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Design >> RF Design >> Question about transconductance relating to cascode LNA
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Message started by baab on Jan 22^nd, 2014, 12:53am

Title: Question about transconductance relating to cascode LNA
Post by baab on Jan 22^nd, 2014, 12:53am

Hi,

I am reading the following paper about LNA.
D.K. Shaeffer, T.H. Lee, “A 1.5V 1.5GHz CMOS Low Noise Amplifier”, IEEE JSSC, Vol. 32, No. 5. May 1997
There is one thing that is confusing. Could anyone help me with the question in the attached picture? Thanks.

Title: Re: Question about transconductance relating to cascode LNA
Post by aaron_do on Jan 22^nd, 2014, 1:25am

Hi baab,

the maths is very easy. Just find the overall Gm and you will know why...

regards,
Aaron

Title: Re: Question about transconductance relating to cascode LNA
Post by baab on Jan 22^nd, 2014, 8:17am

Hi, Aaron.

Could you tell a little bit more? The overall Gm have been given in (9), haven't it?

Title: Re: Question about transconductance relating to cascode LNA
Post by aaron_do on Jan 22^nd, 2014, 4:59pm

Oh i see...I just quickly read the text in the yellow box... :P

You mentioned yourself that the overall Gm is only dependent on the transit frequency. The transit frequency is fixed by the process. But bear in mind that if you were to add additional capacitors here and there (for example across Cgs), you could reduce the effective transit frequency and thereby lower the gain.

Also, don't take the authors words to mean that the design is linear, as gm/Cgs is a nonlinear function of the biasing condition. I think the important point is that your Gm is optimized alongside your fT.

regards,
Aaron

Title: Re: Question about transconductance relating to cascode LNA
Post by baab on Jan 22^nd, 2014, 7:13pm

Thanks.

Quote:

The transit frequency is fixed by the process.

With "process" did you mean "technology"? To be honest, I don't know the difference between "process" and "technology".
If so, in my design, I use TSMC 130nm then "transit frequency" will be fixed, right?

According to the definition above, transit frequency = gm/Cgs. And therefore, it will depend on gm and Cgs. In other words, it will depend on the biasing condition.
Why can we say that it only depends on process?

Quote:

But bear in mind that if you were to add additional capacitors here and there (for example across Cgs), you could reduce the effective transit frequency and thereby lower the gain.

Yes, I see that from the formula transit frequency = gm/Cgs and the product of gain and bandwidth.

Quote:

Also, don't take the authors words to mean that the design is linear, as gm/Cgs is a nonlinear function of the biasing condition. I think the important point is that your Gm is optimized alongside your fT.

Yes, however, I still confused why the author said so. It is clearly that Gm depends on bias conditions.

Title: Re: Question about transconductance relating to cascode LNA
Post by aaron_do on Jan 22^nd, 2014, 9:21pm

Quote:

To be honest, I don't know the difference between "process" and "technology".

join the club :P

I'm sure a lot of people know the difference, but its not important to me so I just use them interchangeably. People understand.

Quote:

Why can we say that it only depends on process?

What I think the author means is that it doesn't depend on device width. However, its not true in practice because if you make the device width really small, then you need a really large gate inductor, and it won't really work because of the finite inductor Q.

Its really not an important piece of information IMO.

regards,
Aaron

BTW, did you figure out what was wrong with your inductance plots?

Title: Re: Question about transconductance relating to cascode LNA
Post by baab on Jan 22^nd, 2014, 9:51pm

Hi, Aaron.

Quote:

join the club

:)
This is the first time I have designed a RF circuit and I will have to learn a lot.

Quote:

What I think the author means is that it doesn't depend on device width.

You meant that Gm doesn't depend on device width, right?
Let's me try to explain that.
As device width changes, gm and Cgs change linearly. Therefore, transit frequency = gm/Cgs remains constant with device width.

Title: Re: Question about transconductance relating to cascode LNA
Post by aaron_do on Jan 22^nd, 2014, 10:38pm

Quote:

As device width changes, gm and Cgs change linearly. Therefore, transit frequency = gm/Cgs remains constant with device width.

Yes. But again, the degree to which it works in practice is limited...

Title: Re: Question about transconductance relating to cascode LNA
Post by baab on Jan 22^nd, 2014, 10:58pm

Hi,
Could you help me with the question in the picture? It is from the same paper. Please let me know if you need more information or the paper. Thanks.

Title: Re: Question about transconductance relating to cascode LNA
Post by aaron_do on Jan 23^rd, 2014, 12:51am

Hi baab,

I don't quite get your question. The author just calculated the transfer function from the noise source to the output. Is that what you want to know?

regards,
Aaron

Title: Re: Question about transconductance relating to cascode LNA
Post by baab on Jan 23^rd, 2014, 2:02am

Hi, Aaron.

Quote:

I don't quite get your question. The author just calculated the transfer function from the noise source to the output. Is that what you want to know?

Yes, I knew that. However, the channel noise, Ind, is already at the output, isn't it?

I want to know why output noise power density arising from Ind is calculated like that. I mean that why we have to divide that for the quantity in yellow box?

Title: Re: Question about transconductance relating to cascode LNA
Post by aaron_do on Jan 23^rd, 2014, 6:13am

U need to draw the small signal circuit with the channel noise as your input source. The drain noise causes a voltage drop across Ls which results in another current determined by gmvgs...

Aaron

Title: Re: Question about transconductance relating to cascode LNA
Post by baab on Jan 23^rd, 2014, 7:00am

Thank you, Aaron.

I will try that now. :)