sgq03507
Newbie
Hi,
My question is about Mixed-Mode S parameter.
First, let consider a differential circuit configuration below.
Now we again consider the circuit above is measured with VNA (Vector Network Analyzer) using single-ended S parameter measurement.
Then the circuit will be rewritten as below. Numbers [1] to [4] are port numbers for single-ended S parameter.
In the next, narrow down the consideration to the Differential Port 1 and Sdd11 parameter only.
If we only consider the Differential Port 1, single-ended S parameter (using VNA) that is needed to obtain Sdd11 is S11, S31, S13, S33.
Using these single-ended S parameters, we can obtain Sdd11 as:
Sdd11 = (1/2)(S11 - S31 - S13 + S33) (1)
We could see this equation in many articles/books.
BUT I am confusing if I think this circuit with much simpler configuration. I will show my confusion below.
Again, let's consider much simpler configuration for Differential Port 1 as below.
In this case, normalized characteristic impedance is assumed as 50 ohm and normalized differential impedance is assumed as 100 ohm.
In the circuit above, single-ended S parameters for port [1] and port [3] will be:
S11 = 0, S31 = S13 = 0, S33 = (100 - 50)/(100 + 50) = 0.333 (2)
Substitute (2) for (1), we can obtain:
Sdd11 = (1/2)(S11 - S31 - S13 + S33) = (1/2)(0.333) = 0.1665 (3)
Further, separate resistors' ground connection and connect RL1 and RL3 with series, then the circuit will be:
In the circuit above, if we calculate differential S parameter Sdd11 with normalized differential impedance of 100 ohm, we can get:
Sdd11 = [(50 + 100) - 100]/[(50 + 100) + 100] = 0.2 (4)
The results (3) and (4) are not match. Why are these results not match? This is my question.
In addition, for the verification, if we consider the Differential Port 1 as balanced single-ended two ports as:
then single-ended S parameters for single-ended port [1] and [3] will be:
S11 = S33 = (75 - 50)/(75 + 50) = 0.2 (5)
(4) and (5) results are match and can be agreed each other. BUT (3) to (4) and (3) to (5) are not much and can NOT be agreed.
Why are these results not match?
Please advise!
My question is about Mixed-Mode S parameter.
First, let consider a differential circuit configuration below.
Now we again consider the circuit above is measured with VNA (Vector Network Analyzer) using single-ended S parameter measurement.
Then the circuit will be rewritten as below. Numbers [1] to [4] are port numbers for single-ended S parameter.
In the next, narrow down the consideration to the Differential Port 1 and Sdd11 parameter only.
If we only consider the Differential Port 1, single-ended S parameter (using VNA) that is needed to obtain Sdd11 is S11, S31, S13, S33.
Using these single-ended S parameters, we can obtain Sdd11 as:
Sdd11 = (1/2)(S11 - S31 - S13 + S33) (1)
We could see this equation in many articles/books.
BUT I am confusing if I think this circuit with much simpler configuration. I will show my confusion below.
Again, let's consider much simpler configuration for Differential Port 1 as below.
In this case, normalized characteristic impedance is assumed as 50 ohm and normalized differential impedance is assumed as 100 ohm.
In the circuit above, single-ended S parameters for port [1] and port [3] will be:
S11 = 0, S31 = S13 = 0, S33 = (100 - 50)/(100 + 50) = 0.333 (2)
Substitute (2) for (1), we can obtain:
Sdd11 = (1/2)(S11 - S31 - S13 + S33) = (1/2)(0.333) = 0.1665 (3)
Further, separate resistors' ground connection and connect RL1 and RL3 with series, then the circuit will be:
In the circuit above, if we calculate differential S parameter Sdd11 with normalized differential impedance of 100 ohm, we can get:
Sdd11 = [(50 + 100) - 100]/[(50 + 100) + 100] = 0.2 (4)
The results (3) and (4) are not match. Why are these results not match? This is my question.
In addition, for the verification, if we consider the Differential Port 1 as balanced single-ended two ports as:
then single-ended S parameters for single-ended port [1] and [3] will be:
S11 = S33 = (75 - 50)/(75 + 50) = 0.2 (5)
(4) and (5) results are match and can be agreed each other. BUT (3) to (4) and (3) to (5) are not much and can NOT be agreed.
Why are these results not match?
Please advise!