psd function argument questions

Hi, there.

I'm trying to understand how these arguments (From/To/Number of Samples/Window Size) of the psd function affect its measurement result.

My original expression 1. is attached below. The way I understood it is To - From = 3.4384e-05s - 1.8e-05s = 1.6384us = 8192*2ns = 8192/500MHz = Number of Samples of 8192/Sampling Frequency of 500MHz = Number of Samples/(2*Nyquist Frequency of 250MHz). And the waveform result (not attached) does display freq range up until 250MHz.

In expression 2. argument From is changed from 1.8e-05 to 3.0288e-05 such that 3.4384e-05s - 3.0288e-05s = 0.4096us = 2048*2ns = Number of Samples of 2048/(2*Nyquist Frequency of 250MHz). And I was expecting the waveform result still displays freq range up until 250MHz but instead it was until 1GHz. Looks like it was the Window Size of 8192 that made the difference. I have read the description in the Doc Assistant but still didn't understand what this argument does? - "The number of frequency domain points to use in the Fourier analysis. A larger window size results in an expectation operation over fewer samples, which leads to larger variations in the power spectral density. A small window size can smear out sharp steps in the power spectral density that might really be present."

In expression 3. the waveform result displays freq range up until 250MHz again instead of 1GHz.

Expression 4. gives the exact same waveform result as expr.2 does up until 1GHz where the value difference of Number of Samples didn't seem to have mattered.

Expression 5. gives the a smoothed version of waveform result up until 1GHz as expr.2 and 4 do.

Can anyone please help explain why 5 expressions give such measurements results because of their different argument settings?

Another question is I have divided all 5 expressions by 50 since my termination resistor is 50 ohms, and this is the right thing to do to divide the measurement by load resistor value?

And when I use Number of Samples of 8192 compared to 2048, shouldn't I expect four times of power according to this post below? Or maybe the video below at around 9:30?

"The power is going to be dependent upon the number of windows, and also the number of cycles - the more cycles, the more power there is in the 1st harmonic."

https://community.cadence.com/cadence_technology_forums/f/custom-ic-design/45464/psd-calculation-of-a-pulse-train-after-a-transient-simulation

www.youtube.com/watch

Thanks and best regards

1. dBm((psd((v("/MDI_P" ?result "tran") - v("/MDI_N" ?result "tran")) 1.8e-05 3.4384e-05 8192 ?windowName "Hanning" ?smooth 1 ?windowSize 8192 ?detrending "None" ?cohGain 1) / 50))

2. dBm((psd((v("/MDI_P" ?result "tran") - v("/MDI_N" ?result "tran")) 3.0288e-05 3.4384e-05 2048 ?windowName "Hanning" ?smooth 1 ?windowSize 8192 ?detrending "None" ?cohGain 1) / 50))

3. dBm((psd((v("/MDI_P" ?result "tran") - v("/MDI_N" ?result "tran")) 3.0288e-05 3.4384e-05 2048 ?windowName "Hanning" ?smooth 1 ?windowSize 2048 ?detrending "None" ?cohGain 1) / 50))

4. dBm((psd((v("/MDI_P" ?result "tran") - v("/MDI_N" ?result "tran")) 3.0288e-05 3.4384e-05 8192 ?windowName "Hanning" ?smooth 1 ?windowSize 8192 ?detrending "None" ?cohGain 1) / 50))

5. dBm((psd((v("/MDI_P" ?result "tran") - v("/MDI_N" ?result "tran")) 3.0288e-05 3.4384e-05 8192 ?windowName "Hanning" ?smooth 1 ?windowSize 2048 ?detrending "None" ?cohGain 1) / 50))