State-of-the-art harmonic-balance simulation of forced nonlinear microwave circuits by the piecewise technique

Abstract

bounds to the PM and AM noise of the second output harmonic, computed by Eqs. (1) and (2)-(6), are shown in Figure 2. The uncertainty on the output PM noise is of the order of 20.3 dB and is almost independent of fD. The expected output-to-input PM noise ratio of 6 dB is obtained for 3 = 0 within 50.005 dB, which indirectly confirms that 0 is the most likely value of 3.The output AM noise is very close to that of the source, with virtually zero uncertainty for f D 2 1 kHz. Only at very low frequency deviations and for 3 > 0 is some loss of numerical accuracy observed, due to the very high PM-to-AM noise ratio that makes the computation ill conditioned. It is thus clear that a valid noise analysis can indeed be performed by Eq. (6) on the basis of a simplified statistical description of the noisy source, consisting of PM and AM noise only. ABSTRACT In this article we present a modified least-squares boundary residual (LSBR) method for the rigorous analysis of microwave integrated circuits (MICs). The method is relatively convergent and a semianalytical relative convergence criterion is found to be very important in optimizing its convergence. Moreover, the problem of the poor conditioning of the least-squares matrices has been rigorouslv resolved.ABSTRACT A simple method for obtaining optical transmission spectra of AI, Ga,.,As epilayer by translucent A B wax is presented. Absorp-tion spectra are measured for x in the range of 0 < x < 0.8. For the Tlii Ti( energy bandgap, the aluminum concentrations, calculated from the experimental data with a formula derived by the ray-optics merhod, are in good agreement with those reported. 0 1992 John Wile! & Sons, Inc.

Wideband Voltage Controlled Oscillators for Cognitive Radio Systems

“…In order to cope with these issues, nonlinear simulation techniques must be employed in the Time Domain (TD) (Silverberg. & Wing, 1968;Sobhy & Jastrzebski 1985) in the Frequency Domain (FD) (Rizzoli et al, 1992) or in a "mixed" Time-Frequency domain (Ngoya & Larcheveque, 1996). In TD simulations, the differential system of equation is numerically integrated with respect to the time variable, delivering the most accurate representation of the solution waveform, which enables the transient 4 and the steady state analysis as well.…”

THz Rectennas and Their Design Rules

“…While the nonlinearity behavior is considered of major importance, several recent papers overlook its importance and just focus on proving the nonlinearity under DC conditions. It is, therefore, necessary to deploy nonlinear solution schemes for circuits such as linearization [81] and harmonic balance [82]. An important feature of nonlinear systems is that any slight change in the working conditions can lead to unpredicted output, out of the operating range solution or even instability.…”

Implementation Of Exact Sensitivities In A Circuit Simulator Using Automatic Differentiation

“…This approach is is often unreliable because the size of the optimum numerical increment for each independent variable is not always known. Inaccuracy (especially for higher-order derivatives) and a decrease in the convergence rate of numerical methods due to numerical differences has been reported in [1][2][3][4]8]. To the knowledge of the author all implementations in available circuit simulators involve numerical approximations of the derivatives at the device level mainly because it is not practical to implement all the required derivative functions at the nonlinear device models.…”