Analysis of TC compensated Voltage Reference / Discrete Linear Regulator

[AG7CK]

In this thread I would like help in understanding and analyzing a certain group of precision voltage reference circuits used in - among other applications - 4.5 to 6.5 (7.5) digits DMMs and voltage reference standard boxes that can be used to calibrate DMMs up to 8.5 digits. We are talking about circuits / devices that usually output "constant" DC voltage 10.0000x volt (x usually less than +- 10 microvolt) to 10.00000x or even more precise (with good long time stability, low noise and low temperature coefficient).

In order to follow and/or contribute to the discussion you will have to understand the tree topologically very similar circuits shown below, and a few very important differences between them.


Fig. 1




Fig. 2




Fig. 3




Equally important is it to recognize that Fig. 3 utilizes the so called +- 2mv temperature compensation scheme of a series connection of a zener (i.e. avalanche) diode and a PN junction (or diode) that has the "highly desirable feature ... that the output is somewhat self compensating for temperature changes by the opposing changes in VZ and VBE for VZ ≈ 10 volts. With the zener having a positive 2 mV/°C TC and the transistor base to emitter being a negative 2 mV/°C TC, therefore, a change in one is cancelled by the change in the other." [Source https://www.onsemi.com/pub/Collateral/HBD854-D.PDF page 34, paragraph after the paragraph containing formula (27)]

I will the similarities and differences I have found in a post below.

[AG7CK]

reserved

[AG7CK]

reserved

[AG7CK]

The first circuit I would like comments about and analysis of is this one from HP 3450A/B (from late 1960s or so - imo a good starting point in order to understand newer circuits that will follow):


Fig. 4



Source: https://www.aef.se/Instrumentmuseum/Hewlett_Packard/3450B/HP_3450B_manual.pdf



Whether you agree or not with my opinion that this circuit is just and application / sophistication of the regulator in post #1, please comment on why this circuit is as it is

and

How it resembles and/or differs from the "general" regulator circuits Fig. 2 and Fig. 3 in post #1.

Thank you.

[David Hess]

They are all the same topology but there are some mind bending alternatives like the first example shown below.

The improvements in figure 4 involve operating the reference and error amplifier at a constant operating point for better performance.  R31 and R32 provide constant currents to the combined error amplifier transistor and reference.  R31 is biased by a higher voltage from CR12 to increase its value for a given current so that the voltage gain of the transistor is greater.  (1) The differential pair buffers the output of the error amplifier preventing a change in operating point to improve regulation and further increases open loop gain.  Also note Kelvin sensing for the reference output although oddly enough not the ground as shown in my second example below.

I remember when RCA was advertising their combined zener+transistor references which have the advantage of placing the temperature compensating PN junction and zener diode in the same thermal environment and if you are going to use a temperature compensating diode, it might as well be the transistor which either acts as the error amplifier or as in the later integrated references like the LM399 and LTZ1000, acts to lower the reference's output resistance.

(1) The transistor's collector resistance limits how effective this can be so only raising the value of R31 further or replacing it with a high impedance constant current source yields diminishing returns.  Plus you only need so much open loop gain before other error sources become dominant anyway.

[AG7CK]

Thank you very much for studying the circuit.

I do understand the following points, but have a few questions related to some of them:

- Fig. 3 and 4 have TC compensation, while Fig. 2 will have temperature drift due to 2 PN junctions in series.

- The operating point of the base in Fig. 2 will generally be unwanted low because the emitter is raised by a single diode voltage drop.

- Fig. 2 and 4 will have constant current bias of the emitter diode (R2) / the emitter zener (R32). Fig. 3 will have current varying with supply level and ripple via R4.

- The auxiliary supply from R30 in Fig.4 and the high R31's effect on gain of the error amplifier. What determines choice of collector current?

- The differential amplifier with operating point R27 / (R27+R28) x 10v = 9.016 volt nominally. Which factors determines the choice of 9v (close to 10v) operating point? This choice of operating point is much higher than for other similar circuits I will present later. Is it an advantage to have this high operating point for the collector voltage?

- The Darlington series element for low output impedance and/or not loading the differential pair? Why has the pair so low emitter current? Not to load / change the collector bias point?

- What is R26 and C4? Power dissipation and transient response?


Edit: I just dicovered that the calculated nominal collector current through R31 is exactly 100.0 microampere. Is this just a "pretty" choice, or does it have any technical reason?
 

[David Hess]

- Fig. 3 and 4 have TC compensation, while Fig. 2 will have temperature drift due to 2 PN junctions in series.

Yep, sometimes you *want* a specific temperature coefficient on the output.  Figure 2 will also operate at much lower input voltages where zener diodes do not work well anyway.

- The operating point of the base in Fig. 2 will generally be unwanted low because the emitter is raised by a single diode voltage drop.

That is not necessarily a problem.  D1 could be replaced by a bandgap voltage reference and temperature compensation could be added to Q2.  It is possible to make a bandgap voltage reverence with an output of 200 millivolts allowing for very low voltage operation; check out the old National LM10 combined reference and operational amplifier.  Note that the voltage gain of the whole circuit multiplies not only the reference voltage produced by Q2's Vbe and D1 but also their noise.

You can make a pretty good low voltage temperature compensated reference with an LED and transistor.

- Fig. 2 and 4 will have constant current bias of the emitter diode (R2) / the emitter zener (R32). Fig. 3 will have current varying with supply level and ripple via R4.

That is right.  R4 in figure 3 impedes the line regulation because the variation in line voltage changes the current through the reference.

- The auxiliary supply from R30 in Fig.4 and the high R31's effect on gain of the error amplifier. What determines choice of collector current?

The collector current affects all kinds of things including the transconductance and voltage noise by altering the emitter resistance of the transistor and it sets a minimum value for the current through the reference.  Offhand I do not know how they selected it so let us see ...

The collector is at 9 volts so R31 provides 0.1 milliamps.  R32 provides 2.9 milliamps.  So the collector current is 0.1 milliamps which is typical for a high beta low noise transistor and the zener diode sees 3.0 milliamps total which is typical.  Those are suspiciously nice round numbers so probably not an accident.  I think that is an RCA part but Motorola made them also they give specifications for a 5 milliamp zener current and 250 microamp collector current.  I think they used such a low collector current in this case to minimize the bias current into the base through the feedback divider.

- The differential amplifier with operating point R27 / (R27+R28) x 10v = 9.016 volt nominally. Which factors determines the choice of 9v (close to 10v) operating point? This choice of operating point is much higher than for other similar circuits I will present later. Is it an advantage to have this high operating point for the collector voltage?

The operating point has to be high enough to support the error amplifier and zener reference; they will not operate much lower.  It also has to be low enough that Q12B does not saturate.  The higher the operating point the higher the value of R29 which contributes to better common mode rejection.  Let us see ...

Collector voltage of the error amplifier is 9.0 volts which is 2.8 volts above saturation.  Collector voltage of Q12B is 11.2 volts which is 2.8 volts above saturation so there is your answer.  They picked an operating point such that the collector-emitter voltages of the error amplifier and Q12B are equally above saturation.

- The Darlington series element for low output impedance and/or not loading the differential pair? Why has the pair so low emitter current? Not to load / change the collector bias point?

My guess is that the tail current of the differential amplifier is low to prevent excessive loading on the output of the error amplifier.  The 100 microamp collector current does not allow much.

- What is R26 and C4? Power dissipation and transient response?

R26 is a simple way to add current limiting for a reference supply which is low current anyway.

I am not sure about C4.  I doubt transient response is an issue but it could affect stability especially with that Darlington configuration; they are not known for being tame.

Edit: I just dicovered that the calculated nominal collector current through R31 is exactly 100.0 microampere. Is this just a "pretty" choice, or does it have any technical reason?

And the collector current plus 2.9 milliamp zener current add up to 3.0 milliamps.  My guess is that the specifications for the zener reference were given at those values but you would need to find the datasheet to know for sure.  As I said above, they are not far off from the values Motorola gave for their zener references.

[AG7CK]

Thanks again. You have some points I never have thought about, so I would like to recapitulate a bit that I think I understand until now - and then introduce a similar circuit for comparison.

The collector is at 9 volts so R31 provides 0.1 milliamps.  R32 provides 2.9 milliamps.  So the collector current is 0.1 milliamps which is typical for a high beta low noise transistor and the zener diode sees 3.0 milliamps total which is typical.  Those are suspiciously nice round numbers so probably not an accident.

I have also noticed that the collector current (10-6.2) volt / 1310 ohm is 2.900 mA. This is probably no accident because most of the circuits I have found and will present have Ic around 3mA. (The "exactness" of 100.0 uA and 2.900 mA is IMO just "old HP engineering math")

Collector voltage of the error amplifier is 9.0 volts which is 2.8 volts above saturation.  Collector voltage of Q12B is 11.2 volts which is 2.8 volts above saturation so there is your answer.  They picked an operating point such that the collector-emitter voltages of the error amplifier and Q12B are equally above saturation.

This I haven't seen before, but for the error amp transistor Vc-Vz = 9-6.2= 2.8 volt and for Q12B as the collector is two PN junctions higher than than the output - it will be at around 10+0.6+0.6= 11.2 volt - i.e. 2.2 volt higher than Vb and 2.8v higher than Ve - as you said: "2.8v above saturation".

I do think I understand your other points about the sampling divider, base current, error amp collector operating point, saturation, loading, common mode rejection and the differential pair low bias current. I will come back to the RCA (I did not know) and Motorola SZA263 Reference Amplifier (RefAmp) later.

I now would like to compare the HP 3450A circuit Fig. 4 with this Fluke 341A circuit Fig. 5 which seems to be from 1969. The HP circuit is positively earlier than the Fluke circuit - HP's first RefAmp use is probably from around 1965 or so (at least as prototype - I will come back to this).

Fig. 5



Source: http://exodus.poly.edu/~kurt/manuals/manuals/Fluke/FLUKE%20341A,%20343A%20Instruction.pdf

I will list my electrical comparison results in my next post - I would just like to state now some very obvious differences:

- 10v vs 15v
- HP uses a cooler for the RefAmp (see Fig. 4) - Fluke uses neither cooler nor heater
- Fluke has a diode in the zener bias resistor path, HP just a resistor
- Fluke trims not only RefAmp base voltage (output), but also collector current
- (ignore the Fluke preregulator), Fluke does not use auxillary supply (because of 15v ?)

[Kleinstein]

The collector current of the ref-amp is used to trim the TC.  Using the collector current, and not the zener current from trimming can have a slight advantage as the power consumption will not change that much. I don't know about those ref amps, but there could be selected / binned (possibly even on chip adjusted) refs to work well with 2.9 mA+100µA current setting.

The extra diode gives a slight temperature dependence of the zener current. This ca give a slight contribution to the second order TC. I have not checked the numbers, but I am afraid this might not be enough.  In a application with a wide temperature range the second order TC can become important if the first order is trimmed to zero.

[David Hess]

The collector is at 9 volts so R31 provides 0.1 milliamps.  R32 provides 2.9 milliamps.  So the collector current is 0.1 milliamps which is typical for a high beta low noise transistor and the zener diode sees 3.0 milliamps total which is typical.  Those are suspiciously nice round numbers so probably not an accident.

I have also noticed that the collector current (10-6.2) volt / 1310 ohm is 2.900 mA. This is probably no accident because most of the circuits I have found and will present have Ic around 3mA. (The "exactness" of 100.0 uA and 2.900 mA is IMO just "old HP engineering math")

None of the operating currents are particularly critical.  250 microamps and 5 milliamps (4.75 milliamps through R32) would have worked also.  But there is likely one best ratio between the zener current and collector current for lowest drift.

Except for drift considerations, I probably would have selected a collector current no lower than the value such that the transistor contributes the same noise as the zener diode and that happens to be somewhere around 100 microamps.  A higher collector current would yield diminishing returns.

Collector voltage of the error amplifier is 9.0 volts which is 2.8 volts above saturation.  Collector voltage of Q12B is 11.2 volts which is 2.8 volts above saturation so there is your answer.  They picked an operating point such that the collector-emitter voltages of the error amplifier and Q12B are equally above saturation.

This I haven't seen before, but for the error amp transistor Vc-Vz = 9-6.2= 2.8 volt and for Q12B as the collector is two PN junctions higher than than the output - it will be at around 10+0.6+0.6= 11.2 volt - i.e. 2.2 volt higher than Vb and 2.8v higher than Ve - as you said: "2.8v above saturation".

I do think I understand your other points about the sampling divider, base current, error amp collector operating point, saturation, loading, common mode rejection and the differential pair low bias current. I will come back to the RCA (I did not know) and Motorola SZA263 Reference Amplifier (RefAmp) later.

9 volts is the value I would have picked for exactly the reason I gave.

I now would like to compare the HP 3450A circuit Fig. 4 with this Fluke 341A circuit Fig. 5 which seems to be from 1969. The HP circuit is positively earlier than the Fluke circuit - HP's first RefAmp use is probably from around 1965 or so (at least as prototype - I will come back to this).

Kleinstein covered the diode in series with the zener supply current.  I did not noticed the selected values but I am not used to Fluke schematics.

I think R19 is for matching the power dissipation in Q15 and Q17 for lower drift.  I was surprised that it was not included in the HP implementation.

It looks like a separate ground is used for the reference and feedback divider return currents to provide Kelvin sensing for the reference output like in the example I posted.

[AG7CK]

Thank you very much - Kleinstein and David Hess.

It looks like a separate ground is used for the reference and feedback divider return currents to provide Kelvin sensing for the reference output like in the example I posted.

As this thread hopefully progress towards cascaded refamps, virtual grounds / potential splitting and current cancellation op amps as in Fluke 5700A and 732B respectively, I will ask more questions about implementation. For now, I concentrate on design / theoretic function.

I have too many questions - I don't know where to start. So I just start:

The collector current of the ref-amp is used to trim the TC.

- The HP 3450 circuit Fig. 4 has a base resistor R1 8k25 (?) in the error amp / refamp. The fluke 341A circuit Fig. 5 has not a base bias resistor. Suppose one trims the output of the HP circuits by a small change in the sampling divider. This will give a small base current change in the relatively low impedance HP divider, and the resulting small change in Ic is sufficient for the output voltage adjustment because of high refamp and diffamp gain. Is this correct?

- Since Fluke has no base resistor (but relies on the divider for current limiting), a relatively higher / more sensitive current change and change of base bias voltage in the high impedance Fluke divider will be the result. Is this correct?

- What is it that Fluke "adjusts" with R21? It is not Ic, because Ic is Beta x Ib? (I appreciate it is a one time "selection" - not a customer adjustment option. But some other Fluke boxes have 2 collector resistors in series, which could mean iterative selection / adjustment - as in "trimming" of the selected part.)

- Is it so that Fluke sets the (already known) current for which the TC is zero by adjusting the tapping point on the sampling divider. Then the divider is adjusted for exact output voltage. Finally the collector resistor is selected for the desired operating point Vc? (HP can skip the last step because of much higher gain and a "constant" temperature cooler?)

In general, I do not yet understand the most important aspect of the refamp "zero TC" regulator: The mechanism and the steps in selection / trimming.

[AG7CK]

...
So the collector current is 0.1 milliamps which is typical for a high beta low noise transistor and the zener diode sees 3.0 milliamps total which is typical.  Those are suspiciously nice round numbers so probably not an accident.  I think that is an RCA part but Motorola made them also they give specifications for a 5 milliamp zener current and 250 microamp collector current.
...

I have found no data/-sheet neither for SZA263 nor DH71005A nor DH80417B nor LTFLU-1, so I wouldn't know. Empirically, almost all hardware I have seen on the forums are run at 3mA or thereabout.

[Kleinstein]

I would consider the base resistor in the HP circuit as a kind of precaution to prevent to much base current, especially on startup. With about 1 µA of base current there is only a few mV of drop on the resistor. The 15 V of the fluke circuit naturally results in a higher impedance of the divider.

The feedback loop adjusts the voltage over R21 to a constant value. The collector resistor R21 in the fluke circuit set's the collector current - the base current is a result of this.

I would expect the adjustment procedure to first adjust the TC with R21 and than adjust the voltage level. Changing the divider would not have a significant effect on the TC.

With temperature control the HP circuit does not need the TC adjustment - especially not at that level of resolution.

[David Hess]

The collector current of the ref-amp is used to trim the TC.

- The HP 3450 circuit Fig. 4 has a base resistor R1 8k25 (?) in the error amp / refamp. The fluke 341A circuit Fig. 5 has not a base bias resistor. Suppose one trims the output of the HP circuits by a small change in the sampling divider. This will give a small base current change in the relatively low impedance HP divider, and the resulting small change in Ic is sufficient for the output voltage adjustment because of high refamp and diffamp gain. Is this correct?

- Since Fluke has no base resistor (but relies on the divider for current limiting), a relatively higher / more sensitive current change and change of base bias voltage in the high impedance Fluke divider will be the result. Is this correct?

I am not sure what is going on with R1 but the higher divider resistance of the Fluke suggests to me that the added base resistance compensates for variation of transistor Vbe or hfe with temperature.  Some current mirror implementations do something similar with added base resistance.

- What is it that Fluke "adjusts" with R21? It is not Ic, because Ic is Beta x Ib? (I appreciate it is a one time "selection" - not a customer adjustment option. But some other Fluke boxes have 2 collector resistors in series, which could mean iterative selection / adjustment - as in "trimming" of the selected part.)

Since the collector voltage and reference output are constant, they are adjusting Ic and I assume trimming Ic for best temperature coefficient like Kleinstein wrote.  Instead of Ic=beta*Ib, in this case it is Ib=Ic/beta.

In a modern design, I doubt it is worth going to all of this trouble versus using a differential pair where the impedance at both bases can be matched instead of selected.  A differential pair doubles the noise but that is easy to make up for with a higher tail current.

- Is it so that Fluke sets the (already known) current for which the TC is zero by adjusting the tapping point on the sampling divider. Then the divider is adjusted for exact output voltage. Finally the collector resistor is selected for the desired operating point Vc? (HP can skip the last step because of much higher gain and a "constant" temperature cooler?)

Fluke is doing something like that.  I don't know how they established the value for R21 but I suspect they tested the reference units at two different temperatures.  See below.

In general, I do not yet understand the most important aspect of the refamp "zero TC" regulator: The mechanism and the steps in selection / trimming.

I doubt the methods were widely advertised or documented outside of Fluke and HP.

The production processes I have seen in the past used a test assembly to measure the temperature coefficient with two different temperatures and then calculated the values for the selected parts for each unit.  I have written the programs for doing these calculations a few times.

[AG7CK]

Thanks again. I think I understand a new point:

The adjustment of / change in Ic is not because they "push" current (Vout - Vc)/Rc into the collector thereby increasing Ib. It is more like the "inverse" relation Ib=(1/Beta)xIc arises because adjusting Rc changes Vc which is the input signal to the diffamp. So a change in Rc marginally adjusts Vout and hence Vb and Ib?

[David Hess]

Thanks again. I think I understand a new point:

The adjustment of / change in Ic is not because they "push" current (Vout - Vc)/Rc into the collector thereby increasing Ib. It is more like the "inverse" relation Ib=(1/Beta)xIc arises because adjusting Rc changes Vc which is the input signal to the diffamp. So a change in Rc marginally adjusts Vout and hence Vb and Ib?

No, the differential amplifier has the same voltage at both bases so the collector voltage of the error amplifier is fixed.  Since the positive end of Rc is also fixed, Rc has a constant voltage across it and changing it only affects the collector current of the error amplifier.  This has only an incidental effect on the output voltage and a significant effect on the temperature compensation of the zener diode.

The reason these voltages are fixed is that the control loop is constantly adjusting them to match the voltage at the base of Q17 which itself is a fraction of the reference output voltage.  The absolute value of this voltage is unimportant but it is important that it not change.

The change in collector current alters the emitter resistance which alters both the transconductance of the error amplifier and its noise; neither is important.  It also affects the base current which is also unimportant.  The temperature coefficient on the other hand is important.

[AG7CK]

Thanks again. I think I understand a new point:

The adjustment of / change in Ic is not because they "push" current (Vout - Vc)/Rc into the collector thereby increasing Ib. It is more like the "inverse" relation Ib=(1/Beta)xIc arises because adjusting Rc changes Vc which is the input signal to the diffamp. So a change in Rc marginally adjusts Vout and hence Vb and Ib?

No, the differential amplifier has the same voltage at both bases so the collector voltage of the error amplifier is fixed.  Since the positive end of Rc is also fixed, Rc has a constant voltage across it and changing it only affects the collector current of the error amplifier.  This has only an incidental effect on the output voltage and a significant effect on the temperature compensation of the zener diode.

The reason these voltages are fixed is that the control loop is constantly adjusting them to match the voltage at the base of Q17 which itself is a fraction of the reference output voltage.  The absolute value of this voltage is unimportant but it is important that it not change.

The change in collector current alters the emitter resistance which alters both the transconductance of the error amplifier and its noise; neither is important.  It also affects the base current which is also unimportant.  The temperature coefficient on the other hand is important.

This solves long time on-and-off thinking about refamps for me. I will have to read more about transistor theory. To me the error amplifier / refamp seemed like a Common Emitter with a (almost) constant low impedance voltage source (the zener) in the emitter. And all I knew was Ib=Hfe*Ic.

I have several of these refamp devices - including one that is running as reference in a Fluke 8505A 6.5-7.5 digit DMM. Even if I could just forget all about the refamps and use LT1021 (non-heated), LM399 and LTZ1000 (depending on need), it is a meaningful lost cause for me to build and (more importantly understand) a discrete reference and oven that matches first LM399 and then LTZ1000 in stability. All these 3 more modern references are TC compensated zeners (a zener in series with a PN junction). So a refamp circuit built from precision junk box parts in a stable external oven should be able to match them.

Thanks a lot to both of you.

[David Hess]

This solves long time on-and-off thinking about refamps for me. I will have to read more about transistor theory. To me the error amplifier / refamp seemed like a Common Emitter with a (almost) constant low impedance voltage source (the zener) in the emitter. And all I knew was Ib=Hfe*Ic.

What really helps in these analysis is recognizing differential pairs used in closed loop feedback circuits like Q15 and Q17.  When the feedback loop is closed, then the voltages between the bases are zero.  This is the same rule where the inputs to an operational amplifier have zero volts across them and no current flows into or out of them.  Of course these are all simplifications and there is a voltage and current does flow in or out of the inputs and in precision designs these need to be taken into account.

I have several of these refamp devices - including one that is running as reference in a Fluke 8505A 6.5-7.5 digit DMM. Even if I could just forget all about the refamps and use LT1021 (non-heated), LM399 and LTZ1000 (depending on need), it is a meaningful lost cause for me to build and (more importantly understand) a discrete reference and oven that matches first LM399 and then LTZ1000 in stability. All these 3 more modern references are TC compensated zeners (a zener in series with a PN junction). So a refamp circuit built from precision junk box parts in a stable external oven should be able to match them.

Those old references are surprisingly stable and high performance.  Even now you can buy 5ppm/C temperature compensated zener diodes but their price and difficulty of use makes references like the LT1021, LM339, and LTZ1000 economical.

[AG7CK]

Yes, it has occurred to me that the input of all op amps is a differential stage. Also, the next development in these reference boxes - the Fluke 731A - uses an identical circuit with an op amp instead of the "long tailed pair".

I will be busy with life stuff a few days. When I come back, I will try to formulate a procedure for a build, selection of parts and adjustment / trim of one of these circuits.

Thanks again. Very generous of you to spend all this time on the topic.

[David Hess]

Yes, it has occurred to me that the input of all op amps is a differential stage. Also, the next development in these reference boxes - the Fluke 731A - uses an identical circuit with an op amp instead of the "long tailed pair".

Differential pairs are the king of precision and integrated differential pairs are both the best and most economical so it is not surprising that Fluke replaced that discrete differential pair with an operational amplifier even though there was nothing special about the 2N3391.

With operational amplifiers being as good as they are, other circuit considerations and especially the reference itself are the primary contributors to errors.

[AG7CK]

Now that I know about the mechanism of adjusting collector current for the ref amp, I think I will read about transistor circuit theory applicable to the refamp, and make a test circuit for adjusting TC.

I looked through other related threads and found this very useful post:

https://www.eevblog.com/forum/metrology/the-ltflu-(aka-sza263)-reference-zener-diode-circuit/msg1066470/#msg1066470

Almost a cookbook template for me. Should give me some hands-on experience before I try to study the more advanced circuits that came later.

Thanks again - David Hess and Kleinstein.