Understanding S21 for an unmatched network

I have a very basic question regarding S21 when there is an impedance mismatch with the characteristic impedance.

I have attached a figure of the test circuit.



Assume that the Transmission line is loseless and has an effective length of λ/4 at Frequency=200GHz. When I plot the S11 at DC, it's simply

S11= (1M-10)/(1M+10)~0.99998 (pretty close to 0dB, it's complete reflection at the input).
S21 obtained is around -44 dB (based on simulation). Is this because, |S11|²+|S21|²=1 for a lossless transmission line?
What I don't get is the following.

At DC, the gain of the above network is 1M/(1M+10) ~ 1, on the other hand, S21 is much below (i.e. -44 dB). What am I missing? I thought S21 is an indication of insertion loss but this result is counter intuitive. I am so confused...:bang:

What matters is the length of the line compared to the wavelength, or for the time domain guy: the propagation delay in the line compared to the signal rise/fall time.

If the line propagation delay is short compared to the signal timing, the line doesn't matter. Whatever is connected at the end of the line will be "visible" at the line input, because the line delay is short compared to the other time responses.

If the line propagation delay is long compared to the signal timing, the signal will first see a load 40 Ohm when it gets to the beginning of the line, keeping constant 40 Ohm on the line, then see an almost open at the 1MOhm load. These discontinuities will cause reflection, and because the rise/fall time is now fast compared to the propagation delay you will see them as individual pulses. So it takes one round trip (source - load - and back) until the voltage at the input is what you expect at DC for that load impedance.

Are you setting port impedances for S parameter calculation to 10 ohm and 1Mohm? Looks just useless.

FvM said:

Are you setting port impedances for S parameter calculation to 10 ohm and 1Mohm? Looks just useless.

Click to expand...

Yes, why do you say it's useless? Note that I am not calculating the s11 or s21 of the transmission line, as in this case I have to set the impedance to 50 ohm. What I am interested in is the reflection coefficient and transfer characteristics in the presence of impedance mismatch.

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volker@muehlhaus said:

What matters is the length of the line compared to the wavelength, or for the time domain guy: the propagation delay in the line compared to the signal rise/fall time.

If the line propagation delay is short compared to the signal timing, the line doesn't matter. Whatever is connected at the end of the line will be "visible" at the line input, because the line delay is short compared to the other time responses.

If the line propagation delay is long compared to the signal timing, the signal will first see a load 40 Ohm when it gets to the beginning of the line, keeping constant 40 Ohm on the line, then see an almost open at the 1MOhm load. These discontinuities will cause reflection, and because the rise/fall time is now fast compared to the propagation delay you will see them as individual pulses. So it takes one round trip (source - load - and back) until the voltage at the input is what you expect at DC for that load impedance.

Click to expand...

I understand this, but my question is if I place this circuit and simulate for s-parameter (ADS or Cadence), I get the above-mentioned result for S21. That's the part I don't understand

S parameters have been invented to specify and analyze RF system that deal with incident and reflected waves. Although you can apply the formalism to DC frequency, you shouldn't expect intuitive insights. You'll rather expend some effort to explain why the results are correct though. Setups with different port impedances are particularly counter intuitive, I fear.

FvM said:

S parameters have been invented to specify and analyze RF system that deal with incident and reflected waves. Although you can apply the formalism to DC frequency, you shouldn't expect intuitive insights. You'll rather expend some effort to explain why the results are correct though. Setups with different port impedances are particularly counter intuitive, I fear.

Click to expand...

The thing is I have seen this analysis to be kind of useful especially when you have impedance mismatch (like 40 ohms Zo and 50 ohm loads), you would see ripples in S21, which can be obtained based on this analysis. That's the reason why I felt it would be useful to know.

That's surely possible and can be useful if you understand the meaning of S-parameters right. Your example describes a huge impedance mismatch which shows in S11 and S21. In S parameter terms, the incident wave is completely reflected.

Hi venn_ng, need to be careful when trying to use and interpret s parameters, especially in cases where you're considering putting things on the ports of the network which aren't 50 ohms.

You should review the basic definition of power waves a and b, and the scattering matrix s, from Kurokawa's paper:



Here, Zi is the characteristic impedance of the network. In theory one can choose Zi arbitrarily, and it can actually be different for each port of a network, but in practice we basically always use 50 ohms (because all of our test equipment happens to be set up for 50 ohms).

However, it's important to realize that the s parameters of a network do not depend on the impedances connected to its ports.

This is contradicted by a lot of references out there which are sloppy with their terminology. For example, if I take an ideal transmission line like yours and connect both ends to a VNA, I should measure |S11|=0 and |S21|=1. But if I disconnect one end of the cable from port 2 of the VNA, I will measure |S11|=1 and |S21|=0. And if I then connect the cable to various impedances (like 10 ohms or 100ohms) I will see the measured S11 change phase and magnitude.

But its incorrect to claim that the S11 or S21 of the cable is actually changing. Those are properties of the cable itself, and I'm not changing the cable. What the VNA measures is everything between its two ports, and when I disconnect the cable it no longer sees just the cable, but a big open circuit along with the cable. Therefore the results displayed by the VNA don't describe just the cable anymore. We have to be careful when discussing S parameters, and always include context on the experimental setup.

Also your comment about DC gain is another good inroad to understanding s parameters better. Voltage gain and S21 are only the same when all ports are terminated with their characteristic impedance. Therefore if your S21 is derived with a characteristic impedance of 50ohms at both ends (like it is in 99.99% of cases), but you terminate its ports with different impedances, you should expect your voltage gain and S21 to be different.