Question about impedance measurement and S11

Dear dskang,

dskang said:

I was trying to make an LNA, and I measured input impedance and S11, to make a matching circuits. (Input impedance was measured by sp sim -> ZP -> Z11 plot)

With the obtained value, I simply calculated S11dB20 and seems like the calculate result and simulation results were different (The two notches are coming from output loads)

calculation : 20log |8.37+ j1.87|/|108.37+j1.87| = -22.xx so it is quite different from -13.64

Am I missing any concepts? Or in this case what is more reliable?

I could not help notice a couple items that I believe may be responsible for the difference between your calculated s11 (expressed in dB) result of -22.01 and the spectre result of 13.64. Let me know your thoughts...

1. First, if you examine the y-axis of the strip where you plot "Z11 imOhm", the units are in kohms - not in ohms. Hence, using an imaginary value of 1.87 in your formula for s11 expressed in dB is not consistent with your measurement result.

2. Second, in an S-parameter simulation, the definition of s11 is for a load terminated in the reference impedance - in this case 50 ohms I assume? I am not clear totally from your text, but I think you simulated Z11 using loads that are not terminated in the reference impedance as you state "The two notches are coming from output loads". Hence, you would not expect your computed S11 in dB to be the same value as spectre provides from an sp analysis. Am I correct?

3. Finally, I assume you have active devices in your LNA. The S-parameter analysis will only perform a small-signal analysis and will not include any device non-linearity. I am not sure once again, but did you simulate Z11 using a large signal analysis where the active devices in your LNA may be exhibiting non-linear responses?

I am sorry I don't fully understand your simulation description and results and hence will need you to tell me if any of my comments are relevant dskang! I am just trying to help!

Shawn

Dear Shawn,

First of all, I really appreciate your kind reply! And I'm also sorry that my question wasn't enough detailed. So let me answer one by one.

1. The y-axis represents k-Ohm, and this is because the peak reaches to k-Ohm. The place where vertical pointer are set, the values are 58 and 1.8 ohm.

2. The "load" I used this term for the upper-part of LNA. The structure is like this (at below figure), I used transformer at  a load for wide inter-stage matching. Two output pins are connected to the another port, to measure S21, or NF ...

So, I think the soaring impedance at two resonant frequency of the transformer and it's impedance at resonant frequency (which will be high) is trespassed to the input impedance (I'm making CG-LNA for now). (This is still just my guess, I'm still not 100% understand in transformer. Still, I think there cannot be other reason for such peaking.)

Another guess coming from here is that : I used ideal capacitor and inductors in here. So at resonant frequency, this will make yellow circled net (which is connected to drain of the transistor)  completely floating, so this is the place where errors starts to begin.

3. Sorry, I couldn't fully understand this question, maybe because I'm not having good understanding about how simulation works or about device modeling. What I can tell you is that I used simulation like this :

I'm glad to answer any additional things if needed. And thank you so much!

Regards,

Dongsuk

Dear Dongsuk,

dskang said:

1. The y-axis represents k-Ohm, and this is because the peak reaches to k-Ohm. The place where vertical pointer are set, the values are 58 and 1.8 ohm.

I believe the marker is providing the y-axis value - which is 1.8705 K - not 1.8 ohm. You can verify this by right clocking on the waveform for the imaginary value and send it to a table. Exine the value in the table and I think you will find it to be 1.8705K. Let me know!

dskang said:

2. The "load" I used this term for the upper-part of LNA. The structure is like this (at below figure), I used transformer at  a load for wide inter-stage matching. Two output pins are connected to the another port, to measure S21, or NF ...

 I don't understand where nodes OUT and OUTB are connected relative to the circled yellow net to their left. 

Shawn

Shawn,

Only a quick and incomplete comment from me. The markers (if I’m not mistaken) show the full value and not referred to the axis scaling. Even if that wasn’t the case, if the value was in k then it would have to be above the maximum y axis value, which seems unlikely. 

Andrew

Dongsuk,

OK, I had a little longer to look at this. I think the most likely situation here is that the original equation you're using to convert z-parameters to s-parameters is wrong. You've done a two-port s-parameter simulation, and your equation to compute S11 is only taking into account Z11 and not Z22. See https://en.wikipedia.org/wiki/Impedance_parameters (countless other other references of course).

Note that spectre actually computes the s-parameters, and I'd say there's little doubt that the s-parameters are correct. The z-parameters are then computed from the s-parameters (either inside the simulator if you ask it to save these on the s-parameter options) or as a post-postprocessing step when you plot ZP if they were not saved by the simulator. There's little doubt that these are correct too as they have been well-proven over many years.

Andrew

Dear Shawn,

1. I just read your advice, and exported results on table. As you can see on the table it showed the full values.

2. They are connected by two inductors, with "mind" in analogLib. As far as I understood it mutual correlation between two inductors. Below can be the equivalent circuit of the above: So OUT and OUTB is somehow connected to the yellow-circled net (I just wrote down what I understood from some manuals and papers, so please let me know if I'm mis-using something.)

Thank you again.

Regards,

Dongsuk

Dear Andrew,

Firstly, thank you for the kind reply. I read your advice and the link quickly, and understood what I missed (not taking into account Z22 in the S11 calculation). So this was more like my conceptual problem, not a technical question. I was only thinking that S11 = |Zs-ZL|/|Zs+ZL| ...

Again, thank you so much!

Regards,

Dongsuk

Dear Andrew and Dosuk,

Andrew Beckett said:

Only a quick and incomplete comment from me. The markers (if I’m not mistaken) show the full value and not referred to the axis scaling.

dskang said:

I just read your advice, and exported results on table. As you can see on the table it showed the full values.

I am sorry for my incorrect information! Thank you you for correcting my error Andrew, and for verifying your correct result Dongsuk. Please excuse my waste of both of your times!!

Shawn