Adam Cooman

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Testing the Large-Signal Small-Signal
simulator in ADS

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2. Testing methodology

The linear system around a periodic solution is a Linear Time-Periodic (LTP) system. The behaviour of such a LTP system can be described perfectly by a infinite series of Frequency Response Functions (FRF) called Harmonic Transfer Function (HTF) [1]. The HTF which describes the frequency response from the excitation frequency ω\omega to a translated frequency ω+lωex\omega+l\omega_{\mathrm{ex}} will be denoted as GUY[l](jω)G_{U\rightarrow Y}^{\left[l\right]}(j\omega). ωex\omega_{\mathrm{ex}} is used to indicate the pulsation of the LTP system.

To test the LSSS simulator, a periodically time-varying differential equation is implemented in ADS. The HTFs of such differential equations can also be calculated in Matlab using techniques described in [1]. By comparing the Matlab results to the results from ADS, we can get an indication of the error made in the simulator. The following periodically time-varying first order differential equation will be used:

dy(t)dt+a(t)y(t)=u(t)(2.1)\frac{dy(t)}{dt}+a(t) y(t)=u(t)\tag{2.1}

The time-variation a(t)a(t) will be a random-phase multisine with a base pulsation of ωex=2πfres=0.5Hz\omega_{\mathrm{ex}}=2\pi f_{\mathrm{res}}=0.5\mathrm{Hz}. The multisine excites all tones up to fmax=5Hzf_\mathrm{max}=5\mathrm{Hz}. The amplitude of each tone in the multisine is set to 11 and random phases are used. A DC offset of 11 was added to the multisine as well. The resulting a(t)a(t) signal is shown in Figure 2.1.

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Figure 2.1 Values of the aa parameter in the differential equation (2.1) as a function of time.

The implementation of this differential equation is done in ADS with a Symbolically Defined Device (SDD) block. The simulation set-up is shown in Figure 2.2. The SDD block in the schematic is configured such that the voltage at port 1 acts as the input signal u(t)u(t) and the resulting current flowing into port 1 is the output signal y(t)y(t). The control of the factor a(t)a(t) is done through the second port of the SDD block. It is important to force a non-zero initial condition in that port, as setting the node to zero leads to errors in the simulation.

The whole circuit is simulated with a HB simulation with a base frequency of 0.5Hz0.5\mathrm{Hz} which is given an order of 100100. The LSSS was run on a logarithmic frequency grid going from 0.1Hz0.1\mathrm{Hz} to 100Hz100\mathrm{Hz} with 100100 steps per decade. With these settings, ADS returns 201201 HTFs sampled at 301301 frequency points.

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Figure 2.2 Simulation set-up in ADS to implement the time-varying differential equation (2.1)

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