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[SOLVED] How to take to account impedance mismatch losses when cascading 2-port networks as RF System?

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fred3991

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I'm trying to learn how to correctly calculate (cascade==RF system cascading) the connection of 2-port networks, taking into account mismatch losses. For example There is a first 2-port network, its S parameters at 10GHz,

2021-06-30T16_47_27.png
2021-06-30T16_47_51.png


And a second 2-port network.
2021-06-30T16_48_13.png
2021-06-30T16_48_33.png

They are shown in the pictures below. If you try to add them up as an RF system (!!!not adding S parameters via ABCD or T matrices!!!) - you have to add their insertion loss ((-0.577)+ (- 0.895) = -1.472 ). So the total insertion loss should be 1.472 - only if the 2-port networks themselves are matched by exactly 50 ohms (perfect impedance matching). But in fact, as you can see in the picture in ADS and ADSimRF - the insertion loss is 1.508.

2021-06-30T16_49_25.png
2021-06-30T16_49_05.png


Снимок.PNG



My question is this. If I know the input and output impedance of the 2-port networks (s11 and s22 impedance on SmithChart) how do I need to account for mismatch losses to get the same results in ADS and ADSImRF ? I think I need to calculate the mismatch loss between port 1(50 ohms) - and the first 2-port network (46.999+j16.888), then between network 1(46.999+j16.888) and network 2 (55.2+j2.594) and finally between network 2(55.2+j2.594) and port 2.


I tried to use the formula


MismatchLosses = -10log(1-Г^2)


but either I calculated something wrong, or it does not fit.


I will be grateful for any help or advice
 

i am not sure exactly what you are trying to say.
if you are trying to simulate the total loss of a network, there is the loss due to mismatch at the input port, the resistive loss of the network itself, and the mismatch loss of the output mismatch.

i do not see where you are taking into account the loss of the middle term.
 

i am not sure exactly what you are trying to say.
if you are trying to simulate the total loss of a network, there is the loss due to mismatch at the input port, the resistive loss of the network itself, and the mismatch loss of the output mismatch.

i do not see where you are taking into account the loss of the middle term.
I'm trying to calculate rf system (like ADSimRF) to see system paremeters. Can you show me how to do this? to achieve proper value
 

(!!!not adding S parameters via ABCD or T matrices!!!)

Why not? ABCD matrix (chain matrix) would be the correct method to get the cascaded result, including mismatch losses between the two non-matched components.

In real life, there is some length of line between them, which must also be considered, so you cascade 3 blocks.
 
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Why not? ABCD matrix (chain matrix) would be the correct method to get the cascaded result, including mismatch losses between the two non-matched components.

In real life, there is some length of line between them, which must also be considered, so you cascade 3 blocks.
The point is that I need to make a system calculation of the RF path, using only the data - noise figure, gain, IP1dB, etc. (and complex input and output impedance of 2-port network)

As it is done in the program ADSimRF - But!

Not under the assumption that each unit is perfectly matched at 50 ohms, but using real values from device design.
 
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Sorry, I don't get your point. Cascading blocks using ABCD matrix is what simulation tools like ADS do, and that includes the effect of cascaded mismatch etc.

That said, your homebrew math looks wrong to me. You can't use 50 Ohm S21 and just add a few mismatch terms. Proper math using ABCD cascade is what we teach in RF classes to solve this exact problem.

Regarding ADSimRF, I agree that this looks too simple if it doesn't account for complex impedances.
 
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Sorry, I don't get your point. Cascading blocks using ABCD matrix is what simulation tools like ADS do, and that includes the effect of cascaded mismatch etc.

That said, your homebrew math looks wrong to me. You can't use 50 Ohm S21 and just add a few mismatch terms. Proper math using ABCD cascade is what we teach in RF classes to solve this exact problem.

Regarding ADSimRF, I agree that this looks too simple if it doesn't account for complex impedances.
I completely agree with you about multiplying ABCD matrices - this is the most proven and accurate method.

However, ADSimRF, as you can see in the screenshot - shows a power gain value of -1.5 - if I set Zin Zout - from my 2-port networks. (only the real part).

I apologize, I just saw in the ADISimRF Help - scalar mismatch loss.
I guess the answer to my question is hidden somewhere in here.
3123123123.PNG
 

Ok, it seems we agree ABCD is the correct math.

And from what I can see, impedances are close enough to 50 Ohm so that ADISimRF with unknown scalar calculation and ADS with complex ABCD calculation agree on the -1.5dB for the cascaded stages.

So your question is if/how to calculate the same result by hand, if you consider ABCD math too complicated? Or what exactly is your question? If you have ADS available, why not use that?

One detail mistake that I spotted your initial post was that you want to add a mismatch loss between source and your first stage input, but that is already included in the 50 Ohm S-params: the S21 there is already under 50 ohm source/load conditions. Same for the output side. So only the inter-stage matching must be considered.

~~

As mentioned above, you would also need to include the LINE (phase shift!) between both devices because that will turn around impedance in Smith chart, and thus change the inter-stage matching.
 

Ok, it seems we agree ABCD is the correct math.

And from what I can see, impedances are close enough to 50 Ohm so that ADISimRF with unknown scalar calculation and ADS with complex ABCD calculation agree on the -1.5dB for the cascaded stages.

So your question is if/how to calculate the same result by hand, if you consider ABCD math too complicated? Or what exactly is your question? If you have ADS available, why not use that?

One detail mistake that I spotted your initial post was that you want to add a mismatch loss between source and your first stage input, but that is already included in the 50 Ohm S-params: the S21 there is already under 50 ohm source/load conditions. Same for the output side. So only the inter-stage matching must be considered.

~~

As mentioned above, you would also need to include the LINE (phase shift!) between both devices because that will turn around impedance in Smith chart, and thus change the inter-stage matching.

I do not even have any doubt about the correctness of the mathematics :) using ABCD , T, Z, and Y matrices, as I already use it for automated synthesis of some passive microwave devices cells (phase shifter and attenuator cells) and do not consider this mathematics too complicated.

My question is exactly how to calculate the interstage losses - as done in ADISimRF, to estimate more accurately total P1dB value using only gain, impedance values and P1dB of individual 2-port network.

I'll try to explain what I need exactly.
Actually these two 2-port networks are the phase shifter cells (providing 22.5 and 90 phase shift). But as you know in a complete phase shifter circuit there can be 4-5-6 cells (bits), etc. Also, by themselves - digital phase shifters have a rather poor matching (S11/S22 ~ -15-10 dB). (Even if the individual cells are perfectly matched, and if not, additional matching circuits (inductors, lines, mimcap) will be used)
And also achieving a high P1dB value is a challenge (for us at least, we are not yet the biggest professionals in this field, but only learning)))

In order to achieve the best performance at almost the final stage of the design, the question appears - about the order of the cells in the RF path (5.625-22.5-45...etc. or 22.5-45.-90...etc.).

This plays an important role in improving the matching of the whole device (better cell order gives better S11/S22 values of the whole device) low RMS value (but maybe the applied circuit of the individual cell plays a big role here), and probably will also give an ability to achieve the highest P1dB value.

At the moment I am developing a program, as part of my PhD thesis, for automated synthesis of the whole device (like a phase shifter or attenuator) and for selecting a particular cell sequence I just use cascading via ABCD matrices to calculate all the small-signal parameters.

Program optimization algorithm, calculating the correct P1dB value every time is a totally different task, more complicated, where numerical methods are used.(as far as I know).
Besides, it will significantly increase the running time of the program.

I know it will not be perfect accurately, but I want to get a result as close as possible to what I get from a commercial CAD (ADS or Cadence) in terms of final S parameters and power characteristics of the device.

That is why I need to calculate the value of the interstage loss in order to make the correct adjustments of the total gain and total P1dB values in a given analyzed sequence of phase shifter cells. (As it is done in ADISimRF in the calculation of the system parameters).
 

I see ... Here is my quick & dirty calculation (ignoring the imaginary part):

Mismatch stage 1 in 50 Ohm environment (as already included in S-Params):
50 <> 47 Ohm: mismatch loss 0.004 dB
Mismatch stage 2 in 50 Ohm environment (as already included in S-Params):
50 <> 55.2 Ohm: mismatch loss 0.050 dB
Sum of both: 0.054 dB

Mismatch cascaded:
47 <> 55.2: mismatch loss 0.080 dB

Mismatch loss cascaded minus mismatch in 50 Ohm: 0.080 dB - 0.054 dB = 0.026 dB

That's my idea. But we would need to use complex impedance to get accurate results.
 
Assuming you have the complex S parameters of each network to begin with:
1. Convert each S matrix to its ABCD matrix
2. Multiply the two (or more) ABCD matrices together
3. Convert The resulting ABCD matrix back to S matrix.

As for P1dB and NF, that's not so straightforward. Strictly speaking, network parameters alone cannot tell you anything about P1dB. NF can be estimated using Friis formula, but only if you actually know the gain and NF of each stage when terminated as they will be in your overall system.
 
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I see ... Here is my quick & dirty calculation (ignoring the imaginary part):

Mismatch stage 1 in 50 Ohm environment (as already included in S-Params):
50 <> 47 Ohm: mismatch loss 0.004 dB
Mismatch stage 2 in 50 Ohm environment (as already included in S-Params):
50 <> 55.2 Ohm: mismatch loss 0.050 dB
Sum of both: 0.054 dB

Mismatch cascaded:
47 <> 55.2: mismatch loss 0.080 dB

Mismatch loss cascaded minus mismatch in 50 Ohm: 0.080 dB - 0.054 dB = 0.026 dB

That's my idea. But we would need to use complex impedance to get accurate results.
Yes, its definitely need to consider the imaginary part in this calculation.

I found one paper

http://utpedia.utp.edu.my/2937/1/Regina_Gani_MSc_Thesis_UTP.pdf

Here on page 26 there is a formula for calculating mismatch losses. I tried to use it, but either I misunderstood something in the calculation, or this formula is not suitable for me.
1626514462359.png



Also, on another forum - one person answered my question using Transducer power Gain and Г.


But still, I can't get results similar to ADS or ADISimRF.

So interesting - it seems like a very simple question, but in fact I still have no idea how to calculate what I need as correctly as possible.:unsure:😔
--- Updated ---

Assuming you have the complex S parameters of each network to begin with:
1. Convert each S matrix to its ABCD matrix
2. Multiply the two (or more) ABCD matrices together
3. Convert The resulting ABCD matrix back to S matrix.

As for P1dB and NF, that's not so straightforward. Strictly speaking, network parameters alone cannot tell you anything about P1dB. NF can be estimated using Friis formula, but only if you actually know the gain and NF of each stage when terminated as they will be in your overall system.
I've already written above why it doesn't work for me to use ABCD or T parameters.

If you try to calculate cascade P1dB with nets AS IF matched at 50 ohms each - you get one value. But, if you take mismatch losses into account - you will get the total P1dB higher, because mismatch losses - will increase the cell losses - accordingly if you look at the cascade P1dB formula - you will see that this leads to an increase in the total P1dB.

So I need to eventually calculate the approximate P1dB without using harmonic balance or numerical methods - as I wrote above.

I still don't understand how do I calculate the interstage mismatch loss (get the total dB(S21) of the two networks = 1.508 as in ADS) AND/OR then - how much should I change the cell loss to get a more accurate total P1dB value.
 

If you try to calculate cascade P1dB with nets AS IF matched at 50 ohms each - you get one value. But, if you take mismatch losses into account - you will get the total P1dB higher, because mismatch losses - will increase the cell losses - accordingly if you look at the cascade P1dB formula - you will see that this leads to an increase in the total P1dB.

So I need to eventually calculate the approximate P1dB without using harmonic balance or numerical methods - as I wrote above.
Just to confirm your intent, for each stage you have the following data:
1. The small signal S parameters
2. P1dB, characterized with specific terminating impedances
3. NF, again characterized with specific terminating impedances (perhaps different from those used for P1dB)

With just that, I don't believe it's possible to calculate cascaded P1dB when the terminating impedances are different from those used to characterize the initial P1dB data. P1dB is an inherently nonlinear phenomenon, and the relationship between P1dB and terminating impedance can't be generalized.

Similarly I don't think you can calculate the effect of different terminating impedances on NF without a detailed model of the DUT. Not so sure about this one though.
 

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