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# CMOS in weak inversion for generating PTAT

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#### bhl777

##### Full Member level 6
Hi All, I referred to some paper and used the circuit in the following to design a PTAT. M1 and M2 are in weak inversion over all temperature, and current source are good. However, I have some questions of this simulated PTAT and hope any of you can advise.
Question:
(1) You can see that this PTAT is not ideally straight, is it the real PTAT? Or the good PTAT should be a straight line?

(2)I used the trend line to calculate the temperature at 0A, and found that it is around -256 instead of ideal -273.It is normal?

(3)In practical design, will we get a ideal straight line for PTAT and has 0A at -273C?

(4) From the theory of book, when Vgs is less than Vth, it is in weak inversion. However, in the real design for weak inversion circuit, is it true? I am wondering the reason of "PTAT is not an ideal straight line" is that even we have Vgs<vth, that is still not good enough.

Ideal is a straight line. But no resistor I've ever seen, has
zero higher-order tempco terms (i.e. curvature) and only
thin film metallics are even close.

The engineering concept of "good enough" applies here.
When you know what that is, then you can criticize the
details of performance and decide whether any more
work is wanted.

bhl777

### bhl777

Points: 2
Regarding (4). I think that you need to have a sufficient margin from Vgs to Vth (my guess is 100m-150mV) otherwise they are going to move from weak inversion. If you use spectre you can see the region of operation. Check that the region=3 for weak inversion. Also the mos (not the one above the resistor) usually has higher Vgs than the other one, so it is more likely to leave from weak inversion.

Dear bh3302

It will be a straight line in case if the has only first order temperature coefficient, practically the resistor has also a second order which becomes effective at higher temperature as you can see

for me, I think the graph you are getting are very good

Hi All, I referred to some paper and used the circuit in the following to design a PTAT. M1 and M2 are in weak inversion over all temperature, and current source are good. However, I have some questions of this simulated PTAT and hope any of you can advise. View attachment 86760
Question:
(1) You can see that this PTAT is not ideally straight, is it the real PTAT? Or the good PTAT should be a straight line?

(2)I used the trend line to calculate the temperature at 0A, and found that it is around -256 instead of ideal -273.It is normal?

(3)In practical design, will we get a ideal straight line for PTAT and has 0A at -273C?

(4) From the theory of book, when Vgs is less than Vth, it is in weak inversion. However, in the real design for weak inversion circuit, is it true? I am wondering the reason of "PTAT is not an ideal straight line" is that even we have Vgs<vth, that is still not good enough.

(1) You can see that this PTAT is not ideally straight, is it the real PTAT? Or the good PTAT should be a straight line?
P in PTAT stands for proportional so yes ideally it should be a straight line going through 0A at 0K but as already mentioned there are many non-idealities in this circuit that induce curvature
(2)I used the trend line to calculate the temperature at 0A, and found that it is around -256 instead of ideal -273.It is normal?
see above
(3)In practical design, will we get a ideal straight line for PTAT and has 0A at -273C?
no - see above
(4) From the theory of book, when Vgs is less than Vth, it is in weak inversion. However, in the real design for weak inversion circuit, is it true? I am wondering the reason of "PTAT is not an ideal straight line" is that even we have Vgs<vth, that is still not good enough.
The region around Vgs = Vth is called moderate inversion and you want to be far from it to have the nice exponential dependence of the drain current (on Vgs) necessary for your circuit. How far is enough depends on the temperature and technology; it is usually quantified through the concept of inversion coefficient and technology current. At room temperature 150mV below Vt is a good ballpark number.
Even in these ideal bias conditions the temperature coefficients (already at the first order contrary to what someone has claimed here) of the resistor are sufficient to create curvture.
Another source of non-ideality in this circuit would be body-effect, both Vth and the substrate factor are affected and would contribute additional curvature. In case you have not already, you can try to tie the NFET source to its body (which in practice would require deep-nwell devices) to improve the curvature of your PTAT source.

bhl777

### bhl777

Points: 2
Hi dgnani, I used matlab command "polyfit" to process my PTAT current, and found that its coeeficient inT^2 is in the same order of CTAT current (for example, both of PTAT and CTAT have around 1e-10 T^2 coefficient).
(1) during all temperature range, Vgs-Vth is from 100mV to 145mV. Do you think this is the critical thing to make PTAT has a "big" T^2 coefficient?
(2) If that is not the case, do you know how can I improve my PTAT design and make its T^2 coefficient much smaller than current level ?
(3) If I use conventional PTAT generator (two diodes and one resistor), can I expect better linearity than this "delta Vgs" PTAT generator?

Thank you very much!

P in PTAT stands for proportional so yes ideally it should be a straight line going through 0A at 0K but as already mentioned there are many non-idealities in this circuit that induce curvature

see above

no - see above

The region around Vgs = Vth is called moderate inversion and you want to be far from it to have the nice exponential dependence of the drain current (on Vgs) necessary for your circuit. How far is enough depends on the temperature and technology; it is usually quantified through the concept of inversion coefficient and technology current. At room temperature 150mV below Vt is a good ballpark number.
Even in these ideal bias conditions the temperature coefficients (already at the first order contrary to what someone has claimed here) of the resistor are sufficient to create curvture.
Another source of non-ideality in this circuit would be body-effect, both Vth and the substrate factor are affected and would contribute additional curvature. In case you have not already, you can try to tie the NFET source to its body (which in practice would require deep-nwell devices) to improve the curvature of your PTAT source.

Hi bhl,

using polyfit on PTAT and mentioning the coefficient in T^2 of the fit might not be the best way to go about this:
- your ideal behavior is not a constant value (as e.g in a resistor) but a straight line through the origin
- in this case you have two basic forms of non-ideality: second order behavior and offset, which of them is problematic depends on your application
- a temperature coefficient also depends on a nominal temperature as it is usually normalized dividing by the value of the ideally constant quantity at the nominal temperature
- in your case the ideally constant quantity is the the first order coefficient so that would make for a better normalization parameter (it is not clear if you used any)
- using a fit is good to describe performance but not to debug a design: the departure from the expected behavior is easier to understand in terms of local properties such as a derivative than in term of global properties such as a fitting coefficient over the whole curve
This is mostly academic in your case (the curvature is very small). More importantly
- If you are trying to build a reference by summing CTAT and PTAT currents, you might have correlated behavior (e.g. matching resistors) that makes the curvature of the sum smaller than the curvature of the individual components. There is no reason to focus on the individual performance in that case as only the residual curvature actually matters...

I have already mentioned inversion level (try pushing the devices in weaker inversion) and body effect. You need to try to see which one dominates.

A BJT-based generator (diodes are not usually modeled with sufficient accuracy) is usually much more accurate than a weak inversion circuit. This depends on the technology though, the closer a BJT behaves according to the ideal diode equation the better a PTAT will be...

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