Kiran K. Gullapalli

Best Practices for Compact Modeling in Verilog-A

Verilog-A is the de facto standard language that the semiconductor industry uses to define compact models. Unfortunately, it is easy to write models poorly in Verilog-A, and this can lead to unphysical model behavior, poor convergence, and difficulty in understanding and maintaining model codes. This paper details best practices for writing compact models in Verilog-A, to try to help raise the quality of compact modeling throughout the industry.

Analysis of oscillator injection locking by harmonic balance method

A new approach to analyze injection locking mode of oscillators under small external excitation is proposed. The proposed approach exploits existence conditions of the solution of HB linear system with degenerate matrix. The method allows one to obtain the locking range for an arbitrary oscillator circuit with an arbitrary periodic injection waveform. The approach can be easily implemented into a circuit simulator. Examples are given to confirm the correctness of the new approach.

Faster statistical cell characterization using adjoint sensitivity analysis

With the adoption of statistical static timing analysis (SSTA), the characterization of standard cell libraries for delay variations and output transition time (output slew) variations, referred to as statistical characterization, is becoming essential. Statistical characterization of intra-cell mismatch variations as well as inter-chip variations need to be performed efficiently with acceptable accuracy as a function of process parameter variations. The conventional approach to this problem is to model these mismatch variations by characterizing each device variation separately. However, this entails a cost that is proportional to the product of the number of devices (nd) in the cell and the number of local statistical parameters (np), and characterization becomes infeasible. In this work, we propose an improved transient sensitivity analysis to accelerate statistical characterization. We compute sensitivities of node voltages with respect to any process/design parameters. These sensitivities are used to extract the sensitivities of delays and transition times. It is more critical to note the sparsity of the circuitpsilas dependence on the statistical parameters (i.e., any given parameter directly impacts only a small portion of the circuit, sometimes only one device). By exploiting this sparsity we obtain a method that is O(np), compared to O(nptimesnd ) of the conventional approach. As an example, for an AOI cell with 40 devices, the sensitivity analysis, compared to the standard approach using multiple simulations, results in more than 18X runtime improvements with better accuracy.

New numerical technique for cyclostationary noise analysis of oscillators

A new numerical technique for cyclostationary noise analysis of oscillators is proposed. This technique is based on the transformation of the frequency conversion linear system for periodic small signal analysis. This transformation provides nonsingular matrix with zero frequency offset that allows to avoid numerical errors at small frequency offset values. The numerical examples are given to demonstrate the efficiency of the new approach.

Smoothed form of nonlinear phase macromodel for oscillators

This paper proposes an improvement to the well-known oscillator nonlinear phase macromodel based on Floquet theory. A smoothed form of the nonlinear phase macromodel is derived by eliminating highly oscillatory terms in the macromodel, resulting in a significant speed-up in transient simulation. For an LC oscillator under sinusoidal excitation the new macromodel is equivalent to the Adler model. Numerical experiments confirm a considerable decrease of computational efforts. It is further shown that the new macromodel allows one to perform phase noise analysis of locked oscillators under arbitrary periodic injection.

Injection locking conditions under small periodic excitations

Injection locking of oscillators subject to small periodic excitations is derived from existence conditions of the solution of the small signal harmonic balance degenerate system. The resulting expression for the locking range can be applied to any oscillator circuit with arbitrary periodic injection waveform, and can be easily implemented into a circuit simulator. The application of the general expression to some special cases is considered, and comparison with known results is given. Theoretical results are confirmed by SPICE simulations.

A numerical technique for time domain noise analysis of oscillators

A new numerical technique for time domain noise analysis of oscillators is proposed. This technique is based on the linear periodically time varying model, with an equivalent transformation of the linear system. This transformation produces a nonsingular matrix when the frequency offset is zero, which avoids numerical errors at small offset frequencies. Examples are given to demonstrate the efficiency of the new approach.

Frequency adjusting numerical technique for oscillator simulation

The special-purpose numerical continuation procedure for oscillator simulation is presented. The procedure allows to extend the convergence region and supports automatic guess of starting frequency point for continuation process.

New Macromodeling Approach to Phase Noise Analysis of Locked Oscillators

A new oscillator macromodel in the form of phase differential equation is proposed. The comparison of new macromodel with the Adler equation and with the macromodel based on Floquet theory is presented. It is shown that the proposed approach allows to perform phase noise analysis of any oscillator circuit with arbitrary periodic injection waveform. The approach can be easily implemented into a circuit simulator.