Full-Wave Quantum


Recently, the memristor (the abbreviation for memory resistor), displaying remarkable electronic properties, has attracted several studies due to its extraordinary role in microwave applications. The unique feature of a memristor is that it behaves as a linear resistor with memory; technically, the resistance (or conductance) at a given time depends on the time integral of the entire history of its current (or voltage) value. Furthermore, a broader quantitative description of a memristor has been mathematically generalized into a memristive system.

A simplified physical model, which is based on a thin film of titanium dioxide, can characterize nanoscale memristive effects, such as negative differential resistance, multiple conductance and switching, and hysteretic conductance. Since the birth of the first memristor, a wide range of nanoscale memristive systems, including spin memristive systems, a polymeric memristor, and a resonant tunneling diode memristor, have been identified and fabricated. The excitement of those memristive devices lies in expanding the electronic information processing methodology by using the state variables instead of using conventional voltage or current.
Wavenology EM as the software simulation tool can use its SPICE circuits to model memristor. The spintronic effect of the memristor is modeled with an equivalent non-linear circuit. Such model is built in Wavenology EM SPICE solver, and the non-linear circuit is embedded at the two corners of a patch antenna and a full-wave simulation was performed.


Fig. 1. Simulated circuit properties of high-frequency voltage-driven memristive system. (a) I-V hysteresis shape. (b) Normalized state variable curve.


Fig. 2. (a) Schematic of dual memristors embedding in an L-band directly modulated patch antenna. (b) Reflection coefficient for microwave patch antenna without the modulation.


Fig. 3. Electric field distribution on the microstrip patch antenna. (a) Antenna is “ON” mode, switch by memristor. (b) Microstrip patch antenna is turned “OFF” by the memristor.


Fig. 4. (Color online) (a) Received near-field time-domain Ex waveform at (0, 0, 20) mm. This electric field is a combined nonlinear response of a 1.455 GHz sinusoidal carrier wave and a 100 MHz baseband signal. (b) Received field time-domain Ex waveform at (0, 0, 200) m. (c) Power spectrum of received modulation signal is normalized by it maximum value. Wideband radiation is clearly observed. (d) Far-field radiation spectrum comparisons between diodes and memristors. The -10 dB level bandwidth is used here. The -10 dB bandwidth of microstrip patch antenna (indicated by the pink box) with memristors is twice the one of microstrip patch antenna with diodes (indicated by the green box).


Josephson Junction

A Josephson junction (JJ) is made by sandwiching a thin insulating layer between two superconducting layers. The Josephson effect has found wide usage. Wavenology EM’s SPICE simulator has an advanced feature for modeling JJ. The following examples demonstrates such an ability, where a JJ driven by an ideal DC current source, as shown in Fig. 5(a). The simulation result of the voltage versus time is plotted in Fig. 5(b). Good agreement is observed between this result and the reference result.


Fig. 5. (a) A JJ of RSJ model is driven by an ideal DC current source. (b) Simulation result for the voltage versus time compared with the reference data.

The second example is used to study the voltage-current relation of a JJ. The circuit we used is similar to the one shown in Fig. 5(a). The only difference is from the DC current source. Here we scan a number of different DC source currents from 0 to 0.23 mA. For each value of the DC current source, the voltage variation with time is simulated and the oscillation results are averaged to obtain a corresponding voltage. Our computational results for the voltage-current relation are shown in Fig. 6.


Fig. 6. Simulation results for the voltage-current relation of a Josephson junction compared with the reference data (the reference data has only available up to 60 uV).


Based on the above equivalent circuit model of a JJ, the circuit model for superconducting quantum interference devices (SQUIDs) can be implemented with Wavenology EM SPICE. A SQUID is a very sensitive magnetometers used to measure extremely weak magnetic fields, based on superconducting loops containing Josephson junctions. For example, a DC SQUID consists of two superconductors separating by thin insulating layers to form two parallel Josephson junctions.

SQUID arrays can form superconducting quantum interference filter. In addition to 1D SQIF, Wavenology EM SPICE supports 2D SQIF, which is an array of SQUIDs arranged in two dimensions, as shown in Fig. 7, which has M SQUIDS in series and N junctions in parallel. Its output voltage is proportional to M.


Fig. 7. A 2D SQIF with M (here is 4) SQUIDs in series and N (here is 5) junctions in parallel.

In this simulation, a small 2D SQIF is investigated. This structure has 4 SQUIDs in series and 5 junctions in parallel. The 4 x 5 cell structure has a uniform cell length of 5 microns along parallel direction and non-uniform lengths along series direction with averaged cell length of 7 microns. Self-inductances is considered. A linearly dynamic magnetic field is imposed on the SQIF. The output voltage across the SQIF is shown in Fig. 8 left.

Since the dynamic field changes much slower compared to the characteristic response times of the SQUID, a simple low pass filter of averaging is employed to get its steady state behavior. The results are shown in Fig. 8 right. In addition, two other simulations are performed. One is to consider a 10% mutual coupling of adjacent inductances to the 2D SQIF. The other is to add a random -15% to 15% variation to the critical currents of JJs in the SQIF. Both results are shown in Fig. 8 right for a comparison. The simulation shows that the small self-inductance and variation has little effects on the performance of the SQIF.


Fig. 8. Left: The output voltage before low pass filtering. Right: The flux-voltage transfer functions of a 4×5 2D SQIF.

At last, SQIF-based device is simulated in a full-wave environment. An extremely sensitive magnetic field receiver is put near to a conventional electric dipole antenna. A Gaussian shape signal is carried in an incoming plane wave. The simulation configuration is demonstrated in Fig. 9.


Fig. 9. Configuration of the simulation of SQIF receiver.

Wavenology EM is able to embed such 2D SQIF arrays into a full-wave simulation. As shown in Fig. 10. The outgoing and incoming electric fields are displayed. The time domain signatures of the outgoing and incoming waves are illustrated in Fig. 11 left, where the outgoing wave is a sinusoid signal and the incoming wave is of a Gaussian shape. The SQIF received signal is shown in Fig. 11 right.


Fig. 10. Snapshots of outgoing and incoming wave propagation.

Fig. 11. Left: Green is the dipole radiated sinusoid signal. Red is the incoming plane wave signal. Right: SQIF received signal.