For a directional coupler, if Pi = Incident Power, Po = Output power, Pf = Forward coupled power and Pr = Reverse coupled power; then, Directivity of directional coupler is

Explanation:

Directional Coupler and Its Directivity

Definition: A directional coupler is a passive RF/microwave device used to sample a small portion of power traveling in a transmission line, either in the forward or reverse direction. It has four ports: an input port (incident power Pi), an output port (output power Po), a coupled port (forward coupled power Pf), and an isolated port (reverse coupled power Pr).

Directivity: Directivity is a measure of how well the directional coupler isolates the forward-coupled power (Pf) from the reverse-coupled power (Pr). It is a critical parameter that indicates the performance of the coupler in distinguishing between the forward and reverse signals.

Formula: The directivity D of a directional coupler is expressed as the ratio of forward-coupled power (Pf) to reverse-coupled power (Pr), typically in decibels (dB). Mathematically,

D = Pf / Pr

In decibels, it is represented as:

D (dB) = 10 × log₁₀(Pf / Pr)

Significance: A higher directivity value indicates better isolation between forward and reverse signals, which is desirable for accurate signal sampling and analysis. Low directivity can lead to interference, reducing the efficiency of the coupler.

The correct option for the directivity of a directional coupler is: Option 1: Pf / Pr

This option is correct because it correctly defines directivity as the ratio of forward-coupled power (P_f) to reverse-coupled power (Pr). This ratio quantifies the coupler's ability to distinguish between the forward and reverse signals, providing an essential metric for evaluating its performance.