To analyze circuits using G-parameters (also known as "scattering parameters" or "S-parameters"), you need to understand how they represent the behavior of a microwave amplifier or any other microwave device. G-parameters are commonly used for modeling and characterizing multi-port microwave devices, such as amplifiers, mixers, filters, and other components.
G-parameters are a set of complex numbers that describe the relationship between the incident and reflected waves at each port of a multi-port device. For a two-port device, the G-parameters are represented as follows:
G11: Represents the forward gain from port 1 to port 1 (transmission from input to output at port 1).
G12: Represents the forward gain from port 1 to port 2 (transmission from input to output at port 2).
G21: Represents the forward gain from port 2 to port 1 (transmission from input to output at port 1).
G22: Represents the forward gain from port 2 to port 2 (transmission from input to output at port 2).
To analyze circuits using G-parameters, follow these steps:
Obtain G-parameters: Measure or simulate the microwave device to obtain its G-parameters. This can be done using specialized vector network analyzers (VNAs) or electromagnetic simulation tools like ADS (Advanced Design System) or CST (Computer Simulation Technology).
Interconnect devices: If you are analyzing a more complex circuit consisting of multiple microwave components, you can interconnect them by cascading their G-parameters. For a two-port device connected to another two-port device, the resulting overall G-parameters can be found using the following equations:
G11_total = G11_device1 + (G12_device1 * G21_device2 * G11_device2) / (1 - G22_device1 * G11_device2)
G12_total = G12_device1 * G22_device2 / (1 - G22_device1 * G11_device2)
G21_total = G21_device2 * G11_device2 / (1 - G22_device1 * G11_device2)
G22_total = G22_device2 + (G21_device2 * G12_device1 * G22_device1) / (1 - G11_device2 * G22_device1)
Where the "device1" represents the first device, and "device2" represents the second device in the chain.
Perform stability analysis: G-parameters can also be used to analyze the stability of an amplifier circuit. For a two-port device, the circuit is unconditionally stable if the following determinant condition is met:
Det(S) = (1 - |S11|^2 - |S22|^2 + |S11 * S22 - S12 * S21|^2) > 0
Where S11, S12, S21, and S22 are the S-parameters, which are related to G-parameters by S = (2G)/(1 + GG^), where G^ is the conjugate transpose of G.
Analyze gain and stability circles: By converting G-parameters to other formats such as Y-parameters or Z-parameters, you can visualize the device's performance on the Smith chart, which helps in understanding gain and stability circles.
Keep in mind that G-parameters are frequency-dependent, so the analysis should be done at the desired frequency range of interest. Additionally, when using G-parameters for stability analysis, it's crucial to ensure that the G-parameters are measured or simulated accurately, as stability is a critical aspect of microwave amplifier design.