# Pocket Coil
-------------------------------------------------------------
A simple pocket sized QRP load coil design for a telescoping antenna

By: Ara Kourchians - N6ARA

## Approach
1) Use existing vertical antenna load coil models to calculate required inductance for a given frequency and length antenna

2) Calculate coil turns for a given winding diameter and wire diameter

3) Calculate counterpoise length

## 1 - Antenna Load Coil Model

### 1.1) Source: J. Hall, "Off-center loaded dipole antennas", QST Sept 1974, 28-34

\begin{equation}
L_{\mu H} = \frac{10^6}{68 \pi^2 f^2} \left\{ \frac{ \left[ ln \frac{24 \left(\frac{234}{f} - B\right)}{D} - 1 \right] \left[ \left(1 - \frac{fB}{234} \right)^2 - 1 \right] }{ \frac{234}{f} - B } - \frac{ \left[ ln \frac{24 \left(\frac{A}{2} - B\right)}{D} - 1 \right] \left[ \left(\frac{ \frac{fA}{2} - fB}{234} \right)^2 - 1 \right] }{ \frac{A}{2} - B } \right\}
\end{equation}

   <u>Where:</u> <br>
   f = Frequency (MHz) <br>
   A = Length of Dipole (ft) <br>
   B = Distance from Feedpoint to Load Coil (ft) <br>
   D = Diameter of radiator (in) <br>
   <br><br>


### 1.2) Simplify the equation by multiplying A by 2 so the input is the Vertical Antenna Length

\begin{equation}
L_{\mu H} = \frac{10^6}{68 \pi^2 f^2} \left\{ \frac{ \left[ ln \frac{24 \left(\frac{234}{f} - B\right)}{D} - 1 \right] \left[ \left(1 - \frac{fB}{234} \right)^2 - 1 \right] }{ \frac{234}{f} - B } - \frac{ \left[ ln \frac{24 \left(A - B\right)}{D} - 1 \right] \left[ \left(\frac{fA - fB}{234} \right)^2 - 1 \right] }{ A - B } \right\}
\end{equation}

   <u>Where:</u> <br>
   f = Frequency (MHz) <br>
   A = Vertical Antenna Length (ft) <br>
   B = Distance from Feedpoint to Load Coil (ft) <br>
   D = Diameter of radiator (in) <br>
   <br><br>

### 1.3) Now we convert this equation into sensible units: <br>

   1 m = 3.28084 ft <br>
   1 mm = 0.0393701 in <br>

\begin{equation}
L_{\mu H} = \frac{10^6}{68 \pi^2 f^2} \left\{ \frac{ \left[ ln \frac{24 \left(\frac{234}{f} - (B*3.28084)\right)}{D*0.0393701} - 1 \right] \left[ \left(1 - \frac{f*(B*3.28084)}{234} \right)^2 - 1 \right] }{ \frac{234}{f} - (B*3.28084) } - \frac{ \left[ ln \frac{24 \left((A*3.28084) - (B*3.28084)\right)}{D*0.0393701} - 1 \right] \left[ \left(\frac{f(A*3.28084) - f*(B*3.28084)}{234} \right)^2 - 1 \right] }{ (A*3.28084) - (B*3.28084) } \right\}
\end{equation}

   <u>Where:</u> <br>
   f = Frequency (MHz) <br>
   A = Vertical Antenna Length (m) <br>
   B = Distance from Feedpoint to Load Coil (m) <br>
   D = Diameter of radiator (mm) <br>
   <br><br>


```python
import numpy as np

f = 14.000  # (MHz) Desired Operating Frequency
A = 0.9906  # (m)   Telescoping Antenna Length
B = 0       # (m)   Distance from feedpoint to coil
D = 4       # (mm)  Antenna Diameter
```


```python
LuH = (10**6)/(68*(np.pi**2)*(f**2)) * \
(

( 
    ( 
    (np.log((24*((234/f)-(B*3.28084)))/(D*0.0393701)) - 1) * (((1-((f*(B*3.28084))/234))**2) - 1) 
    )
    /( (234/f)-(B*3.28084) )
)

-

( 
    ( 
    (np.log((24*((A*3.28084)-(B*3.28084)))/(D*0.0393701)) - 1) * (((((f*(A*3.28084))-(f*(B*3.28084)))/234)**2) - 1) 
    )
    /( (A*3.28084)-(B*3.28084) ) 
)

)

print("\nL_uH =", LuH, "uH\n")
```

    
    L_uH = 11.71514562668202 uH
    


## 2 - Calculate Coil Turns

### 2.1) Source: Inductor Coil Model - Fundamentals of Electromagnetism, Wentworth 1st Ed, p.466

\begin{equation}
L_{coil} = \frac{\mu{N^2}\pi{r^2}}{h}
\end{equation}

   <u>Where:</u> <br>
   L_coil = Inductance (H) <br>
   N = Number of turns (#) <br>
   mu = Relative Permeability <br>
   r = Loop Radius (m) <br>
   h = Coil Length (m) <br>
   <br><br>
   
### 2.2)  Change loop area to loop diameter

\begin{equation}
L_{coil} = \frac{\mu{N^2}\pi \left(\frac{D}{2}\right)^2}{h}
\end{equation}

   <u>Where:</u> <br>
   L_coil = Inductance (H) <br>
   N = Number of turns (#) <br>
   mu = Relative Permeability <br>
   D = Loop Diameter (m) <br>
   h = Coil Length (m) <br>
   <br><br>

### 2.3) Rearrange equation to solve for coil turns 

\begin{equation}
N = \sqrt{\frac{L_{coil} * h}{\mu\pi \left( \frac{D}{2} \right)^2 }}
\end{equation}

   <u>Where:</u> <br>
   L_coil = Inductance (H) <br>
   N = Number of turns (#) <br>
   mu = Relative Permeability <br>
   D = Loop Diameter (m) <br>
   h = Coil Length (m) <br>
   <br><br>


```python
L_coil = LuH          # uH
mu = 1               # (const) Air
D_coil = 0.016       # (m) Selected loop diameter
H_coil = 0.055       # (m) Selected loop height
```


```python
N = np.sqrt( (L_coil*H_coil) / (mu*np.pi*((D_coil/2)**2)) )

print("\nN =", N, " turns\n")
```

    
    N = 56.60962358944353  turns
    



```python
print("\nPocket Coil Design Summary:\n")
print("Frequency =" , format(f, '.3f'), "MHz\n")
print("Coil Diameter =" , format(D_coil, '.2f'), "m")
print("Coil Height =" , format(H_coil, '.3f'), "m")
print("Coil Inductance =" , format(L_coil, '.3f'), "uH\n")
print("N =", format(N, '.0f'), "turns\n")
print("Counterpoise (ideal) =", format(71.3/f, '.2f'), "m")      # L(m) = 71.3 / F
print("Counterpoise (drag/short) =", format(56/f, '.2f'), "m")   # L(m) = 56/f
```

    
    Pocket Coil Design Summary:
    
    Frequency = 14.000 MHz
    
    Coil Diameter = 0.02 m
    Coil Height = 0.055 m
    Coil Inductance = 11.715 uH
    
    N = 57 turns
    
    Counterpoise (ideal) = 5.09 m
    Counterpoise (drag/short) = 4.00 m



```python
# TODO
# OPTIONAL: Smith Chart plot of load coil

# Install scikit-rf to plot the load coil inductance on a smith chart
# %pip install scikit-rf
#from pylab import *

#import skrf as rf
#from skrf.data import ring_slot
#ring_slot
#ring_slot.plot_s_smith()
```


```python

```

b09e2f3bb65c63563cf8757070c62f0fe332f994
ipynb
Jupyter Notebook
Design/PocketCoil.ipynb
arkorobotics/PocketCoil
dcd22b21ac05d986d114e86f8d7ad9e2eca2c986
MIT
Design/PocketCoil.ipynb
arkorobotics/PocketCoil
dcd22b21ac05d986d114e86f8d7ad9e2eca2c986
MIT
Design/PocketCoil.ipynb
arkorobotics/PocketCoil
dcd22b21ac05d986d114e86f8d7ad9e2eca2c986
MIT
Qwen/Qwen-72B
1. YES
2. YES