why there's an ICMR for an op-amp. You basically just set Vgs to give you the right overdrive voltage AND you may have to use more gate voltage to make sure Vds is far enough away from Vds(sat). Short-channel devices don't have an easy to define Vds(sat) so you basically have to decide where to bias Vds based on the desired amount of output resistance.

Does that answer your question? I think you know what you are talking about but you just had some doubts about the design philosophy.

Title: Re: Biasing circuit for telescopic amplifier
Post by steven on Jan 25^th, 2006, 10:38pm

Hi Marc,

Thanks for your comments. I understand what you said, however, I don't quite understand what is going on in this circuit. For exmaple, in the attached figure, bias voltages have been labeled. I didn't draw the bias network and CMFB network. Vb1 and Vb2 are from the bias network. Vbias comes from CMFB. As can see from M1 to M4, the bias is not right, ie. Vds are too small than Vds(sat). I tried to achieve the big "AND" in your post but no avail so far. Something is wrong.

Thanks,
Steven

Title: Re: Biasing circuit for telescopic amplifier
Post by Cri Azzolini on Jan 27^th, 2006, 12:36am

Hi Steven,

regarding your telescopic OTA, the source voltage of M1/M2 is defined by the input-common mode of the opamp and by the ratio Id1 / (W/L)1: in my opinion you should try to properly bias the M1/M2 since the CMFB loop will work fine only if the opamp's tail device is out of triode region (it seems to me that your CMFB is not working at all if the output common mode is 0.104V!!). You may want to enlarge your differential pair or raise the input common mode.

As a second matter, the voltage at the drain of M1/M2 is defined by the gate voltage of M3/M4 and by their size: again, you should enlarge M3/M4 since, in my opionion, a gate-to-source voltage equals to 2.45 is too high for M3/M4. The biasing of M3/M4 and M7/M8 is quite delicate for they should be properly saturated event when the opamp's output voltage is completely unbalanced (full swing condition): generally speaking, the telescopic architecture is suitable for medium-low output swing: if you require more swing (1.5V-2 V) you may design a replica-tail feedback loop (quite complicated for high-speed applications!) or change your topology toward a folded-cascode (more power-hungry!).

In order to find the appropriate biasing and size of M3/M4 you can also substitute MB5 with a voltage source and, once all is fixed, come back to MB5. That is a standard routine during the first design activities. ;)

Bye,
Cri

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Jan 27^th, 2006, 7:40pm

steven wrote on Jan 25^th, 2006, 10:38pm:

One nasty problem is that Vsd7 is far too big...it eats up all your voltage.

I'd say you haven't sized the transistors to handle the current sourced by M5, Mb4, and M6. I would need to know the branch currents and transistor sizes to make any useful comments. You'll also need to size Mb5 so that it has Vds5 > Vgs + Vds(sat).

Make sure vbias MOS is 3x to handle all branch currents.
Mb5 should be sized to give the targeted Vgs + Vds across it when you run the branch current through.

Other sizing tips: pick the gm you want, and vgs you want. size each transistor type so that it gives you the desired gm at the vgs you selected. do a vgs sweep with vds set to the target vds when you are trying to get gm

What Vgsn, Vsgp, Vdsn(sat), and Vsdp(sat) are you targeting?
What is Vth for each MOS?

What is v+, v- at?

Title: Re: Biasing circuit for telescopic amplifier
Post by steven on Jan 27^th, 2006, 9:01pm

Marc Murphy wrote on Jan 27^th, 2006, 7:40pm:

steven wrote on Jan 25^th, 2006, 10:38pm:

Hi Cri and Marc,

Thanks for both of you commenting on the circuit. As Marc said, I didn't size it correctly when I posted but tried to illustrate how to get around the Vsd7. I can size them to have open-loop gain at around 85dB but GBW is too small. Still I don't feel comfortable on something. Here are the parameters I used:

V+ and V- are at 1.5.

Vthn is 0.6, Vthp is -0.8. I tried to set |Vds(sat)| around 0.2. Actual Vds(sat) is about 0.3~0.4 (absolute value). Vds(Mb5) now is about 1.2V. It was really hard to set Vds(Mb5)=Vgs+Vds(sat) (I am happy to listen your tricks on doing this).

M10 is in trio mode though, Vds10=0.04 < Vds10(sat)=0.9. I don't if I still need to adjust it or not. The others are at Saturation.

Half branch current is 3.3mA, Id(Mb5) is 31uA. Maybe I should redraw the circuit to show the sizes. Before that, I want to ask these to Marc,

1. When you said make sure vbias MOS is 3x, what is the 3x compared to?

2. How do you do a vgs sweep? This is very useful since I didn't know how to set M3 and M4 efficiently before I posted the original post.

Regards,
Steven

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Jan 28^th, 2006, 3:43am

I will answer your questions in more depth later...gotta go to a seminar! There is a simple, systematic way to handle things.

3x is in relation to the other NMOS.

Just take a single MOSFET. Hook up a voltage source to the gate and another to the drain. I don't know what tool you are using but they all can do a DC-sweep of voltage. Just sweep Vgs.

If you didn't know how to set M3 and M4 than the rest of them are probably off too!

Try the sizing tip I gave and that is where you need to start.

Gotta run!

Title: Re: Biasing circuit for telescopic amplifier
Post by steven on Jan 28^th, 2006, 11:16am

Marc Murphy wrote on Jan 28^th, 2006, 3:43am:

Just a quick reply. Here I guess (really guessing) we had a misunderstanding of each other:

When you said "Vgs sweeping", you meant that connecting a *single* transistor and do a DC sweep to find correct Id and (W/L), right? (But hand calculation is quite close if I check with this sweeping setting up). If this is the case, I believe I asked a wrong question. I was thinking you were referring to Cri's comment, ie., fixing some voltage source then sweeping the other to find the appropriate Id and (W/L) while keeping the *whole* OTA topology. If this is not what meant, I need more comments from you.

Regards,
Steven

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Jan 28^th, 2006, 12:59pm

steven wrote on Jan 28^th, 2006, 11:16am:

I wasn't referring to Cri's comment, although now that I look at it, he is also concerned with the odd voltage drops and probable sizing problems. I was basically saying you need to properly size your transistors for the vgs and gm that you want. You can figure out the right size for your basic transistor NMOS, PMOS by using a single transistor. There isn't a need to change the OTA topology.

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Jan 28^th, 2006, 1:27pm

Let's say we want Vov=Vgs-Vth=0.1*Vdd=300 mV
So, Vgsn=Vthn+0.3=0.8 V
Vsgp=Vthp+0.3=1.1 V
sounds like Vds should be around 0.3 V for saturation
pick fT, which leads to your gm
do the vgs single tran sweep to find out what size gives you the right gm at your desired vgs (vds is set to around or more than vds(sat))

now you know the sizes for all NMOS and PMOS in your circuit. M1, M2, M3, M4 are going to be the same size. All PMOS are the same size. I think the thing that may have messed you up is that the PMOS were not sized right relative to the NMOS. The KEY to making the rest of the circuit work is the proper sizing of MOSFETs and now you have almost all of the sized to sink the right current at the chosen bias voltages.

Each PMOS branch will have roughly the same current when in saturation. You size M10 to take all the current, so it is 3x bigger than the other NMOS. You make Mb5 smaller to raise its voltage to at least vgs+vds, to keep M3 & M1 happy.

steven wrote on Jan 27^th, 2006, 9:01pm:

Title: Re: Biasing circuit for telescopic amplifier
Post by steven on Jan 28^th, 2006, 9:36pm

Marc Murphy wrote on Jan 28^th, 2006, 1:27pm:

Hi Marc,

Thanks for your quick clarification. I know what you mean now. The way you pick gm is new to me. I used Id, W/L, and Vds(sat) (Vds(sat)~0.3) to size transistors. Your way is an interesting way. I sure will give a try with your sizing tips and get back to you soon.

Regards,
Steven

Title: Re: Biasing circuit for telescopic amplifier
Post by steven on Jan 30^th, 2006, 7:02pm

Hello Marc,

I tried the sizing method you suggested. Here are some followups and thoughts.

1. you are right that the ratio between PMOS and NMOS can easily mess sizes obtained from single tran sweep results. In other words, Vsd7 would be still too big even though individual tran has been sized correctly in single tran sweep. So when connecting PMOS and NMOS, the sizes have to be redone again. I hope I didn't do anything different than what you said regarding this.

Some sizes I adopted at single tras sweep are: NMOS (W/L)=200/0.5 leads to gm=14.5mS, PMOS (W/L)=500/1 leads to gm=12mS. Put them in the circuit place, Vsd7 is around 1.6 (after some minor tweaking), still too big.

2. I think using fT to pick gm should be the same as using Id, (W/L), and Vgs method in single tran connection. Besides, you may have other ways to choose fT, which is a function of parasitic cap also the transistor size and gm.

3. I think since Mb5 is simply to generate bias voltage for M1~M4, it may not require to have the same branch current as M1 and M2 branch. Of course, assuming the three branch have the same current can greatly siimplify the design.

Regards,
Steven

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Feb 1^st, 2006, 7:37am

Re: 2 I prefer to pick my transistor sizes and biasing based on performance. If you simply go with Id, Vgs, and W/L you could pick a small Vgs, big W/L, and big Id...getting a slow circuit with big transistors that burns lots of power.

Re: 3 If the PMOS is saturated, it should have roughly the same current as the other branches.

You are always going to have a Vds larger than Vds(sat) somewhere in the stack; you need to drop the voltage somewhere in the stack.

I would suggest trying something similar tothis topology from Baker's CMOS 2nd Ed.

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Feb 1^st, 2006, 7:45am

FYI, here is an attempt I did this morning. I didn't bother to beautify the schematic but you should be able to see the operating points.

Title: Re: Biasing circuit for telescopic amplifier
Post by huber on Feb 1^st, 2006, 9:16am

steven:
It definately looks like your cmfb isn't working. Until you fix that it is pointless to talk about transistor sizing. If you are using a transistor-level circuit for cmfb it may be tricky to initialize, expecially if it is a switched-cap cmfb circuit. Try using an idealized cmfb network built with vcvs's. It seems like all your problems with devices in triode would be fixed if your output was at 1.5V-2V where it should be.

Title: Re: Biasing circuit for telescopic amplifier
Post by steven on Feb 1^st, 2006, 10:57am

huber wrote on Feb 1^st, 2006, 9:16am:

Hello Marc and Huber,

Thanks both of you commenting on the circuit, espeically Marc's illustration example. I see why Marc picked fT rather than Id in sizing. What is your rule of thumb in picking fT?

I can use VCVS to force the CMFB work, i.e., make Voc~1.8V. In this case, Huber's comment is definitely right. However, since the circuit is using SC CMFB, there is not too much adjust on the SC CMFB network except the transistor sizes (CMFB consists of just ideal switches). I am not using transistor CMFB. This comes back Cri's comment, which he also suggested to use VCVS in CMFB. But I ended up still needing to re-size the trans after returning SC CMFB. Did I do something inefficiently?

Regards,
Steven

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Feb 1^st, 2006, 11:15am

It's hard to say that there is a rule of thumb...rather, there are tradeoffs. In the end, you have to design to fit your application.

a higher vgs gives you higher fT, but reduces swing
a shorter L gives you higher fT, but reduces output resistance

I am not totally clear on how the CMFB circuit would solve your biasing issue...as it is now, you can just manually set vbias to whatever the CMFB circuit would give.

Title: Re: Biasing circuit for telescopic amplifier
Post by steven on Feb 2^nd, 2006, 6:29pm

I made it work but not completely understand why previously the circuit didn't work: I picked Vcm=1.5 in SC CMFB previously, which didn't work. Now if picking Vcm=-1.5, everything works perfectly, the sizing, phase margin, and gain. I don't know why yet. Someone can provide a clue?

By the way, since now the GBW is only about 700MHz. Can someone provide reference on how to further improve GBW? Marc's fT selection is obviously a good way. Other ways?

Thanks

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Feb 3^rd, 2006, 7:53am

steven wrote on Feb 2^nd, 2006, 6:29pm:

Great! For any circuit where a PMOS drain meets and NMOS drain it is pretty tough to say what the voltage will be without CMFB. You basically can just visualize the Ids vs. Vds curves intersecting at a point which determines the voltage.

To increase GFT (gain*fT), increase Vgs. The gain suffers a little but fT ~ Vov/L...Vov = Vgs - Vth. The tradeoff is the swing suffers.

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Feb 3^rd, 2006, 8:08am

Hi, someone asked me a question about gm/Id and fT. Hopefully my answer is helpful to others, and if I am wrong in my understanding, please correct me! :)

---

Re: cascode tail current source. The cascode current source is just used to get a higher output resistance, and thus performs as a better current source. The downside is it limits the minimum input swing of the amp; it requires a larger voltage drop than a simple source to get it looking like a current source.

gm/id is about efficiency...you want to get a lot of current change, i.e. high gm, at the lowest bias Id possible. The best efficiency occurs at around subthreshold. However, at subthreshold the overdrive voltage Vov=Vgs-Vth is small, and so fT is small. People are interested into weak/moderate inversion design because both the gm/Id and fT aren't that bad. For high-speed design you just pick a big fT knowing that gm/Id will be low.

fT is the point where short-circuit current amplification stops happening...i.e. id/ig=1 I think of it as a figure of merit...the higher the fT, the faster your circuit can potentially be. In a real circuit you want some gain and have a load so fT isn't a reachable operating frequency. It isn't related to the model 'falling apart'.

Title: Re: Biasing circuit for telescopic amplifier
Post by steven on Feb 4^th, 2006, 9:50am

My understanding about fT is like this: fT is the frequency when gi=id/ib=1 and can be expressed as

fT~gm/Ctot (1)

where ~ stands for proportional and Ctot is the total capacitance. Then since gm~Id~Vov, therefore increasing Id or Vov can improve fT. However, for geometric parameters, the proportional relation is more involved since

Ctot~W*L and gm~sqrt(L/W)

Plugging back to (1), fT and L (or W) has nonlinear relation.

Title: Re: Biasing circuit for telescopic amplifier
Post by vhdl00 on Feb 4^th, 2006, 2:19pm

HI steven, Marc and all,

I am still kind of confused about gm/id, ft . Just like Marc said: "the higher the fT, the faster your circuit can potentially be." we may tweak the transistor to make the ft big, does that mean the speed of the transistor is fast? from my understanding, "potentially faster" doesn't really mean high performance?

thanks

Title: Re: Biasing circuit for telescopic amplifier
Post by steven on Feb 4^th, 2006, 7:59pm

Hi Vhdl,

I had a typo in my post (now I corrected) on the definition of fT. Marc was right the definition. fT is the frequency when the current gain (not gm) equals 1.

I think you are confused fT and the bandwidth of an amplifier, or -3dB frequency. For one dominant-pole open loop response, the speed is determined by the -3dB frequency. However, in certain case, fT or GBW is useful in setting up a benchmark of amplifier speed. For example, when talking about amplifier settling time, fT (somewhere labeled fu or omega_u) is frequently used.

Title: Re: Biasing circuit for telescopic amplifier
Post by holddreams on Feb 16^th, 2006, 5:54am

What's the meaning of "fT"?
Thanks.

Title: Re: Biasing circuit for telescopic amplifier
Post by Marc Murphy on Feb 17^th, 2006, 10:57am

holddreams wrote on Feb 16^th, 2006, 5:54am:

What's the meaning of "fT"?
Thanks.

fT is the transistion frequency. It is the frequency where the short circuit current gain, id/ig=1. At this frequency, the MOSFET transitions from being an amplifier to not being one. The drain has to have a DC voltage so that the drain is ac-shorted to the source.

You can do an AC analysis and see where id/ig=1. Another way is to do a DC op-point analysis and do a small signal analysis:
ft=gm/[2*pi*(Cgs+Cgd)]

EDIT: Oops, I think I already answered this question in this thread. Oh well, maybe this post is more helpful.