Methods of analysis

Methods Models Tolerances SPICE2G6 ELDO APLAC

• Direct current analysis
• Small-signal analysis
• Transient analysis
• Harmonic balance

---

Direct current analysis

Only the components that are essential for direct current, take part: capacitors into open circuits and coils into short-circuit. Are used to calculate the operating point (.OP in Spice) or to analyze the direct currents in terms of the wanted voltage or current source (or temperature etc.) (.DC). Are calculated also in other types of analysis to get the initial values. Problems will occur if the circuit has several stabile states (PTAT-reference, circuit containing hysteresis), in which case it’s better to do the simulation in time domain with transient analysis.

---

Small-signal analysis

First the operating point is solved with direct current analysis. After that, the non-linear circuit that is analyzed is linearized, that is, the non-linear components are replaced with the first-degree Taylor series in the operating point. Because the circuit is assumed to be entirely linear, the signal won’t be cut and the amplitude of the input impulse doesn’t affect the analysis (the impulse is usually 1, in which case the output voltage, for example, is directly the voltage amplification).

With this method of analysis the characteristics of the circuit can be calculated in frequency domain. These characteristics are frequency response, input and output impedances, S-parameters etc. Also the noise of the circuit is analyzed with small-signal analysis. Only a few simulators know how to control the noise of non-linear circuit (APLAC). In some simulators (e.g. HSPICE) you can give the sampling frequency for the small-signal analysis, in which case the high-frequency noise folds.

---

Transient analysis

The initial condition t=0 is an operating point that is analyzed with direct current analysis. Alternatively you can give the initial values of the voltages manually (IC). The simulation moves from one point in time to another using numeric integration methods. The capacitors and coils of the circuit need lots of time to settle to a continuous state, because the simulation of the circuit is started from a direct current operating point. A circuit that converges badly can more easily be analyzed by connecting the operating voltage to the circuit after the zero-point. Even then the rise time of the operating voltage must be longish.

There are many methods for calculating the points of time. Usually if there are problems in the convergence, you should back up to the previous point of time and continue with a shorter time step. Respectively the time step is lengthened if the changes in the voltages and currents have been small during the previous time points. In this case there’s a risk of loosing short impulse peaks in some less developed simulators.

There might occur some numeric oscillation in the simulated signals, especially when integrating with the trapezoid method. You shouldn’t mistake them for the instability of the circuit. You can figure out the oscillation mechanism by changing the integration method in the options of the circuit. NB! When changing the integration method you usually must also change the calculation method of the time step.

If you analyze the distortion characteristics of the circuit, you’ll usually have to enhance the accuracy of the transient analysis, e.g. by shortening the maximum time step (SPICE: DELMAX-option). You should also check the distortion of the actual sinoidal impulse to evaluate the accuracy.

Generally transient analysis is long but it requires fairly little memory and it’s a simulation method that converges fairly easily.

---

Steady state analysis, alias harmonic balance analysis

In harmonic balance, the circuit is divided into two parts, linear and non-linear. After this, the circuit is duplicated for as many harmonic components of the basic frequency as is wanted in the analysis. Then the voltages of the non-linear part are guessed and used to solve the linear part. After this, the results of the different parts are compared and a suitable integration algorithm is used to calculate new values for the non-linear part. Then the linear part is solved etc.

If there is enough memory in the computer to describe a circuit with all the wanted frequencies and if that iteration converges, the simulation gives the result either as spectrum components or as waveforms in time domain. The outcome of the analysis is the continuous state of the circuit. Sometimes transient analysis requires a long settling time before the result of the simulation describes the continuous state accurately enough. This can be avoided by using the analysis of harmonic balance.

Unfortunately, the harmonic balance requires very much memory and the final convergence of the simulation is uncertain. It is thus fairly easy to guess that with complicated circuits there might occur some simulation problems regarding the harmonic balance. In some cases some assumptions that ease the analysis, can be made, e.g. the RF-signal the frequency mixer should mix can be assumed as a small-signal and this way simplify the analysis (e.g. APLAC’s small-signal steady state).

There is a different version of harmonic balance for oscillators. There is no impulse frequency when simulating an oscillator and thus the fundamental frequency must be solved in simulation. Respectively there is an own version of harmonic balance in APLAC for analyzing SC-circuits.

---

Updated 18.08.2005.