Simulation Experiments for Neural Pulses - Brain Theory from a Circuits and Systems Perspective - page 186

Fig. A.4 A control voltage v 1 to start sodium current

Fig. A.5 Amplifier to generate v 1

translated through a floating fixed source of 1 V to be 0, +1 V. These are the output
levels for v 1 .
A reference voltage V R to the “

” input determines the threshold, V R ¼

10 12 F, with an
initial condition of 100 mV assures that the amplifier forces v 1 to 0 at t

55 mV. One hundred picofarads (pF) of capacitance, or 100

0. Not
shown is a small capacitance of 1 femtofarad (fF) or 10 15 F, which is included
from the “+” input to ground to ensure numerical stability.

¼

Stopping Sodium Current Stopping the sodium current at about +40 mV requires a
voltage v 2 that goes true at +40 mV, but which stays true until node voltage is safely
below the threshold for triggering at about 55 mV. This sort of behavior may be

accomplished with a nonlinear amplifier that generates a hysteresis loop. The
desired loop appears in Fig. A.6 .
A circuit that provides this loop is shown in Fig. A.7 . Note that the reference
voltage is

150 G.
The sodium current is stopped by a simple expedient, making control voltage v 1
zero by switching it to ground with a controlled switch as in Fig. A.8 . Switch S2 is a
voltage-controlled switch that closes when v 2 goes true or high.

5 mV and the feedback resistor R f ¼