mark@mips.COM (Mark G. Johnson) (07/19/89)
Here's a design problem that I had some with; hopefully you will too. I enjoyed the tightwad-tradeoff aspects. 0. The overriding goal is to have the cheapest possible parts cost. Saving $0.01 is Ultimate Victory; cost table is below. 1. Given a transducer and a load to drive. Design a controller circuit that varies the voltage applied to the load (approximately) linearly with the transducer "reading". 2. The transducer is a pressure sensitive resistor. Its resistance is <= 5Kohms when there is too little pressure, and >10K if too much. 3. The circuit and the load operate from 12VDC (+/- 10%). 4. When there is too little pressure, apply the full 12V (99% of VCC) to the load. Not (VCC-2*Vbe), VCC. 5. When there is too much pressure, apply only 6V to the load. 6. When the transducer reading is between 5K and 10K ohms, linearly control the voltage applied to the load as shown in the curve below. 7. The load is basically a 50 ohm resistor (240 mA at 12V). Voltage applied to load (% of 12V supply) | | >99% |----------+ | \ (approximately linear curve but | . \ not required to be perfectly precise) | . \ | . \ !! NOTE: 50% | . +-------------- | . . resistance of pressure- o----------|----|----------------> sensitive transducer 5K 10K ohms Here are the prices of components; minimize the total parts cost: Resistors 1 cent Capacitors <= 0.5uF 3 cents Capacitors > 0.5uF 15 cents Diodes 2 cents Zener Diodes 5 cents Transistors rated < 0.5 Watt 8 cents Transistors rated > 0.5 Watt 20 cents Power MOSFET, > 0.5 Watt 45 cents Dual Opamp, 0.5 Watt 20 cents Quad Opamp, 0.5 Watt 20 cents Transducer (REQUIRED) 100 cents (My "solution" costs 152 cents; I suspect it can be done for about 141 cents by a sufficiently clever design). Transistor and diode VBE is between 0.45 and 0.85 volts (mfg variability plus temperature sensitivity). Beta (Hfe) is 40-200 for the small transistor, 10-80 for the big one. Vcesat is 0.05 to 0.10 volts. MOSFET VT is 1.5 to 3.0 volts, and RON is 0.05 to 0.15 ohms. Resistors, capacitors, and Zeners are 5% tolerance. The circuit should not oscillate or exhibit other instabilities. -- -- Mark Johnson MIPS Computer Systems, 930 E. Arques, Sunnyvale, CA 94086 ...!decwrl!mips!mark (408) 991-0208
tomb@hplsla.HP.COM (Tom Bruhns) (07/22/89)
mark@mips.COM (Mark G. Johnson) writes: > > >Here are the prices of components; minimize the total parts cost: > Resistors 1 cent > Capacitors <= 0.5uF 3 cents > Capacitors > 0.5uF 15 cents > Diodes 2 cents > Zener Diodes 5 cents > Transistors rated < 0.5 Watt 8 cents > Transistors rated > 0.5 Watt 20 cents > Power MOSFET, > 0.5 Watt 45 cents > Dual Opamp, 0.5 Watt 20 cents > Quad Opamp, 0.5 Watt 20 cents > Transducer (REQUIRED) 100 cents > >(My "solution" costs 152 cents; I suspect it can be done for about 141 > cents by a sufficiently clever design). - Are the two opamps really both $.20? - What does it mean to call the opamps "0.5 Watt"? - What accuracy is required, beyond the low "on" drop specified? - If your parts costs are right, and with reasonable accuracy, seems like $1.41 might be tough. (You immediately toss out many of the parts as too expensive :-) BTW, what about the PC board cost? Connectors? Mounting/enclosure? If this were a _real_ problem, an obvious thing to work on is lowering the cost of the transducer :-).
mark@mips.COM (Mark G. Johnson) (07/30/89)
Recetly I posted a design problem which was claimed to be "a whole lot of fun" to solve, mostly because it required a minimum-parts-cost design. (And thus rewarded "clever" circuits). The problem was to vary the voltage applied to a 50 ohm load depending on the value of a variable-resistance sensor, with this xfer function: Voltage applied to load (% of 12V supply) | | >99% |----------+ | \ (approximately linear curve but | . \ not required to be perfectly precise) | . \ | . \ !! NOTE: 50% | . +-------------- | . . resistance of pressure- o----------|----|----------------> sensitive transducer 5K 10K ohms The two most interesting replies used very different approaches. One circuit employed two discrete transistors: X1 VCC 1 /* (Transducer: 5K - 10K) $1.00 */ R1 1 GND 11K /* $0.01 */ R2 1 2 30K /* $0.01 */ Q1 VCC 2 3 NPN-small /* $0.08 */ DZ1 4 3 4.7V /* Zener diode $0.05 */ R3 4 GND 4.7K /* $0.01 */ Q2 5 4 GND NPN-power /* $0.20 */ R4 2 5 150K /* $0.01 */ D2 5 3 diode /* $0.02 */ RX VCC 5 50 /* load */ ---------------------------------------------------------------------------- TOTAL COST $1.39 The second approach used an opamp. Although one way to account for this is to charge 1/4 the cost of a quad opamp pkg, I decided to count it as 1x the full cost of a dual opamp pkg. Computing parts cost the other way, the price would be $1.39 (same as the previous design). R1 VCC 1 100K /* $0.01 */ R2 GND 1 5K /* $0.01 */ R3 1 2 33K /* $0.01 */ R4 2 3 1.5M /* $0.01 */ A1 3 0 5 2 /* OPAMP with out = 3, in+ = 5, in- = 2 $0.20 */ R5 3 4 250 /* $0.01 */ Q1 6 4 VCC PNP-power /* $0.20 */ R6 6 5 100K /* $0.01 */ X1 5 GND /* (Transducer: 5K - 10K) $1.00 */ DZ1 6 4 4.7V /* Zener diode $0.05 */ C1 6 4 0.1U /* $0.03 */ ---------------------------------------------------------------------------- TOTAL COST $1.54 The discrete circuit is rather non-precision, as it does not compensate for the temperature-sensitive VBE's or the finite base currents. However it certainly *is* inexpensive, mostly because it doesn't need any capacitors for stability. The opamp circuit *does* need frequency-compensation elements (R3,R4,C1) which adds $0.05 to the cost. However, this topology is much more likely to be linear than the previous circuit. Note that the opamp must handle input signals very near GND, and put out an output signal near VCC. Interestingly, both circuits used the same "trick" to get the breakpoint at (10K, 50%-of-VCC). A zener diode is placed across the collector-base junction of the power transistor, to limit the collector-emitter voltage drop at 6 volts or less. (DZ1 and D2 in the first ckt, DZ1 in the second). Special thanks to Charles Flaig of Apple and TomB of HP for the two most interesting (and lowest cost) solutions. -- -- Mark Johnson MIPS Computer Systems, 930 E. Arques, Sunnyvale, CA 94086 ...!decwrl!mips!mark (408) 991-0208