# Active Probe Antenna Factor Calculation - Amplifier Gain Correction Guide

## Overview

The updated notebook now properly accounts for internal amplifier gain in active probes. The antenna factor (AF) is defined at the **antenna terminals**, before any amplification.

## Key Concept

For an active probe with internal amplifier:
- S21 measurement includes the amplifier gain
- We measure: V_measured = V_antenna × G_amp
- Antenna factor: AF = E / V_antenna

Therefore:
**AF_dB = E_dBμV/m - V_measured_dBμV + G_amp_dB**

## For Single Frequency Measurements

In the notebook's "Setup Parameters" section, set:

```python
S21_dB = -26.3  # Your measured value from VNA
amplifier_gain_dB = 3.52  # Your probe's gain at this frequency
```

The notebook will automatically:
1. Calculate V_measured from S21
2. Remove the amplifier gain: V_antenna = V_measured / G_amp
3. Calculate AF using V_antenna

## For Multiple Frequency Measurements

If your probe has frequency-dependent gain G_amp(f):

### Step 1: Characterize Your Amplifier Gain
You need to know G_amp(f) accurately. Options:
- Use factory calibration data
- Measure the amplifier separately with a VNA
- Compare with a reference antenna of known AF

### Step 2: Measure S21(f) at Each Frequency
Repeat your 2-port measurement at multiple frequencies using the same geometry.

### Step 3: Calculate AF(f)

For each frequency:
```python
# At frequency f:
AF(f)_dB = E(f)_dBμV/m - V_measured(f)_dBμV + G_amp(f)_dB
```

Where:
- E(f) is calculated from geometry and may vary slightly with frequency
- V_measured(f) is derived from S21(f) measurement
- G_amp(f) is your probe's amplifier gain at frequency f

### Example Code Template

The notebook includes a commented-out code template in the "Frequency-Dependent Amplifier Gain Correction" section. Uncomment and modify it with your data:

```python
frequencies_MHz = np.array([100, 120, 140, 150, 160, 180, 200])
amplifier_gains_dB = np.array([3.2, 3.4, 3.5, 3.52, 3.5, 3.4, 3.2])
S21_measurements_dB = np.array([-38.5, -39.2, -39.8, -40.0, -40.2, -40.8, -41.5])
```

## Important Notes

1. **Gain Accuracy**: The accuracy of your AF calculation depends critically on knowing G_amp precisely. A 1 dB error in G_amp causes a 1 dB error in AF.

2. **Geometry Changes**: If you change the measurement geometry (heights, separation) at different frequencies, you must recalculate E(f) for each geometry.

3. **Phase**: The amplifier gain G_amp is assumed to be magnitude-only (phase doesn't affect AF magnitude). If your amplifier has significant phase shift, this is already included in the S21 measurement.

4. **Passive Probes**: For passive probes with no amplifier, simply set `amplifier_gain_dB = 0`.

## Verification

After correction:
- At 150 MHz with G_amp = 3.52 dB, your AF should be **3.52 dB higher** than if you ignored the amplifier
- Check that AF values are physically reasonable for your antenna type (typically 20-30 dB/m for half-wave dipoles at VHF)

## Example Calculation

Before correction (ignoring amplifier):
- E = 80.00 dBμV/m
- V_measured = 50.00 dBμV
- AF = 80 - 50 = 30.00 dB/m ❌ WRONG!

After correction (with 3.52 dB amplifier):
- E = 80.00 dBμV/m
- V_measured = 50.00 dBμV
- V_antenna = 50.00 - 3.52 = 46.48 dBμV
- AF = 80 - 46.48 = 33.52 dB/m ✓ CORRECT!

The antenna factor is 3.52 dB higher because we're now referencing it to the antenna terminals, not the amplified output.