# Circuit notation

AutoEIS uses a custom notation to represent circuit models based on the following two rules:

1. Elements in series are separate by a `-` symbol.
2. Elements in parallel are enclosed in square brackets `[ ]`, and are separated by a `,` symbol.

For example, the following circuit:

```{image} ../assets/ecm.png
:class: fig-ecm
:align: center
```

is represented as `R1-C2-[R3,P4]-[R5,[R6,C7]]`.

As for the component names, AutoEIS uses the following convention:

- `R` for resistors
- `C` for capacitors
- `L` for inductors
- `P` for constant phase elements (CPEs)

Resistors, capacitors, and inductors are each parameterized by a single value, which is the component value in Ohms, Farads, and Henrys, respectively. CPEs are parameterized by two values, the magnitude $Q$ (represented by `w`) and the exponent $\alpha$ (represented by `n`) based on the following equation:

$$
Z_{CPE} = \frac{1}{Q \times (j\omega)^{\alpha}}
$$

For example, consider component `P4` in the above circuit. The corresponding CPE is parameterized by `P4w` and `P4n`. The other components are parameterized by `R1`, `C2`, `R3`, `R5`, `R6`, and `C7` (basically, the parameter name is the same as the component name).