Modelling and design of an optical receiver

Dear TUKA,

TUKA said:

The TIA gives me input referred noise current and the VGA gives me input referred noise voltage. Is there any formula to convert these input referred noise quantities into an equivalent noise figure for the whole system?

There is a relationship between the noise figure of an amplifier and its input referred noise and its source noise since the noise figure relates the S/N at the output to the S/N at the input. When you cascade amplifiers with known noise figures there is a relationship that can easily be driven between the gains of the each stage and the output noise figure as shown below. This relationship assumes the impedances between the amplifiers are all matched.

I hope I understood your question and this is useful. This information can be found any basic text that includes amplifier noise.

Shawn

Dear TUKA,

My reply was posted before it allowed me to upload the relationships. 

Shawn

Dear Shwan,

Thank you for your reply and thanks for the useful information.

Dear TUKA,

I must apologize! After I posted my reply last night, I realized I made an error in my equation. I hope it did not confuse you! The corrected equation is include below. The initial expression I provided did not properly display the cascaded amplifier gains in the denominator of the sum. To hopefully make it more clear, I include an example for a cascade of 3 amplifiers.

Shawn

Dear Shawn,

Thank you once again for getting back to me, and thanks a lot for providing me the right set of equations once gain.

However, now things are fine with me regarding these equations and hand calculations of Noise figure. But, my aim is to plot the noise figure consisting of (flicker, thermal and shot noises) versus frequency.

I am attaching a part pf my verilogA code below (these only contain noise related parameters and functions):

In the ADE L simulator setup, I choose the "noise" analysis, and swept frequency as a variable from 1 to 100 GHz. For the output noise, I choose the 'voltage' and then selected the positive output node. I left the negative output node empty and for the input noise, I choose 'none'.

Then, I went to direct plot, main form and and tried plotting the noise figure and input referred noise voltage. But all it shows is a constant 0 dB horizontal line throughout the spectrum. It would be great if you could let me know where I am going wrong.

Thanks a lot once again for your helpful comments to my post!

Dear TUKA,

TUKA said:

However, now things are fine with me regarding these equations and hand calculations of Noise figure.

Great!

TUKA said:

In the ADE L simulator setup, I choose the "noise" analysis, and swept frequency as a variable from 1 to 100 GHz. For the output noise, I choose the 'voltage' and then selected the positive output node. I left the negative output node empty and for the input noise, I choose 'none'.

Then, I went to direct plot, main form and and tried plotting the noise figure and input referred noise voltage. But all it shows is a constant 0 dB horizontal line throughout the spectrum. It would be great if you could let me know where I am going wrong.

From the code snippet you included, I don't see an expression for your LNA output. I only see an expression for the noise at your pin "in". You also added:

TUKA said:

For the output noise, I choose the 'voltage' and then selected the positive output node. I left the negative output node empty

1. I do not see any expression for the LNA  pin "out" in your code snippet. I think that will be an issue! Did you define an output expression for pin "out" in your code?

2. Why did you choose to leave the negative output node empty? I think you need to include a reference node as the negative node. There is no implicit reference node, and any signal is meaningless without some type of reference signal.

Shawn

Dear Shawn,

Thank you once gain for getting back to me, and thanks a lot for your detailed explanation.

Yes, you were right, the issue was because I did not include the "out" pin at the output node. Now I am able to plot both thermal noise and flicker noise versus frequency. Also, as you suggested, I have included ground as a reference node in place of the negative output node.

To be more specific, I have used the predefined functions flicker_noise( ) and white_noise( ) to plot the flicker noise and thermal noise respectively.

Is there any way to plot shot noise as well? I am especially concerned about the collector shot noise that is given by:

where Ic is the collector current and fT is the transit frequency. As seen form the formula, this noise varies with frequency, thus I am unable to use white_noise( ) fucntion to plot shot noise.

(Here, Please assume that I have already included the values for collector current and transit frequency as real parameters in my behavioral model code). I would wish to know if there is any predefined function to plot shot noise versus frequency? If no, it would be nice if you could tell me any other approach to have all the three noises (flicker, thermal and shot noise) in one single plot.

Thank you once again for your helpful feedback comments!

TUKA said:

To be more specific, I have used the predefined functions flicker_noise( ) and white_noise( ) to plot the flicker noise and thermal noise respectively.

Is there any way to plot shot noise as well?

 The term flicker noise generically is not limited to noise whose exponential dependence on frequency is limited to -1. A short review on the different sources of flicker noise may be found in Section 2.2 of a note at URL:

I cannot include the entire link as my response will be classified as spam. However, if you type the prefix through "....com/" into your web browser, you may copy and paste the remainder of the URL shown below to access the note.

s/5za1ilay6sqa06b/phase_noise_response_081422v1p0.pdf?dl=0

www.dropbox.com/s/5za1ilay6sqa06b/phase_noise_response_081422v1p0.pdf?dl=0

I am not sure if this was Cadence's motivation for their definition of the flicker_noise() function, but from the verilog-A manual, the function allows for an exponent other than -1.

Hence, you should be able to use this function to synthesize noise whose exponential frequency dependence is -2.

Shawn

ShawnLogan said:

Hence, you should be able to use this function to synthesize noise whose exponential frequency dependence is -2

Dear Shawn,

Thank you so much for your response, and thanks for sharing the URL and giving me the right insights.

Thanks!

Dear TUKA,

Of course, you are most welcome and I just hope they help!

Shawn