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Design >> RF Design >> Confusion about noise factor in LNA
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Message started by baab on Dec 12^th, 2013, 9:00am

Title: Confusion about noise factor in LNA
Post by baab on Dec 12^th, 2013, 9:00am

I am reading a paper about LNA called "CMOS Low Noise Amplifier Design
Optimization Techniques ".
The author gave the schematic of a cascode LNA topology adopted to apply the CNM technique and noise factor.
I spent two days to prove it but get nothing now. And I wonder why there is no conductance gg in the noise factor of F.
Ing = 4kT*gg*δ*Δf and therefore, I think the final expression of F has to have gg.
PS. I attached the noise factor expression in the second post as the site allowed only one picture per post.

Title: Re: Confusion about noise factor in LNA
Post by baab on Dec 12^th, 2013, 9:01am

Noise factor expression:

Title: Re: Confusion about noise factor in LNA
Post by tm123 on Dec 12^th, 2013, 10:27am

The i_ng² noise source appears to be included in the parameter 'c' shown as equation (4) on page 2. I think the i_ng² represents the equivalent gate noise which includes the noise generated by the conductance g_g, as shown in (3).

Title: Re: Confusion about noise factor in LNA
Post by baab on Dec 12^th, 2013, 11:15am

Well, thanks. I think you are right.
I have derived many expressions from that paper. However, the one above may be the most difficult. It took me a lot of time to get them but I learnt more.
I will try to get the expression now. BTW, if you know any reference telling how to derive that expression, please let me know.

Title: Re: Confusion about noise factor in LNA
Post by aaron_do on Dec 12^th, 2013, 5:17pm

Hi,

T.H. Lee derives expressions for LNA NF in his book.

Aaron

Title: Re: Confusion about noise factor in LNA
Post by baab on Dec 13^th, 2013, 8:25am

Thanks Aaron.

I have read almost two chapters in the book about noise and LNA but the formula above is not derived.
I have just found an online lecture cover this well.
Now I have a problem need help.
I use TSMC 0.13um then is it short channel or long channel?
How can I find transit frequency, gama, delta, gd0?

Title: Re: Confusion about noise factor in LNA
Post by tm123 on Dec 13^th, 2013, 8:51am

I suggest assuming long channel approximation for a first cut calculation. If you expect your calculated NF to exactly match the simulation you definitely need to account for short channel effects, but the calculation will become too complicated to gain any insight.

When doing calculations like this I never expect my calculation to exactly match simulation, but I expect to be relatively close and more importantly to gain insight into the circuit operation, what the primary contributors to the NF are, and how could I improve the NF of the given circuit architecture.

Title: Re: Confusion about noise factor in LNA
Post by baab on Dec 13^th, 2013, 4:29pm

Hello tm123,

I will be very happy if my calculations relatively close to the simulation results. 8-)
Thanks for the advice. I am using the cascode structure. Is it really hard to get NF less than or equal to 2 (assuming that we don't need to much gain, for example, gain = 15dB)?

Title: Re: Confusion about noise factor in LNA
Post by baab on Dec 14^th, 2013, 6:40am

Hello,
I can't work out the formula above. I tried a lot but don't get it.
I found this lecture: http://www.ece.ucsb.edu/yuegroup/Teaching/ECE219Winter2013/Lecture%20slides%20and%20notes/ECE219-Lec3-4-notes-LNA.pdf
At the page 9, the professor derived the formula for the same problem. I understand the lecture perfectly. However, as I checked two formulas (the first one is that in original post and the second is the one in the lecture), they are NOT the same. I am sure that the formula in the lecture is correct but can't tell if the one above also right.
I also checked both of them as delta δ =0 and they are different!

The only error I can see in the original is Rs^2 - sLs^2. It should be Rs^2 - (sLs)^2.

If you have derived that formula, please tell me how to do that. Thanks.

Title: Re: Confusion about noise factor in LNA
Post by Kevin Aylward on Dec 15^th, 2013, 4:48am

Analyzing colliding, rotating black holes tells one that using formulas as above in real designs, is completely futile. So long as you *understand* the global principals of what is going on, running a brute force multiple parameter spice sweep of all relevant components is the way real, optimum commercial designs are done. Sure, academics like to produce formulas and frown on the trained monkey approach. They are wrong.

Title: Re: Confusion about noise factor in LNA
Post by baab on Dec 15^th, 2013, 5:36am

Hello Kevin,

I agree with you. However, I want to derive the formula myself to get much insight.
I got a document in which they give relatively detailed how to design a LNA and therefore I really want to prove that.