The VSWR is given by:
A. <span class="math-tex">\(\frac{{{V_{max}}}}{{{V_{min}}}}\)</span>
B. <span class="math-tex">\(\frac{{{V_r}}}{{{V_i}}}\)</span>
C. <span class="math-tex">\(\frac{{{V_i}}}{{{V_r}}}\)</span>
D. <span class="math-tex">\(\frac{{{V_{min}}}}{{{V_{max}}}}\)</span>
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
The voltage standing wave ratio is defined as the ratio of the maximum voltage (or current) to the minimum voltage (or current).
\(VSWR = \frac{{{V_{max}}}}{{{V_{min}}}} = \frac{{{I_{max}}}}{{{I_{min}}}}\)
Important Derivation:
The general expression of the voltage across a transmission line is given by:
\(V\left( l \right) = {V^ + }{e^{j\beta l}}\left( {1 + \left| {{{\rm{\Gamma }}_{\rm{L}}}} \right|{e^{ - j2\beta z}}} \right)\)
l = distance from the load
β = Phase constant
ΓL = Reflection coefficient at the load calculated as:
\({{\rm{\Gamma }}_L} = \frac{{{Z_L} - {Z_0}}}{{{Z_L} + {Z_0}}}\) - - - (1)
The maximum and minimum voltage is given by:
\({V_{max}} = \left| {{V^ + }} \right|\;\left( {1 + \left| {{{\rm{\Gamma }}_{\rm{L}}}} \right|} \right)\)
\({V_{min}} = \left| {{V^ + }} \right|\;\left( {1 - \left| {{{\rm{\Gamma }}_{\rm{L}}}} \right|} \right)\)
\(VSWR = \frac{{{V_{max}}}}{{{V_{min}}}} = \frac{{1 + {{\rm{\Gamma }}_L}}}{{1 + {{\rm{\Gamma }}_L}}}\)