docs: def z_transfer_functions():
      r'''
      Return a symbolic equality representation of the transfer function of RMS
      voltage measured by either control board analog feedback circuits.
  
      According to the figure below, the transfer function describes the
      following relationship::
  
            # Hardware V1 #                        # Hardware V2 #
  
              V₂      V₁                               V₂   Z₁
              ── = ───────                             ── = ──
              Z₂   Z₁ + Z₂                             V₁   Z₂
  
      where $V_{1}$ denotes the high-voltage actuation signal from the amplifier
      output and $V_{2}$ denotes the signal sufficiently attenuated to fall
      within the measurable input range of the analog-to-digital converter
      *(approx. 5V)*.  The feedback circuits for control board **hardware version
      1** and **hardware version 2** are shown below.
  
      .. code-block:: none
  
            # Hardware V1 #                        # Hardware V2 #
  
            V_1 @ frequency                        V_1 @ frequency
                ┯                                      ┯
              ┌─┴─┐                                  ┌─┴─┐    ┌───┐
              │Z_1│                                  │Z_1│  ┌─┤Z_2├─┐
              └─┬─┘                                  └─┬─┘  │ └───┘ │
                ├───⊸ V_2                              │    │  │╲   ├───⊸ V_2
              ┌─┴─┐                                    └────┴──│-╲__│
              │Z_2│                                         ┌──│+╱
              └─┬─┘                                         │  │╱
               ═╧═                                          │
                ¯                                          ═╧═
                                                            ¯
  
      Notes
      -----
  
       - The symbolic equality can be solved for any symbol, _e.g.,_ $V_{1}$ or
         $V_{2}$.
       - A symbolically solved representation can be converted to a Python function
         using `sympy.utilities.lambdify.lambdify`_, to compute results for
         specific values of the remaining parameters.
  
      .. _`sympy.utilities.lambdify.lambdify`: http://docs.sympy.org/dev/modules/utilities/lambdify.html
      '''
      # Define transfer function as a symbolic equality using SymPy.
      V1, V2, Z1, Z2 = sp.symbols('V1 V2 Z1 Z2')
      xfer_funcs = pd.Series([sp.Eq(V2 / Z2, V1 / (Z1 + Z2)),
                              sp.Eq(V2 / V1, Z2 / Z1)],
                             # Index by hardware version.
                             index=[1, 2])
      xfer_funcs.index.name = 'Hardware version'
      return xfer_funcs