To the issue of restrictions

Your false happiness is a dynamic process. He is unsatisfied in principle. And we are primarily talking about genuine, fundamental happiness. Its conditions are determined by a single word.
- What?
He waited - and waited.
- The restriction ..

The topic of this post was prompted to me by young colleagues who came up with a question regarding the linearity of the circuit, which we will continue to consider. When I answered their question and explained that it should be so and the engineer’s zero rule once again proved its infallibility and “There are no miracles in the world,” the next question, how to do it right, I suddenly found it difficult to answer. After some thought, I came to the conclusions that I’m going to share. But let's get it in order.

The research topic will be a simple resistive voltage divider, which in this particular case is designed to change the voltage range in front of an analog-to-digital converter (scaling).

So what problems can be associated with such a simple device?

For starters, a little simple theory. We formulate the problem - there is a voltage that needs to be measured and it varies from Umin to Umax. There is a microcontroller with a built-in ADC (it could also be an external device, it doesn’t matter for business, but the severity of the wording is preferable), which is capable of receiving a signal from U1min to U1max to the input. It is necessary to ensure the conversion of the input voltage U to the voltage at the input of the ADC U1, which can be carried out by a simple mathematical formula:

U1 = (U - Umin) * (U1max - U1min) / (Umax - Umin) + U1min

There is a more beautiful equivalent formula U = U1min * (Umax - U) / (Umax-Umin) + U1max * (U-Umin) / (Umax-Umin), but here we are not talking about beauty, but about physical realizability, but with its Lagrange polynomial is not too good.

The question immediately arises of determining the values ​​included in this formula - if for the maximum input we can get data from the TK (I hope you have it), then for the minimum it is not so simple and there is room for imagination - should we measure negative values ​​and etc. Of course, it is possible to set the minimum voltage to zero by directive, but in this case we can significantly lose accuracy if, in fact, the input voltages we are interested in are in the range, for example, 20-50V. And there is also uncertainty for the ADC input signal - I know how rail-to-rail amplifier circuits are implemented (recently, quite unexpectedly for myself, I found a similar device in the Microchip line, I really didn’t think that they were doing it) and I'm not sure what standard MK did exactly what is needed - but here we can (and should) trust the documentation until we are convinced of the opposite. And if the documentation indicates the lower measured value 0V, then the upper one will usually be Ucc-0.5V or so, and in any case, the measured voltage at the input should not exceed the voltage of the ADC support, if Vref is taken as the latter, then it usually amounts to 1.2-2.5V and always lower than the supply voltage (pay special attention to the spread of this parameter in the documentation for MK, it is very significant, but more on that later).

Let us return to our formula and if we nevertheless (of course, after analyzing the problem) assume that Umin = U1min = 0, then the expression will take the form U1 = U * U1max / Umax, and provided k = U1max / Umax <= 1 this transformation can be performed on a simple resistive divider, for which we need resistors with a ratio of nominal values ​​R / r = 1 / k - 1, from which the restriction on k <= 1 is immediately obvious, since in our universe a negative ratio of resistor values ​​can hardly be realized ( of course, when it comes to a passive circuit).



Everything seems to be clear and understandable, but a new restriction comes into play - you cannot just take it and get in the general case the ratio of resistors we need. The fact is that constant resistors are produced in quite specific values ​​from the standard series and this means that neighboring resistors, for example in the E24 series, differ 1.1 times (in fact, in 1.10068, but we do not need such accuracy, because otherwise we have dealing with precision measurements and the post is not at all about them - everything is very, very complicated there), and this means that any possible ratio of resistor values ​​will be a degree of this number and intermediate values ​​are impossible in principle. For example, if we need to attenuate the input signal by 5 times and the corresponding required value of the ratio of resistors 4, then we can get either 3.83 or 4.21 when using the E24 series. Which of these values ​​should be preferred - depends on the situation and internal conviction - if you agree to lose a little (by 10%) in the value of the least significant bit over the entire range, then we select the lower value if we consider an acceptable fee of 10% error in the upper part of the range, then more. My personal opinion in the general case is undoubtedly less important, since in this case the error is predictable, monotonous and compensable, but it is up to you.

But when making a decision, one should not forget about another factor - in an ideal world, resistors have exactly the value indicated on the package, but in the real world there is still a deviation, and it is 5% or 2.5% or 1% (or 0.1% if you are rich Pinocchio) for each of the two resistors.

Fortunately, our calculation formula is successful in terms of accuracy and we should not multiply the error of the resistor by 2, nevertheless, it cannot decrease, therefore, 5% for ordinary resistors is “pull out”. And taking into account the initial deviation of the ratio of the nominal values ​​from the required result can deviate from the required by as much as 10%. Therefore, in this particular case, with the necessary ratio of 4, we need to choose the ratio of 3.83 and make sure that 3.83 * 1.05 = 4.012 is within the required value of 4 (as we agreed, we neglect an error of less than one percent, since the measurements are not precision) and the linearity of the transformation into The entire input voltage range is guaranteed.

At the same time, we must clearly understand that the possible deviation of the transmission coefficient from the accepted for implementation can be - + 5% for a given accuracy of resistors. If this result does not suit us, then we should either use more accurate resistors, or build a more accurate composite resistor from less accurate ones (I had a post about this) or use a tuning resistor.

What do I mean when I talk about a tuning resistor, and not about a variable resistor, although these are the subtleties of terminology - the main work on the formation of the transmission coefficient should be performed by constant resistors, and the variable resistor can only change it, and not too much (on those same maximum 10%). Why should we do just that, although we could confine ourselves to a variable resistor of the corresponding nominal value - there are many reasons for this, I will give only a few.

1. Initial values ​​- immediately after the correct assembly, this part of the circuit will begin to work with acceptable parameters, and it is guaranteed not to put the signal on the stops and not to overload the source, no matter how the engine is in a variable resistor.

2. Ease of understanding - just glance at the diagram to understand the transfer coefficient from the nominal values ​​(taking into account the comments on the nominal values ​​a little lower), otherwise you will have to separately indicate the necessary parameter in the form of text (although I still recommend doing this anyway, the information is superfluous can not be).

3. Ease of adjustment both after assembly and after replacing key elements of the measuring unit (for example, MK, or an external support), since the values ​​of the reference voltage, if you did not use high-precision components, will float from copy to copy very significantly.

And finally, I highly recommend multi-turn resistors because of their accuracy and insensitivity to mechanical and climatic influences (those who repaired black-and-white televisions, I realized the rest just believe it - it was just a plague, not variable resistors, and their resistance could change from a sidelong glance), the more they are quite affordable and not too expensive (although, of course, more expensive than permanent ones).

Now about the ratings - one more consideration should not be overlooked - the same ratio of resistor ratings (and, accordingly, the transmission coefficient) can be obtained with different values ​​and different (but agreed) factors, so which ones should you choose?
First of all, it should be taken into account that the input resistance of the divider circuit will be R + r at best, and R at worst, and we should strive to raise this value. Therefore, the factor should be as large as possible, even if our signal source is low-impedance, we should not drag extra current from it. On the other hand, the larger the resistor, the worse the deal with noise, so you should think carefully before leaving for dozens of megaohms. In addition, you should take into account the limitations of the input circuit of the ADC, usually it makes requirements for the maximum allowable output resistance of the signal source, due to the need to recharge the input capacitance. And finally, with very high ratings, you will have to calculate and take into account the voltage drop across the input resistor from the leakage currents of the MK inputs, and they are not zero at all.

Now about the ratings - I highly recommend taking a smaller resistor with a nominal value of 1 per factor (10kΩ, 100kΩ, 1MΩ), because then, just by looking at the circuit, you can immediately calculate the division coefficient in your mind. For this case, we can offer 380 and 100 kilos, or 3.8 and 1 meter. Since we take it with a drawback, the variable should be added to a larger resistor, its value should not be less than 10% of the value of the constant resistor, otherwise we will lose (in the extreme case) in the range, the restriction from above is due to practical considerations, but we don’t want to catch 24 kilo on a 10 meter resistor, even if multi-turn. And one more thing - we separate the variable from the measuring point with an input resistor, otherwise we can get the influence of the tuner capacity on the results, and we don’t need it at all,

Now about another important component of the input divider - the capacitor (I hope you have not forgotten about it). Despite its obvious usefulness, far from all schemes this element is present, which is very sad. The fact is that the circuit without it is simply wrong, since it is impossible to use the ADC without an input filter (low-frequency if you work in the first Nyquist zone or bandpass for all other cases), since the result becomes unpredictable. Of course, you can put different types of digital filters after the ADC, but if your circuit has noise in the mirror channel, then you can’t (from the word at all) isolate it from post-processing. Well, the presence of a capacitor in the input divider will definitely not require you to allocate additional MK resources for signal processing.

Of course, you are not going to work outside the first Nyquist zone, otherwise you would not read such simple posts, so we will put a low-pass filter, and this is easy to achieve by turning on the capacitor in parallel with a smaller resistor. Since the capacitor is absolutely necessary (if I did not convince you, then "you just believe, but you will understand later"), it remains only to solve the issue with its face value. Everything is obvious here - it should be increased as long as possible, but no more than that - by the way, it’s a pretty universal rule, it’s a pity that I didn’t come up with it.

Translated into engineering, this phrase means that our input divider should significantly attenuate out-of-band signals, but should not introduce significant distortions at the fundamental harmonic of the measured signal. You did not think about this parameter and do not really understand what it is about - you are not alone in your errors and this is sad. A large (everyone emphasizes this word on the basis of the level of misanthropy, I am inclined to the letter “o”, although the letter “a” is also not happy) some young engineers at best consider this to be half the sampling frequency over time, the rest they don’t believe anything at all. But this is a key parameter in the development of a measurement system and we had to build on it. So, the cut-off frequency of our input filter should be several times (minimum 2 but better 10 times) higher than the above fundamental harmonic,

Given that the cutoff frequency is expressed as fs = 1 / (2 * Pi * r * C)> = 10 * fo, from here we get the value of the capacitor C <= 1 / (2 * Pi * r * (2..10) * fo ) Is another argument in favor of increasing the multiplier of resistors, we will get the same cutoff frequency with a smaller capacitor, but also a reminder that with a resistor too large, we will get a low cutoff frequency and, accordingly, distortion of the fundamental harmonic even on stray capacitors. Pay attention to the size of the letter denoting the resistance of the resistor - this is the value of a smaller resistor, and by no means an input one, which follows from simple calculations, which, unfortunately, did not fit on the margins of my tablet. In fact, there should be the resistance of the parallel connected resistors r * R / (r + R), but for simplicity we leave only the smaller, especially

This should not be forgotten, especially when your divider is related to dozens, for example, when measuring mains voltage, otherwise unpleasant surprises await you.
Well, at the end of the topic, we calculate the value of the capacitor with a divider of 380 by 100 kilos and the sound frequency range (3300 Hz) C = 1 / (2 * 3.14 * 100e3 * 2 * 3.3e3) = 10 / (2 * 3.14 * 2 * 3.3) e-9F = 240 pF and estimate the frequency range with a stray capacitance of 3 pF - for a sinusoidal signal it will be 150 kHz (in fact, much smaller and that's why).

Let us ask ourselves what will be the transmission coefficient at a frequency that is 2 times lower than the cutoff frequency ... somewhat unexpected 0.89, that is, a decrease of 10%, which should not be neglected at all. But for a frequency 10 times less than the cutoff frequency, everything is much better - 0.995, that is, the transmission is very close to ideal - that’s why we need a stock 10 times the cutoff frequency. All this is true only for a first-order filter, but we are not considering anything more complicated.

We ended up with resistors and a capacitor (there may be more than one of them, but we will leave frequency compensation schemes for another post, although the topic is unusually interesting and I do it with slight regret) and consider the last component of the circuit that is discussed in this post, namely Zener diode, since everything that we considered earlier could not lead to non-linearity of the amplitude characteristic in direct current (and in AC, strictly speaking, too). Obviously, it was he who was the cause of the problem that we discussed, since all other possibilities were already excluded. First of all, why did the zener diode appear on the circuit - its task is not to allow the ADC input stage to be overloaded when a voltage appears at the input that exceeds the maximum expected values,

Of course, in this case (with the appearance of overvoltage) there can be no talk of linearity, and it is not required, since we left the work area, but nonlinearity also occurred with voltage values ​​within the expected values. At first I didn’t really understand the question and explained that it was necessary to provide a guaranteed stabilization current in order to get a guaranteed voltage value, but then I got into the essence. The fact is that the idea of ​​an ideal zener diode, the I-V characteristic of which is shown in the figure, in no case can be transferred to the real world, where the zener diode does not work at all (not at all) like on this graph. And how exactly it works is described (should be described) in the documentation.

Let us turn to this source of information for the 3v3 device (a specific BZX84 device, but it will not be better with others) and what we will see there is, first of all, the stabilization voltage at a strictly defined current through the device, and in the normal documentation we should see the minimum and maximum value ( we can still see the typical one, but to be honest, I don’t quite understand why I might need it), but if we see the maximum and typical or minimum and standard, and even more so typical, then for the zener diode this is clearly not enough and we will take out Dena consider the documentation is not normal. What to do in this case, I do not presume to advise, the only right decision is not to work more with the products of this manufacturer, but in life there is always room for a feat, so it's up to you.



In this case, we are dealing with normal documentation and we are given both necessary (actually three, but we don’t need a third) values, moreover for different types of devices in terms of accuracy, and we can plot them on the I – V curve - points 1 and 2. Immediately, we note that these values ​​do not contain any information about the behavior of the device at a current other than the specified one and should not enter into unsteady ground of conjecture and speculation. You can, of course, look at the graph of a typical I – V characteristic, but, as I said above, consider typical values ​​(including graphs) - “this is nothing”. Therefore, we pay attention to another parameter - the current through the device at a voltage of 1 volt, for which the maximum current value is set, and this is quite enough to plot point 3 on the graph and postpone a segment of possible current values ​​from it down. In this case, we must decide on the lower boundary of this segment, since we have not been given the minimum current. A good value will be zero, since in the framework of passive devices, a negative current at a positive voltage appears to be nonsense and such a solution looks natural. These considerations are purely theoretical in nature, since in our case and at our scale we see only a point on the graph. Now we can build a whole family of possible characteristics (green lines) passing through the marked points, and only a few of them will be linear and there is no reason to prefer one of them to the other. The only thing we should avoid in our assumptions is negative resistance, because their physical nature is somewhat mysterious (at least for me, you may have a different opinion).

What other parameters are given to us that can narrow the range of possible curves? We read the documentation and see the differential resistance at a voltage of 1 volt and at a stabilization voltage, which allows us to construct several limiting lines. If these lines closed, then we could put forward (quite bold and unreasonable) the assumption that the differential resistance in the whole section retains its value, but they did not. We can make the assumption (also quite bold, but more or less justified) that the differential resistance is monotonous throughout the entire plot and draw the region of acceptable I – V characteristics that flows from this, and we did it (I could not color the region, so it is determined by points 1 -2-2'-3-3), but prefer one of the green lines that fall into this area, we can not. Since the zener diode is obviously connected in parallel with the lower resistance, it will have a shunting effect on the latter, leading to the observed non-linearity, as soon as the voltage at the ADC input exceeds 1 V (non-linearity will be earlier, but much less noticeable), and it would have been predictable non-linearity, which can be fought with the linearization table, but it can quite obviously (and will) change from one instance to another. To illustrate this fact, in the figure you can find the I – V characteristics of the resistor and the zener diode connected in parallel, and two load lines are plotted, pay attention to the expected and real intersection points. The cause of the problem has been discovered, how to fix it - this is the problem. then it will have a shunting effect on the latter, leading to the observed non-linearity, as soon as the voltage at the ADC input exceeds 1 V (the non-linearity will be earlier, but much less noticeable), well, it would be a predictable non-linearity, which can be fought with the linearization table, but it can quite obviously (and will) vary from instance to instance. To illustrate this fact, in the figure you can find the I – V characteristics of the resistor and the zener diode connected in parallel, and two load lines are plotted, pay attention to the expected and real intersection points. The cause of the problem has been discovered, how to fix it - this is the problem. then it will have a shunting effect on the latter, leading to the observed non-linearity, as soon as the voltage at the ADC input exceeds 1 V (the non-linearity will be earlier, but much less noticeable), well, it would be a predictable non-linearity, which can be fought with the linearization table, but it can quite obviously (and will) vary from instance to instance. To illustrate this fact, in the figure you can find the I – V characteristics of the resistor and the zener diode connected in parallel, and two load lines are plotted, pay attention to the expected and real intersection points. The cause of the problem has been discovered, how to fix it - this is the problem. but much less noticeable), well, it would be a predictable nonlinearity, which can be fought with the linearization table, but it can obviously (and will) change from one instance to another. To illustrate this fact, in the figure you can find the I – V characteristics of the resistor and the zener diode connected in parallel, and two load lines are plotted, pay attention to the expected and real intersection points. The cause of the problem has been discovered, how to fix it - this is the problem. but much less noticeable), well, it would be a predictable nonlinearity, which can be fought with the linearization table, but it can obviously (and will) change from one instance to another. To illustrate this fact, in the figure you can find the I – V characteristics of the resistor and the zener diode connected in parallel, and two load lines are plotted, pay attention to the expected and real intersection points. The cause of the problem has been discovered, how to fix it - this is the problem. Pay attention to the expected and real intersection points. The cause of the problem has been discovered, how to fix it - this is the problem. Pay attention to the expected and real intersection points. The cause of the problem has been discovered, how to fix it - this is the problem.

The zero solution is to do nothing, accept the situation as it is (“smile and wave”), but change the input range of the measured voltages so as to work until the zener diode opens, that is, to 1V and recalculate the input divider. The first minus of this solution is obvious - we significantly lose in the dynamic range at least 10 dB. The second is less obvious - even in this case there will be no linearity, but, probably, this can be neglected, especially if the input resistor is not too large. In general, like any solution trying to ignore a real problem (“this is not a bug, this is such a feature”), it’s not very impressive, so we’ll look for other possibilities.

The first solution is to completely remove the zener diode, relying on the built-in protective MK diodes, which together with a significant input resistance should limit the voltage at the input of the ADC, and the presence of a capacitor (as it turns out to be in place) will limit the emissions that the built-in diodes can not cope with. The advantages of such a solution are obvious, the most important thing is that you do not have to do anything (in the sense of adding anything, you still have to do something, this is not a zero solution), only remove the zener diode, but it also has disadvantages:

1) we rely on on poorly documented MK functions (really weak, read the corresponding section of the documentation),
2) in the general case, these diodes may not be present on some legs of some MKs (I have not seen such a thing with general-purpose legs, this is usually characteristic of a reset, etc., but who knows ...),
3) the level of restriction will be more than voltage power supply and is definitely unknown (in no case rely on Vcc + 0.7V, we already hoped for a direct voltage of the zener diode and miscalculated, a direct drop on a diode at low currents behaves no better),
4) for 5V tolerant legs there will be an even higher voltage limitation and, although this should not lead to damage to the MK legs (otherwise why would they be called that), the behavior of the ADC in this situation is difficult to predict. Most likely, it will fall on the stops from above, but this is not guaranteed in any way, since we are clearly beyond the scope of TU. And I emphasize once again - as soon as we go beyond the limits of TU, ​​nothing is guaranteed to us. We can make various assumptions about the behavior of the device in this area, sometimes they will even be very justified and believable, but if it behaves in a completely different way, not as we expected (for example, it will fail), then it will be our fault as developers.

The second solution is to make the effect of the zener diode on the divider insignificant, for which reduce the resistor so that the shunt effect of the zener diode is not noticeable. Given that the dynamic resistance of the zener diode at 1 V is 600 Ohms, and near the stabilization voltage of 80 Ohms, you will have to choose the resistance of a smaller resistor in units of Ohms, which seems somewhat impractical.

The third solution is to replace the badly acting zener diode with something more predictable (but this is a very sound idea and we will develop it later), as a result of which (not by me) series-connected diodes were proposed. After all, it is well known that a diode does not conduct current at a direct voltage of less than 0.7V at all (yeah, of course) and everything will be fine. It’s not that such a circuit did not occur in my practice (when cutoff was needed at low voltage levels, in a coupled communication equipment, two parallel diodes at the input of the cascade stood at every step, but it was used with low-resistance signal sources), but with high-resistance output linearity if it will differ from the existing scheme with a zener diode, it is not at all for the better.

But the following solution of this type was proposed by me and, at first glance, it looked quite beautiful - put a three-pin type Zener diode type 431 and get perfectly controlled and very stable (I can not express the admiration that I experienced when I first measured the stabilization voltage in a batch of such devices - a deviation of less than 0.2% on 50 samples of the device with a stated accuracy of 1% is really cool) voltage limitation, and the circuit has long been known and a little less than all, power supplies with galvanic isolation use (use a little differently, but these are trifles, and we boldly neglect trifles).

The devil, as always, was in the details - when I guessed to look into the documentation (not that I didn’t do it before, but looked at this device for the first time in this context), I saw that this magnificent device is not capable of solving such a simple task and its behavior in the voltage range from 1V to 2.5V can in no way be called suitable for our case. It turns out that in addition to the graph with tens of mA along the vertical axis, there is another one with microAmps, and it follows from it the sad fact that the device does not open at all by a jump, but there is an opening zone from 1V to 2.5V. Yes, the differential resistance of the device is significantly higher in this area than that of the zener diode and is almost 4 kOhm, but it is a typical parameter and therefore not predictable. It was a hard blow, as it turned out, I don’t know the component well enough,

But we continue the search for the third solution, which requires the presence of a component, in whose parameters we do not doubt in a certain (wide enough) area. I recalled how a good friend of mine used (when we were limited in the choice of the element base) instead of the KC133 zener diodes, the range of values ​​of which was simply unlimited (although completely within the framework of the TU), AL307B LEDs, which fit the accuracy requirements much better, but it was from hopelessness, since the documentation was not regulated in any way. A quick search showed that the LEDs (of course, modern ones, although I looked at 307) do retain a closed state longer, but still have a pronounced zone of nonlinearity before opening and there can be no solution.

The correct solution (as often happens, all of a sudden) came from a similar emission control problem, where the upper limitation diodes are reduced to a zener diode that sets the response level. It turns out that you just need to work not at the forward bias, which is so non-linear, but at the reverse - because the diode in the reverse bias is the device I was looking for - its current does not exceed the "dark" current in the entire range of permissible reverse voltages. But this fact can be considered fully proven, since this parameter is clearly spelled out in the documentation, and we agreed to believe it.

Simple series connection of the diode and the zener diode does not lead to the desired result (we build a current-voltage characteristic and continue to observe significant non-linearity), so the circuit is somewhat complicated to ensure a guaranteed voltage at the zener diode and is shown in the figure. Here, everything is fine with linearity up to measured voltages not exceeding the stabilization voltage; everything is almost fine with a voltage limiting, which will be no more than 0.7V higher than the voltage limiting the zener diode. Of course, there will be no linearity in the cutoff region, but we must understand that this is no longer the measurement domain and by choosing the appropriate zener diode to achieve the desired value.

One more remark - you should not take the Schottky diode in the calculation of its smaller forward drop, since its reverse current is significantly (by an order of magnitude, or even not one) higher than the reverse current of a conventional diode, and our resistors are significant, therefore, an extra drop in the measurement accuracy we are not compensated for in any way by a possible (not guaranteed) decrease in the cutoff voltage. Well, or very carefully read the documentation and calculate the drop in the input resistor associated with the reverse current, decide, as always, to you, I just give advice.



There is only one question left for this circuit - the resistance rating Rv. The first and obvious value that provides the stabilization current of the zener diode Rv <= (Uv - Uf) / If = (36-3.3) / 5e-3 = 6.5kOhm leads to significant currents of consumption from the measured source (yes, I consider units of mA a significant current) over the entire range of input values, especially during overvoltage. Another not obvious feature should be taken into account - where we guarantee that at voltages less limited the diode will be biased in the opposite direction, that is, the voltage at the zener diode will always be higher than at the measurement input (on the divider). After all, I have repeatedly emphasized that the behavior of the zener diode at currents lower than the stabilization current is not defined. I don’t refuse my words, but, as one very indecent joke said, “and the rest is nuances,”



Now we will do it - watch your hands.

We found that the curve of the I – V characteristic of a real device lies below the broken line 0-3-3'-2. We stand the transfer characteristic of the system from the input resistor and the zener diode, for which we draw the load line and begin to shift it to the right, increasing the input voltage. Up to point 1, the voltage on the zener diode practically repeats the input voltage, up to a drop on the input resistor, the current does not exceed the initial current, that is, the transfer coefficient is close to unity. Starting from point 3, the current through the zener diode increases and the voltage lags more and more behind the input, the transmission coefficient decreases, but cannot become less than the equivalent resistive divider with a pull-up resistor equal to the differential resistance of the device. After point 3 ', the resistance changes stepwise (of course, but cannot change in this way, the restrictions that describe it change) and the transmission coefficient drops even more (although it does not become equal to zero). Therefore, if we ensure that the transmission coefficient in the 3-3 'section is not less than that of the main resistive divider, then we can easily achieve the required condition - the diode is back biased over the entire input voltage range. It can be seen from the figure that the green line (voltage at the zener diode) is always higher than the red line (voltage at the divider) until it becomes lower and then the red line is bounded (blue curve). From here we get k1 = Rv / (Rv + R1)> = r / (r + R), and then by simple manipulations we get R1 <= Rv * r / R, which for our values ​​will be 600 * 11 = 6.6 kOhm, i.e. everything went well. Therefore, if we ensure that the transmission coefficient in the 3-3 'section is not less than that of the main resistive divider, then we can easily achieve the required condition - the diode is back biased over the entire input voltage range. It can be seen from the figure that the green line (voltage at the zener diode) is always higher than the red line (voltage at the divider) until it becomes lower and then the red line is bounded (blue curve). From here we get k1 = Rv / (Rv + R1)> = r / (r + R), and then by simple manipulations we get R1 <= Rv * r / R, which for our values ​​will be 600 * 11 = 6.6 kOhm, i.e. everything went well. Therefore, if we ensure that the transmission coefficient in the 3-3 'section is not less than that of the main resistive divider, then we can easily achieve the required condition - the diode is back biased over the entire input voltage range. It can be seen from the figure that the green line (voltage at the zener diode) is always higher than the red line (voltage at the divider) until it becomes lower and then the red line is bounded (blue curve). From here we get k1 = Rv / (Rv + R1)> = r / (r + R), and then by simple manipulations we get R1 <= Rv * r / R, which for our values ​​will be 600 * 11 = 6.6 kOhm, i.e. everything went well. It can be seen from the figure that the green line (voltage at the zener diode) is always higher than the red line (voltage at the divider) until it becomes lower and then the red line is bounded (blue curve). From here we get k1 = Rv / (Rv + R1)> = r / (r + R), and then by simple manipulations we get R1 <= Rv * r / R, which for our values ​​will be 600 * 11 = 6.6 kOhm, i.e. everything went well. It can be seen from the figure that the green line (voltage at the zener diode) is always higher than the red line (voltage at the divider) until it becomes lower and then the red line is bounded (blue curve). From here we get k1 = Rv / (Rv + R1)> = r / (r + R), and then by simple manipulations we get R1 <= Rv * r / R, which for our values ​​will be 600 * 11 = 6.6 kOhm, i.e. everything went well.



Why did we succeed - because if we need to know the exact value of the transfer coefficient for the measurement, then for the auxiliary circuit we need it to be not less than a certain limit, and the specific value is completely irrelevant. Nevertheless, a certain smack of trickery remains (we made some assumptions regarding the behavior of the differential resistance of the Zener diode, which are quite functional, but are not directly stated in the documentation), and this should be avoided. In addition, we have to select a significant current (units of mA) from the source of the measured voltage, and if it is, for example, a battery? Therefore, it is highly desirable to use not a signal source, but some internal voltage of the device to obtain the cut-off voltage, it must also have power, which leads us to modify the circuit in the following figure. There is nothing to worry about at all, the voltage at the zener diode is fixed and stable, regardless of the input voltage, and the diode cannot be shifted in the forward direction until the input values ​​are above the boundary, never if we believe in technical documentation (“we believe in God, everything the rest requires evidence. ”)



Let's pay attention to the fact that instead of the usual zener diode, the so-called "three-output zener diode" of the 431 series is included, which I already mentioned and temporarily postponed. What gives the use of just such a device is, first of all, unsurpassed voltage stability, it seems to us that this is not particularly necessary in this situation, but it’s better to get used to good solutions right away. Secondly, it can significantly reduce the requirements for direct current through the device (at times) and, although we do not consume this current from the input signal, but from the supply voltage, why take too much. Here is the last aspect I would like to consider in more detail.

Those who have already read my posts will not be surprised, but for my beginning readers I’ll say right away that the “cry of Yaroslavna” will begin. Yes, I like to speculate on the degree of greenness of the grass, but first you read my opinion, then look at the sources, then compose your own, and only then judge (or join).

So, we begin the discussion of documentation on 431.

We are talking about a completely wonderful electronic device, which was really developed by the masters of their craft, which is mass-produced by many well-known companies and mass-produced in millions of copies (and maybe tens of millions) around the world, and there is not a grain of sarcasm in this phrase. I have been using this device for more than 20 years and always left the best impression of myself, but today I carefully looked at the documentation for it (I didn’t look at other manufacturers from ON, Motorola, NSC, TI, but I think it was enough) and found that it is not complete (well, or I'm dumb, I ask with the justification of the last thesis in the commentary). We consider the electrical parameters and see:

- stabilization voltage at a fixed current (never mind the current, you say, as much as 10 mA, and you will be right, but wait a bit), and the minimum and maximum values ​​are set (also typical, which is unclear why, but let it be);
- the effect of temperature on the value of the stabilization voltage (for some reason, a typical graph of this dependence is given under the table, but I do not see any harm from it if you remember that this is a TYPICAL graph and, therefore, is not guaranteed by anything);
- the effect of the cathode voltage on the reference voltage (very slight, attenuation of almost 40 dB, which is remarkable);
- the value of the differential resistance at the current is again 10 mA, and very small - substantially less than one Ohm (a really wonderful device);
- the minimum stabilization current, with a typical value of 0.4 and a maximum of 1 mA (here it is, we laugh at the little believers who were scared off by the 10 mA line at the beginning of the table) - "but from now on, more in detail, please."

What kind of parameter is this - no, I understand what all three words in the parameter name mean, I can clearly imagine what their combination means, but I'm sorry, we are dealing with technical documentation, and there should not be room for interpretations. The only documentation where an attempt is made to somehow hint at the behavior of the device at this current is the domestic description on EN19, where the phrase about the stabilization current from 1 to 10 mA is found, but even there it is not expanded into a normal description. And in the documentation of foreign manufacturers this parameter is simply set and that’s it.

Indicate the stabilization voltage, or differential resistance, or the deviation of any of these parameters from the nominal value in the range of collector currents, starting with the minimum stabilization current, and I will remain completely satisfied. But this has not been done - from the word at all.

There are beautiful pictures (if the word “typical” were not above them, they could be called graphs, and these are pictures), from which we can assume that when the collector current is reduced to 1 mA, the stabilization voltage does not change significantly. But, firstly, these are pictures, and, secondly, I was taught at the institute to take values ​​even from graphs (especially from a picture) by applying a ruler with divisions to them. If you require specific values, they must either be listed in the table or analytical formulas for the curves restricting the parameter, figures and graphs given — the material is illustrative. Moreover, some manufacturers with a special arrow on the I – V characteristics show a minimum stabilization current in the low current region (but for some reason it’s not the maximum, but the typical one, I conjure it again - don’t be fooled by the typical values), that is, guess

Yes, for many years I myself set the initial stabilization current to 1 mA, and all the circuits worked perfectly and showed excellent repeatability of the results, And on the circuit presented to your attention, such a current is installed, but all this is wrong, although it works.
If one of the readers of this post works in one of the listed companies, tell your colleagues that in distant Russia at least one engineer asks them to clearly register the behavior of 431 devices with a minimum stabilization current.

As it was said in one good film, “But in general, we came to congratulate you”, so I like the resulting scheme, it solves the main tasks, who can, let it do better, “where is that young punks that will erase us from the face of the Earth” .