Introduction

Quasi-static curves (or characteristics) are a collection of curves describing the behavior of an electronic device in terms of voltages and currents at its terminals. An instrument useful for tracing those characteristics is called curve tracer. Several curve tracers have been fabricated, ranging from very cheap and simplistic boxes to be connected to an oscilloscope in XY mode, to professional instruments able to test devices from tiny 25 nm transistors on silicon wafers, to high voltage/high current power devices and vacuum tubes. Notable examples are the venerable Hewlett-Packard HP4145 [HP4145], on which generations of technicians have cut their teeth, or the more recent Agilent B1505A [B1505A]. A few years ago, I got a dismissed curve tracer, a Textronix 577 D1 with a 177 fixture. I repaired it recently, and I started to investigate a little the characteristics of some electronics devices in my possession. This article comes from the observations I have done in the last few months.

Even if the curves do not cover all the aspects of a device (for example, high frequency behavior requires a different kind of investigation), they are a true signature of what is happening inside a device. I would like to present here a few experimental results as well as some thoughts relating the characteristics to the context on which devices are (or were) fabricated. Figure 1 gives an ensemble view of some of those we are about to get acquainted in this article. Of course, giving a complete detailed description of each device can not be in the scope of an article. Moreover, there are dozens of different device families, each of them literally counting hundreds of relatives. Some sort of arbitrary choices will therefore be done.

Fig. 1: some of the devices discussed in the article. We have ECC83, ECC82 and ECC88 miniature double triodes, a 5Y3GB rectifier, a 6080WA double power triode, 2N3055 and MJL4281A power transistors. A BC546B bipolar transistor and a BF244C JFET on the Tek adapter. The keyboard of the laptop will not be described here, but has proven to be useful for typing this text. The highlighter has also been employed while preparing the bibliography section.

The article is organized as follows. At first, I will describe how a curve tracer works and I will give you a short description of my Tex 577. In this part, I will also focus on why knowing the curves of a device is so useful. Then I will present and comment some devices characteristics. Some sort of historical perspective being underlining all the article, I will try not to restrict only to currently used solid state semiconductor devices, but I will also give the characteristics of a few vacuum tubes. We will at first see a few rectifiers (a vacuum tube diode, a mercury low pressure rectifier, a silicon diode). Then we will concentrate on low and (relatively) high power three-terminal devices, such as triodes and transistors of different sizes. This article ends with a conclusion which summarizes all obtained results, with a special emphasis on measured small signal parameters.

I must warn that some audiophiles might be disappointed: I will in fact describe some tubes, but I will never try to justify or argument about the tube sound, nor it is my aim to prove vacuum tubes are better for audio circuits.

Device curves with the Tek 577 curve tracer

The scope of this paragraph is to clarify some jargon and describe briefly what one means with device curves and then show the Tektronix 577 D1 with a 177 text fixture. To begin with something very simple, let's consider a semiconductor diode, called D in the schematic of Fig. 2 (a). The quasi static characteristic of a diode is the curve obtained by tracing i_c(t) as a function of v_c(t). Quasi static simply means that one must vary v(t) to span a certain range, sufficiently slowly that all time-dependant transient of the device have enough time to complete. One might wonder why I have made a difference between the excitation voltage and v_c(t), the voltage applied to the device. After all, if the ammeter used to measure current i_c(t) is perfect, those two voltages are identical. On the other hand, in a more realistic situation, there will always been a small voltage drop on the ammeter and one has to be careful about its influence in the characteristics.

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Fig. 2: (a) an idealized way of tracing the characteristics of the D diode. By varying the excitation voltage v(t), the curves i_c(t) versus v_c(t) describe the behavior of the device. (b) the characteristics measurement setup for a NPN bipolar transistor (control through current i_b). (c) the setup for a N-channel JFET (control through voltage v_g).

If a three-terminal device such as a bipolar, junction field effect transistor or a triode has to be characterized, a more complex setup must be adopted, such as those shown in figures 2 (b) and (c). In fact, usually, the collector (or drain) voltage is varied and the corresponding intensity i_c (respectively i_d) is traced. This is repeated several times by keeping the base current i_b(t) (respectively v_g) constant. Each new value of this parameter will give a new curve. A curve tracer is an instrument automatically repeating this procedure. To remain coherent through the paper, I will always adopt symbols defined in figure 2 (c), whose indexes recall terminals of bipolar and field effect transistors.

Tektronix has produced several curve tracers, from the classic vacuum-tube era 570 [Tek570] to the programmable 370 [Tek370], now discontinued. I own the Tektronix 577 curve tracer shown in figure 3. It is a nice wholly analog 1970-era design, making use of split screen analog phosphor memory (D1 storage unit). This feature is very useful when tracing curves, since it avoids completely the flickering which is otherwise inevitable when the refresh rate is slow. All the screen captures shown in this article have been taken from a stored image. Then, some information was digitally superimposed to ease reading.

Fig. 3: a photograph of a Tek 577 curve tracer. This is the D1 variant, with the analog phosphor memory. Curves shown belong to a BC546B bipolar transistor. No computers or microcontrollers there. Some knobs are not the original ones, revealing the age of this machine...

The curves on the screen of the Tex 577 in figure 3 have been obtained from a BC546B NPN all-purpose silicon transistor. The vertical axis represents the collector current i_c with a scale of 1mA/div., the horizontal axis is the applied collector voltage v_e with a scale of 0.5V/div. The measurement is repeated 11 times, with the base current i_b ranging from 0µA to 20µA in steps of 2µA. The emitter is kept to the 0V reference. Curves of the same device will be commented in a later moment and are visible in figures 11 and 12 (with different scales).

A lot of people love vintage Tektronix instruments and it is easy to find technical literature about them (user manuals, calibration procedures, schematics, etc...) I had to do several small repairs and the calibration on my 577 and I truly enjoyed the way Tektronix used to trace schematics [Tek577]. Figure 4 depicts a small part of the schematics of the 577, taken from the reference manual. Note how the relevant oscilloscope measurements are reported directly in the schematics, at some key points of the circuit. Everything is conceived to ease repair interventions.

By the way, a double N-channel JFET was fried in my unit, which I replaced with two discrete BF244A's. In this case, no soldering was needed, since all active devices are socketed (single transistors included). While testing tubes for this article, a high voltage diode in the collector supply suddenly shorted. It was promptly replaced with two 1N4007 in series. An external DC adjustable power supply has been used to power up filaments. It barely managed to heat up the AX50 rectifier and almost caught fire with the 6080WA triode. After a few days of testing, my laboratory was quite a battleground...

Fig. 4: electronics can be a form of art. Behold this beautifully drawn portion of the 577 schematics, traced ages before CAD systems were available.

Rectifiers

Diodes: comparing 5Y3GB and 1N4007

Modern electronics was probably born when vacuum diode was invented and patented by John Fleming in 1905 [Fleming1905]. Its working principle is based on the thermionic emission of a heated cathode: emitted electrons can be then collected by a plate when an electric field is applied in the right direction. The asymmetry of temperature and shape between cathode and plate therefore gives an asymmetrical characteristic on the electrical side.

To start our journey, I have therefore selected such a device, a 5Y3GB tube. The impressive size of the diode is appreciable in figure 5, as well as in figure 1. As visible in the inset of figure 5 (obtained from its datasheet [5Y3GB]), two plates connected to pins 4 and 6 share the same cathode. In fact, this tube was conceived to obtain a full wave rectifier combined with a center tap transformer. I characterized one half of the device. As said before, the correct power supply for the filament must be provided externally: the Tek 577 was not made for vacuum tubes and does not provide it. Note that this is not a detail: the 5YGB requires 1.7A at 6,3V for the heaters, about 11W. Those were happily provided by my DC power supply. This tube has a maximum reverse plate/cathode voltage of 1400V and can rectify up to 125mA [5Y3GB].

Fig. 5: a 5Y3GB full wave rectifier, mounted on a home-made test fixture, equipped with octal and noval sockets. The user can configure the connections via 2 mm banana plug cables to fit different tubes. Normal size bananas are used for the connection with the Tek 577. The book behind is definitely worth reading, but it is not about vacuum tubes.

Figure 6 is a screenshot (literally, you bet it!) of the measured characteristics of the 5Y3GB. The arrow represents the 0V reference. The excitation is applied to the plate and is AC: on the right we thus have a positive plate with respect to the cathode and current flows, at the left it is negative and the diode is blocked. The usual asymmetric characteristic of a rectifying diode is therefore visible in the picture.

Fig. 6: the anode/cathode characteristic of half of a 5Y3GB vacuum rectifier, compared with the one of a 1N4007 silicon diode.

The curve suggests that the knee of the diode in direct bias is 5V and, if a current of 50mA is flowing in the device, the voltage drop between the plate and the cathode is about 27V. This tube was apparently introduced in 1937 [5Y3GB_radiomuseum]. Those were times where such a voltage drop was considered normal.

The comparison with the behavior of a 1N4007, a very common silicon rectifier diode can be done in figure 6. The silicon diode was developed around 1966 [1N4007_first] and its design is about thirty years younger than the 5Y3GB. The silicon diode is tiny, weights a fraction of a gram, does not need any filament power and has a much harder knee. At 50mA (a very moderate current nowadays), the voltage drop is less than 0.8V and the diode can withstand 1000V of reverse bias [1N4007].

AX50: hot cathode mercury rectifier

The relatively high voltage drop seen in the previous paragraph for the 5Y3GB has motivated the development of more efficient rectifiers. Mercury rectifiers (invented around 1902) were thus optimized for small power operation [Marti_Winograd_1930]. The voltage/current characteristic of (a little overdriven) AX50 rectifier is shown in figure 7. It required a 4V, 3.75A power supply for the filament. My DC power supply had a hard time supplying it!

Fig. 7: the current/voltage characteristics of an AX50 hot cathode mercury rectifier. The effect of mercury vapor ionization is visible as the small bump at the beginning of the conduction region. Note that the vertical scale is 5 times wider than the one of figure 6.

It is apparent that the forward drop of the AX50 (developed around 1938 [AX50_Radiomuseum]) is much smaller than the one of 5Y3GB and the curve is pretty much vertical, once the gas discharge is ignited. We note that for a current of 50mA the forward voltage drop is about 12V. This has to be compared with the 27V seen with the 5Y3GB rectifier. In fact, a small bump is visible (along with a negative differential resistance part) for currents lower than 20 mA, where the ionization is ignited. The low voltage drop obtainable with mercury rectifiers is due to the reduction of the space charge region which appears in the conduction region of vacuum rectifiers. A blue purplish glow due to mercury ionization is visible during normal rectifier operation.

Several major drawbacks existed with those rectifiers. In fact, they need a consequent pre-heat time in order to correctly vaporize the mercury. This avoids damages due to arcing when plate voltage is applied before enough vapor is present. The correct timing was often achieved by thermally delayed relays. Moreover, the negative differential resistance of some points of the characteristics can amplify switching noise. Of course, a certain degree of concern arises about mercury, which is a highly toxic metal. But after all, the same problem exists today with those nice high-efficiency compact fluorescent lamps, marketed as an efficient way to reduce CO₂ emissions and be environmentally friendly... O tempora o mores!

Low power triodes and solid state devices

The ECC82 double triode

The invention of the triode, patented by De Forest in 1907 [DeForest1907], came from the introduction of a control electrode between the cathode and the plate of a diode. This enhancement allowed amplifying electrical signals, since the voltage of the control electrode influences the flux of electrons between the two other terminals. The control electrode is called grid, being often realized with a dense network of closely spaced metallic wires. If it is strongly negatively biased with respect to the cathode, it will screen completely all the electrons emitted by thermionic emission: in this case, no current can flow between the positively biased plate and the cathode. If, on the other hand, the grid bias become closer to 0V, an appreciable current can flow. Very few electrons are captured by the grid: only a tiny current flows there when a triode is correctly operated. In other words, grid is a high impedance (in reality mainly capacitive) terminal. The voltage on the grid should not become positive, as it will begin collecting electrons from the cathode, thus giving rise to a current flowing in it.

The ECC82/12AU7 is a popular tube used for audio and RF signal amplification, introduced around 1951 [ECC82_radiomuseum]. It is a relatively small double triode with a subminiature (noval) socket. Its filaments require 6,3V at 300mA in parallel, or 12,6V at 150mA in series. Figure 8 represents the characteristics of one of its two halves.

Fig. 8: characteristics of a section of an ECC82/12AU7 double triode. The measurement setup is similar to the one depicted in fig. 2 (c) and the voltage on the grid is kept negative with respect to the cathode. The red circle represents the (interpolated) bias point v_g=-8.5V and v_s=250V, giving i_d not far from 10mA

First of all, for those who are only used to see characteristics of silicon devices, it is worth noticing that the scale of voltages and currents are quite different for vacuum tubes. As we noticed with the 5Y3GB diode, it is not uncommon with vacuum tubes to deal with rather high voltages (a few hundreds of volts) and comparatively low currents. The 1969 Philips datasheet for ECC82/12AU7 is quite complete [ECC82]. We can try to get some important characteristics to compare with those of the literature.

A reasonable bias point (which we will call Q) corresponds to a plate current of i_d=10.5mA, which is obtained at v_d=250V between the plate and the cathode and corresponds to a gate voltage of v_g=-8.5V, always measured with respect to the cathode. By interpolating the curves of figure 8, it appears that v_g=-8.5V and v_s=250V is obtained with a current around i_d=10mA. Fabrication tolerances being of a few percent, this can be considered acceptable. A second possibility is that the tube I own is a bit worn down.

The second important information is the transconductance g_m, which is a small signal parameter to be determined once an appropriate bias point Q is chosen. It states how much the plate current is changed when the gate voltage is changed a little around the bias point, by keeping the voltage constant. Mathematically, if we continue using the notations seen in fig. 2 (c), it is a partial derivative, calculated around the bias point Q:

.

Being a ratio between a current and a voltage, its measurement unit is the siemens (amper over volt), whose international symbol is 'S' . It was current to see in the old tube datasheets mho or an upside down capital omega ℧. Those funny puns are now explicitly deprecated by the international system of measurement units [SI] (be serious, please!). Some datasheets use the symbol S for indicating the slope, but we avoid here that practice, not to risk a confusion with the correct measurement unit. From a much more practical point of view, we can estimate the transconductance from curves shown in fig. 8. By keeping the plate voltage v_d=250V, we see that the current decreases of approximately 4.4mA when the grid voltage passes from -8V to -10V. Thus, the transconductance might be roughly estimated to be g_m=2.2mS, exactly what expected from the datasheet.

The third important parameter is the internal conductance g₀ of the tube. It is a measure of how much the current i_d changes when the plate voltage v_d is varied, holding constant the grid voltage. Once again, this parameter is measured in siemens. It is the tangent to the curves traced in fig. 8 with v_g=const. in the bias point Q. Mathematically, we can write:

.

By interpolating a little bit and following the curve for v_g=-8V, we can evaluate a change of 3.1mA for a voltage variation of 24V, thus giving g₀=0.13mS. Much more frequently, datasheets document the inverse of the internal conductance, which is the internal resistance r₀=1/g₀. The measured internal resistance is in our case r₀=7.74kΩ.

For tubes, datasheets report the maximum voltage gain µ, which is the product between the transconductance and the internal resistance: µ=g_m r₀. Physically, µ represents the voltage amplification we would obtain in a common-cathode operation, by biasing the plate with an ideal current source, without any load connected to the triode. A pretty ideal and useless situation: in a real circuit the voltage amplification of the tube will be lower than µ. In our case, with the Q bias point seen above, µ=17, perfectly agreeing with the datasheet.

The ECC88 double triode

The value of µ found for the ECC82 is moderate. Other twin tube were developed with different characteristics and optimized for higher gain (note that higher µ does not mean a better device, just a different one) or higher transconductance. Figure 9 represents measurement results for curves obtained with an ECC88/6DJ8 twin triode. It is a low noise tube developed by Philips around 1958 [ECC88_wikipedia] and the datasheet reports that the intended usage was as cascode amplifier in television tuners.

Fig. 9: characteristics of a section of an ECC88/6DJ8 double triode. The red circle indicates the (interpolated) bias point of v_d=90V, i_d=18mA and v_g=-1.3V

First of all, as we did with ECC82, can choose a bias point to test the characteristics reported by the datasheet. By taking v_d=90V and v_g=-1.3V, we get a bias point Q of i_d=18mA, reasonably close to the nominal 15mA indicated by the Philips datasheet. To evaluate small signal parameters around the selected bias point, we find that a change of 0.2V in v_g is translated to a change of about 2.4mA in i_d. This gives a transconductance g_m=12mS, which is in an agreement with the 12.5mS given in the datasheet. In the same way, we evaluate an internal resistance of r₀=2.1kΩ, thus giving a maximum voltage gain of µ=r₀g_m=25.5. This value is a little less than what reported in datasheets (µ=33).

ECC82 and the ECC88 are two different tubes developed with different trade-offs. First of all, ECC88 is clearly optimized towards a high transconductance, this parameter being almost six times higher than the ECC82. On the other hand, the ECC82 has a higher internal resistance, so the maximum internal gain of the tubes is not as different. The relatively low internal resistance of the ECC88 is not a problem when this tube is operated in the cascode configuration, as suggested in the datasheet and shown in figure 10. In fact, two triodes (which may have different characteristics) are vertically stacked and the plate load of the first triode is the cathode of the second. The cathode is usually a low-impedance terminal, so the voltage is almost constant there. The internal resistance of the lower triode thus has very little effect. By a frequency analysis of the circuit (out of the scope of this paper), it can be shown that the cascode configuration is particularly convenient for high frequency operation... such as in a TV tuner.

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Fig. 10: a cascode amplifier making use of two triodes. They might not be of the same model.

Of course, it is easy to see that when one changes the bias point Q, the small signal parameters g_m and r₀ change, so also µ is modified. This is due to the nonlinearity of the triodes. From the ECC88 curves shown in figure 9 (but this is visible also with ECC82 in fig. 8) it can be noticed that the transconductance tends to be reduced when the bias current is decreased. This effect was purposely exploited in some tubes such as the UBF-80 (which is a double diode variable µ pentode) to fabricate automatic gain control stages. The bias point was shifted according to the input signal amplitude, in order to keep the output amplitude as constant as possible.

A great number of different low-power triodes with different trade-offs exist. We cite the well-known ECC83, optimized for high gain, achieving µ=100 [ECC83].

The BC546B bipolar transistor and the BF244C JFET

It is interesting to compare the performances triodes with those of more recent semiconductor devices. Figure 11 depicts a comparison of the characteristics of a BC546B, a small general purpose NPN silicon bipolar junction transistor (BJT) with a BF244C junction field effect transistor (JFET). The first evident difference with vacuum tubes is that the voltage scale has to be greatly reduced. The second one is that the characteristics tend to be much more horizontal than those of triodes seen above.

Fig. 11: (top) characteristics of a BC546B NPN bipolar junction transistor, obtained with the configuration of figure 2 (b). (bottom) curves of a BF244C N-channel JFET, acquired using configuration of figure 2 (c). The curves of the two devices have been stored on the screen in different times.

For what it concerns the BC546B, its behavior becomes very nonlinear when v_c is less than 0.5V. This region is called saturation region for bipolar transistors. When v_c is greater than 0.5V, we find a region where the characteristics are almost equally spaced (even if a little tilt is visible, expecially for high collector currents). This region is called active region and is where bipolar transistors are used in linear circuits. The base/emitter junction is forward-biased there, and the base/collector junction is reverse-biased.

The modulation of the collector current i_c is made by the control of the carrier injection in the base of the bipolar transistor, modulating the potential barrier of the base/collector junction. Both type of carriers are involved in the process (electrons and holes), thus justifying the name "bipolar". The curves of a bipolar transistor are therefore traced by increasing in steps the base current, as visible in figure 2 (b).

Watching figure 11, it appears that the curves are approximatively equally spaced, suggesting that we might consider the ß=i_c/i_b parameter constant. This is useful for a simple modeling, but it is not true in general: the ß parameter is strongly affected by the current range used during the measurement. To compare the dynamical performances with those seen above for triodes, let us choose arbitrarily a bias point Q given by i_c0=10mA and v_c0=5V. This corresponds to a base current i_b0=30µA, giving a large signal current gain ß close to 333 (quite classical for this transistor [BC546B]).

Once chosen the bias point Q, we can evaluate h_FE, the small signal current gain. In fact, h_FE is a differential parameter evaluated at the bias point, thus mathematically described by the following equation:

.

In our case, observing the curves i_b=25µA and i_b=35µA and by keeping constant v_c=5V we get h_FE=310, which is (given the large uncertainties of the curve reading) quite similar to the ß previously found.

The second small signal parameter we can determine is the small signal collector/emitter resistance r₀. It is physically related to the modulation of the length of the base terminal, due to the change of the width of the depleted region at the (inversely biased) collector/base junction. This effect is called Early effect, from James M. Early who first described it in 1952 [Early]. The small signal parameter r₀ is the inverse of the slope of the curve i_b=30µA where it crosses the bias point. It is difficult to determine the slope from figure 11. In any case, to give a rough estimation, we can say that we have a variation of the current of around 0.7mA for a 7.5V change of v_c, thus giving r₀=11kΩ. This value changes considerably when the operating point of the transistor is changed, and tends to be inversely proportional to the collector current. The third very important parameter of a bipolar transistor can not be extracted directly from the curves shown in fig. 11 and is the base resistance h_ie. Fortunately, it can be shown that it is almost the same for every transistor and equal to:

,

where U_T is the thermal voltage given by the equation:

,

where T is the absolute temperature, q=1.6x10^-19C is the electron charge and k_B=1.38x10^-23J/K is the Boltzmann constant. U_T is around 26mV at an ambient temperature of 27°C, giving T= 300K. At this temperature, we find h_ie=0.867kΩ. This allows to calculate the transconductance of the bipolar transistor g_m=h_FE/h_ie=358mS.

It is specified rarely for discrete bipolar transistors, but we can define a parameter µ= g_mr₀=3940. Compare those values to what found for the ECC88!

While something similar to the curves of figure 11 is very frequently shown in the textbooks, the analysis of the device breakdown is much less common. This is shown in figure 12.

Fig. 12: The BC546B characterized at a much larger voltage scale than the one of figure 11. Currents have been kept to a reasonable range in order not to heat up too much the device. Some looping is clearly visible due probably to thermal heating.

It is not very well known that in some cases a bipolar transistor in the breakdown region can exhibit a negative resistance behavior and it is not destroyed if the dissipated power is kept small. Figure 13 shows a case on which this effect is evidenced. In fact, this effect is classically exploited in very clever high-speed pulse generator circuits, such as the one depicted in fig. 8 of ref. [Williams_AN94]. Very few transistors are specified to be operated in this working regime (one notable example being those provided by Zetex), but the vast majority of low power bipolar transistors exhibit this behavior and can be useful in this purpose. For more information, you can consult Zetex AN8 [Zetex_AN8] or some of the historical articles such as [Spirito1972].

Fig. 13: a negative resistance region in an appropriately biased transistor at breakdown. Some self-oscillating effect of the curve tracer prevented tracing the complete characteristics, but the negative slope is clearly visible.

A totally different device is the N-channel junction field effect transistor (JFET) BF244C whose characteristics are shown in figure 11, just below those of BC546B. In fact, there, a channel is present between the source and the gate of the transistor. A PN junction connected to the gate is located in the middle of the channel and can modulate the channel width depending on the extension of the depleted region. If the gate is very negative, a depleted region extends through all the channel. The channel is thus said pinched and no current can pass between the drain and the source. If the voltage on the gate is increased, the channel is no longer pinched and an appreciable current is allowed. The JFET is, as the bipolar transistor, a charge controlled device, but since normally the gate current is negligible (the PN junction with the channel being reverse-biased), the curves are traced by keeping a constant voltage v_g on this terminal. In fact, the measurement setup is almost the same for triodes, except that the voltage scales are reduced.

A notable difference with the BC546B BJT is that the nonlinear region of the characteristics is visible in a much larger voltage extent. After it, the curves become almost parallel to the voltage axis. The first region is called triode region (maybe since it bears a certain similarity with triode curves seen above). The second region is (unfortunately) called saturation region for field-effect transistors, which gives a high risk of confusion with the usual terminology used for bipolar transistors. Moreover, in JFET's, the frontier between the triode and the saturation region is not fixed at a given (low) voltage such as in BJT's, but depends on the voltage applied to the gate terminal. It is worth noticing that in the part of characteristics very close to the origin, the transistor behaves in a way very close to a voltage controlled resistance.

Since for linear operation one might want to keep the JFET in its saturation region, it is evident that for a given power supply voltage the bipolar transistor allows a bigger voltage variation range. We can choose as the bias point Q a drain current i_d0=10mA and a drain voltage v_d0=5V (thus a similar situation to what chosen for the BC546B transistor. This gives an (interpolated) gate voltage v_g0=-1.25V.

Around the chosen bias point, we can (exactly as seen with triodes) evaluate the transconductance g_m=2.3mA/0.5V=4.6mS. The source/drain resistance can be evaluated as being around r₀=7.5kΩ, thus giving a maximum voltage gain of µ=g_mr₀=34.5. This value is of the same order of magnitude of what obtained with the ECC88 tube and it is two orders of magnitude smaller than what found with the BC546B bipolar device.

Power three-terminal devices

6080WA triode

An interesting power triode is the 6080, a double unit optimized for use as series DC regulator element and appeared in 1951 [6080_radiomuseum]. Its curves are shown in figure 14 and the tested device was precisely a 6080WA, a ruggedized version of the 6080. It was tweaked to withstand shocks and vibrations (lo and behold, for what permitted by the glass envelope!).

Fig. 14: curves of one section of the 6080WA double triode. It is a r

We select a bias point Q given by i_d=50mA and v_d=85V as we imagine using a 6080WA tube as regulator after the rectifiers seen in the previous paragraphs. Interpolating the curves, we find that this is obtained with v_g=-28.5V. The transconductance around Q is g_m=5.5mS and the internal resistance r₀=410Ω, thus giving µ=g_mr₀=2.3. As we noticed before, by increasing the operating current, µ tends to increase.

The data we have found for g_m andr₀are a little different from those given by the datasheet [6080WA] due to the fact that we have chosen a different bias point for the evaluation (after all, a curve tracer is especially useful for doing that). The maximum voltage gain is quite low might seem strange to someone. In fact, this is confirming again that it is just one of the characteristics of a tube and it does not tell anything about its quality. Having a low internal resistance is for example more useful for the use as a line regulator rather than having a high gain.

The 6080 requires a filament supply of 6.3V and 2.5A, i.e. almost 16W. After a while, my small bench power supply decided that it has been sufficiently stressed by all my abuses and went into a rather catastrophic failure with smoke and bad smell.

Bipolar transistors: comparing 2N3055 and MJL4281A

The 2N3055 is a classic NPN silicon power transistor. It is somewhat historic, as it has been one of the very first affordable and effective power transistors. It has been developed by RCA in the period 1959-1964 [Ellis2001] and the first devices were fabricated with a process called "hometaxial base". This gave a homogeneous base region with uniform resistivity between the emitter and the collector. In fact, at the time those transistors were fabricated on 19mm mono-crystalline silicon wafers, which were very thin (between 155µm and 175µm). The transistor was vertical and, to create the collector, phosphorous was diffused through almost 100µm from the backside of the wafer. This gave a base thickness of about 20µm, which is quite large compared to today standards. Nowadays wafers are much larger, reaching a size of 300mm and a thickness of about 800µm for state of the art processes [SiliconWafers]. Therefore, the fabs have switched to an epitaxial fabrication which changed a bit the characteristics of the transistor, but was compatible with fabrication methods on modern wafers (probably not the 300mm wafers, but in any case larger than 19mm). Diffusion through a wafer thicker than 200µm would be far too slow. The original fabrication method gave a transistor which was relatively slow (f_T=1MHz), but remarkably immune to the double breakdown process, with a very crisp transition between the saturation region and the active region. Figure 15 shows the characteristics of a 2N3055 at a moderate collector current (the maximum rating is 15A).

Fig. 15: characteristics of a 2N3055. A certain degree of nonlinearity of current gain can be seen.

If we compare the characteristics of the 2N3055 with those of the BC546B shown in figure 11, it is evident that the current gain is not constant. In fact the curves which correspond to a constant base current i_b tend to become closer when the current is increased, thus indicating that the large signal gain ß=i_c/i_b decreases. In other words, the ß parameter is no longer a constant. We choose a bias point Q such that i_c=2A, v_c=10V, thus corresponding to a base current (interpolated) i_b=22.5mA. This gives ß=88. In a small signal analysis around Q, we get approximatively h_FE=52, which gives g_m=45S. In reality, this value is greatly affected by the base resistance which is probably higher than h_ie=1.15Ω calculated with equation (4). I estimated a slope of the characteristics of g₀=1/r₀=9.4mS, thus giving r₀=106Ω and therefore µ=g_mr₀=4770.

I believe the 2N3055 transistor I tested is a modern epitaxial version and not one fabricated with the original method. In fact, the transition between the saturation region and the active region is somewhat less clean than what reported in figure 8 of [Ellis2001]. In epitaxial transistors, a way to decrease the collector resistance is to make use of a buried heavily doped layer. The transistor structure is then composed by four layers, with the collector being split in a lightly doped region and a highly doped one (the buried layer). This alters the behavior of the transistor giving rise to a quasi-saturation region, intermediate between the hard saturation region and the active region. It is however barely visible in figure 15.

Another reason for adopting such a four layers structure is to withstand high voltages, this time with a thin base and a wide, lightly doped collector [TcIng1, TcIng2]. In this case, the quasi-saturation region becomes quite evident since the collector resistance is non-negligible and plays a role. Figure 16 shows the curves of a MJL4281A NPN power transistor, with maximum ratings of 15A and 350V, specifically conceived for audio applications.

Fig. 16: curves of a MJL4281A, a device specifically developed for high power audio applications.

It is apparent that the MJL4281A has a behavior in saturation which is very different from the one seen in figure 15 with the 2N3055. In fact, the quasi-saturation region is evident, and there is a visible frontier with the active region. The frontier is a line whose inverse of the slope has the dimension of a resistance and can be evaluated in our case being R_C0=1.4Ω. Physically, this represents the resistance of the lightly doped collector region. In fact, the quasi saturation region exists because, at collector voltages intermediate between the hard saturation and the active region, the charges injected in that region are not enough to fill it completely. When the voltage is enough that there are enough carriers injected, all the lightly doped region is entirely filled by them and its resistance becomes almost negligible.

A second interesting observation is the fact that the lines i_b=const. are spaced in the active region at a remarkably constant interval. This transistor is clearly optimized for achieving a high linearity, such as required for audio applications.

As we did for the 2N3055, we adopt a bias point Q such that i_c=2A, v_c=10V. This gives a base current i_b=10mA. The ß therefore is 200. At the bias point, we evaluate h_FE=225, we calculate h_ie=2.6Ω and therefore g_m=86.5S. It is difficult to evaluate the slope of the characteristics. With a great degree of uncertainty, we can say that the order of magnitude of r₀ is around 250Ω, giving µ=22000.

A few words about... measurement incertitudes!

A measurement result means nothing without a proper evaluation of uncertainties. In fact, in our case, two main sources of measurement errors should be taken into account:

• Errors from the measurement instrument.
• Errors from the operator in reading curves.

The service manual of the Tex 577 [Tex577_service] helps us to quantify the first point. With the setup used for acquiring curves shown in this paper, here are some useful characteristics:

• Accuracy of the step generator is within 3% of step amplitude or the total output, whichever is greater.
• Display accuracy is within 3% of highest on-screen value.

I performed an accurate calibration of the curve tracer following the factory procedure described in the service manual, just before acquiring data for this article. I noticed during this process that a little non-linearity of the vertical and horizontal deflection of the CRT is present, introducing errors less than approximately one third of a minor division on the screen. For this reason, I avoided working too close on the borders of the CRT while collecting data.

Combining the instrument accuracy with operator skills is more delicate. In practice, it is quite easy to read the position of bias points, within half of a minor division of the screen. I would say that those value are affected by an uncertainty of about 5%. When an interpolation is done, we may put ourself on the safe side by considering a 7% uncertainty. Things tends to become worse (or much worse) in the determination of slopes, since errors tend to amplify in the calculation. I would take a 10% for those values which were easy to determine, such as transconductances and internal conductances for triodes (figures 8, 9, 14). For transistors, determination of the resistance r₀ was affected by the highest uncertainty, about 20% or even 30%.

Zooming on the curves is possible with the Tex 577 and has been done when useful, even if the zoomed curves are not shown in this article.

Conclusion

During our journey, we commented the quasi-static curves of a few electronic devices fabricated in a span of about 65 years. I hope I have convinced the reader that such measurements are quite informative. Of course, it should be clear that it is impossible to obtain hints about the frequency behavior from them. However, they helps to shine light on the true heart of the devices being studied.

Table 1 summarizes data extracted from the curves for the various devices analyzed in this article. I remind that the choice of the bias point is arbitrary. Sometimes, I followed suggestions given by the datasheet, in other occasions I did not. The small signal parameters are then extracted and describe the linearized behavior of the device, sufficiently close to the bias point.

Tab. 1: the bias point and the small signal parameters measured in all the devices described in this article.

From the table, it is apparent that the devices giving the higher transconductances are the 2N3055 and especially the MJL4281A. In reality, those very high figures are obtained at bias points at much higher current than for any other devices. It is thus meaningful to normalize the transconductance on the (collector, drain or plate) current which defines the bias point. This term is known as transconductance efficiency and it is the inverse of a voltage. It is clear that bipolar transistors still outperform all other players. That does not come without a price, if we remember the relatively low input impedance calculated with those devices (whereas for triodes and JFETs is very high and mainly capacitive).

It is clear that no journey like this can be ever complete, given the thousands of devices invented by the fertile imagination and ingenuity of some of the best minds of our era. Some devices and phenomena have not been described on purpose. It would have taken too much space to describe the behavior of pentodes, MOS transistors, to investigate the characteristics of Zener diodes or neon gas voltage references. So the perspectives of this work will include testing of other semiconductor devices, for example comparing silicon with germanium ones. After a repair (or better, a rebuilt) of my poor bench power supply, filaments of other vacuum tubes might shine again, as the one of figure 17.

Fig. 17: of course it is a waste of energy, but the filament glow of the old glassware is still source of feelings for a lot of people.

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