Hi Everyone,
 I've been having a problem with trying to verify the calculation method of the gate noise gain of a Transistor in V/V units in LC oscillators according to the Book "The Designer's Guide to High-Purity Oscillators".  According to the book the Chap 3. Eq. (41)  

Vo,n=Vn*(L*omega_0^2)/(4*R*omega_m)                (41)

where Vo,n is the output noise, Vn is the gate noise, omega_0 is the oscillation frequency, and omega_m is the offset frequency where noise is measured


gives the gate noise gain, and Fig. 15 gives the noise gain plot of simulated values VS calculated values.
Does anyone have this book and tried these simulations out?  I have several problems with this.  

Problem1.

First off it seems strange to me that Eq. (41) looks the same as Eq. (32)  the tank gain with the noise voltage simply changed to noise current

Vo,n=in*(L*omega_0^2)/(4*omega_m)                     (32)

Which makes me think that the plots in Fig. 15 and Fig. 12 are just the same plots by changing the gain from V/A to V/V.  Is this coincidental?  Or do I miss understand something?  It makes me very confused as it seems that the book is trying to show how these two noise gains are derived differently and verified separately, when they look like the same thing using different units.

Problem2.
I'm trying to verify Eq. 41 with Spectre RF simulation to get to Fig. 15 without much success.  It seems that when I specify the output of Spectre RF's oscillator simulation as voltage nodes, and use pnoise for noise separation, all the noise sources will be in terms of current (A/sqrt(Hz)) or (A^2/Hz), and the noise gains will be in terms of V/A or V^2/A^2.  Is there a way to get noise gain in units of V/V in Spectre RF? (the noise sources of the transistor are Id noise, fn noise, and rs noise all in current form A/sqrt(Hz))
I tried converting these noise gains (V/A) into (V/V) by multiplying the output noise gain (V/A) by 1/R but it does not seem to coincide with the values in Eq. 41 or Fig. 15 in Chapter 3.  Am I doing something wrong?  

I've been on this book, trying to varify this equation for quite a while now, but without much success  :-[ .  It would be great if someone who's got the book and tried to verify this equation could point me in the right direction.   Thanks!

Win

First of all thanks a lot for the reply!  I've been stuck on this for quite a while now, so I'd be glad if there was anybody who had the same experience, but I wasn't expecting an author of the book!

Okay, now back to the problem.  

Problem1:
I see what you mean by Fig. 12, eq (32) being almost constant with bias current and Fig. 15, eq (41) being almost linear with current.  However it can be seen that eq (32) is not a function of bias current or tank resistance, we would expect it to be constant with bias current.  eq (41) however is inversely dependent on the resistance of the tank.  And since from the simulation example in the book the I*R product is kept constant, increasing the current will automatically decrease the tank resistance making the gate gain automatically increase with bias current.  This makes me feel like the equivalent of calculating the transconductance gain of an amplifier, then calculating the voltage gain of the amplifier and saying that they are some how separate gain.  Is there something wrong with this logic?

In other words while this is obvious from the equations, what I don't understand is how eq (32) and eq (41) can be said to be separate gains since it seems that just by replacing the current noise in (32) with a Vn/R eq (32) becomes eq (41), which, like I said in the initial post, make them seem like the same gain values measured with different units, (V/I) VS (V/V)  ie. just scaled differently.  Is there something wrong with this logic?  For example is it not valid to replace "In" by Vn/R?  And if so why not?  This is what I don't understand.  I mean while they maybe derived separately, they seem to refer to the same gain.

So the way I saw it is that when you calculate the tank gain, you are also calculating the gate gain as well, however, just with different units (just replacing In with Vn/R).  Is there something wrong with this logic?

Problem 2:  I will try out the method that you have suggested and see what happens.

Thanks for the reply!  I actually have some other points I don't understand about the book, but maybe later.


Win