Frequent contributor Christopher Paul just lately supplied us with a painstakingly conservatively error-budget-analyzed Design Concept (DI) for a state-of-the-art pursuit of a 16-bit-perfection PWM DAC.
The DI introduced beneath, whereas shamelessly kibitzing on Chris’ wonderful design course of and product, ought to under no circumstances be construed as criticism or perhaps a prompt modification. It’s neither. It’s only a voyage into the unusual land of final precision.
Wow the engineering world along with your distinctive design: Design Concepts Submission Information
In his pursuit of good precision, Christopher creatively coped with the restrictions of the “artwork.” Maybe essentially the most intractable of those limitations within the context of his design was the temperature coefficient of obtainable reasonably priced precision voltage references. His selection of the wonderful 35xxx household of references, for instance, reveals a temperature coefficient (tempco) of 12 ppm/°C = 0.8 lsb/°C = 55 lsb over 0 to 70°C, decreasing this factor of conversion precision to solely an efficient 10.2 bits.
Since that was greater than an order of magnitude worse than different error elements (e.g., DNL, INL, ripple) in Christopher’s easy and chic (and good!) design, it received me musing about what potentialities may exist to mediate it.
Let me candidly admit upfront that my musing was unconstrained by a priority for the sensible injury such potentialities may suggest in direction of the simplicity and class of the design. This included injury, equivalent to doubling the elements depend and vastly growing the facility consumption.
However with these caveats out of the way in which, right here we go.
The apparent chance that got here to thoughts, in fact, was what if we diminished the significance of thermal instability of the reference by the easy (and brute-force) tactic of placing it in a thermostat? Through the years, we’ve seen plenty of DIs for utilizing transistors as sensors and heaters (generally combining each capabilities in the identical machine) for controlling the temperature of single elements. Determine 1 illustrates the thermo-mechanics of such a scheme for this software.
Determine 1 Thermally coupling the transistor sensor/heater to the DAC voltage reference to stabilize its temperature.
A nylon machine screw clamps the heatsink hotspot of a TO-220-packaged transistor (TIP31G) in a cantilever vogue onto the floor of the reference. A foam O-ring supplies a modicum of thermal insulation. A dab of thermal grease on the mating surfaces will enhance thermal coupling.
Determine 2 exhibits the electronics of the thermostat. Right here’s how that works.
Determine 2 Q1 is a combo heater/sensor for a ±1°C thermostat, nominal setpoint ~70°C. R3 = 37500/(Vref – 0.375).
Q1 is the core of the thermostat. Beneath the management of gated multivibrator U1, it alternates between a temperature measurement when U1’s “Out” pin is low, and heating when U1’s “Out” pin goes excessive. Setpoint corresponds to Q1 Vbe = 375 mV as generated by the voltage divider R3/R4, detected by comparator A1, and timed by U1.
I drew Determine 1 with the R3/R4 divider linked to +5 V, however in follow, this may not be the best selection. The thermostat setpoint will change by ~1.6°C per 1% change in Vref, so sub-percentage-point Vref stability is essential to realize optimum 16-bit DAC efficiency. The +5-V provide rail could subsequently not be steady sufficient, and utilizing the thermostatted DAC reference itself could be (a lot) higher.
Any Vref of sufficient stability and a minimum of 365 mV could also be utilized by merely setting R3 = 37500/(Vref – 0.375). For a similar cause, R3 and R4 ought to be 1% or higher steel movie varieties. The purpose isn’t setpoint accuracy, which issues little, however stability, which issues a lot.
Vbe > 375mV signifies Q1 junction temp < setpoint, which gates U1 on. This permits U1 “Out” to transition to +5 V. This activates driver transistor Q3, supplying ~20 mA to the Q1, Q2 pair. Q2 capabilities as a fundamental present regulator, limiting Q1’s heating present to ~0.7 V/1.5 Ω = 470 mA and subsequently heating energy to 2 W
The suggestions loop thus established, Q1 Vbe to A1 to U1 to Q3 to Q1, adjusts the U1 obligation cycle from 0 to 95%, and thereby tweaks the heating energy to take care of thermostasis. Observe that I omitted pinout numbers on A1 to accommodate the chance that it may be contained in a multifunction chip (e.g., a quad) used elsewhere within the DAC.
Q.E.D. However wait! What are C2 and R2 for? Their cause for being, usually phrases, is to be present in “Fixing a basic flaw of self-sensing transistor thermostats.”
As “Fixing…” explains, a basic limitation on the accuracy of thermostats like Determine 1 is as follows. The junction temperature (Tj) that we are able to truly measure is barely an imperfect approximation of what we’re actually considering: controlling the bundle temperature (Tc). Determine 3 exhibits why.
Determine 3 The deadly flaw of Determine 1: the junction temperature is an imperfect approximation of the bundle temperature.
Due to the nonzero thermal impedance (Rjc) between the transistor junction and the floor of its case, an error time period is launched that’s proportional to that impedance and the heating energy:
Terr = Tj – Tc = Rjc*Pj
Within the TIP31 datasheet, Rjc is specified within the “Thermal Traits” part as 3.125 °C/W. Subsequently, as Pj goes from 0 to 2 W, Terr would go from 0 to 6.25 °C. Recalling that the REF35 has a 12 ppm/°C tempco, that would depart us with 12 x 6.25 = 75 ppm = 5 lsb DAC drift.
That’s 11x higher than the 55-lsb tempco error we began with, nevertheless it’s nonetheless fairly a approach from true 16-bit accuracy. Can we do even higher?
Similar to the R11, R12, C2 community in Determine 2 of “Fixing a basic flaw of self-sensing transistor thermostats” that provides a Pj proportional Terr correction to the thermostat setpoint, that’s what R2 and C2 do right here on this DI. C2 accumulates a ~23 ms common of 0 to 100% heating obligation cycle = 0 to 700 mV, and provides by way of R2 a proportional 0 to 14 mV = 0 to six.25°C Terr correction to the setpoint for web ±1°C steady thermostasis and < 1 lsb reference instability.
Now Q.E.D!
Stephen Woodward’s relationship with EDN’s DI column goes again fairly a good distance. Over 100 submissions have been accepted since his first contribution again in 1974.
Associated Content material
- Fixing a basic flaw of self-sensing transistor thermostats
- A pleasant, easy, and fairly correct PWM-driven 16-bit DAC
- Double up on and ease the filtering necessities for PWMs
- Inherently DC correct 16-bit PWM TBH DAC
- Self-heated ∆Vbe transistor thermostat wants no calibration
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- 1kHz per Kelvin temperature sensor
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