To determine the voltage transfer function and stability of a feedback amplifier with dominant poles and zeros, you can follow these steps:
Feedback Amplifier Configuration:
Identify the configuration of the feedback amplifier. The most common types are voltage-series and current-series feedback amplifiers.
Feedback Network:
Determine the feedback network used in the amplifier. It could be series or shunt (parallel) feedback.
Open-Loop Gain (A(s)):
Find the open-loop gain of the amplifier without considering the feedback network. This is the gain from the input to the output when the feedback loop is open. It includes the effects of all active and passive components of the amplifier, except for the feedback network.
Feedback Factor (β(s)):
Calculate the feedback factor, which is the fraction of the output signal that is fed back to the input. It is the transfer function of the feedback network.
Closed-Loop Transfer Function (T(s)):
The closed-loop transfer function, also known as the voltage transfer function, is the transfer function from the input to the output of the entire feedback amplifier system. It is given by the formula:
T(s) = A(s) / [1 + A(s) * β(s)]
Dominant Poles and Zeros:
Identify the dominant poles and zeros of the closed-loop transfer function (T(s)). Dominant poles and zeros are those that have a significant effect on the system's behavior and stability. These poles and zeros typically lie closest to the origin on the s-plane.
Stability Analysis:
The stability of the feedback amplifier can be determined by checking the locations of the poles of the closed-loop transfer function (T(s)). For a system to be stable, all the poles of T(s) should have negative real parts.
If all poles have negative real parts, the system is stable.
If any pole has a positive real part, the system is unstable.
For a feedback system to be stable, the poles should not lie on the right half of the s-plane (i.e., have positive real parts).
Phase Margin and Gain Margin (Optional):
To further analyze the stability, you can calculate the phase margin and gain margin. Phase margin is the amount of phase lag the system can tolerate before becoming unstable, and gain margin is the amount of gain reduction the system can tolerate before instability occurs.
Remember, the analysis becomes more complex if the feedback network is nonlinear or if there are multiple feedback paths. In such cases, you may need to use advanced stability analysis techniques. Additionally, it's crucial to use appropriate modeling techniques and accurate component values to obtain reliable results.