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A Power Supply With A Negative Output Resistance
Maintains constant speed of a lightweight hobby drill as the load changes.

Photo 1. The power supply is a regulator that I place between the output
of one of my bench supplies and the drill motor. There are no
adjustments. The green LED indicates voltage across the output
terminals and the red LED indicates that the power supply has
entered current limit. When operation crosses over to current
limiting mode, the red LED begins to glow and the green LED dims.


In one of the dark back alleys in Bangkok, I bought something that I could not have bought anyplace else. I bought a light hobby drill that is based on a surplus capstan motor from a video tape recorder (remember those?). I also bought an assortment of collets and drills, and on a later visit to the capital city, I bough some router bits.

The drill works pretty well for drilling holes in circuit boards but the drill's tendency to change speed with load made it difficult to use in the delicate task of cutting patterns in the foil of printed circuit boards. Some sort of regulation or compensation would help reduce the change in speed with changes in the load on the shaft.

One approach which was considered but rejected based on the complexity and difficulty was to monitor the interruptions in current that resulted when the motor's brushes switched contact from one set of armature contacts to the other. A much simpler, and I would like to think elegant approach, that of increasing the voltage delivered to the motor as the current increases, was chosen.

The values shown are appropriate for my particular drill motor. The DC resistance is approximately 27 ohms, when running at 20 volts, the unloaded shaft current is 50 milliamps and having the onset of current limit at 200 milliamps allows enough torque for my light use. The circuit and its topology are suitable for other motors and other voltage and current combinations. I urge anybody considering a project based on this design to learn about the voltage and current requirements of his motor and then use this project as an example but not a universal design.

Chart 1. Above is the plot of the current-voltage response curve of
the power supply. As the load current increases from zero
milliamps to 200 milliamps, the output voltage increases from
approximately 20 volts to approximately 24 volts. Data for this plot
was captured on a voltage recorder using a battery powered attenuator/preamp.

The circuit's output voltage as a function of current is plotted in chart 1. With no load, the output voltage is 19.8 volts and increases at the rate of 23 volts per amp, corresponding to a negative output resistance of -23 ohms. Beyond 200 ma the output voltage decreases, reaching 6.4 volts at 240 milliamps
because of the action of the current limiting circuit. The current limit protects the motor and also makes it possible to operate the circuit without any heat sink.

The Circuit

The Basic Voltage Regulator

Schematic 1. Basic TL431 shunt regulator circuit

shown in Schematic 1 the simplest TL431 regulator would be composed of U1 (the TL431),  Bias resistor R1 and resistive voltage divider R6 and R7. A circuit to increase the current output capability, a circuit that increases voltage as current increases, and a current limiting circuit were added to this basic circuit.

Schematic 2. The circuit is based on the TL431 voltage regulator.
A second feedback loop increases voltage with current while a
third loop limits and regulates the maximum current.

The compete circuit is shown in Schematic 2.

Buffer Stage
The current boosting stage is a compound transistor made of Q2 and Q3. This configuration was chosen because its maximum output voltage (Collector of Q3) can be very close to the input voltage (Base of Q2). I could have made the highest possible output voltage a few hundred millivolts closer to the +26 volt input by using two inverting transistors, but I didn't want to have to worry about the cumulative frequency dependent phase shift because that cause oscillation and make it more difficult when it came time to modify the design for a different motor. High current gain transistors were used for Q2 and Q3 to keep the maximum output voltage high.

D2, a green LED indicates the voltage out of the regulator and thus is related to the voltage across the motor. It glows when the motor runs and dims as current limit is reached.

Current Feedback
To get the current feedback signal needed to obtain a negative output resistance and for the current limiting function, R5, a low value resistor is used to sense the current through the motor.  The voltage developed by the IxR drop is fed to the anode of the TL431, which serves as the non-inverting input to the shunt regulator. This small voltage is amplified by the closed loop voltage gain of the regulator circuit (1+ (R6/R7) = 7.818 with the component values shown in Schematic 2. Ignoring the TL431 anode current through R5 to simplify the problem, negative resistance should be approximately R5 x (1+R6/R7). In the case of  the values shown in Schematic 2, the output resistance is approximately -23.5 ohms. The output voltage is approximately equal to (Vref + Vr5)
(1+ (R6/R7), where Vref is 2.5 volts for the TL431's internal reference voltage and Vr5 is the load current inducted voltage drop across R5.

The easiest means of setting the negative resistance is by selecting the best value for R5. The larger the value of R5, the greater the negative resistance. Too much negative resistance results in instability. I selected the highest value for R5 that at which the motor's speed sounded constant whether the shaft was unloaded or loaded by pressing my finger against the chuck.

Current Limit
The voltage drop across R5 is also used to sense current for the current limiter. As shown in Schematic 2,  when the voltage across R5 becomes sufficient, transistor Q1 begins to draw collector current with the result that the output voltage is reduced. Since D1 is in series with the collector of Q1, D1 will begin to glow as the circuit enters current limit.

It is a happy coincidence that the value of 3 ohms for R5, which produces the desired negative output resistance,  results in an onset of current limit at 200 ma, which is a nice value for this particular drill motor. If I wanted to increase the current at which current limit begins, I would place a resistor across the base and emitter of Q1 so as to form a voltage divider with R4. For example, if I added 1k across the base and emitter of Q1, the onset of current limit would be approximately doubled to 400 ma. Take note that the onset of current limit decreases by approximately 0.3% per degree C. With more sophisticated circuitry, this can be made very stable, but this is only a hobby drill motor, not a surgery-assist robot servo (grin).

Snubber circuit
The main load for the power supply is the permanent magnet motor and it is inductive. I chose 100 ohms as the snubber resistance because it was low enough to keep the voltage at a safe value no matter how fast the output might change. If the inductance were high Q and the maximum current was 250 ma, then the maximum voltage that can be developed as the magnetic field around the motor collapses is 250 ma x 100 ohms = 25 volts. The 100 uf capacitor is probably way larger than what I need, but it was one of the few capacitor values that I have on hand of reasonable size and voltage rating. The snubber probably is not needed for this small motor, but its inexpensive insurance.


Photo 1. The circuit is quite small and can be housed in a
pretty small container. In this specific implementation, the
TO-220 transistor does not need a heat sink because the power
dissipation is low.

All of the components except for the input and output banana connectors are mounted on a phenolic pad-per-hole prototyping board, or 'donut board'  at Alan Yates refers to themUsing old-fashioned through-hole parts, the circuit could fit into a very small enclosure. Wiring was point-to-point without too much attention to wire length, but with some care about not creating ground loops that would affect the output Resistance of the power supply.

I am pretty happy withe the performance of the circuit. I might not bother using it for merely drilling holes, but
I will definitely use it for anything more delicate, such as routing so I can get more accurate shapes and cleaner edges.

As expected, the no-load output voltage is a mild function of the input voltage
. This happens because current through the R1 and the cathode of U1 adds to the current through current sense resistor R5, thus raising the output voltage. An acceptable price to pay for the simplicity of using a three terminal regulator.

If a higher input voltage were available, this could have been done with an LM317
, greatly reducing component count. In that case,
the Adjust pin on the LM317 would connect to R5. Because of the larger input-to-output voltage difference needed by an LM317, its power dissipation will be higher than that of Q2 in the circuit presented on this page, thus more attention would need to be paid to the temperature of the LM317.

Special thanks are due to Joe Goodart of Texas for suggestions of improvements to the circuit description and schematic.

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First posted in February, 2013. Lightly edited in April 2013.

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