# How gate voltages are established to turn on mosfets?

I am a bit confused about how the gate voltages of M13, M14, M15 are established here.

With M9, M10 by diode connected or feedback the gate voltages can be established from the biasing current.

However, I don't see how gate voltages of M13, M14, M15 are formed to turn on these mosfets.

Could anyone explain the mechanism for establishing these voltages here?

Thank you. • What is the model you have to use for the MOSFETs? – clabacchio Oct 24 '16 at 18:43
• It is just from text book, no specific model. – anhnha Oct 25 '16 at 15:04
• OK, based on the exercises you've done so far, what model would you use? How would you start attacking the problem? – clabacchio Oct 25 '16 at 15:13
• It is not related to model. And this is also not a homework question. They are enhancement mosfets. No more info and I don't think we need more! – anhnha Oct 25 '16 at 15:32
• What's the title of the textbook? – Mario Oct 28 '16 at 18:05

## 1 Answer

The circuit of interest is a simple regulated cascode circuit, the NMOS variant is shown below. If T3 doesn't conduct, the voltage at the drain of T3 will rise and T2 will deliver more current therefore the drain voltage at T1 increases so that the gate voltage of T3 increases, too. In case the gate voltage of T3 is too high, the feedback loop will cause a reduction.

This feedback action leads to a stable biasing voltage.

• Thanks. That makes sense. In the picture, the left circuit is equivalent to a super transistor on the right. This transistor will have the same transconductance but a much larger output resistance. Question: what is the purpose of showing gate current here? – anhnha Oct 28 '16 at 19:26
• The current is shown because the three transistors are driven by a current (I1). – Mario Oct 28 '16 at 20:46
• Sorry I meant the current at the gate of T1. – anhnha Oct 28 '16 at 20:48
• The current i1 is needed in the AC model of the transistor, it can be ignored for biasing considerations. – Mario Oct 29 '16 at 7:01