I was reading the chapter about Low Noise Amplifiers from the book "The design of cmos radio-frequency integrated circuits" by Lee, and I have seen this example:
I do not understand the part inside the red circle. It is used to set the correct bias point for M1. The book says that:
Transistor M3 essentially forms a current mirror with M1, and its width is some small fraction of M1's width to minimize the power overhead of the bias circuit. The current through M3 is set by the supply voltage and Rref in conjunction with the Vgs of M3. The resistor RBIAS is chosen large eniugh that its equivalent noise current is small enough to be ignored. In a 50 Ohm system, values of several hundred ohms to a kilohm or so are adequate.
Precisely, I have the following questions:
1) Why do we need a current mirror? The current that flows on M3 is not given to any other circuit, what is its aim? I'd say that M1 needs a biasing voltage (and not current) and that may be achieved through for instance a simple voltage divider with two resistances.
2) I do not understand its considerations about RBIAS and noise: higher resistance means higher thermal noise, so I do not understand that statement.
Best Answer
The clue is in the title... "The design of ... integrated circuits".
You are correct that you could set the bias voltage with a resistive divider ... IF you knew what the correct voltage was.
But you don't ...
Look at some MOSFET datasheets : note that there isn't a specific value given for Vgs(at some current) e.g. Vgs(th) often refers to a threshold current of 0.1 mA - but a range, say 1V to 3V.
All you can be reasonably sure of is that M1 and M3 require (reasonably closely) the same voltage, as they are made in the same process, and at the same temperature, by virtue of being close to each other on the same die.
If it helps to think of M3 as an analog computer calculating the correct voltage for Vbias, that's pretty much what it is.
EDIT : the point of Rbias is to isolate the RF path from all the parasitic capacitances around M3, and to attenuate any RF signals reaching M3 (which would attempt to amplify them onto Rref...) M3 is supposed to be DC only, and you can make R3 as high as you like because Ibias is practically 0. (If the book recommends kilohms, that is about keeping the physical size down)