How can you calculate the current gain from S-parameters?
1 Answer
To calculate the current gain (also known as current transfer ratio or current gain ratio) from S-parameters, you'll need to have access to the relevant S-parameter data for the device or circuit under consideration. S-parameters describe the relationship between incident and reflected/received waves in a multi-port network. These parameters are usually provided in the form of a matrix, commonly known as the S-matrix.
For a two-port network (like a transistor or amplifier), the S-matrix takes the following form:
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[ b1 ] [ S11 S12 ] [ a1 ]
[ ] = [ ] [ ]
[ b2 ] [ S21 S22 ] [ a2 ]
Where:
a1 and a2 are the incident waves at Port 1 and Port 2, respectively.
b1 and b2 are the reflected/received waves at Port 1 and Port 2, respectively.
S11, S12, S21, and S22 are the S-parameters that define the characteristics of the two-port network.
For calculating the current gain (current transfer ratio) of the network, we are interested in the current flowing into and out of the ports. Assuming the input current at Port 1 is Iin1 and the output current at Port 2 is Iout2, the current gain Ai is given by:
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Ai = Iout2 / Iin1
To extract the current gain from S-parameters, you'll typically need to perform some conversions. For instance, if you have the scattering parameters (S-parameters) S11, S12, S21, and S22, you can find the current gain using the following steps:
Find the voltage gain Av from S-parameters:
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Av = S21 / (1 - S11 * S22)
Calculate the input impedance Zin and the output impedance Zout using S-parameters:
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Zin = (1 + S11) / (1 - S11 * S22 - S12 * S21)
Zout = (1 + S22) / (1 - S11 * S22 - S12 * S21)
Convert the voltage gain Av to the current gain Ai using the input and output impedances:
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Ai = Av * (Zout / Zin)
It's important to note that S-parameters are typically frequency-dependent, so the current gain calculated using the above method will be valid at a specific frequency for the two-port network. If you want to determine the current gain across a range of frequencies, you need to repeat these steps for each frequency point using the corresponding S-parameters.
For a two-port network (like a transistor or amplifier), the S-matrix takes the following form:
css
Copy code
[ b1 ] [ S11 S12 ] [ a1 ]
[ ] = [ ] [ ]
[ b2 ] [ S21 S22 ] [ a2 ]
Where:
a1 and a2 are the incident waves at Port 1 and Port 2, respectively.
b1 and b2 are the reflected/received waves at Port 1 and Port 2, respectively.
S11, S12, S21, and S22 are the S-parameters that define the characteristics of the two-port network.
For calculating the current gain (current transfer ratio) of the network, we are interested in the current flowing into and out of the ports. Assuming the input current at Port 1 is Iin1 and the output current at Port 2 is Iout2, the current gain Ai is given by:
makefile
Copy code
Ai = Iout2 / Iin1
To extract the current gain from S-parameters, you'll typically need to perform some conversions. For instance, if you have the scattering parameters (S-parameters) S11, S12, S21, and S22, you can find the current gain using the following steps:
Find the voltage gain Av from S-parameters:
makefile
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Av = S21 / (1 - S11 * S22)
Calculate the input impedance Zin and the output impedance Zout using S-parameters:
scss
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Zin = (1 + S11) / (1 - S11 * S22 - S12 * S21)
Zout = (1 + S22) / (1 - S11 * S22 - S12 * S21)
Convert the voltage gain Av to the current gain Ai using the input and output impedances:
makefile
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Ai = Av * (Zout / Zin)
It's important to note that S-parameters are typically frequency-dependent, so the current gain calculated using the above method will be valid at a specific frequency for the two-port network. If you want to determine the current gain across a range of frequencies, you need to repeat these steps for each frequency point using the corresponding S-parameters.