Gate Source Voltage Drop Approximation

Question

When dealing with BJTs in an approximate large signal analysis, Vbe is often chosen to be 0.7 Volts (Given the component is operating in active mode). My question is: Is it possible to do the same for MOSFETs?

I'm asking this because I'd like to find an approximate expression for the output current in the following current mirror setup:

For the BJT case, I often saw the output current being approximated by (Vcc-0.7/R) so I was wondering whether a similar approach would be valid for the MOSFET structure.

Answer 1

BJT and MOSFET have different working mechanism. But there are similar aspects indeed. As you see, no matter MOSFET current mirror or BJT mirror, the two transistor have same gate-source (or base-emitter) voltage, but because BJT and MOSFET have different working mechanism, so the (Vcc-0.7/R) approximation won't work for MOSFET current mirror.

But this won't prevent you to find a 'rule' to simplify the analysis:

When short the drain and gate of M1, it will forcing it to operate in the saturation mode, because \$ V_{GS} - V_{DS} = 0 < V_{tn} \$. So, we have $$ I_{M1} = I_{REF} = \frac{V_{DD}-V_{GS}}{R}\qquad(1)\\ I_{M1} = \frac{1}{2}k_{n}'(\frac{W}{L})_{1}(V_{GS}-V_{tn})^\qquad(2)\\ I_{OUT}=I_{D2}=\frac{1}{2}k_{n}'(\frac{W}{L})_{2}(V_{GS}-V_{tn})^2\qquad(3)\\ $$

From equations (2) and (3), we get

$$ \frac{I_{O}}{I_{REF}}=\frac{(W/L)_2}{(W/L)_1}\qquad(4) $$

So, Equations (1) and (4) are the rules for MOSFET current mirror. They are easy to remember and use.

Answer 2

The difficulty with MOSFETs is that this outcome is not entirely as universal as the 'standard single BJT' situation.

As you say, the estimation for a broad analysis that the transistors will be similar and the left one would be in diode-conduction, gives decent results.

Unfortunately a MOSFET, has all these parameters that differ from one type to another, depending on the exact build-up of the semiconductor layers inside. Of course a BJT has these differences, but there's always that nifty predictable PN conduction junction that prescribes the behaviour you 'quote'.

To simplify the MOSFET parameters, the most important first step in identifying the set-point is the gate threshold voltage. If you assume that as the voltage under the resistor you will get near to the right value, but it may still be off by a measurable amount. If you want to get a closer approximation without all the channel maths you'll need the graph(s) in the data-sheet of the MOSFET to find where the resistor's voltage vs current graph crosses the Vge vs Id and/or Vde vs Id graph(s).