This paper presents a virtual circuit controller (VCC), which provides a systematic structured method to stabilize the resonance of an LCL filter in a grid-connected voltage source converter. The semiconductor switches are controlled to mimic the behaviour of a virtual reference circuit. The properly-damped circuit by a resistor in parallel with a filter capacitor is focused on and selected as the reference circuit. A linear transformation matrix is introduced indicating the resemblance between the physical and virtual circuits, and is employed to map the states between both circuits. Accordingly both analog and digital control laws are systematically computed. The insight into the feedback of the capacitor current and voltage through proportional gains is clarified. While the consequence of the former is conventionally known to emulate a resistor for damping purpose, the latter is newly used to emulate an inductor for adjusting the inner-loop control bandwidth and improving the robustness. A Kalman filter is used to deal with the inherent time delay. The detailed discrete-time state-space model of the complete system is derived. The design example of the proportional current controller is demonstrated. The simulation results illustrate the effectiveness of the damping and the robustness of the system against component-value variations.

This paper presents a new, frequency-domain based method for modeling and analysis of phase-locked loop (PLL) small-signal behavior, including time-varying aspects. Focus is given to PLLs with sampling phase-frequency detectors (PFDs) which compute the phase error only once per period of the reference signal. Using the harmonic transfer matrix (HTM) formalism, the well known continuous-time, linear time-invariant (LTI) approximations are extended to take the impact of time-varying behavior arising from the sampling nature of the PFD, into account. Especially for PLLs with a fast feedback loop, this time-varying behavior has severe impact on, for example, loop stability and cannot be neglected. Contrary to LTI analysis, our method is able to predict and quantify these difficulties. The method is verified for a typical loop design.

This paper presents a method for constructing behavioral models for harmonic oscillators and sets of coupled harmonic oscillators. These models are useful for system-level simulations and tradeoff analysis. The modeling method allows capturing the steady-state and transient behavior of the target oscillators through a sequence of transformations of the circuit equations. Model extraction is based on ideas of perturbation analysis and averaging. The resulting models are evaluated at a computational cost that is well below that of solving the original circuit equations. Another major advantage of the approach is the explicit separation of the slow- and fast-varying components of the oscillator's behavior. This allows using a much larger time step during numerical simulations. The technique is illustrated for both a single harmonic oscillator and a harmonic quadrature oscillator.

A new approach is presented for the construction of behavioral models for harmonic oscillators and sets of coupled harmonic oscillators. The models can be used for system-level simulations and trade-off analysis. Besides the steady state behavior, the model also takes the transient behavior of the oscillation amplitudes and phase differences into account. This behavior is modeled using a set of linear differential equations. Their extraction from a netlist description is based upon the ideas of perturbation analysis and stochastic averaging. The modeling equations are valid in the neighbourhood of the oscillator's steady-state operating point and can be evaluated at very low computational cost. Another major advantage of the approach is that it explicitely separates the fast-varying steady-state behavior and the slow varying transient behavior. This allows for straightforward application of multi-rate simulation techniques, greatly boosting simulation speeds. The technique is illustrated for a quadrature oscillator.

A new technique is presented for generating symbolic expressions for the harmonic transfer functions of linear periodically time-varying (LPTV) systems, like mixers and PLL's. The algorithm, which we call Symbolic HTM, is based on the organisation of the harmonic transfer functions into a harmonic transfer matrix. This representation allows to manipulate LPTV systems in a way that is similar to linear time-invariant (LTI) systems, making it possible to generate symbolic expressions which relate the overall harmonic transfer functions to the characteristics of the building blocks. These expressions can be used as design equations or as parametrized models for use in simulations. The algorithm is illustrated for a downconversion mixer.

This paper describes the similarities and differences between two widely publicized methods for analyzing oscillator phase behavior. The methods were presented in [3] and [6]. It is pointed out that both methods are almost alike. While the one in [3] can be shown to be, mathematically, more exact, the approximate method in [6] is somewhat simpler, facilitating its use for purposes of analysis and design. In this paper, we show that, for stationary input noise sources, both methods produce equal results for the oscillator's phase noise behavior. However, when considering injection locking, it is shown that both methods yield different results, with the approximation in [6] being unable to predict the locking behavior. In general, when the input signal causing the oscillator phase perturbations is non-stationary, the exact model produces the correct results while results obtained using approximate model break down.

This paper presents an algorithm for generating symbolic expressions for the harmonic transfer functions of linear periodically time-varying (LPTV) systems, like mixers and PLLs. The harmonic transfer functions characterize the up- and downconversion behavior of the wanted and unwanted signal components. The algorithm, which the authors call Symbolic HTM, is based on the organization of the harmonic transfer functions into a harmonic transfer matrix. This representation allows one to manipulate LPTV systems in a way that is similar to linear time-invariant systems, making it possible to generate symbolic expressions relating the overall harmonic transfer functions to the building block parameters. These expressions can be used as design equations or as parameterized models for use in simulations or synthesis. Comparison of the symbolic models with numerical data shows them to be accurate, even for small numbers of modeling terms.

This paper presents an efficient time-domain simulation approach for telecommunication frontends at architectural level. It is based upon the use of complex damped exponential modeling functions. These allow to construct accurate signal models for digitally modulated telecom signals, requiring only few modeling functions. Since these models are valid over a long range of time, they allow for a large timestep, which greatly speeds up time-domain simulation of the telecom frontends. Details of a simulation approach based upon this signal model are discussed. The approach is verified by experimental results.