# Stability of a RF Amplifier

It's written that (page 2):

In an RF transmission network, if the reflection coefficient of a certain port is greater than 1, positive feedback will be introduced which may cause the amplifier unstable. In order to ensure unconditional stability, the real part of the impedance of the signal source, the load, the amplifier input, and the amplifier output, respectively, should be greater than 0.

1. To understand it, I think I should firstly understand what is meant for stability. Is it BIBO stability (Bounded Input Bounded Output) or does it mean that the amplifier starts oscillating?

2. The author speaks about load (or input) resistance and positive feedback. If the first one is negative, the last one occurs. Why? If the author refers to absolute negative resistance, it means that the latter changes its voltage proportionally to the current (like a positive resistor) but adds it to the input voltage (instead to subtract). I can't see what this has to do with positive feedback.

3. Positive feedback doesn't necessarily mean instability. It depends on the poles of the resulting transfer function. So, which is the point of this analysis?

1. Stability in rf amplifier design:

Unconditional stability - The amplifier is always stable no matter the input and output impedances of the source/load you present to it.

Conditional stability - There's a range of impedances for the source and load for which the amplifier will be stable. If the source or the load impedances are outside this range, the amplifier may become unstable.

If the amplifier is unstable it means oscillations can occur.

1. I haven't fully read the article and could not find the statement you mention. What I know is that unconditional stability in an amplifier design can be verified using the S-parameters of the amplifier, by checking Rollet's condition: $$K = \frac{1-|S_{11}|^2-|S_{22}|^2+|\Delta|^2}{2|S_{12}S_{21}|} > 1$$ and that: $$|\Delta| = |S_{11}S_{22}-S_{12}S_{21}| < 1$$

If you check literature around the formulation of these expressions, you'll also find that if the input/output impedance of the amplifier have a negative real part impedance (not to be confused with the concept you mentioned), then the reflection coefficient at the input/output would be greater than 1, hence leading to possible oscillations.

1. If positive feedback occurs in an amplifier, means that part of the output signal is adding to the input of the amplifier, this is an essential condition to start oscillation in an amplifier design. As stated before, positive feedback will mean a reflection coefficient higher than 1 at either port, this means the unconditional stability criteria can never be met.
• Which is the physical link between negative resistance and positive feedback/instability? Apr 28 at 3:20