Fig 1. Connecting both ends of a potentiometer yields a parabolic curve for resistance versus wiper position.
Fig 2. This circuit uses the parabolic resistance curve of an end-connected digital potentiometer to compensate for changing pneumatic pressure in a paint gun as shots are fired.
Even the most ordinary and commonplace components can serve in extraordinary and unusual applications when connected in uncommon ways. Consider a linear potentiometer (either digital or electromechanical) with total resistance Rt that has both ends of its resistance element wired together (Fig. 1). This peculiar topology yields a parabolic resistance curve as the wiper (Rw) moves from one end of the element to the other. The resistance swings from zero to a peak of Rt/4 and then back to zero with R = Rw(Rt – Rw)/Rt.
This resistance curve has application in compensating for pneumatic pressure variations in a wide variety of popular sport and recreational equipment—ranging from so-called “paintball markers” to precision, short-range, indoor target rifles—that use compressed air as a propellant. The typical pneumatic power plant in such devices uses a spring-driven striker to open a poppet valve. Opening the valve releases behind the projectile a small volume of air from a pre-charged reservoir, sending the projectile on its way.
The trouble with this simple mechanism is that the volume released will change as the (finite) air charge is expended and the pressure remaining in the reservoir declines from shot to shot. The result is a variation in projectile velocity from shot to shot, which translates directly into inconsistent trajectories, decreased shooting accuracy, and missed targets.
This variation usually follows a parabolic function of velocity versus shot count. Early shots achieve a relatively low velocity because the reservoir is at maximum pressure and the striker’s ability to lift the poppet against that pressure is limited. Consequently, the striker achieves only a brief and partial opening of the valve.
With subsequent shots releasing air from the reservoir, the pressure drops and the striker is increasingly able to open the valve, resulting in a gradual rise in projectile velocity. The system reaches an inflection point and provides peak projectile velocity when dropping pressure (and slower air flow) balances the effect of increasing valve actuation. Following shots see decreasing velocity as pressure continues to drop.
The velocity variation problem can be addressed with mechanical pressure regulators, but at increased cost and decreased reliability. The parabolic pot provides the possibility of an electronic solid-state solution (Fig. 2).
The solid-state solution adds to the basic spring-and-striker assembly a relatively low-power solenoid (the striker’s spring provides most of the needed energy), arranged so the solenoid assists the spring to increase the striker’s kinetic energy and thus the valve’s opening. Timing circuitry adjusts the solenoid drive pulse’s duration as a function of shot count to compensate for falling pressure and maintain a consistent projectile velocity. A digital pot in a parabolic connection generates the necessary timing to compensate and cancel the pneumatic power plant’s parabolic velocity variation.
A shot cycle begins with the striker’s initial release and spring-driven acceleration, which passively moves the connected solenoid. Because of residual magnetization, the solenoid’s movement generates a trigger pulse that comparator A2 detects. The comparator then turns on current source transistors Q1 and Q2 and their current causes comparator A1 to switch on the ZTX drive transistor, adding the solenoid’s force to the striker spring’s.
The digital pot’s resistance (R) determines the drive duration (and therefore the kinetic energy the solenoid contributes to the striker) by adding at A1 pin 2 the voltage Iq2 × R to the timing ramp that Rcal and the 1-µF capacitor generate. The nearer this added voltage is to the reference voltage Iq1 × Rzero at A1 pin 1, the shorter the timing ramp and solenoid drive pulse and the less added energy in the striker.
Each trigger pulse increments the DS1804’s internal counter, causing the voltage Iq2 × R to follow a parabolic curve versus shot that accurately tracks—and therefore cancels—the poppet valve’s parabolic projectile velocity curve.
Calibration of this circuit involves adjusting the Rcal and Rzero trimmers and programming the DS1804’s nonvolatile power-up wiper position to match the solenoid’s timing function to the pneumatic equipment’s actual characteristics and shot capacity. Powering down the circuit when filling and recharging the reservoir ensures that the digital counter inside the pot remains synchronized with shot count.
Often the case with electronics in sporting equipment, this circuit will need to operate over a wide range of ambient temperatures. Unfortunately, the DS1804 has a large, positive temperature coefficient of 750 ppm/°C, representing more than 5% of drift over 0°C to 70°C. To cancel this error, a thermal compensation Rtc utilizes part of Q1’s 300-ppm/°C Vbe temperature coeffecient so rising temperature makes the voltage Iq1 × Rzero rise to track the thermal drift in R.