MOS Folded-Cascode Differential Amplifier

[AMSA84]

Hello there guys.

I want to design a differential amplifier, more especifically a Folded-Cascode differential amplifier. I'm using the reference book of razzavi.

Before starting I want to find some values. I've some currents already defined for each branch and the L, but the main problem is that I don't know how to start doing the calculations to determine the W/L to design the transistors. The technologie is 0.35um and I'm using cadence.

Can anyone give me a tip for how to start? I've already been told to count with an overdrive voltage of 200mV. Is from there that I've to start, but I've some doubts.

 

[upvl]

Usually, you just need ~200-mV overdrive for the current mirrors. For the amplification transistors and the cascode transistors, you can use small overdrive, even pushing them to subthreshold, if you don't have other special concerns.

 

[AMSA84]

Thank you very much for your reply.

But, anyway, my major doubt is about how to start. I mean, I want to do some calculations to have a starting point. Taking in to account that I need that overdrive voltage, and that I know my L and the current in each branch, what I have to do, where I need to start. What kind of aspects I need to take in to account so that I can start to make the "model" of my transistor. Maybe starting to get the W?

W = (2 Id L) / (u Cox Vov^2) ?

By the way, where can I find the Cox and u for the C35B3 AMS kit 3.7?

Best regards.

 

[Braski]

If you have the current defined for each branch and the L, then there is no problem.

You have to start from the specifications: what are them?
Noise?
Gain?
Offset?
Slew rate?
Input-output ranges?

Start from the diff pair and the current mirrors. Forget about knowing an exact value of unCox because it depends on the biasing through un.

My advice is:

if You have BSIM3v3 model you can read the model file of your mos and find tox and u0. tox is the gate oxide thickness, from which Cox. u0 is the mobility at 0 voltage, i.e. with vgs and vds equal to 0. This value u0 overestimates thea ctual mobility in design conditions, but you can use it as an estimation. If you calculate with un equal to let's say 75% of u0 it should be better.

Then, you can set gm from your specs, both using expressions 2Id/(VGS-VTH) or sqrt(2*beta*ID). For a diff pair the former is more useful.

If you have an input offset spec and L fixed, the W is directly obtained from the offset formulas.

If you have flicker noise, the large the W the better.

If you have thermal noise, the more the gm, the better-> if Id fixed, the more the W the better (weak inversion and sub-threshold)


If you don't have any experience with your DK, the better thing is to do some simple simulation to understand what are the typical W/L for a given ID and VGS-VT. It is not practical to do too much hand calculations. Thus, first estimate uncox and try values following the specs, then sweep the parameters to adjust. Gaining experience with your DK is the best.

 

[erikl]

... where can I find the Cox and u for the C35B3 AMS kit 3.7?

These are company confidential data. After registration and NDA you can download this HIT Kit as well as additional design docs from . From the simulation model files you can extract those data.

 

[AMSA84]

Thank you so much for your replies.

Braski, about the specifications I do have. I can post later.

About the "if You have BSIM3v3 model" I don't know what is the BSIM3v3 model. Can you tell me where can I confirm that?

When you say VGS-VT is the same as Voverdrive? Because, according to wiki "The overdrive voltage is defined as the voltage between transistor gate and source (VGS) in excess of the threshold voltage (Vt) where Vt is defined as the minimum voltage required between gate and source to turn the transistor on (allow it to conduct electricity)."

"forget about knowing an exact value of unCox because it depends on the biasing through un" I asked that because I don't know where to start. The first thing that I thought was:

"If the Voverdrive is about 200mV, the VGS-VT is the Vov, now according to the formula W = (2 Id L) / (u Cox Vov^2) I can get the W" It was that.

Later I'll post here the specs.

Best regards and thanks in advance.

 

[Braski]

1) BSIM3v3 model is a kind of MOSFET description through a set of parameter. You should know what model file your DK uses. If you don-t know, check the DK manual or the model files themselves.

2) VGS-VT is the overdrive.

3) unCox can be estimated in the way i told you. but it remains an estimation, not valid in all the cases,, but useful to start. You can also estimate it simulating a mos and making calculations starting by the ID current, but the estimation will be rough.

 

[erikl]

W = (2 Id L) / (u Cox Vov^2)

For preliminary estimations you can use values from various other published 0.35µm process parameters, e.g. from MOSIS.
For 0.35µm processes, good mean values are k_0n = µ_0n*C_OX = 160 µA/V² and k_0p = µ_0p*C_OX = 60 µA/V² , s.a. David M. Binkley "Tradeoffs and Optimization in Analog CMOS Design", p. 42 .

 

[AMSA84]

Thank you guys for your quick replies.

To be honest, what I want to do is a Band-gap Voltage Reference. First, I am starting to do the Differential Amplifier. The output voltage is 1.235V, the bias current is 1uA and the PSRR, from 1Hz to 1MHz, is 40dB. These are the main objective.

About the model that you refered to, BSIM3v3 model, I think that is that one that the cadence that I am using have. I will check that.

When I asked for the values of µn and Cox, of course that would be a estimation. But, even so, I'd like to do the math in order to know what to expect. More or less, and of course, to present some calculations.

The circuit that I am using to do the Folded Cascode Differential Amplifier is present in the CMOS Circuit Design, Layout, and Simulation book, in page 715. The Vbias3 is obtained by connecting the gate of two series NMOS transistors.

The Vbias1 and Vbias2 is obtained by two diode connected PMOS. There, exist a 1uA bias current.

For example, how do I have to think to know / what I need to count in order to calculate the Vbias3? I know the L, the ID, the Vov (=200mV) and the Cox and µn, so I do have everything to calculate the W -> W = (2 Id L) / (u Cox Vov^2). Now I ask, I am thinking well? Another doubt is related to those 2 transistors M5 (and above that one) and M6 (and the one above that).

I am really confused. Lost. Don't know how to start. Maybe drawing the circuit in cadence and them simulating until get the desired current in the branchs is easy, but I don't want to do that way.

 

[erikl]

Don't know how to start.

Suggest to read the a.m. book from Binkley about choosing the Inversion Coefficient in order to get the right trade between power consumption and bandwidth -- this will allow you to calculate the appropriate W/L ratios.