How to transfer S11 to impedance?

[mrf245]

Hello everyone,
These days I try to design a RF amplifier base on RD15HVF1, for calculate of input and output match network, I need get this MOSFET input and output impedance value.
Now datasheet give me S11 and S22 value, which include mag and ang value. But I need R+JX format value for future calculation.
Impedance in 175MHz is 2.34-j8.01 ohms and mag/ang is 0.748 and -173.6.
Anyone know how to transfer it? Thank you very much.

[helius]

It appears the angle is being reported in degrees (although it could also be in grads!).
You need to convert that to radians, and then feed it to the cis function (cos + j sin) to get the unit vector. Then multiply by the magnitude in your table.

The conversion of degrees to radians is multiplication by \$ \pi \over 180 \$.

[mrf245]

It appears the angle is being reported in degrees (although it could also be in grads!).
You need to convert that to radians, and then feed it to the cis function (cos + j sin) to get the unit vector. Then multiply by the magnitude in your table.

The conversion of degrees to radians is multiplication by \$ \pi \over 180 \$.

OK, just try calculate 175MHz data.
First, transfer degrees to radians: -173.6*(PI/180)= -3.03
cos(-3.03)=0.9986
Second, amplitude=0.748*0.9986=0.7469
This 0.7469 is very different from normal impedance real? I think it need more transfer...

[ThomasDK]

It appears the angle is being reported in degrees (although it could also be in grads!).
You need to convert that to radians, and then feed it to the cis function (cos + j sin) to get the unit vector. Then multiply by the magnitude in your table.

The conversion of degrees to radians is multiplication by \$ \pi \over 180 \$.

OK, just try calculate 175MHz data.
First, transfer degrees to radians: -173.6*(PI/180)= -3.03
cos(-3.03)=0.9986
Second, amplitude=0.748*0.9986=0.7469
This 0.7469 is very different from normal impedance real? I think it need more transfer...

One last step: Multiply by Z0 (50)

[rfeecs]

No.

S11 is the reflection coefficient at the input.  You need to convert from reflection coefficient to impedance:

A calculator (Gamma is S11):
https://leleivre.com/rf_gammatoz.html

Some equations:
http://www.pilloud.net/op_web/one_port.pdf

The equation is:

Z=Z0 (1 + S11) / (1 - S11)

S11 and Z are vectors, Z0 is your system impedance, a scalar, usually 50 ohms

[mrf245]

Ok, Thanks for everyone help, I understand all transfer process.

just try calculate 175MHz data again in RD15HVF
First, calculate real and imaginary of Γ
real  =cosθ*MAG=-0.993*0.748=-0.7433
imag=sinθ*MAG=-0.111*0.748=-0.083(j)
So Γ is -0.7433-j0.083
Now transfer Γ to R+jX model:
Z=Zo*((1+Γ)/(1-Γ))=50*((0.26-j0.08)/(1.74+j0.08))=7.35-j2.63
Finished.

[in3otd]

Z=Zo*((1+Γ)/(1-Γ))=50*((0.26-j0.08)/(1.74+j0.08))=7.35-j2.63

Note that this is the input impedance of your device only when its output is terminated to 50 ohm; this comes from the definition of S-parameters.
If the device is terminated in a different impedance (and it will surely be if you want to get some power from it) the input impedance will also change, due to the internal feedback (S12).
Moreover, the S-parameters assume that the device is linear, that is the signal amplitudes are small. For a power amplifier this will not be the case so the impedances you will get for large signals will be different. In practice you may use the S-parameters to get a first approximation of the amplifier gain and the matching networks needed but you will likely need to tweak the networks to optimize the operation at full power.

[mrf245]

Z=Zo*((1+Γ)/(1-Γ))=50*((0.26-j0.08)/(1.74+j0.08))=7.35-j2.63

Note that this is the input impedance of your device only when its output is terminated to 50 ohm; this comes from the definition of S-parameters.
If the device is terminated in a different impedance (and it will surely be if you want to get some power from it) the input impedance will also change, due to the internal feedback (S12).
Moreover, the S-parameters assume that the device is linear, that is the signal amplitudes are small. For a power amplifier this will not be the case so the impedances you will get for large signals will be different. In practice you may use the S-parameters to get a first approximation of the amplifier gain and the matching networks needed but you will likely need to tweak the networks to optimize the operation at full power.

Thank you very much for your answers

[OwO]

The S11 of the transistor isn't necessarily the input impedance, because S11 is measured with port 2 terminated with 50 ohms. In a typical amplifier the transistor's output doesn't see 50ohms but rather an "optimal" load impedance that was determined by load pull (trial and error) measurements. The datasheet of rd15hvf1 tells you what the optimal load impedance is (see attached), and what the input impedance is when presented with that load. Alternatively you can import the S parameters into RFSim99 and do a simulation to determine input impedance.

[re1177]

mrf245: Your summary was really helpful for me. You mentioned an example. But how to calculate cosθ? I don't have any phase value.
Only I am getting data # Hz S RI with Nanovna

5000000 -0.558689675490485 0.8049481718630415

5386904 -0.5036385824989272 0.8397630336146349
Do you know how to solve this issue?

[mio83]

I have made a video with all the calculations (mostly as a reminder for myself in the future).
It's 25mins long, and in italo-english  , so watch it at your own risk