# 1. $\pi$-Model and $T$-Model equivalent equations

- Equivalent capacitive model for 4 plates


```python
# Libraries
from sympy import*
import numpy as np

# To define automatic printing mode
init_printing()
```

## $\pi$-Model:


```python
# Define the symbolic variables

# Capacitance
c_1, c_2, c_M = symbols('c_1 c_2 c_M', real = True)

# Angular frequency
w = symbols('w', real = True)
```


```python
# Common denominator
com_D = (1/(w*I))*(1/c_1 + 1/c_2 + 1/c_M)
```


```python
# T-model equivalent c'_1
Zp_1 = ((1/(w*I))**2)*((1/c_1)*(1/c_M))/com_D
simplify(Zp_1)
```


```python
# T-model equivalent c'_2
Zp_2 = ((1/(w*I))**2)*((1/c_2)*(1/c_M))/com_D
simplify(Zp_2)
```


```python
# T-model equivalent c'_M
Zp_M = ((1/(w*I))**2)*((1/c_1)*(1/c_2))/com_D
simplify(Zp_M)
```

## $T$-Model:


```python
# Define the symbolic variables

# Capacitance
cp_1, cp_2, cp_M = symbols('cp_1 cp_2 cp_M', real = True)
```


```python
# Common numerator
com_N = ((1/(w*I))**2)*((1/(cp_1*cp_M)) + (1/(cp_1*cp_2)) + (1/(cp_M*cp_2)))
```


```python
# Pi-model equivalent c_1
Z_1 = (com_N)/(1/(w*cp_2*I))
simplify(Z_1)
```


```python
# Pi-model equivalent c_2
Z_2 = (com_N)/(1/(w*cp_1*I))
simplify(Z_2)
```


```python
# Pi-model equivalent c_M
Z_M = (com_N)/(1/(w*cp_M*I))
simplify(Z_M)
```

ea7ccf4fa86e497a0e5efca90cc12130542cda70
ipynb
Jupyter Notebook
.ipynb_checkpoints/Active_CN_Model-checkpoint.ipynb
SanTT19/Symbolic_Python
3bfaec4fc62de52e6a592cf3db333e605a35fcbc
MIT
.ipynb_checkpoints/Active_CN_Model-checkpoint.ipynb
SanTT19/Symbolic_Python
3bfaec4fc62de52e6a592cf3db333e605a35fcbc
MIT
.ipynb_checkpoints/Active_CN_Model-checkpoint.ipynb
SanTT19/Symbolic_Python
3bfaec4fc62de52e6a592cf3db333e605a35fcbc
MIT
Qwen/Qwen-72B
1. YES
2. YES