Stability is arguably the most critical aspect of RF amplifier design. An amplifier is stable if it remains free from unwanted oscillations under all specified operating conditions. An unstable amplifier will not perform its intended function; instead, it will act as an oscillator, converting DC power into unwanted RF signals, potentially damaging components, or severely degrading system performance. S-parameters provide direct methods to assess the stability of active two-port networks.

The concept of unilateral or bilateral nature is fundamental to understanding feedback and stability.
- Unilateral Network: An ideal unilateral network is a theoretical construct where there is absolutely no signal transmission or feedback from the output port back to the input port.
- S-parameter Condition: For a two-port network, this means S12 =0.
- Implication: If a device is truly unilateral, its input characteristics (like Γin) are completely independent of the load connected to its output, and its output characteristics (like Γout) are completely independent of the source connected to its input. This significantly simplifies design, as input and output matching networks can be designed independently.
- Reality: Perfect unilateralism is rarely achieved in real active devices like transistors due to unavoidable parasitic capacitances and inductances that provide a feedback path. However, many RF amplifiers are designed to be 'approximately unilateral' by ensuring very high reverse isolation (very small ∣S12∣).
- Bilateral Network: A bilateral network is one where there is some degree of signal transmission or feedback from the output back to the input, meaning S12 > 0.
- Reality: Almost all practical active devices at RF frequencies are bilateral. Even a tiny S12 can become significant at high frequencies or high gain.
- Implication: The input impedance of a bilateral device is dependent on the load connected to its output (Γin depends on ΓL), and its output impedance is dependent on the source connected to its input (Γout depends on ΓS). This interdependence makes the design of simultaneous matching networks and the analysis of stability more complex.

An active two-port network (like a transistor or an amplifier stage) is considered unconditionally stable if it will remain stable (i.e., not oscillate) regardless of what passive source impedance (ZS, corresponding to ∣ΓS∣ ≤1) or passive load impedance (ZL, corresponding to ∣ΓL∣ ≤1) is connected to it. This is the most desirable characteristic for a general-purpose amplifier that needs to operate reliably in various system environments.
The unconditional stability of a two-port network can be mathematically determined from its S-parameters using two key criteria: the K-factor (Rollett stability factor) and the Delta (Δ) parameter.
The conditions for unconditional stability are:
1. K > 1: The K-factor (stability factor) must be greater than 1.
- K=(1−∣S11∣2−∣S22∣2+∣Δ∣2)/(2∗∣S12∗S21∣)
- Where Δ (Delta) is the determinant of the S-matrix, calculated as: Δ=S11∗S22−S12∗S21
2. ∣Δ∣<1: The magnitude of the determinant of the S-matrix must be less than 1.

• If K > 1 AND ∣Δ∣<1: The network is unconditionally stable.
• If K < 1: The network is conditionally stable. This means the device can be made stable for certain source and load terminations, but there exist specific passive source and load impedances that will cause it to oscillate. In this case, designers must use stability circles (a graphical tool plotted on the Smith Chart, which will be covered in a later module) to identify the regions of source and load impedances that cause instability.
• If K = 1: The network is marginally stable, sitting right at the boundary between unconditional and conditional stability. Any slight change in parameters or operating conditions could push it into instability.

• The K-factor essentially quantifies the inherent 'stability margin' of the device. It compares the internal positive feedback (related to S12 ∗S21) to the reflections at the input and output. A higher K-factor implies that the device is less likely to oscillate.
• The Δ parameter (determinant of the S-matrix) is also related to the internal feedback and transfer characteristics of the device. The condition ∣Δ∣<1 is necessary to ensure that the network is 'passive at the boundary,' meaning it cannot self-oscillate simply from energy circulating within the network itself when terminated reactively.