In Part 2 of Optimize Power Transfer Link Efficiency, we compare the benefits of simulating the wireless power linkage using an RF simulator, such as the Agilent’s ADS with a typical SPICE simulator. There are many benefits to using the ADS simulator for an application such as a resonant converter or resonant link. Here, we’ll focus on three benefits, which are:

- Simulation speed
- Parametric DC sweep simulations
- Post processing functions

A simplified ADS simulator model of the resonant link allows simulation of the link and display of the various waveforms in the link. The ADS platform offers many types of simulators allowing analysis in the frequency, time, modulation, and algorithmic domains. These include Harmonic Balance (see sidebar), Envelope, Momentum and SPICE to name a few. Each of these serves a different purpose and offers a different set of capabilities. In this case, we will use the Harmonic Balance (HB) simulator, which is a Fourier based solver to perform a fast, steady state simulation of the resonant link. The simulation produces a frequency domain solution, while also allowing the results to be transformed into the time domain. This is analogous to the transformation of a transient domain SPICE model to a state space average SPICE model. Since the Harmonic Balance engine is a large signal simulator, the simulation results include non-linear, as well as small signal effects. The Harmonic Balance engine simulates much faster than the transient time domain solver such those found in SPICE.

The ADS simulator model shown in Fig. 1 includes a variable frequency square wave at the input to simulate the “H” Bridge and four ideal diodes to simulate the synchronous output rectifiers. The ideal diodes are much simpler to model than the synchronous rectifiers and, for our purposes, are more than adequate.

Harmonic Balance |

Harmonic Balance (HB) is a large signal frequency domain analysis primarily used to assess non-linear effects such as distortion and compression in RF systems. The HB engine also includes the transformation of frequency domain to time domain. In this way, the steady state solution of a nonlinear circuit can be solved quickly and the answers can be displayed in the frequency domain (spectrum plots) or in time domain. A major benefit of this simulation engine is that it performs sweeps within an analysis For example, we can look at the output voltage of the rectified resonant link while sweeping the coupling of the transmit and receive coils. |

The “smoothness” of the HB waveforms is a function of the number of harmonics that are evaluated. The tradeoff is the larger the number of harmonics, the longer the simulation computation time and the more computing power that will be required.

Fig. 2 shows a comparison of the secondary current and output DC voltage waveforms resulting from Harmonic Balance and transient simulations, along with the simulation times

The ADS software allows a selection of the number of harmonics to include in the HB simulation, as well as the maximum time step for the transient simulation. While we could use any SPICE simulator for the transient simulation, we used the ADS SPICE engine to obtain a fair comparison.

The “fuzzy” DC waveform in the HB simulation results is due to the 32 harmonic limit that we arbitrarily set. More harmonics would result in a sharper waveform at the expense of longer simulation times. For comparison purposes, 48 harmonics required 5.96 seconds.

Fig. 3 shows the output display in a slightly different way, it shows the input current waveform as a frequency spectrum (a) and as a time domain output (b).

While it is certainly a benefit to simulate large signal steady state solutions quickly, this is only one benefit of the HB simulation engine.

The spectrum nature of the results allows the determination of frequency dependent terms, such as skin effect in the coil wires.

A second and possibly even more significant benefit is the ability to perform DC parametric sweeps within this resonant simulation. This is not easy to perform using a SPICE simulator.

For example, any parameter can be swept in the HB simulation, including component parameters, such a resistance, inductance and coupling or simulation variables, such as frequency or input voltage.

The third major benefit of simulating in ADS is the post processing power, which exceeds the capabilities of those found in many, if not most SPICE simulators.

Since the HB simulator is Fourier based, any waveform can be evaluated at any harmonic, including DC (harmonic 0) and mathematical functions can easily be represented. For example, the ratio of the receive coil to the transmit coil at the fundamental frequency is:

Where:

I_{OUT} = Receive coil current

I_{IN} = Transmit coil current

These results show:

Where:

rms(pri[1] )= Transmit coil voltage

Freq[1] = Fundamental frequency

rms(lin.i[1] = Transmit rms current

rms(out[1]) = Receive rms current

The transmit and receive coil losses can be calculated as can the overall efficiency, which you will note is very close to the value predicted in Part 1.

Using the values of 28.3uH and 12.8uH with the respective Q and k for a 4mm separation results in a calculated efficiency of:

These are just a few of the benefits of simulating wireless power using the harmonic balance simulation. There are many additional benefits, such as the Optimizer Cockpit, which allows the automatic adjustment of parameters in order to optimize a particular result, such as efficiency.

Our simulation model was kept simple to clearly show the simplicity of the HB engine. It is possible to add additional characteristics, such as the Q’s of the coils and coupling as a function of the distance between the coils. This can be accomplished using a 3D EM simulator, such as Agilent EMPro . The results from the EM simulator can then be imported into and simulated within ADS. Fig. 4.

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