Adding linear resistance

[zlatko-minev]

• Cap is experimental feature now (to be tested). Cj is set to a fixed value right now
• Adding in resistance calculation in a more unified way

Nick Materise

[nmaterise]

I tried to hack the pyEPR/core_distributed_analysis.py file to compute the current across an external resistor as a crude attempt to model an RSCJ Josephson junction with a nonzero normal resistance.

• To do this, I modified get_junctions_L_and_C to return Ljs, Cjs, and another variable Rjs
• Then, I modified calc_p_junctions to take Rjs as another input and called calculate_current_line_voltage with Rjs as another input
• Assuming that the junction is a parallel combination of Rj, Lj, Cj, then the current becomes the ratio of the voltage V and the impedance Z, i.e. the code below

722 omega = 2*np.pi*freq  # in SI radian Hz units
723
724        Z = omega*junc_L_Henries
725        if abs(float(Cj_Farads)) > 1E-29:  # zero
726            #print('Non-zero Cj used in calc_current_using_line_voltage')
727            #Z += 1./(omega*Cj_Farads)
728            print(
729                '\t\t'f'Energy fraction (Lj over Lj&Cj)= {100./(1.+omega**2 *Cj_Farads*junc_L_Henries):.2f}%')
730            # f'Z_L= {omega*junc_L_Henries:.1f} Ohms Z_C= {1./(omega*Cj_Farads):.1f} Ohms')
731
732        I_peak = V/Z  # I=V/(wL)s

could be replaced by something like this

722        omega = 2*np.pi*freq  # in SI radian Hz units
723        if (junc_L_Henries > 0) and (Rj_Ohms > 0) and (Cj_farads > 0):
724            ZLR = 1./(1./(omega * junc_L_Henries) + 1./Rj_Ohms + omega * Cj_farads)
725        elif (junc_L_Henries > 0):
726            ZLR = omega * junc_L_Henries
727        elif (Rj_Ohms > 0):
728            ZLR = Rj_Ohms
729        else:
730            ZLR = 0.
731        Z = ZLR
732        if abs(float(Cj_Farads)) > 1E-29 & abs(float(junc_L_Henries)) > 1E-29:  # zero
733            #print('Non-zero Cj used in calc_current_using_line_voltage')
734            #Z += 1./(omega*Cj_Farads)
735            print(
736                '\t\t'f'Energy fraction (Lj over Lj&Cj)= {100./(1.+omega**2 *Cj_Farads*junc_L_Henries):.2f}%')
737            # f'Z_L= {omega*junc_L_Henries:.1f} Ohms Z_C= {1./(omega*Cj_Farads):.1f} Ohms')
738
739        I_peak = V/Z if (Z > 0) else 0. # I=V/(wL)s

Notes on the experimental capacitance feature: It is set to a constant (2 fF) in master pyEPR/core_distributed:

1075 Cjs[junc_name] = 2E-15  # _parse(
1076                # 'Cj_variable') if 'Cj_variable' in val else 0

[zlatko-minev]

Yes,Cjs[junc_name] = 2E-15 should be an optional property of the junction properties, I agree.

The voltage is in parallel, so all the voltages are equal across RLC, but if there is an R, the R will such some of the energy and current out