Improvement: add Zarc element (#268)

* add Zarc element

Author: etrevis

impedance/models/circuits/elements.py

@@ -313,6 +313,25 @@ def K(p, f):
     return Z
 
 
+@element(num_params=3, units=['Ohm', 'sec', ''])
+def Zarc(p, f):
+    """ An RQ element rewritten with resistance and
+    and time constant as paramenters. Equivalent to a
+    Cole-Cole relaxation in dielectrics.
+
+    Notes
+    -----
+    .. math::
+
+        Z = \\frac{R}{1 + (j \\omega \\tau_k)^\\gamma }
+
+    """
+    omega = 2*np.pi*np.array(f)
+    R, tau_k, gamma = p[0], p[1], p[2]
+    Z = R/(1 + ((1j*omega*tau_k)**gamma))
+    return Z
+
+
 @element(num_params=3, units=["Ohm", "F sec^(gamma - 1)", ""])
 def TLMQ(p, f):
     """Simplified transmission-line model as defined in Eq. 11 of [1]

impedance/tests/test_circuit_elements.py

@@ -68,6 +68,11 @@ def test_each_element():
             (0.038772663673915 - 0.048723166143232j),
             (6.332569967499333e-08 - 7.957742115295703e-05j),
         ],
+        "Zarc": [
+            (0.08900974-0.00486384j),
+            (0.04818879-0.01198904j),
+            (0.00969182-0.00436265j),
+        ],
     }
     input_vals = [0.1, 0.2, 0.3, 0.4]
     for key, f in circuit_elements.items():