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aaron_do

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inductive degeneration analysis
Oct 23^rd, 2008, 1:17am

Hi all,

I'm trying to analyze inductive degeneration (LNA) using basic feedback analysis. Assume i break the loop at the source terminal of the transistor. So the open-loop transconductance is simply g_m, while the feedback factor should be sL_s making the loop gain g_msL_s. Therefore, the overall transconductance is,

G_closed = g_m/(1+g_msL_s)

which seems to be correct. For the input impedance, it should be something like,

Z_in = (1/sC_gs)*(1+g_msL_s)
=1/sC_gs + ω_TL_s

However, the actual solution for Z_in should be,

Z_in = 1/sC_gs + ω_TL_s + sL_s

I have a feeling i've gone wrong somewhere by not considering the loading, but i'm a bit confused how. Any help is appreciated.

thanks,
Aaron

BTW i have assumed that the circuit is fed by a voltage source, not a 50 ohm source...

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there is no energy in matter other than that received from the environment - Nikola Tesla

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buddypoor

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Bremen, Germany

Re: inductive degeneration analysis
Reply #1 - Oct 23^rd, 2008, 3:17am

aaron_do wrote on Oct 23^rd, 2008, 1:17am:

Hi all,

I'm trying to analyze inductive degeneration (LNA) using basic feedback analysis. Assume i break the loop at the source terminal of the transistor. So the open-loop transconductance is simply g_m, while the feedback factor should be sL_s making the loop gain g_msL_s. Therefore, the overall transconductance is,

G_closed = g_m/(1+g_msL_s)

which seems to be correct. .

I did not recalculate all the formulas, however, I think the overall transconductance is not correct as you did not take Cgs into consideration. If you like to consider Cgs during Zin calculation you should do this also for the gain resp. overall transconductance as a part of the current through the source terminal originates from the current through Cgs. May be that is the cause of the discrepancy.

Added some time later:
In the mean time I have thougt a little about the problem - and I think there is another reason for the discrepancy (but it is connected with the above mentioned arguments):
The input impedance is increased by the same factor which decreases the gain (resp. transconductance) due to feedback only in the case that there is a CLEAN voltage feedback without any disturbance.
But in your case, the element Cgs disturbs this feedback - and therefore the situation is a bit more complicated and we cannot expect that there is a common factor (1+gmwLs) for the main parameters. �

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« Last Edit: Oct 23^rd, 2008, 4:19am by buddypoor »

LvW (buddypoor: In memory of the great late Buddy Rich)

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RFICDUDE

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Re: inductive degeneration analysis
Reply #2 - Oct 26^th, 2008, 7:07pm

I think it is simply because you end up with the series impedance of the element plus a feedback term. The feedback term is what produces ωTLs (combination of sCgs and gm transforms the inductive reactance into a real resistance) while the impedance simply do to the inductor in series with the input is sLs.

A similar thing happens with series series feedback for common emitter amplifiers with resistive degeneration.

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aaron_do

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Re: inductive degeneration analysis
Reply #3 - Oct 26^th, 2008, 7:43pm

Hi,

thanks for all the help.

I think this point by buddypoor may have been the main thing...

Quote:

But in your case, the element Cgs disturbs this feedback - and therefore the situation is a bit more complicated and we cannot expect that there is a common factor (1+gmwLs) for the main parameters.

Anyway i got the right answer using blackman's formula...obviously kvl and kcl works too...

cheers,
Aaron

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there is no energy in matter other than that received from the environment - Nikola Tesla

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