Experiment 3 : Voltage Standing Wave Ratio and Standing Wave

            

           

             The terms matching, inverse standing wave ratio m, mismatching, reflection, reflection coefficient g, reflected wave, standing wave, VSWR (voltage standing wave ratio) are all concerned with the fact that, in microwave system, not all the energy from generator reaches the load, but that small parts of the outgoing wave are reflected due to small mismatches.

 

             Mismatches reduce not only the efficiency of a system but also influence other components in their functioning. For example, the operating point of an oscillator may be shifted by returning energy thus operating on another frequency and with a different power than without this reflected power. That is why, in this experiment, an isolator is always built after the oscillator in order to decouple the rest of the system. An isolator will absorb the reflected power caused by mismatching of the other components.

 

            If the load does not ideally match the generator, part of the power transported from the generator to the load is reflected at the load. A unit of measure for the matching is the inverse standing wave ratio, m, which is 1 when matching is ideal and 0 in the case of total mismatching: 0% of the power is received by the load. 0 ≤ m ≤ 1, m is a measure for the power absorbed by the load. The reciprocal of m is VSWR or s,

 

                                                       m =1/s = (1-ρ) /(1+ρ),

 

With ρ as reflection coefficient. Whereas the reflection coefficient ρ is applied for voltage measurements generally as: 

 

                                                             ρ = U_r/U_v

 

With r as reflected and v as outgoing part of the voltage U, the ref lection coefficient in power measurement, such as in this experiment can be interpreted as:

                                                             ρ = P_r/P_v

 

            Used in the above formula, the voltage standing wave ratio, s, and the inverse standing wave ratio, m, can be expressed with the advancing or outgoing wave. Here the reflected wave is identified by the index r and the advancing wave with v. the reflected power can also be expressed by:

 

                                             Pr = [Pv (s-1) ²] / [(s+1) ²] = Pv. ρ²

 

ρ can be applied as reflection coefficient of the voltage and ρ² as reflection coefficient of the power. Refer appendix figure 10, Power, P over displayed voltage, V.

 

Power reflection coefficient, ρ =Pr / Pv ≤ 1