Evolution in Simulation of Buildable Circuits

The use of real reconfigurable hardware ensures that the properties of the physical electronic medium are available without restriction, to be exploited by the evolved circuits. Evolution using a detailed simulation is also possible, but a simulator inevitably neglects some details, while spuriously affecting others, for all but the smallest of circuits. Simulations are attractive, being more controllable, observable, and in some cases faster (in others infeasibly slower), than using real reconfigurable hardware running in real time. Noise levels can be controlled in a simulation, which can affect the evolutionary dynamics [70]. In the following, we give an example of the special precautions that must be taken to ensure that bipolar transistor-level simulation results are valid: that the evolved circuits will actually work when built. The commercial simulator SMASH will be used, but the comments apply equally to the use of other well-known packages such as SPICE.

The most elementary precaution is only to allow components in the simulation that are really available. This not only implies the use of `preferred values' for resistors, capacitors, etc. [71], but also adjusting the transistor model parameters, such as the saturation current $I_{s}$ and $\beta$, to match closely the components to be used in the real implementation.

It is also necessary to check during the simulations that the transistors would not be damaged by overcurrent conditions. This can be done by checking that the base-emitter voltages and collector currents do not exceed limits (usually $\approx$0.7V, and around 100mA for low-power transistors). Without this check, it is common to evolve a circuit that seems to work in the simulation, but which will instantly destroy the transistors at power-up if built.

As an example, consider the evolution using a GA of a transistor amplifier. The genotype was a linear string using integer encoding: it consisted of a separate `gene' corresponding to each component. The gene determines the nature, value and connecting points of the related component. Experimental details can be found in [10]. In this particular set of experiments, the genotype was made up of eight genes, with a total of 10 connecting points available for the evolutionary algorithm to arrange the components. Half of these points are external ones, being connected to: a positive power supply (12V), a negative power supply (-12V), ground, the input signal, and the circuit output. The other five points are internal to the circuit. The biased input voltage represents a differential circuit input.

The fitness evaluation was based on a dc transfer analysis, in which the input signal was swept from the negative to the positive power supply voltages, in $n$ increments of 100mV. The function:

$$Fitness = Max_{i=1}^{n-1}\vert V(i+1) - V(i)\vert$$ (5)

was used, where V(i) describes the circuit output voltage as a function of the dc analysis index, i, which spans the swept range of the input signal. This evaluation function aims to identify the maximum voltage gradients between consecutive input voltage steps; the higher the gradient, the larger the amplifier gain will be. Ideally, the amplifier transfer function should include two saturation regions separated by a narrow, linear and steep gain region [11].

In a first set of experiments, a penalty term was included in the fitness function, in order to eliminate circuits presenting over-current or over-voltage conditions. In a second set, these restraints were not applied during the evolutionary process, but the final circuits were inspected before any attempt was made to build them. For the first set, there was a low success-rate for GA runs, but the solutions had a greater probability of working when built. For the second set, there was a higher apparent success rate for GA executions, but most of the evolved circuits would not work in practice. This finding gives a context to some reports in the literature of highly complex transistor circuits evolved in simulation not using preferred values, matched transistor models, or any check on over-current or over-voltage, and for which no attempt was made to implement using real components (e.g. [72]).

Fig. 31 depicts the schematic of the best amplifier synthesised in the second set of tests. In this run, approximately $10^{5}$ individuals were evaluated, taking about 20 hours running on one processor of a Sun Ultra Enterprise 2 workstation. Fig. 32 compares the dc transfer function obtained in simulation with that experimentally measured from the circuit actually implemented on a prototyping board (Fig. 33).

Figure 31: The best evolved amplifier from the second set of GA runs.

Figure 32: Comparison between the dc transfer function obtained in simulation (solid line) and the one achieved by actually measuring the circuit output (dashed/crosses).

Figure 33: The evolved circuit built on a prototyping `breadboard' for testing.

The topology of the circuit shown in Fig. 31 is very unconventional: the input is being applied to the collector, and not to the base, of transistor Q1. The circuit is not exactly equivalent to any standard transistor stage. Transistor Q3 is redundant.

By running an operating point analysis, it was discerned that transistors Q2 and Q4 were working as current amplifiers, whereas transistor Q1 was biased in its reverse region. Q1 and Q2 act so as to set the dc operating point of Q4, which is delivering the amplification of the overall circuit.

The diode shown was inserted after evolution to remove a bias voltage of -0.7V from the circuit. The resistor values produced by the GA have also been slightly changed, using human knowledge, to improve the circuit linearity. Interactive involvement from an expert is not necessarily undesirable, but in cases such as this, linearity could alternatively be improved by a further application of an optimisation algorithm to the component values within the evolved structure.

From Fig. 32, it can be observed that both the implemented and the simulated versions behave as inverting amplifiers. The shift between the responses is due to a mismatch between the real diode parameters and the default ones employed by the simulator. An important feature of this amplifier, which had to drive a 10k$\Omega$ resistive load during all tests, is that the saturation voltages approach the power supply values, an enhancement over our previous results [10].

Figure 34: Frequency response of the evolved amplifier (in simulation).

At first glance, it might seem that this circuit is comparable to a commercial bipolar operational amplifier, such as the NE5534 [11]. The latter has a gain of 100dB and a gain-bandwidth product of 10MHz when driving a capacitive load of 100pF, while the evolved circuit has a gain of 56dB and a gain-bandwidth product of over 100MHz for the same load, with both circuits dissipating around 100mW. Fig. 34 depicts the frequency response of the evolved amplifier. However, such a comparison is not warranted, because the specification of the NE5534 includes good performance by many other criteria. These criteria were not included in our experiment but are necessary for a useful OpAmp [73]. A promising multi-criteria evolutionary method is given in [15]; here we simply aimed to show that if simulations are to be used at all, then buildability must be a primary criterion.