If this is the first time you read about the uTracer, perhaps a little explanation is in order. About two years ago I had an idea to construct a tube tester / curve tracer. By using a pulsed measurement principle, the whole circuit could be kept very small. After several iterations, this led to the uTracer3. Many people liked the concept, and after many requests I decided to make a kit so that everybody could build their own DIY tube tester.
In the mean time some 60 uTracers are up and running in more than 20 countries and 4 continents! Although, without exception, people are very enthusiastic about their uTracer, there is always room for improvement. Both from people who have actually built the uTracer3 as well as from the thousands of people who have read the weblog, I received many emails with requests for improved / extended performance and added functionality.
Figure 1.1 A set of vintage beauties waiting for restoration left to right: Pilot T501 (done), NSF h207u, Philips LX452AB (battery tube radio), Philips BX200U (set for tropics).
On this page I want to make an inventory of these requests, and I want to test and compare circuit ideas to realize them. I have to emphasize here again that the goal is not to design the best all round, most complete tube tester that money can buy, but to find the balance between performance and complexity / costs! Having said that, I do not want to raise false expectations: I really have no idea if this will eventually result in a complete working system, let alone a commercial product! I write these pages primarily for my own documentation, and for communication with other enthusiasts. Making the uTracer3 kit has cost me a lot more time than I could have ever imagined, and besides making tube testers, there are many other projects waiting, such as the restoration of four beautiful vintage radios.
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Higher Anode and Screen voltages
This point is undoubtedly on top of the list of most people who have given me feedback. The maximum anode / screen voltage of 300 V is by many people regarded as the most severe limitation of the uTracer3.
So, why are the anode and screen voltages limited to 300V? At the beginning of this project I did some initial experiments, and I found that with standard available components the maximum output voltage of a straightforward boost converter is limited to approximately 450V. Since 100uF/ 400V electrolytic capacitors are commonly available and relatively cheap, I decided to limit the output voltage to 400V. And then again, during the experiments with the high voltage switches I decided to limit the output voltage to 300V because, given the simple circuit concept of the uTracer3, is was difficult to guarantee fully short-circuit proof outputs.
Personally I am not into Power Audio Amplifiers. For me the main motivation to build the uTracer was to have a means to visualize and study the phenomena which occur in more standard “small signal” tubes, so for me 300V was already more than enough. In the mean time I have learned that especially people developing and building power amplifiers are interested in triode characteristics up to much higher voltages. So the question is: how high? Values mentioned in emails I received vary from 400V, via 700V, all the way up to 1500V! I really could use some more input here: what tubes are commonly used in the somewhat bigger PA’s, and to what voltages and currents need they be characterized keeping in mind that there is always a trade-off between price and performance? Is there only a need for higher voltages for triodes, or are there also people who want to test pentodes to much higher voltages? Would a curve-tracer just for triodes be OK for most people? What type of tubes are you using? Any additional wishes ….
Extended grid bias range
More or less the same questions apply to the grid bias circuit. The grid bias voltage range of the uTracer3 is 0 to -50V. The choice for this range was on one hand given by practical reasons, such as supply voltage ranges of OpAmps and the maximum input voltage of the LM339 voltage regulator, and on the other hand by the fact that this range covers some popular tubes including the very popular EL34.
Figure 2.1 A PL509 tested at grid biases of -60 to -80 V with the aid of an external 50V voltage source.
Some creative solutions can be used to increase the grid bias range of the uTracer3. To be able to characterize a PL509 in the relevant bias range, Derk Reefman for example inserted an external 50V voltage source in series with the grid connection (Figure 2.1). I understand however that a somewhat higher (more negative) grid bias would be welcome.
Figure 2.2 The 801A is designed to be used for grid biases between -160 V up to 160 V.
I received one or two questions from people who would like to test tubes at positive grid biases. I have to admit that I had no idea that tubes were also sometimes used in this regime. As it turns out some tubes like the 801A, are even designed to be used at positive grid biases so that a higher output power can be achieved (More1,More2). The 801A is even specified for grid biases ranging from -160 V up to 160 V (Fig. 2.2)! A positive grid bias automatically results in a grid current which also needs to be measured.
Again, I am highly interested in the specifications that people “in the field” would like to see for the grid bias!
Larger heater bias range
To keep the uTracer cheap and simple an old laptop power cord is used as power supply. The idea is that most people have an old power cord lying around anyway, and if not they can by bought practically for free at flea markets, surplus shops etc. These power cords can easily deliver tens of Watts of power at an output voltage of approximately 19 V. With so much power available, it was natural to use some of it for the heater. By simply pulse-width-modulating the output of the power cord, heater voltages between 0 and 19V can be obtained with only a few transistors and an inductor. As it happens this covers quite a large range of tubes commonly used, but of course not all.
In the meantime it has become clear that the internal heater supply has difficulties with low voltages (< 4V) in combination with high currents (>1 A). It has become clear that this is a result of the PWM principle in combination with inductances in the heater circuit (More). This is certainly one of the things on my list to look into.
A number of people have asked me if it is possible to include a converter so that the uTracer can be extended to higher heater voltages. Personally I do not think it is worth the effort. Such a circuit will greatly increase the complexity, while it offers little additional functionality. Fortunately, the design of the uTracer3 is such that both for directly, as well as for indirectly heated tubes an external heater supply can be used. What I recommend as the most practical and economical solution is to use a simple external lab power supply for tubes with a heater voltage higher than 19V. For indirectly heated tubes, even a simple transformer can be used.
For low voltage / low current heaters, such as for delicate 1,5 V battery tubes (DL96, DK96, etc.), as well as for valuable vintage tubes, I personally always use a battery as heater supply. With a PWM regulator it is not so easy to accurately control the equivalent DC output voltage down to a tenth of a volt, especially not for low voltages. Additionally, in this way, under no circumstances, the heater can be damaged due to a hardware or software error. Next to these more rational arguments, I have to admit that emotionally I do not feel too comfortable to subjecting fragile heaters to a PWM signal with an amplitude of 19V! A few dry “A” cells can easily be included in the case and made accessible on the front panel.
USB Communications
A recurring “complaint,” especially on forums, is the lack of an USB interface. The good-old serial RS232 interface is considered to be outdated and obsolete. Well, what can I say? It certainly is a bit outdated, but by far not obsolete! There are still zillions of devices with a serial interface around interfaced to USB ports through cheap USB-to-serial converters. Even recent projects in leading magazines like Elektor are often RS232 based but use on board USB to serial converter. Basically there are a number of options:
Next to these “hot topics” there are some more minor issues which are on my personal wish list:
This list is by no means complete and will probably be expanded as this project develops. If you have suggestions, ideas, please mail them to me!
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Georg Beckman is one of the people who bought a uTracer3 from the first series. He actually wrote a very nice review about it on the RadioMuseum forum. He also wrote me a few emails with some very interesting circuit ideas. One of these ideas was to get rid of the “high-side” high-voltage switch altogether by using a transformer. He reasoned: “transformers can transform a low voltage pulse to a high voltage pulse. If we generate a low voltage pulse on the primary side of a transformer which is used backwards and transform it up to a high voltage, we can get rid of the high-voltage switch.” The principle of the idea is shown in Fig. 3.1. We have some “low-voltage” adjustable voltage source and a MOSFET switch which generates a pulse on the primary side of the transformer. On the secondary side of the transformer we then find a pulse with, depending on the turns ratio, a higher voltage which drives the anode or the screen. Since the secondary winding is floating with respect to the primary winding, current measurement can be simple done by adding a current sense resistor to the “cold side” of the secondary winding.
Figure 3.1 Principle of the transformer based high voltage bias circuit.
I have to admit that my first reaction was not very enthousiastic; one of the very nice features of the uTracer3 is that it doesn’t contain any heavy and difficult transformers, keeping the circuit small, cheap and light. Introducing a transformer seemed to me a step back in time. When we talk about low-loss switched-mode power supplies we always use low-loss ferrite based inductors and transformers. So (obviously) my first assumption was that Georg wanted to use some fancy, specially made, ferrite transformer. A quick “back-on-the-envelope” calculation showed that, given a measurement pulse length of about 1 ms, that would be almost impossible because of magnetic saturation of the ferrite.
The idea continued to intrigue me however. If it would work, it has some very nice features. The fact that the whole rather complex and “sensitive” high-side (PMOS/PNP) switch can be replaced by a normal robust low-side NMOS is obviously very attractive. Also current sensing by means of a small series resistor at the cold-side of the secondary side of the transformer is straightforward. On top of that the galvanic isolation between the high-voltage side and the low-voltage driving electronics seems attractive, although this argument might be more emotional rather than rational.
When I confronted Georg with my reservations he explained to me that it was not his intention to use a fancy ferrite transformer, but an ordinary, cheap, off-the-shelf mains transformer. I did some experiments on which I will report in subsequent sections, and became convinced that the idea might work. So assuming for the moment that the transformer idea works, how could a uTracer based on that look like?
Figure 3.2 Two power supplies are needed to test tetrodes and pentodes.
First of all we need two of those transformer stages to bias both the anode and the screen grid independently (Fig. 2.1). Here already we run into a difficulty. One of the implications of using a transformer to generate high voltage bias pulses is that due to resistive losses in both the primary, but especially also the secondary (high-voltage) windings, as well as losses in the core, the voltage on the anode cannot be predicted accurately because it will depend on the current drawn by the tube! This doesn’t need to be a problem: although it cannot be predicted with great accuracy, it can be accurately measured! For a triode that is fine. Suppose we want to make an anode sweep, we then just make a best guess for the needed Uvar values (Fig. 3.1), but use the actually measured anode voltages for the plot. For a pentode or tetrode this is more difficult because here the anode sweep is made under the assumption that the screen bias is constant! Keeping the output voltage of the transformer bias circuit constant under varying load conditions is much more complicated and probably will require some iterative procedure. But nevertheless, let’s assume for the moment that we can fix that.
Figure 3.3 When a triode is tested the high-voltage supplies can be stacked or connected in parallel.
One of the very, interesting features of the concept is that the high voltage side is isolated from the driver side. This makes it possible to play some interesting tricks, provided that a triode is tested so that a separate screen supply is not needed. Occasionally I get questions from people who ask me for an option to test triodes to anode voltages in excess of 1000 V! By stacking two supplies (Fig. 3.3A) that is possible. Assume that each supply is capable of generating a pulse of 600 V at 200mA, then testing triodes to an anode voltage of 1200 V (@ 200 mA) becomes feasible. Alternatively, the two supplies might be connected in parallel to increase the output current to 400 mA (@ 600 V). These are indeed very nice specifications.
Figure 3.4 Idea for practical circuit implementation
Georg’s idea was to go directly from a low voltage to the required high voltage. What does that imply? Suppose that we use a power supply of 20 V and set the maximum high voltage at 600 V. This means a transformation ratio of 600/20 = 30 at least. In reality we will need a higher transformation ratio to make up for the losses. This means that the current at the primary side is at least a factor 30 higher than the current at the secondary side. So if we set – just as for the uTracer3 - the maximum anode current to 200 mA, this results in a primary current of at least 6 A, but more likely in excess of 10 A. Although that is not impossible, I am not really over-enthusiastic about the idea. I think it a better idea to use an intermediate high voltage of say something like 150 V and from there to use a transformer to step-up the voltage to 600 V. In that way the currents remain “manageable,” and since it requires less volume to store the same amount of energy at a higher voltage in a smaller capacitance (E=0.5*CV^2 with C inversely proportional, and V proportional to the volume) it also results in a (physically) smaller reservoir capacitance.
The actual circuit implementation I have in mind is something like the circuit shown Fig. 3.4. It consists of a small boost-converter identical to the one used in the uTracer3. The boost converter (L1,T1,D1) charges reservoir capacitor C2. If needed, C2 can be discharged through T2. Zener diode D3 removes the 19.5 V offset inherent to a boost converter. T3 pulses the transformer, while flyback diode D2 dissipates the energy that is released when T3 opens again.
Figure 3.5 Generating negative and positive grid bias pulses.
Continuing along the same line of thought it may even be attractive to use a transformer in the grid bias circuit. In the uTracer3 a constant grid bias was used, generated by an OpAmp with a special “high-voltage” discrete output stage. There is actually no reason why the grid bias voltage should be a constant voltage. Just as the anode and screen supplies, also the grid bias circuit can be pulsed provided that the grid bias pulse precedes the anode and screen pulses to prevent unwanted anode current transients. By using a transformer with a center tap and an additional NMOS switch, it becomes possible to generate in a very simple and elegant way both negative as well as positive grid bias pulses (Fig. 3.5).
All this sounds very nice and attractive, however, the biggest problem as I see it right now is – as already discussed – the difficulty to predict the correct driver settings for a certain bias condition. The losses in the transformer combined with the fact that currents drawn by the tube are inherently unknown will require some kind of clever iterative scheme or mathematical procedure. Having uttered these words of caution, I cannot conclude else than that the whole idea seems attractive. Time for some experiments!
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Transformers can be tricky components to understand. Most people are more or less familiar with the operation of a transformer for AC sinusoidal signals, but when it comes to (DC) pulses, most of us feel a bit uncomfortable. To explain how a transformer behaves for pulses, we first have to build an equivalent circuit model of the transformer. Central component in such a model is a device which only exists in theory: an ideal transformer. Figure 4.1A gives the circuit symbol of an ideal transformer. The current voltage relations of this imaginary device are identical to the equations we know for the real transformers we are all familiar with, with this exception that these relations are valid for any waveform be it AC or DC.
Figure 4.1 Left - ideal transformer, Right – the simplest model of a real transformer includes the magnetization inductance.
A real transformer (unfortunately) doesn’t behave like this. The reason is that we have used magnetic principles and effects to implement a practical version of this ideal device. Our everyday transformer is basically nothing more than two inductors which are magnetically coupled.
Figure 4.2 sketches what happens when a constant voltage is applied to the primary winding of a transformer with a turns ratio of n1:n2 = prim:sec = 1:2. The secondary winding of the transformer is left open in this example. The three rows of graphs in the figure show respectively the applied primary voltage, and the primary current and secondary voltage. The four columns show different moments in time. When the input voltage is first applied (Fig. 4.2A), the current through the primary winding increases linearly with time according I = V*t/L, with L the inductance of the primary winding. Since the magnetic flux (B) increases proportionally with the current (Ampere’s law), the voltage induced in the secondary winding (proportional to dB/dt, Lenz’s law) is constant. Since the ratio of the windings is two, the induced voltage at the secondary side will be twice the input voltage.
Figure 4.2 A constant voltage applied to a transformer with open secondary windings.
As long as the magnetic core of the transformer is not in saturation, the current will continue to increase linearly, and consequently the output voltage will remain constant (Fig. 4.2B). At a certain moment however, the core saturates. All the magnetic dipoles of the iron have now aligned with the magnetic field, and cannot help anymore to sustain a further increase in the magnetic field strength. In other words for a further increase in current, the transformer behaves as if the core was not there, resulting a sharp decrease in inductance and coupling between the windings. Due to the decreased inductance, the current through the primary winding will now show a sharp increase (Fig. 4.2C.) The output voltage of the secondary winding will collapse as a result of the vanishing coupling between the windings. Finally, the primary current is limited by the series resistance in the primary branch (Fig. 4.2D). When the current has become constant, the voltage at the secondary winding has become zero.
The simplest model of a real transformer is shown in Fig. 4.1B. In this model Lm represents the inductance of the primary winding with open secondary terminals. Lm is called the magnetizing inductance referred to the primary winding. The magnetization inductance models the magnetization of the core material. It is a real inductor showing saturation and hysteresis.
If we want to use a simple mains transformer as pulse transformer, what are then the boundary conditions for the input pulse (amplitude, duration) so that saturation is avoided? Iron cores saturate at a magnetic field strength B of around 2T (Bsat = 2T), but for off the shelf components the construction details needed to calculate the magnetic field are usually not available. Fortunately there is another method! We use the knowledge that mains transformers are designed to operate close to saturation under normal operating conditions. Knowing this, it can be shown (Appendix A) that the product of the pulse amplitude (V) and duration (t) should be V*t < 4.5 ms⋅Vrms (for 60 Hz transformers V*t < 3.8 ms⋅Vrms). For example, if we have a transformer with a primary winding of 36 V, then the V*t product of the input pulse should be less than 162 msV to avoid saturation. To take some extremes: a voltage pulse of 1 V during 162 ms, or a pulse of 162 V for only 1 ms.
Back to the idea of using a transformer to “boost” the high voltage pulses for anode and screen. The first choice is the transformation ratio. A high ratio results in high primary currents, while for a low ratio we could have saved ourselves the trouble of using a transformer. For the first experiments I picked a 10 VA transformer with two primary windings of 18 V (at nominal currents), which in series give 36 V, and a secondary winding of 220 V. Using a 6 V AC voltage I measured the transformation ratio of the secondary to primary windings which turned out to be 4.8. We have seen that for a 1 ms measurement pulse, the maximum amplitude of the input pulse for this transformer theoretically is 162 V, resulting in an unloaded output pulse of 4.8*162V = 780 V!
Figure 4.3 First test circuit used to test the pulse transformer principle
The circuit shown in Fig. 4.3 was used to test the new principle. Readers of my other tubes-tester weblogs will undoubtedly recognize my “standard” pulse generator circuit in the left part of the circuit diagram. The components have been chosen such that when S1 is pressed, the circuit produces a positive pulse of 1 ms. The energy for the primary high-voltage pulse is stored in a 1000 uF / 200 V electrolytic capacitor which is connected via a 0.39 ohm current sense resistor to ground. The capacitor is charged via R4 by a variable high-voltage power supply. R4 is selected such that during the pulse almost all the current through the transformer is supplied by the buffer capacitor. In that case the (negative) voltage drop over R5 is directly proportional to the current through the primary winding of the transformer. Flyback diode D2 absorbs the energy stored in the transformer when T1 switches off again. At the output I added a resistive voltage divider to reduce the output voltage to safe limits for my scope. The resistor values are a bit odd, but I happen to have these 1% resistors lying around. The division relation is
Vout = 11*Vscope.
Figure 4.4 Primary current and output pulse for different input pulse amplitudes, and unloaded output.
Figure 4.4 shows in each photo both the current through the primary winding (top trace) as well as the output pulse (bottom trace). By the way, the current is measured over the sense resistor against ground, it appears as a negative signal. The output pulse amplitude increases linearly with the input pulse voltage (Fig. 4.6). For input voltages up to 150 V there are no signs of saturation. At that point the output pulse amplitude is 660 V! Note how the current almost linearly increases with time. At 175 V we observe, as expected, the onset of saturation near the end of the pulse. For 200 V the saturation becomes really pronounced, and we observe a sharp almost exponential increase in current.
Figure 4.5 Primary current and output pulse for different input pulse amplitudes with a 3k3 resistor connected to the output of the transformer.
The next step is to test the circuit under load conditions. The simplest test was to redo the measurement above, but now with a 3k3 (10W) resistor connected to the output of the transformer. The output current will now be proportional to the output voltage. Just for reference, for an output voltage of 660 V the output current will be 200 mA, more or less my target output current value. We observe a number of striking differences.
First of all observe that the primary current is now much larger than in the unloaded case. A quick calculation: For an input pulse amplitude of 150 V, we find an output voltage of ca. 550 V. This results in a secondary current of 550V/3300Ω = 166 mA. This again results in a primary current of 4.82*166 mA = 800 mA, exacty the value we read from the photo.
We will consider the change in the slopes of the pulse and the absence of saturation in a next section, but first concentrate on the amplitude of the final pulse.
Figure 4.6 Output pulse amplitude versus input pulse amplitude taking losses into account.
In the graph in Fig. 4.6 the output voltage amplitude of the transformer has been plotted as a function of the input pulse amplitude for the case that the output of the transformer is left open and for the case that a 3k3 resistor is connected to the output (solid lines). For the loaded transformer the output voltages are obviously lower due to losses in the transformer. The circuit diagram in Fig. 4.6 shows the equivalent circuit of the transformer as far as DC resistive losses are concerned. The relation gives the output voltage of the transformer as a function of input voltage taking resistive losses into account. The dashed line in the graph gives the predicted input-output relation based in this relation and the measured DC resistances of the primary and secondary windings. We observe that most, but not all of the losses can be explained from the DC resistances of the transformer windings. Other losses can be caused by: discharging of the reservoir capacitor, series resistance of the capacitor, the current sense resistor and other losses in the transformer core and windings.
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When a load is applied to the output of the transformer, the shape of the pulse changes from a nice rectangular shape to a pulse with pronounced leading- and trailing edges (Fig. 4.5). This effect is caused by the leakage inductances of the transformer. These leakage inductances are associated with magnetic field lines originating from the primary winding which are not coupled into the secondary winding and vice versa. In the transformer model they are represented by two separate inductances in series with the terminal leads (Fig. 5.1A). In Fig. 5.1A also the series resistances of both windings have been included. For our purpose we will rewrite the transformer model of Fig. 5.1A into a slightly different model where the secondary leakage inductance and resistance have been referred back to, and included into, the primary leakage inductance and resistance (Fig. 5.1B). As long as Ls is much smaller than Lm, the transformer ratio of the ideal transformer hardly changes so it can still be approximated by n. By the way, a very simple method to measure Ls, is to short circuit the secondary winding and then measure the inductance at the primary winding. Short circuiting the secondary winding will short circuit Lm, leaving only Ls (Appendix C).
Figure 5.1 Complete model of a transformer including series resistances and leakage inductances.
If we neglect the magnetization current for a moment (which is a valid assumption under significant loads, compare Fig. 4.4 and 4.5), then all the output current has to pass Ls. The leakage inductance in combination with the output resistance forms an L-R combination with time constant τ = L/R. If we estimate from one of the graphs in Fig. 4.5 the time it takes for the current to increase to 63% (1/e) of its final value, we find ca. 200 us, this in combination with the output resistance of 3k3 gives a leakage inductance of L = τ*R = 200us*170Ω = 34 mH, which is for such a simple estimation close enough to the measured value of 22 mH (Fig. 5.2).
Figure 5.2 Estimation of the leakage inductance from the leading slope of the output pulse.
Note, that although in the measurements of Fig. 4.5 input voltages of up to 200 V were used, so well in excess of the “theoretical” saturation value of 162 V (for a 1 ms pulse), no saturation is observed! The reason is that it is the integral of the voltage over time (the area of the pulse) which counts, and which has to be less than the aforementioned 162 msV. So although it takes more time for the pulse to reach its plateau value, we can compensate for that by increasing the pulse length. The output pulse can be described by a simple first-order system resulting in an exponential behavior (Fig. 5.3). The time constant of this system is determined by the leakage inductance and the total series resistance referred to the primary winding. As long as the integral of the pulse over time is less or equal than the saturation criterion, no saturation will occur.
The leakage inductance results in a significant complication of the whole transformer pulse idea! With increasing load, the slope of the trailing edge of the output pulse decreases. As a consequence the length of the measurement pulse will have to depend on the load. On the one hand the pulse length has to be chosen such that the final plateau value (say to a value of 4τ, corresponding to 98% of the final value) is reached, while on the other hand it should not be chosen too long because otherwise the criterion for non-saturation is violated.
Figure 5.3 The output pulse shows a first-order exponential behavior.
When the MOSFET switch opens again, the current through the leakage inductance wants to remain constant. To achieve this, a voltage across Ls will develop so that the primary current continues to flow through the snubber diode. Gradually, the energy stored in the inductor will be dissipated in the load resistor, and the current will drop, resulting in a trailing edge of the pulse with the same time constant as the leading edge. Note, that when the diode is extended with a zener diode, Ls will have to develop a higher voltage to maintain the same current. The higher voltage will result in a faster “discharging” of Ls (t=V*t/L) and hence a reduced fall time. This at the expense of a significant dissipation in the zener diode and a higher breakdown voltage of the MOSFET.
The measurement of Fig. 4.5 with a constant load resistor connected to the output of the transformer obviously results in an output current which is proportional to the output voltage. A pentode and tetrode however have output characteristics which much more resemble a constant current sink. In this case the pulse circuit has to be able to deliver high currents at low voltages. To investigate how the pulse circuit behaves under true constant output current conditions, a slightly different measurement was performed whereby the circuit was evaluated for a number of different output voltages rather than input voltages. So for each output voltage set point, a load resistor was connected which resulted in a current of either 100 mA or 200 mA, after which the input voltage was adjusted so that the desired output voltage was obtained.
Figure 5.4 Input voltage required to reach a certain output voltage for a current of 100 mA or 200 mA.
Figure 5.4 shows the result of this measurement. Next to each measurement point the pulse length required to reach the plateau value is noted. The good news is that with a simple 10 VA transformer pulses up to 600 V at currents of 200 mA can easily be obtained. The bad news is that both the input pulse amplitude, as well as the optimal pulse length are a function of the load (current) which is not known beforehand. A measurement even will therefore inevitably involve some kind of iterative procedure to obtain the optimal settings.
What seem most challenging are high current pulses at low output voltages. In this case the load impedance is lowest, resulting in a large LR-time constant. The question is whether a plateau value can be reached, while still avoiding saturation. Figure 5.5 shows a measurement where the output voltage was set to 50 volts while the load resistance was decreased resulting in an increase of load current. So for every new measurement with a lower load resistance, the amplitude of the input pulse (noted in Fig. 5.5) was adjusted so that a 50 V output pulse was obtained. Remarkably, the output current could be increased to 500 mA without any sign of saturation. At an output current of 600 mA the onset of saturation can be observed. At that point the input pulse amplitude is 108 V!
Figure 5.5 “worse case” test with a low output voltage and high output current (low output impedance situation). The output voltage was kept constant at 50 V while the load resistance was decreased.
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Lets try to summarize what we learned so far. A simple mains transformer can be used to “boost” a voltage pulse. When the transformer is unloaded, the output pulse will be rectangular, and the “boost factor” will be almost equal to the ratio of number of turns secondary/primary. To avoid saturation, the area of the input pulse (amplitude times duration) should be smaller than a certain non-saturation criterion which depends on the design of the transformer. When the output of the transformer is loaded, two effects complicate the situation. In the first place the amplitude of the output pulse will drop due to resistive losses in both the primary, as well as the secondary windings. In principle this is not so bad because we can compensate for that by just increasing the amplitude of the input pulse. The other effect is that the leading edge of the output pulse changes from a rectangular shape into more gradual “first order” increase characterized by a time constant τ. This time constant is proportional to the leakage inductance of the transformer, and inversely proportional to the load resistance. As a result higher load currents require a longer measurement pulse duration than smaller load currents. At the same time care has to be taken not to violate the non-saturation criterion. Fortunately nature helps a bit here: the higher the load current, the longer the pulse, but also the more gradual the increase in voltage, and since it is the integral of voltage versus time that counts, the integral also increases at a slower pace. For high load resistances on the other hand the measurement pulse cannot be too short, because we need some time for the electronics to stabilize and for the AD conversions themselves. In short, both the amplitude as well as the duration of the measurement pulse are variables which depend on the actual load being measured, which is in principle unknown!
Figure 6.1 Saturation criterion calculation for a pulse length of 4*τ.
In this section I want to have a look at how the optimum duration of the measurement pulse has to be chosen in relation to the output current and voltage. As mentioned, the output pulse behaves like a first order system characterized by a time constant τ (Fig. 5.3). In order for the pulse to stabilize to a certain constant plateau value, I decided that the pulse length should be at least 4 times τ. In that case the voltage has stabilized to within 2% of its final value. In order to avoid saturation, the integral of the voltage over time from 0 to 4*τ has to be less than the saturation criterion (162 msV for our test transformer). Figure 6.1 shows the calculation of this integral, and quite remarkably we find that this integral only depends on the output current, and not on the output voltage. As long as the 3*n*Ls*Iout is less than 162 msV, saturation is avoided.
Figure 6.2 Vout / Iout selection plane and boundaries.
Figure 6.2 shows in a (rather complicated) graph the complete output voltage (x-axis) and output current (y-axis) space. In the area below line A, the integral of the voltage over time from 0 to 4*τ is less than the saturation criterion of 162 msV. So the conclusion is that as long as we can scale the duration of the measurement pulse with the time constant τ inversely proportional to Req (see Fig. 6.1), saturation will only occur above a certain current level, regardless of the output voltage. However, the higher the output voltage, the shorter the measurement pulse. Unfortunately, the measurement pulse cannot be made too short. Some time is needed for the electronics to stabilize and also the AD conversions take some time. So let’s say the minimum measurement pulse length is, just as in the uTracer3, 1 ms. How does that then limit the possible output voltage/current values?
Figure 6.3 Saturation criterion calculation for a fixed pulse length of 1 ms.
To find that limit we have to calculate for which Vout/Iout pairs the area of the input pulse for a fixed length of 1 ms equals the saturation criterion (Fig. 6.3). Unfortunately the resulting equation cannot be solved analytically (at least I couln’t), but the numerical solution is shown in Fig. 6.3 by line B. So for a constant pulse length the area right to line B is forbidden. The total operation range is now reduced to the uncolored area below line A but left to line B. The highest output voltage that can be obtained is with an unloaded output, indicated by point C.
Figure 6.4 Calculation of lines with constant pulse length.
The dashed lines in Fig. 6.2 indicate the measurement pulse length corresponding to 4*τ. The calculation of these lines is straightforward and given in Fig.6.4. In the shaded area below the line for 1 ms the pulse length corresponding to 4*τ is less than 1 ms. So in this area a constant pulse length of 1 ms is used as explained above. As a result this area is on the right side limited by line B. Above the 1 ms line the optimal pulse length has to be increased as indicated. Finally, the dotted lines in Fig. 6.2 give the required amplitude of the input pulse for a certain Vout / Iout combination, based on a simple model only including resistive losses.
Figure 6.5 Checking the validity of the model.
In Fig. 6.5 the validity of the theory is explored along the boundary of the valid measurement region. For each measurement first a target output voltage was selected and a load resistor was connected which would result in the desired output current. Next the amplitude of the input pulse was increased so that the target output voltage was obtained. The standard time base was 200 us/div, for some measurements the time base had to be increased. In general I would say that there is a very reasonable agreement between the experiments and the simplified model. For all the points in the “forbidden” area, saturation is observed (white arrows), while the points within the white area are saturation free. Also the predicted input amplitude and measurement pulse length are in fairly good agreement.
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When a constant voltage V is applied to a simple air coil with a certain inductance L a current will start to flow through the inductor. The current will obviously start at zero and then increase linearly according to I = (V*t)/L. Since the inductance of an air coil is usually very low, the current will increase very fast to the point where the current is limited by the resistance of the coil. At that point the current will remain constant at a value I = V/R.
When an iron core is inserted in the coil, the inductance of the inductor will increase by something like three orders of magnitude. What happens is that the magnetic moments of the individual iron atoms start to align with the external magnetic field so that the total magnetic flux is increased dramatically. Since the inductance is increased, the rate of increase in current when a constant voltage is applied will be much slower (I = V*t/L). At a certain magnetic field however, all the magnetic moments of the iron atoms are aligned, so that the metal core no longer can make a contribution to the increase in flux. This point, which is called saturation, occurs in iron at a magnetic field strength of typically 1.5 - 2.0 T. What is basically left after saturation of the core is an air coil with a very low inductance, resulting in a sharp and unwanted increase of the current.
We now add a second coil to the iron core to make a transformer. Again a constant voltage is applied to the first (primary) coil, while the second (secondary) coil is left unconnected. As we have seen, the current and the magnetic flux will start to increase linearly at a rate given by I = (V*t)/L. The increasing flux will induce a voltage in the secondary coil which is proportional to the derivative of the flux increase to the time and to the ratio of the number of turns in the primary and secondary coils according to: V = (n2/n1) * dB/dt (Lenz law). So a constant voltage applied to the primary winding of a transformer will result in a constant voltage at the secondary winding of the transformer. Unfortunately this only holds for as long as the core is not in saturation. As soon as the core reaches saturation, it - from a magnetic point of view – disappears, resulting in a loss of magnetic coupling between the primary and secondary windings which in turn will result in a sharp drop of the voltage at the secondary winding, while the current in the primary winding will show a dramatic increase.
So, if we want to use a standard iron core transformer as a pulse transformer, it is important to avoid saturation of the core. To avoid saturation, the product of the amplitude of the voltage pulse and the duration of the pulse (remember I = V*t/L) will need to be kept below a certain maximum value. This value obviously depends on the inductance of the primary coil, but also on the properties of the iron that is used in the transformer, and on the way the transformer is constructed. Most of these details are unfortunately unknown for most transformers. So is it nevertheless possible to say something about this maximum V*t product? The answer is Yes! The reason is that manufacturers of transformers make their products as small, cheap and light as possible, and therefore design transformers in such a way that in normal use they just operate under saturation! It is this piece of information that we use to calculate the v*t product.
To explain how this can be done a bit of physics and math is unavoidable. The first physics law that we use is Ampere’s Law, which relates the magnetic field to current. In its most general form:
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In a transformer both the primary winding as well as the secondary winding have a series resistance. It is possible to combine these resistances to one equivalent resistance that is placed at either side of the transformer.
The figure above shows an ideal transformer with a turns ratio np : ns = 1 : n with a series resistance Rp at the primary side and a series resistance Rs at the secondary side. At the secondary side a load is connected to the transformer which “pulls” a current Is. The question now is, “what input voltage Vin do we need to apply to obtain an output voltage Vout.”
We simply calculate the output voltage taking into account the losses:
It is thus possible to define an “Equivalent Series Resistance” which is completely related to the secondary side of the transformer:
The required input voltage Vin for a given output voltage:
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A transformer has many equivalent circuit models which all can describe the electrical behavior of the transformer equally well. The figure above shows a convenient circuit model of a transformer whereby all the inductances have been referred to the primary side. The transformer used in the example here is a SPITZNAGEL SPK 0801818. It is a small 10 VA PCB transformer with one 220 V winding and two 18 V secondary windings which I use in series. Since in this project the transformer is used the other way around as compared to normal I call the 36 V (2 x 18V) winding the primary and the 220 V winding the secondary winding. Measuring the component values is easy:
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