VSWR, return loss (RL), reflected power, and transmitted power

The relationships between Voltage Standing Wave Ratio (VSWR), return loss (RL), reflected power, and transmitted power are interconnected through the reflection coefficient (Γ). Below are the key formulas and steps for conversion:

### **Core Formulas**
1. **Reflection Coefficient (Γ)**:

\Gamma = \frac{\text{VSWR} - 1}{\text{VSWR} + 1}

2. **VSWR** from Γ:

\text{VSWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|}

3. **Return Loss (RL)** in dB:

\text{RL (dB)} = -20 \log_{10}(|\Gamma|)

4. **Reflected Power (%)**:

P_{\text{refl}} = |\Gamma|^2 \times 100\%

5. **Transmitted Power (%)**:

P_{\text{trans}} = \left(1 - |\Gamma|^2\right) \times 100\%

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### **Conversion Steps**
#### **1. Starting with VSWR**:
- Calculate Γ:

\Gamma = \frac{\text{VSWR} - 1}{\text{VSWR} + 1}

- Use Γ to find RL, reflected power, and transmitted power using the formulas above.

#### **2. Starting with Return Loss (RL in dB)**:
- Calculate Γ:

|\Gamma| = 10^{-\text{RL}/20}

- Use Γ to find VSWR, reflected power, and transmitted power.

#### **3. Starting with Reflected/Transmitted Power**:
- For **reflected power** (\(P_{\text{refl}}\)):

|\Gamma| = \sqrt{\frac{P_{\text{refl}}}{100}}

- For **transmitted power** (\(P_{\text{trans}}\)):

|\Gamma| = \sqrt{1 - \frac{P_{\text{trans}}}{100}}

- Use Γ to compute VSWR and RL.

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### **Example Table**
| **VSWR** | **Return Loss (dB)** | **Reflected Power (%)** | **Transmitted Power (%)** |
|----------|----------------------|-------------------------|---------------------------|
| 1.0 | ∞ (Perfect match) | 0% | 100% |
| 1.5 | 14.0 dB | 4% | 96% |
| 2.0 | 9.5 dB | 11.1% | 88.9% |
| 3.0 | 6.0 dB | 25% | 75% |

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### **Key Notes**
- A **VSWR of 1:1** means no reflection (Γ = 0, RL = ∞).
- **Higher VSWR** or **lower RL** indicates more reflected power.
- **Transmitted power** is maximized when VSWR ≈ 1.

Use these formulas to interconvert between parameters for impedance matching in RF systems.