MOSFET (common source) current paths

[Renshai]

Why is the voltage gain of a common source MOSFET negative?

I have a schematic below and I get the voltage gain to be -gm(ro||Rd). I say that is what I get, but the truth is that is what my professor said we should get. I do not understand why the Gain (Av) is negative. It will go a long way (I think) in also helping me understanding the current path for finding Gm, Rin, and Rout.


Sorry about making the schematic a thumbnail attachment. I know it would be much easier to put it in this workspace, but I do not know how to embed the schematic into this workspace.

 

[Renshai]

Anyone have any ideas? I could really use the help. Thanks.

 

[vk6kro]

Just consider signal currents and voltages and ignore any DC voltages or currents.

First, the negative sign just means the signal is inverted. I will omit this to make the following clearer.

Then, the definition of gm is
gm = drain current / gate voltage

so, drain current = gm * gate voltage.

Voltage across load resistor RL = drain current * RL

So, Voltage across load resistor RL = gm * gate voltage * RL

Gain = Voltage across load resistor RL / gate voltage = gm * RL

RL means the actual load resistor plus the output resistance of the FET plus any load from the following stage, all in parallel.

 

[Renshai]

That is a very good way of putting that information. I appreciate that very much. I will be able to see the MOSFET a little more clearly now. As far as the negative gm, you said that the signal is just inverted. I guess my question is why? If I do a very basic design of the common gate I get a gain of gm*RL (taking ro and gmb out of the equation). That gain is not negative or inverted, so I guess I am still a little confused by the negative sign or inversion. Thank you for your information so far. It is very helpful.

 

[vk6kro]

The gm isn't negative.

If the input waveform is Vin = sin(wt)
Then the output is {gain} * {-sin(wt)}

So the gain = -sin(wt) * gm * RL / sin(wt)
= - (gm * RL)

Note the negative sign.