Recently, we’ve seen Design Ideas for programmable current sources with improved accuracy using the LM3x7 series of three-legged regulators. These designs also take advantage of those classic devices’ built-in anti-overheating features. 

Some are very good, like “Improve the accuracy of programmable LM317 and LM337-based power sources.”

Others perhaps not so much…“Cross-connect complementary current sources to reduce self-heating error”…

All of them, however, had to accommodate the LM3x7 family’s need for about 5-V of supply voltage headroom when used this way. That is the voltage drawn from the supply that can never be delivered to the load. It therefore creates significant inefficiency in power utilization. It might have been picky of me, but I couldn’t resist wondering what could be done to improve (reduce) the loss.

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Current source without overtemperature protection

Figure 1 shows what I started with: A simple, straightforward, accurate, 0 to 1 A current source programmed with 0 to 2.5 V. It needs only about 1.25 V of headroom, consisting mostly of the drop of current sense resistor R1 (plus a modicum more from the Ron of Q1), thus fixing the problem I started out to solve.

Figure 1 An improved efficiency precision current source has no overtemperature protection. With no protection, if the Q1 heatsink is inadequate, high power or ambient temperature might destroy it.

But sadly, in fixing one problem, I created another. 

The same elimination of LM3x7s that reduced the headroom requirement also eliminated overtemperature protection. Without a substantial external heatsink, the Si7489DP FET is rated for only ~6 W at 25 °C. If power dissipation, ambient temperature, or both happen to go higher, there’s now nothing to prevent Q1 from being cooked.

Current source with overtemperature protection

So now I wondered what might be done about that. Figure 2 shows what said wondering (wandering?) inspired.

Figure 2 External junction temperature protection for the Q1 pass transistor. Since Q1’s internal junction temperature can’t be directly measured, it must be inferred from power dissipation, junction to ambient thermal resistance, and ambient temperature. If it tops 150 ^oC, A1d stops the show. 

What was needed was an external version of the now missing LM3x7’s internal junction overtemperature cutoff. Of course, the challenge with implementing an external junction temperature limiter is that internal transistor junctions are a second cousin to the classic Schrodinger’s cat.

Well, maybe not exactly. Unlike the famous quantum kitty, whose temperature (whether body or room) is theoretically unknowable. Junction temperature, while difficult to directly observe, might at least be calculated. 

And in fact, this is what the right-hand half of Figure 2 does. 

The necessary junction temp math is:

Tj = (Ij Vj)/Sja + Ta 

Where:

Tj	Junction temperature
Ij	Amperage through the junction
Vj	Voltage across the junction
Sja	Thermal conductivity (watts/degree) from junction to ambient from Q1 datasheet
Ta	Ambient temperature

The analog arithmetic

Figure 2’s circuitry performs analog arithmetic by relying on the nifty 17th-century invention of John Napier for multiplication and division: adding and subtracting logarithms. Here’s how the Figure 2 circuitry divides (and multiplies!) up the work.

Q3’s Vbe is the logarithm of the Q1 current programming signal sensed via R6. Meanwhile, Q4’s Vbe logs the voltage across Q1 monitored by Q8 and R6. 

Q3 and Q4 are connected in series, so their log voltages sum. About 400 years ago (now that’s really legacy technology!) Napier showed that adding logs is equivalent to multiplication. So, the sum of Vbe’s becomes the IjVj product term in the Tj math.

The IjVj signal is applied to A1c’s non-inverting input, which then subtracts Q5’s Vbe present on the inverting input. Because subtracting logs equates to division (thanks again, Johnny!), if R8 is properly scaled, this division provides the Sja normalization term for Rja. The quotient yields the log of junction temperature rise above ambient..

The antilog transistor Q6’s collector current, in concert with the R9/R10 network (at long last!) converts A1c’s output to a 2 mV/^oC junction temperature signal. That’s summed by A1d with Q7’s ambient temperature signal.

When the sum bumps against Q1’s 150 °C safety limit, A1d’s output ramps positive, overriding the programmed source current to a safe value.

Which you might say is the cat’s meow. 

Stephen Woodward’s relationship with EDN’s DI column goes back quite a long way. Over 100 submissions have been accepted since his first contribution back in 1974.

Related Content

• Cross connect complementary current sources to reduce self-heating error
• Improve the accuracy of programmable LM317 and LM337-based power sources
• Calculator or Slide Rule?
• Special day for physicists’ cats
• Is that a banana in your pocket (or are you just glad to see me)?

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