for the second problem I found other equations. I think the Vgs should be negative to get a positive temperature coefficient (TC). But Id0 and n are still problems... Maybe anyone has an idea for these two parameters?

Regards,
Ronny

Hi Andre,

the output branch of the bandgap includes a pMOS, a resistor and a diode-connected PNP (from vdd to gnd). Now the intention is to calculate Vout over the resistor and the PNP with: Vout = Iout * R + Vpnp where Iout is Id of the pMOS. Vout should be at 1.2 V with a TC < 100 and relatively independent from vdd.
Vg of the pMOS is set to vdd-250mV to ensure weak inversion. The equation for Vout must be derived to find the point where the TC is zero. My problem is that this curve strongly depends from Id0 and the curve doesn't have a point where the TC is near zero, I got very different results for Id0

The complete bandgap is shown at the pages 12/13 of
http://users.ece.gatech.edu/rincon-mora/classes/ece4430/handouts/l39_bg.pdf
I have no idea what are reasonable values for all W's, L's and the resistors there! And it's also difficult to get a feeling what are feasible performances for this circuit.

Thanks and regards,
Ronny

Andre,

unfortunately I'm not a real designer just a beginner but I know what a current mirror is. My question concerns your last equation (seems to be a similar equation as in the slides). Why is there a relation between IM6 and IR1? The X is ok, it is the current mirror between M2 and M6. I verified your equation by simulation and it fails as expected from my side. Can you explain it to me?

Do you have a link or title for the Vittoz paper? I cannot find a paper where the inversion factor is explained. This criteria for weak inversion is new to me since I know that Ugs < Uth and Id < 1uA.

For the output branch of the circuit Id must be 50uA to establish a voltage over Q5 with -2mV/K. Therefore in my opinion M6 cannot be in weak inversion. But I'm not sure  :-/

I think it's quite difficult to choose the W's to get a good TC and a good supply independency.

Ronny

Guys:

Instead of getting mired in the equations, why don't you just run a set of bias curves for the transistors you are using and go from there with geomaetry scaling? Or do it on a simulator?

Remember that a lot of the equations being cited are academic simplifications for the purpose of illustration.

If these transistors could be accurately represented with those equations then, the BSIM 4.5 would not have 230 odd parameters in it. (dont get me started on that issue!)

Jerry

loose-electron: You don't need bias curves, since you don't care about the Gate Source Voltage on any of the Transistors. When you have a mirror you don't care about the VGS. It changes over process and temperature anyways. It doesn't help you to understand a circuit either. I see this every day. If you understand how it works you can run as many sweeps as you want. I am not sure how hard it is to understand IM6=IR1. The only other equation you need is the inversion factor if you want to determine if the transistor is in WI or not. In simulation you could determine this by looking at gm/Id and find the plateau, but that is not really a simplification. Further the equation for if is amazingly accurate (it only depends on beta and UT). But if you look at the OP, there is clearly a question for ID(VGS) of the MOST in WI.

Ronny: The only reason why a mirror has a mismatch in the currents is a difference in drain source voltages or triode mode operation. One of the mirror transistors has VGS=VDS and the other one has VDD-Vout. So you have to use cascodes and if you have constraints on VDD use low voltage cascodes.
If you neglect mismatch (I don't think you are running monte carlo?), a current mirror will always work, no matter if it is in WI or SI.
The only thing that can make a difference is when one of the transistors goes out of saturation  (in WI a good assumption is VDS>100mV for saturation) or if the VDS are differing a lot.

Forget about the mosfets VGS. It doesn't do anything for you in this circuit.


A good summary on low voltage mirrors can be found here:
http://amesp02.tamu.edu/~sanchez/lvtutorial-2000.pdf

The Vittoz paper I mentioned earlier is titled:
"CMOS analog integrated circuits based on weak inversion opearaton"
Its on the IEEE servers.