Question

The VSWR can have any value between :

• A. \(0 \text{ to } 1\)
• B. \(-1 \text{ to } +1\)
• C. \(0 \text{ to } \infty\)
• D. \(1 \text{ to } \infty\)

Hint:

Important VSWR values: \[ VSWR=1 \Rightarrow \text{Perfect matching} \] \[ VSWR\rightarrow \infty \Rightarrow \text{Total reflection} \]

Answer 1

The Correct Option is D

Concept: VSWR stands for: \[ \text{Voltage Standing Wave Ratio} \] It is defined as: \[ VSWR=\frac{V_{max}}{V_{min}} \] where:
• \(V_{max}\) is maximum standing-wave voltage
• \(V_{min}\) is minimum standing-wave voltage VSWR is also related to reflection coefficient: \[ VSWR=\frac{1+|\Gamma|}{1-|\Gamma|} \] where: \[ 0\le |\Gamma| \le 1 \]

Step 1: Determine minimum value of VSWR. For perfect impedance matching: \[ \Gamma=0 \] Substituting: \[ VSWR=\frac{1+0}{1-0} \] \[ VSWR=1 \] Thus: \[ \text{Minimum VSWR}=1 \]

Step 2: Determine maximum value of VSWR. For total reflection: \[ |\Gamma|=1 \] Substituting: \[ VSWR=\frac{1+1}{1-1} \] \[ VSWR=\frac{2}{0} \] \[ VSWR\rightarrow \infty \] Thus: \[ \text{Maximum VSWR}=\infty \]

Step 3: Write the range of VSWR. Therefore: \[ 1\le VSWR < \infty \] Hence VSWR can vary from: \[ 1 \text{ to } \infty \]

Step 4: Write the final answer. Thus, the correct option is: \[ \boxed{(D)\ 1 \text{ to } \infty} \]