Appendix A:  The Issue with Unfiltered PWM Heater Voltage

As discussed in Part I of this article, it can be a challenge to get accurate effective heater voltage from the built-in supply on the µTracer main board. That is what led me to add a separate, heater regulator board (HRB). The problem stems from the use of unfiltered pulse width modulated (PWM) output to drive the tube’s heater. At right, the µTracer is seen pro­duc­ing (roughly) an effective 6.3Vrms. It’s a curious fact that there is a big difference between using filtered versus un­fil­tered PWM heater voltage, as the µTracer does.

When a PWM signal is lowpass filtered, the DC result is the average DC voltage (Vavg) of the PWM waveform:

Vavg = Vpk × Dcy, where Vpk is the peak voltage and Dcy is the duty cycle of the PWM.

- If we reduce Dcy by a factor of 4, then Vavg is reduced by a factor of 4.

- Power delivered is P = (Vavg)˛/R. where R is the heater resistance...

—so the 4X reduction in Vavg becomes a 16X reduction in power.

But if the PWM waveform is applied without filtering:

- Power while the pulse is high is (Vpk)˛/R, and the power is zero when the pulse is low.

- Average power delivered is P = (Vpk)˛/R × Dcy

The important thing is that unfiltered, a 4X reduction in Dcy only reduces power 4X, whereas there was a 16X reduction for the filtered case. Looking at it in terms of effective voltage, Veff = √(R×P) so the Dcy reduction only reduces Veff by a factor of 2, whereas it is reduced by a factor of 4 if the waveform is filtered!

If we filter the PWM signal, DC voltage is proportional to duty cycle but if we don’t filter it, effective DC voltage is proportional to the square root of duty cycle! No problem, you say, we’ll just adjust the duty cycle to produce the effective DC voltage (Veff) needed. The problem is, the duty cycle needed for lower voltages is now much shorter than it would be for filtered PWM. From the 19V main supply, filtered PWM would use a Dcy = 6.3/19 = 33.2% whereas it would use  Dcy = √6.3/19 = 11.0% for unfiltered PWM. The resolution of the PWM is limited and at 6.3V output, it gives us a resolution of about 0.48%. It’s adequate for tube testing but gets worse at lower Veff. If we require at least 1% resolution, the minimum Veff is 4.4V, which leaves out Zenith Trans-Oceanic radio tubes and the legendary 2A3, as examples. Of course, you can always connect an external heater supply!

Blurring the Line Between Filtered and Unfiltered

Since there is such a drastic difference in effective voltage between filtered and unfiltered PWM, you can imagine that anything which partially filters the signal can have a significant effect, especially since we’re concerned about maintaining measurement-quality accuracy. Now, it has been found that high-Gm vacuum tubes are prone to oscillate when plugged into the wiring of a tube tester. The VTA project was first built without protection for this and it turned out that tubes with Gm of around 10,000 and higher would quite reliably oscillate in the 200MHz region. Investigation pointed to the wiring in the socket field itself. You can see the situation in slide 44 of the VTA gallery. The only sure-fire fix was to put an RF bead on every wire going to a tube socket pin. (For the µTracer/HR, I’ve followed a less drastic approach similar to that recommended by Dekker, which you can see in slides 18 and 20 of the µTracer gallery.) The beads effectively insert a small lossy, inductance in the wire, which dampens the resonances that lead to the oscillations.

The concern is that these inductances, combined with the very high rates of current change of the PWM signal, will filter the waveform enough to cause error in effective heater voltage. As noted in Part I of this article, even high-end TRMS meters cannot measure the RMS voltage to 1% accuracy. That’s due to the double-whammy of high peak-to-average ratio and wide bandwidth of the signal. As a result, hobbyists cannot set the built-in heater voltage accurately, even if they try to measure and adjust it. My solution was to add the heater regulator board.

Why Doesn’t the µTracer filter the heater voltage?

Of course, Ronald Dekker could answer that better than I but here are what my thoughts might have been, had I been working on that design: It occurs to me that, since heater temperature is slow to change, it can easily smooth over the ripple of a PWM running at an inaudible 20kHz, so there’s no need to provide filtering on the µTracer, thereby saving the cost of components, extra PCB space and some complexity. But what about the interference from the switching? Oh—since the measurement only takes 1ms or so, I can easily afford to stop the PWM for that and again, the slow heater will smooth right over it.

This means, for little more than the cost of one small inductor and the MOSFET switch, the unit can provide a powerful, adjustable heater supply! There is nothing apparent which would suggest the strange issue of unfiltered versus filtered PWM resolution. In fact, by pushing the PWM frequency down to 20kHz, I’ve maximized the resolution of the period setting. When the resolution issue at low heater voltages comes up much later, the fact that it’s running at only 20kHz makes the inductor and capacitor needed for filtering, quite large. Depending on trade-offs, resistance in the inductor could impair voltage accuracy, require feedback or cost a lot. Trying to add the filtering components would abandon the simplicity and thrift of the basic concept and wouldn’t fit in the available board space. Raising the PWM frequency would reduce voltage resolution.

Surely, there must be some software trick of dithering which could improve the resolution, I would say to myself. The issue of beads and wiring affecting the waveform and its RMS value hasn’t come up; neither has the issue that modern, TRMS multimeters can’t accurately measure the pulsed signal. It’s Murphy’s perfect trap: lure them in with an oh-so-cost-effective concept, then strike with an issue so obscure that it’s tough to really visualize exactly why filtering makes such a difference in the RMS value! Finally, “strafe their orphans” with the beads and TRMS problems! Har! Murphy savors the moment ;-)

A Possible Fix for the µTracer Heater Supply?

What could be done to make the µTracer heater supply more accurate? It seems that it would have to be filtered. If that’s not practical at the present, 20kHz pulse rate, it may need to be raised to a higher frequency to keep the cost and size of the components down. It will reduce the resolution of the PWM duty cycle but that could be fixed by dithering the duty cycle between adjacent values to produce an average, in-between. The slowness of the heater response can smooth over the result. This approach might even lead to a lot more heater voltage resolution. One other thing: The filter may introduce enough series resistance, that the output voltage would vary with loading. If so, one of the unused ADC channels of the PIC microcontroller could be used to measure the heater voltage, allowing the PIC to adjust it.

The added cost would be the additional inductor and cap for filtering and maybe a few other parts. One way to get additional space for these in the layout would be to stand-up C13, which is close to the heater section. An alternative for those who need lower height would be to move C13 to the bottom of the board, laid horizontally and secured with insulating adhesive. To retrofit existing units, owners could make a small perfboard for the new components.

Of course, this would require a change in the software and some development. I imagine the µTracer has already claimed far more of Dekker’s time and attention than even his worst fears could have envisioned, so I certainly would not expect him to pursue anything like this. We hobbyists have to remember that he has a couple of important day-jobs in addition to this project. It’s fun to contemplate “what-ifs,” though. I guess adding the HRB or an equivalent is the best practical solution, for now.

Appendix B:  All About the Heater Regulator Board (HRB)

[Appendix B was referenced here. Also here.] The idea behind the HRB (at right) is to provide a simple, low-cost, precision heater supply which fits in the diminutive packaging for the µTracer and runs from the same AC adapter. By “precision,” I have in mind something like 0.1% accuracy. It needs to supply plenty of current for all common receiving tubes and to have accurate, preset voltages for most. Heat dissipation has to be low to avoid a fan or having to ventilate the enclosure. Knowing that a lab supply can easily be substituted for odd cases makes it easy to whittle it down to just three voltages (5.0, 6.3, 12.6V). That, in turn, allows the use of a miniature toggle switch to select voltage. The size, power supply and dis­si­pa­tion limitations dictate that it has to be a switching supply.

Design Choices

To simplify development, I’m employing a switching regulator module (SRM) widely available on eBay for just \$2 each, including shipping (quantity-5). It would cost more than that just to buy the parts to do that function.  (Incidentally, I bought a cache of 20 of the modules to insure availability for future readers.) The quality of the volt­age reference and loop amplifier on such modules (chips) is hardly up to measurement accuracy though, so I wrap the module in a precision feedback loop, based on the LT1884 precision opamp and MAX6325 voltage reference (at right). There were loop stability issues to sort out but those were easily vanquished.

Concern about possible interference with the µTracer measurements motivates adding stages of LC filtering to both the input and output of the SRM. Negative sup­ply voltage for the opamp is tapped from the µTracer main board. A highly accurate heater voltage source would be of little value if nothing were done about voltage drops in the heater and ground connections. With the connectors and wires, it’s pretty easy to find 0.1Ω or more. At 3A, that drops 0.3V or about 5% of 6.3V, which is way too much error from that one contributor.

Hence, I decided that remote sensing for the heater supply is necessary. With remote sensing, the regulator sets the voltage at the socket, rather than at the regulator’s own output. It does that by using separate wires to bring back the voltages at the two heater pins. Very little current flows in these sense lines, insuring that the regulator is seeing what is actually at the socket pins. Notice, however, that this implies that two separate lines must be connected to each pin: drive and sense. That requires two-pole connectors.

Schematic Discussion

Please refer to the schematic, linked at right. You may want to right-click and open it in a new window, for reference while reading. For most purposes, we can consider the drive lines as combined with the sense lines, since they are connected at the tube socket. To begin with, let’s pick out the main blocks: There’s the switching regulator module at upper left. That’s con­trolled by the Loop Integrator below. The three feedback dividers with pots are at right and the Voltage Reference is below the loop integrator. Remote sensing is associated with P204-207 at right.

Switching Regulator Module (SRM)
It drives the output voltage, depending on input from the Loop Integrator below. You can think of the SRM as an inverting opamp, with “Pin2” being its inverting input. There is also a built-in 10K feedback resistor going from out+ to Pin2. The Loop Integrator drives it through R211, so the SRM “opamp” circuit is an inverting amplifier with a gain of -10K/2.7K = -3.7. One other thing is that Pin2 is referenced to +0.8VDC. So to drive +6.3V out, IC201-1 will be about -0.685V. I added C207 to improve stability of the SRM itself. The module includes circuits for adjustable voltage and current limiting, which we don’t use. Those should be at maximum clockwise setting. Still, the regulator chip internally limits at about 8A. While the module may be able to produce 3-5A at up to 12.6V output, I’ve found that it’s necessary to keep continuous loads down to 3A at 6.3V and 2A at 12.6V. The chip has internal thermal limiting but I don’t recommend exercising it. I experienced strange operation and scary temperatures. It’s nice to know there is some extra capability though.

Loop Integrator
The next block is the Loop Integrator, IC201A. This is a differential integrator circuit, in­te­grating the difference it sees between the reference voltage and what comes out of the feedback dividers. C203 and R212 set the inverting side time constant at 66ms (2.4Hz unity gain bandwidth). On the noninverting side, C205 sets the time constant along with the source resistances of the divider circuits. Each of those is intended to be roughly 20K, yielding about the same time constant as the inverting side. The overall bandwidth of the loop is far less than that of the SRM and the LC lowpass filters. Although the SRM is a low-Z source when charging C202, it’s very weak at discharging the cap. When there’s no tube load, R214 sets the discharge time constant. This nonlinear effect dictated a low bandwidth for the (outside) loop. That’s no problem though, it’s still plenty fast enough for our purposes.

 Why All the Precision? Since vacuum tubes are so drifty, you might wonder why I chose an accuracy goal of 0.1% for the heater regulator board. The reason isn’t that I think it must have that. Actually, I generally like to have at least 1% accuracy for my lab measurements. Having a goal of 0.1% greatly increases confidence that it will achieve at least 1%, over time and after mishaps. This goes back to experience with classic HP in­stru­ments. They often seemed to perform far better than specified. That was a source of the great confidence we had in them. Another thing: As we saw in the testing in Part II of this article, the µTracer board may deviate much more than the 1% standard I mentioned above. Some might see that as a license to let the heater regulator vary as well. Au contraire! There is that much more need to keep heater error down, so as not to add to the existing error! With this heater supply, I can be pretty confident that I’m getting all the accuracy of which the µTracer is capable.

Feedback Dividers
Next, we consider the feedback dividers, which deter­mine the three voltages. The switch selects among the divider networks. Since pots can only be relied upon to stay put within say, 1% of their range, it’s important to minimize the adjustment range. Of course, to avoid running into the stops with com­po­nent drift, this implies making sure that the range is accurately targeted initially and that it won’t drift too far over time and temperature. Hence 0.1% 10ppm/C precision metal film resistors were used where available. Then, secondary re­sis­tors (which can have looser specs, due to their minor effect) were used in parallel to more closely target the ideal ratio, where needed. As a result, a ±1.2% adjustment range is achieved. It is so well centered that all three pots ended up very close to center. That bodes well for handling drift over time.

Voltage Reference
To support the accurately-targeted dividers and narrow ranges, I needed a voltage reference with excellent initial accuracy and very low drift. The voltage value has to be substantially less than 5V, since it sets the minimum output voltage in this circuit. That, and the need for high accuracy led to the MAX6325. This superb IC boasts 0.04% initial accuracy and 1ppm/C max drift. While it’s a bit pricey at \$11.84, I was thrilled to find it. In the context of the over-\$500 being spent (plus countless hours of my time), that seems like a small price to pay to nail this down so solidly.

Remote Sensing Arrangements
There is not much that’s esoteric about remote sensing. Mainly, it just boils down to connecting the feedback to the load, rather than the output of the HRB itself. The main thing is that current must not be allowed to flow in the sense lines. Above, I said that for most purposes, we can consider the drive lines as combined with the sense lines, since they are connected at the tube socket. Now we need to look at drive and sense separately. For discussion, let’s say that 5V output is selected. If we didn’t have remote sensing, R201 would be connected directly to HtrDrv. Voltage at that point would indeed be held to 5V but the drop across the HtrDrv line and connectors going to the socket might result in only 4.9V at the load, a 2% error. By connecting R201, through HtrSen, separately to the tube socket, the regulator holds that point to 5V, eliminating the error.

Now let’s look at the ground side of things. The regulator’s internal ground reference is the line connecting IC202-4 and other parts. Let’s call that point, GndRef. The output voltage is exactly 5V above that point. If we didn’t have remote sensing, GndRef would be connected directly to HGDrv. Output voltage would indeed be 5V above that but the drop across the HGDrv line and connectors going to the socket might result in +0.1V at the socket pin, reducing the voltage across the tube by that amount. By connecting GndRef, through HGSen, separately to the tube socket, the regulator holds the output voltage to 5V above that point, eliminating the error. IC201B has ultra-low offset so it’s a lot like connecting GndRef directly to HGSen. With the buffer, IC202’s 2mA operating current and the voltage divider currents are kept off of the HGSen line, avoiding a small error from that. Notice that in this example, remote sensing has saved a total of 4% error.

Finally, diodes D203-206 insure that sense and drive lines don’t get too far apart when connections are being made. In normal operation, the 200mV or so maximum voltage across the diodes will not make them conduct significantly.

Appendix C: Testing the Heater Regulator Board Accurately

I hope I’m not belaboring the point about separate drive and sense lines but they come into play both for the HRB operating in the system and for testing the HRB accurately. The paragraph in Part III which references this appendix offers a good introduction:

Exactly how you connect the load resistor, meter, drive and sense lines is critical to accurate load testing. If done properly, you should be rewarded with find­ing that the load has almost no effect on the voltage. The main thing is the meter should not connect directly to the drive line or the socket; rather, it should connect to the sense line and the sense line connects to the drive line at the socket. This goes for the ground side as well as the voltage side of the heater connections.

At upper right, since there’s very little current in the sense line, the V-meter sees exactly what the sense input sees. The problem below is that heavy current flows through the wire between the V-meter and the sense input, so they see different voltages due to wire resistance.

Now let’s extend this approach to the ground side as well, as seen at right. Here, the meter is seeing the same voltage as the sense lines on both terminals of the power supply. Note that this illustration is for pur­poses of testing the HRB. In an actual ap­pli­ca­tion, there would be em­pha­sis on locating the sense-line-to-drive-line connections close to the load.