A Vacuum Tube Audio Primer

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The purpose of this booklet is to introduce the reader to the fundamentals of vacuum tubes and their use in audio preamplifiers and power amplifiers. Interest in vacuum tube audio equipment by both audio manufacturers and audiophiles has greatly increased during the last several years. This increased interest has had two effects. Many new tube amplifiers have been introduced by both existing and new companies. In addition, much has been written to explain the resurgence of the “obsolete” technology of vacuum tubes. The merits of tube versus transistor sound have been heatedly debated. Sadly, many of these discussions have contributed little to an understanding of vacuum tube audio and the unique benefits that vacuum tube amplifiers offer the listener, and instead have only made the issues more confusing. This booklet, and the brief, factual discussions of vacuum tubes and vacuum tube audio that it contains, is intended as a first step in overcoming this confusion.

Vacuum Tubes: Diodes, Triodes, and Pentodes

The simplest type of vacuum tube is the diode (Fig. 5). Although vacuum tube diodes are rarely used in modern audio amplifiers, an understanding of how they work will make it easier to explain how triodes and pentodes function.

The name “vacuum tube” is not very revealing of how these devices operate. True, the inside of all triodes and pentodes, and most diodes, is (or should be) a vacuum. A much more instructive name is the British “thermionic valve.” In the diode of Fig. 5, the inner electrode, called the cathode, is heated to a temperature of about 10000 Kelvin (about 13000 Fahrenheit) by a tungsten alloy wire situated along the inside wall of the cathode. When a current is passed through this wire, called the heater, the cathode (which is electrically insulated from the heater) heats up. The surface of the cathode is treated with a material which freely emits electrons when heated. The emission of electrons from a heated metal or metal oxide (thermionic emission) is called the Edison effect. The number of electrons emitted from a given area of the cathode’s surface depends on the temperature of the cathode: the hotter the cathode, the more electrons are emitted. Of course, the thermal stresses on the heater and cathode also increase as their temperatures are increased. Many years of research have gone into developing coatings for the heater to increase its ability to heat up the cathode, and coatings for the cathode to increase its ability to emit electrons at reduced temperatures which will prolong the life of the tube.

Fig. 5. Vacuum tube diode. Nore its parts: ANODE (PLATE); CATHODE; HEATER

Fig. 6. A simple diode circuit.

Now let’s consider what happens inside the diode when the heater is first turned on, but the cathode and the outer electrode, the anode (also called the plate), are not connected to any electrical circuit. The cathode begins to emit electrons, negatively charged particles. The first electrons to be emitted from the cathode encounter only the vacuum of empty space around the cathode, and some reach the anode. This is not the case for electrons emitted later. The early electrons form a cloud of negatively charged particles around the cathode, called the space charge. This cloud grows and begins to repel the electrons which the hot cathode is still trying to emit. After a while an equilibrium condition is reached, and no further electrons can be emitted from the cathode.

So far, this isn’t very useful behavior from a circuit designer’s viewpoint. Power is being expended to heat the cathode, but the electrons emitted by the cathode are repelled by each other in the cloud of charged particles which forms around the cathode, and only a few electrons reach the anode.

Now suppose that the cathode and anode are placed in the circuit shown in Fig. 6. The battery B maintains a voltage V_ak between the anode and the cathode. This in turn produces an electric field between the diode’s anode and cathode which will affect the motion of the electrons emitted by the cathode. When the anode is at a positive voltage with respect to the cathode, the electric field causes the electrons to accelerate towards the anode. In this state the diode can conduct a current. No longer do all the electrons emitted by the cathode remain in the space charge region, the electric field removes some electrons by accelerating them towards the anode. This allows additional electrons to be emitted from the cathode. An equilibrium condition will be reached in which the number of electrons removed by the electric field will be equal to the number of additional electrons the cathode can emit into the electron cloud. In Fig. 6 a complete electrical circuit exists: electrons emitted by the cathode and accelerated by the electric field to the anode proceed from there back to the cathode via the battery B. These electrons constitute the circuit’s electrical current I_a Because of a convention introduced by Benjamin Franklin (who believed that it was positive charges which circulated in an electric circuit, whereas in fact it is the negatively charged electrons which are responsible for electric currents), the direction of the current I_a is taken to be the reverse of the direction of the electrons’ motion.

Fig. 7. Diode saturation anode current versus anode to cathode voltage. Note: CURRENT; MAXIMUM CURRENT; HEATER

The number of electrons which are accelerated to the anode (and therefore the magnitude of the electric current I_a) in a given time interval depends on the strength of the electric field within the diode. For a given spacing between the anode and cathode, the electric field strength in turn depends on the voltage V_ak between the anode and cathode. As this voltage is made greater, the strength of the electric field increases. This increases the acceleration of the electrons, so that more of them can reach the anode in a given time interval. More electrons per second circulate from cathode to anode and back to cathode, so the current I_a is increased. As the voltage V_ak is made very great, a maximum current is finally reached (see Fig. 7). At this point all the electrons emitted by the cathode are accelerated towards the anode, and there is no space charge. The maximum current which the diode can conduct is limited by the number of electrons which the cathode can emit. As was mentioned above, the electron emission characteristics of the cathode are determined by its composition and temperature.

Now suppose that the battery B is connected the other way around in Fig. 6, so that the anode is at a negative voltage with respect to the cathode. In this case the electric field points the other way, causing the electrons to be accelerated back towards the cathode, and not towards the anode. The result is that once again no electrons pass from the cathode to the anode, so the current I_a is zero: the diode is non-conducting in this state. Thus we have shown how a vacuum tube diode can function as a rectifier (a device which conducts a current only in one direction).

The vacuum tube diode is not useful as an amplifying device. The current T conducted by the diode depends only on the anode to cathode voltage V_ak and the cathode temperature. There is no way to make a small external voltage or current control the current I_a and therefore allow the diode to function as an amplifier.

This is corrected in the triode (Fig. 8). The triode is basically a vacuum tube diode with one additional electrode, called the control grid, or sometimes just the grid. As illustrated in Fig. 8, the control grid is a spiral of wire, located between the cathode and plate, and electrically insulated from these other two electrodes. The addition of the control grid makes the triode a much more versatile device than the diode, and allows it to function as an amplifier.

First let us consider how the circuit of Fig. 9 works. This circuit is exactly like the one in Fig. 6, except the diode has been replaced with a triode, and there is a variable voltage source connected between the control grid and cathode of the triode. With the voltage source temporarily disconnected from the control grid, the tube will act like a diode. For a fixed cathode temperature and plate to cathode voltage V_ak, the current through the triode is also fixed.

Now suppose that the variable voltage source is reconnected to the control grid, and the control grid to cathode voltage V_gk is set to some moderate positive value (say, a few volts). The control grid is not a solid metal electrode, but is instead an open wire spiral, so that it does not physically interfere with the motion of the electrons from the cathode to the plate. When the control grid is connected to a voltage source, however, it creates an additional electric field within the triode which can affect the motion of the electrons. When V_gk is positive, the control grid does nothing to inhibit the stream of electrons emitted by the cathode. Some in fact are intercepted by the control grid, so in this case there is a current through the control grid circuit ‘g (cathode to control grid and back to the cathode via the variable voltage source) in addition to the plate current I_a

Now suppose that the grid to cathode voltage V_gk is slowly reduced. The control grid then begins to have a greater effect on the electric field in the vicinity of the cathode. When V_gk is made negative, the control grid begins to inhibit the flow of electrons from cathode to plate. The electric field due to the control grid opposes the greater electric field due to the plate to cathode voltage V_ak. The more negative V_gk is made, the greater is the effect of the control grid on the flow of the electrons from the cathode to the plate, and the less the plate current I_a becomes. In addition, the grid circuit current 1 is greatly reduced, just as I_a dropped to zero for the diode when the plate to cathode voltage was made negative.

This behavior explains why the triode’s additional electrode is called the control grid. The control grid to cathode voltage V_gk controls the plate current I_a. When V_gk is negative, a small change in its value can produce a large change in the plate current. As V_gk is made more and more positive, the control grid has less effect on I_a. If V_gk is made sufficiently positive, the control grid ceases to control the plate current, and the tube then functions exactly like a diode. In most triode amplifier circuits, the grid to cathode voltage is always negative.

The circuit of Fig. 9 may be used to make a series of measurements of the triode’s electrical behavior, and from this a graph could be generated showing the relationship between the plate current 1 plate to cathode voltage V_ak , and control grid to cathode voltage V_gk. This graph would display the characteristic curves of the particular triode. There are several different but equivalent ways in which the information could be graphed to form a set of characteristic curves. The most common is the plate characteristics curves, shown in Fig. 10. These curves show the relationship between V_ak and I_a for a number of different values of V_gk. The plate characteristics curves are very useful in explaining how a triode amplifier stage works.

Fig. 8. Vacuum tube diode.

Fig. 9. A simple triode circuit.

Fig. 10. Triode characteristic curves.

Fig. 11 Triode amplifier circuit.

Fig. 11 illustrates a simple triode amplifier stage. Instead of being connected directly to the main power supply (battery B of voltage Ebb), the plate is now connected to a resistor RL. For simplicity the heater is no longer illustrated. It is assumed that the heater is connected to an appropriate power supply. The variable control grid voltage supply of Fig. 9 has been replaced by a second battery B of voltage Eg in series with a signal generator with output voltage V

First let us consider the state of the triode when the signal generator’s output voltage V is zero. In this case the net control grid to cathode voltage V_gk is determined solely by battery BV_gk o = — Eg (the voltage is negative because the positive end of B is connected to the cathode). This biases the triode to a convenient (and unique, for a given value of Ebb and RjJ quiescent operating point, marked Q in Fig. 12. The plate to cathode voltage V_ak o is not equal to the plate supply voltage Ebb because there is a current I_ao through the triode, and this current produces a voltage drop of magnitude IaoRL. The sum of the voltages dropped across the triode and the load resistor RL must equal the supply voltage, so V_ak o = Ebb — IaoRL.

Now suppose that the signal generator is turned on, and set to deliver a very low frequency triangular voltage V At first the voltage V slowly increases, which has the effect of slowly decreasing the control grid to cathode voltage: V_gk = V - Eb. From the description above the affect of V_gk on the plate current I_a we remember that as V_gk is made less negative, the plate current I_a increases. This in turn increases the voltage drop across the load resistor RL, which means that V_ak must decrease. As V slowly increases to its maximum positive value, the voltage across RL slowly increases, while V_ak slowly decreases, such that the sum of these two voltages remains equal to Ebb. As V decreases from its maximum value back to zero, the process is reversed, until when V = 0 again, I_a = I_ao and V_ak = V_ak o. As V becomes increasingly negative, I_a continues to decrease to values less than the quiescent value I_ao This means that less and less voltage is dropped across RL, 50 V_ak increases to greater than its quiescent value V_ak o. Finally, as V again returns to zero at the end of one cycle of the triangle wave, the values of V_ak , V_gk and I_a revert back to their quiescent values.

The instantaneous values of V_ak , V_gk and I_a can be plotted on the plate characteristics curves of Fig. 12. When this is done, a straight line is formed. This line is called the loadline, and its slope depends on the value of the load resistor RL. When the value of RL is very large, the loadline is nearly horizontal. When the input signal is applied to such an amplifier stage, the changing value of V (and therefore the changing voltage dropped across RL) will produce only a small change in the plate current 1 If the value of RL were made in finitely large, the loadline would be horizontal. A horizontal loadline is illustrated in Fig. 13. In this case, a given small change in the grid to cathode voltage A V_gk produces the greatest possible change in the plate to cathode voltage AV_ak . I_a does not change. The ratio A V_ak / A V_gk is called the amplification factor j of the tube. A simple tube amplifier stage can not have a voltage amplification (voltage gain) of greater than i. Usually the value of the load resistor RL is not great enough to produce a nearly horizontal loadline, and the voltage gain will be less than the amplification factor u.

When RL is made equal to zero, the loadline becomes vertical. A vertical loadline is also illustrated in Fig. 13. Now a given small change in the grid to cathode voltage A V_gk produces the maximum possible change A I_a in the plate current. In this case V_ak does not change. The ration delta_I_a/delta_V_gk is called the mutual conductance (or transconductance) gm of the tube. The ratio /g, is called the plate resistance rp of the tube, and is equal to the slope of the plate characteristics curves.

The quantities , u, gm, and rp are often misleadingly referred to as tube (or valve) constants. The term is misleading because they are not constant. This is most evident for rp. The characteristic curves in Fig. 13 are obviously not straight lines, so the slope of the line (and therefore rp) depends on the values of V_gk, V_ak and I_a The values of both u and g also depend on he instantaneous operating point of the tube. It is this variation in tube constants which produces amplifier distortion. It is the task of the circuit designer to properly choose the tube type, quiescent operating point, load resistor, and so forth to make the amplifier as distortion-free as possible. The amplification factor t depends primarily on the physical construction of the tube: the spacing between the grid and cathode, and the spacing between the helical wound wires of the grid. The value of the plate resistance rp depends more on the instantaneous value of the plate current I_a than on the instantaneous value of the plate to cathode voltage V_ak . This means that the linearity of the amplifier can be maximized by minimizing delta_I_a for a given output voltage. This can be achieved by making RL large, which has the added benefit of increasing the voltage gain. However, RL should not be made too large for a given plate supply voltage Ebb, or the loadline will fall in the shaded region shown in Fig. 13. The characteristic curves are most strongly curved in this region of very low plate current, so the value of rp becomes very sensitive to the instantaneous value of I_a voltage which would appear if there were no local feedback. The net distortion in the amplifier stage ‘s output voltage is thereby reduced. The local feedback produced by the signal current through the cathode resistor Rk lowers the amplifier’s distortion.

Fig. 12. The loadline.

Fig. 13. Tube constants and triode plate characteristics curves.

Another common and useful type of amplifier stage is the cathode follower (also called a common plate amplifier stage). A simplified schematic of a cathode follower stage is shown in Figure 15. In a cathode follower there is no plate load resistor. Instead, the output voltage is developed across the cathode resistor Rk. The value of this resistor is usually much greater than would be used in a common cathode amplifier stage. This provides a great deal of negative feedback (the cathode follower is sometimes said to have 100% negative feedback), but the voltage gain of the cathode follower is always less than one. Although the cathode follower is not useful as a voltage amplifier, it finds wide application as a buffer amplifier. The circuit’s large amount of local negative feedback has three beneficial effects: it makes the amplifier more linear, it increases its input impedance, and it lowers its output impedance.

At DC and low audio frequencies, the intrinsic input impedance of most vacuum tube amplifier stages is very high. When the grid is biased sufficiently negative to the cathode, almost no grid current is drawn by the tube, so very little signal current is drawn from the previous amplifier stage. This is not always true at higher frequencies, however. The plate, cathode, and the various grids of a vacuum tube are basically air spaced metal plates, and as such form capacitors which affect the performance of vacuum tube amplifier stages. The impedance of a capacitor drops with increasing frequency. To maintain a given signal voltage across a capacitor, twice as much current must be forced through the capacitor at 2 kHz as at 1 kHz. The interelectrode capacitances of the vacuum tube will combine with other circuit elements to form low pass filters, which will cause the frequency response of the amplifier to roll off a high frequencies.

The input capacitance of a common cathode amplifier stage can be as high as 150 picofarads or more. The input impedance of such a stage would be quite low at high frequencies, and the frequency response of the complete amplifier containing this stage would probably begin to roll off at 20 kHz or below. If the complete amplifier contained two stages with similar, comparatively low roll-off frequencies, its performance at high frequencies would probably be quite poor. If the complete amplifier did not use overall negative feedback, then the response of the complete amplifier would be noticeably rolled-off at high audio frequencies. If the amplifier did use overall negative feedback, the frequency response of the amplifier with feed back might be acceptable, but there are still several problems with the design. The amount of negative feedback around the amplifier decreases at high audio frequencies when the frequency response of the individual stages begins to roll off, so the amplifier’s linearity at high audio frequencies is poorer than at lower frequencies. The amplifier may also be unstable, causing it to overshoot or ring on fast changing signal waveforms, or perhaps even oscillate. To ensure the stability of a feedback amplifier, the frequency response of the individual amplifier stages must be carefully tailored so that the amplifier’s overall frequency response (before feedback is applied) does not fall off too abruptly at high frequencies. The high input impedance of the cathode follower allows such tailoring.

The input capacitance of a cathode follower can be as low as a few picofarads. Its input impedance therefore remains high at high frequencies. It does not load down the preceding amplifier stage, so its frequency response can remain flat to a higher frequency. In addition, the output impedance of a cathode follower will be much lower than the output impedance of a common cathode amplifier using the same type of tube. This means that the gain of the stage is little affected by changes in its output loading. In the discussion of the common cathode amplifier stage, it was noted that when the load resistance RL was made much greater than the plate resistance rp that the amplifier’s gain became constant (approximately equal to the amplification factor u (Greek mu)). The cathode follower circuit exhibits this same behavior. When the effective load impedance (consisting of the cathode resistor Rk in parallel with the input impedance of any following amplifier stages or networks) is much greater than the effective plate resistance rp’, the voltage gain reaches a constant value equal to the effective amplification factor u (mu). Because rp’ is so much lower than rp the gain of the cathode follower is much less influenced by changes in the load it must drive than is a common cathode amplifier stage. Therefore the cathode follower is a very effective buffer amplifier: its low effective plate resistance allows it to drive relatively low impedance loads with good linearity without a loss of voltage gain, while its high input impedance prevents the frequency response of the previous stage from prematurely rolling off.

Fig. 16 shows a typical complete low level amplifier for a preamplifier, such as would be used for a moving magnet cartridge. The amplifier consists of three stages: two cascaded common cathode amplifier stages followed by a cathode follower stage. The first two stages provide the necessary voltage gain, while the cathode follower drives the overall negative feedback network and any other external load (volume controls, tape recorders, etc.) The feedback network consists of R0, R1, C1 and C2 which controls the voltage gain of the complete amplifier to provide the necessary RIAA equalization. This is discussed in more detail in a later section. The capacitor Cc couples the first stage to the second for audio frequencies.

Fig. 15. Cathode follower amplifier stage and circuit model.

Fig. 16. Complete low level amplifier.

Another variety of vacuum tube is the pentode. Its internal construction is similar to that of the triode, but an additional two wire helix grids are introduced between the control grid and the plate. The additional grid nearest the control grid is called the screen grid, and is usually connected to a power supply of some sort. The grid nearest the plate is called the suppressor grid, and is usually connected to the cathode of the tube, either in the external circuit or within the envelope of the vacuum tube.

These additional grids affect the electric fields within the tube in a rather complicated manner, but their effect is to produce a tube with a much higher amplification factor ,u , and often a proportionally higher plate resistance rp. This means that although an amplifier stage employing a pentode with an amplification factor of 1000 is capable of giving a voltage gain of nearly 1000, in practice the gain is likely to be much less. The voltage gain of an amplifier stage approaches the amplification factor p of the tube when the load resistance RL is made much larger than the tube’s plate resistance rp. Because the value of rp is very large for most pentodes, the value of RL is not likely to be large compared with rp, so the gain will be considerably less then p. A typical amplifier stage using a triode with an amplification factor of 100 might have a voltage gain of 70, while a typical amplifier stage employing a pentode with an amplification factor of 1000 might have a voltage gain of 200 or less. In some circuits this extra factor of three in gain may be useful, but the vast majority of voltage gain stages (not power output stages) in tube amplifiers use triodes.

Pentodes offer improved performance over triodes for voltage amplifier applications in one other area: input capacitance. The pentode’s screen grid acts as a shield between the tube’s output (at the plate) and its input (at the grid). The increased isolation between the plate and grid lowers the tube’s effective input capacitance. For a given gain, the input capacitance of a pentode amplifier can be much lower than for an equivalent triode amplifier. While this can be extremely important in amplifiers designed to operated at radio frequencies, it usually is not significant at audio frequencies. More important is that a pentode amplifier will usually exhibit more tube induced noise than an equivalent triode amplifier. For this reason, and because of the additional power supply circuitry necessitated by the pentode‘s screen grid, pentodes are little used in audio amplifiers except in output stages. Pentodes or beam power tetrodes (a similar type of tube) are very commonly used in the output stage of power amplifiers because they offer much greater efficiency than triodes.

Amplifier Types

While the characteristic curves of a tube are very useful for selecting a quiescent operating point, they are not very convenient for determining the voltage gain Av of an amplifier stage. What is needed is a simple model for the triode amplifier stage, and an equation describing its behavior, which relates the voltage gain Av to the tube constants p , g and rp and the value of load resistor RL. Such a model is shown in Fig. 14. The triangle represents a perfect amplifier with voltage gain - u . In series with this amplifier is a resistor of value rp, related to the plate resistance of the tube rp’. For the simplest possible amplifier without any local feedback (such as the amplifier of Fig. 11), rp’ = rp. If a cathode resistor Rk is inserted between the cathode and ground is used to bias the tube or provide local feedback, and if Rk is not paralleled by a bypass capacitor, and value of rp’ becomes: rp’ (u + 1)Rk + rp. This resistor, and the load resistor RL, form an attenuator, reducing the overall gain. The voltage gain of the overall amplifier is then: Av = - u RL/(RL + rp u) = - u RL/ + (u + 1)Rk + rp). This equation shows the behavior mentioned above: when the value of RL is very large (much larger than rp’) the voltage gain of the stage is - u. The gain is negative because the amplifier is inverting: a positive-going input signal produces a negative-going output signal. The circuit model for a pentode operated with its suppressor grid connected to the cathode and the screen grid operated at a constant positive voltage with respect to the cathode is the same as for a triode.

Fig. 14. Common cathode amplifier stage and circuit model.

The circuit of Fig. 14 is known as a common cathode amplifier stage. Most voltage gain stages in preamplifiers or power amplifiers use several such stages connected in series. A coupling capacitor is used to connect the various stages for audio signals, while isolating the different DC voltages at the inputs and outputs of the stages.

The resistor Rk serves two purposes. It biases the cathode of the tube to a positive voltage with respect to the grid, so that the tube is operated in its most linear region where no grid current is drawn. The resistor Rk also provides some local negative feedback. This feedback stabilizes the voltage gain and improves the linearity (lowers the distortion) of the amplifier. It accomplishes this by making the voltage gain more dependent on the value of Rk and RL (which, if good quality components are used, do not change as an audio signal is being amplified) and less dependent on the tube characteristics p and rp, which will vary slightly when the tube is amplifying a signal. From the equation for Av it is easy to see how a large value of Rk reduces the effect of rp and p on the amplifier’s voltage gain. As Rk is made very large, ( u + 1)Rk becomes much larger than rp + RL. In this case the equation for Av reduces to Av = u RL/ u +1)RKI. Usually the amplification factor p is much greater than 1, so when Rk and p are large the gain becomes approximately Av = —RL/Rk. Such an amplifier stage will have a gain of much less than — u , but because the effect of p and rp on the gain are negligible, the distortion will be very low, and the gain will not change as the tube ages and its characteristics change.

The manner in which the cathode resistor Rk improves the linearity of the amplifier can also be explained in terms of feedback. The voltage appearing across the cathode resistor is a fraction Rk/RL of the output voltage V. This is true because the same signal current i passes through both Rk and RL. When the control grid of the tube is negatively biased with respect to the cathode, the control grid does not draw any current, so there is only one electrical circuit and one signal current which circulates from the ground, through Rk, the tube, RL, and back to ground (via the power supply Ebb. The output voltage Vo is given by Vo = —is RL. The voltage across Rk is given by Vk = isRk = -(Rk/RL)Vo.

The vacuum tube amplifies not the input voltage V but V_gk : the voltage appearing be tween the grid and cathode. This voltage is the difference between the input voltage V and the cathode voltage Any distortion appearing in V at the amplifier’s output will also be reflected in Vk. The voltage V_gk will contain this distortion component, which is inverted in polarity with respect to the distortion in the output voltage V When this distortion component is amplified by the tube, it may be considered to subtract from the larger output distortion


quency signals, while blocking the DC voltage appearing at the output of the first stage. There is no coupling capacitor between the output of the second common cathode amplifier and the cathode follower amplifier stages. In this case the DC voltage appearing at the second stage’s output helps to bias the cathode follower stage tube. This DC voltage is typically quite high, on the order of Ebb! This allows a large value resistor Rk to be used to bias the cathode follower output stage, ensuring good linearity for the stage.

The amplification factor of the tubes usually employed in preamplifier voltage gain stages ranges from about 30 to 100. Because the voltage gain of a common cathode amplifier stage is usually only about 0.5 u to 0.8 u, the overall open loop (before negative feedback is applied) gain of an amplifier like that shown in Fig. 12 is limited to 6400 or less. Most often the gain will be on the order of 2000 (66 dB). This is not enough gain if a moving coil cartridge is to be used without a separate head amplifier. Consider the case of a low level amplifier for moving coil cartridge use with a gain at 1 kHz of 50 dB (a reasonable figure). Due to the necessary RIAA equalization which must take place, the amplifier’s closed loop gain at 20 Hz is nearly 80 dB (an increase in gain by a factor of 10 times corresponds to exactly 20 dB). The amplifier’s open loop gain must be greater than this by the desired amount of negative feedback at low frequencies. For stable, low distortion operation, at least 12 dB of feedback and preferably more should be used. The open loop gain of the low level amplifier should therefore be on the order of 82 - 90 dB.

One obvious way of increasing gain is to increase the number of amplifier stages. There are several problems with this proposed solution. Adding another common cathode amplifier stage would provide sufficient gain, but the amplifier would probably become unstable when feedback was applied around the circuit. Also, because three polarity inverting stages are in cascade, the overall amplifier becomes inverting. A different configuration feedback circuit would then have to be employed, and such a circuit introduces other technical difficulties. The solution of adding a third common cathode amplifier stage is not an acceptable one.

A pentode common cathode amplifier stage might be tried in place of one of the first two triode stages, but this too has several drawbacks. Pentodes tend not to be as quiet as triodes, and the need for a screen grid power supply complicates the design of the preamplifier. A good solution is to use two triodes in a compound circuit called a cascode (as opposed to cascade) amplifier stage.

A typical cascode amplifier stage is illustrated in Fig. 17. Two triode tubes, connected in series, are used in this circuit. The bottom tube functions as a conventional common cathode amplifier stage. The upper tube functions as a common grid amplifier stage. In a common grid amplifier, the input voltage is applied between the cathode and ground, while the grid is connected to ground for audio signals. In the circuit of Fig. 17, the capacitor connecting the grid of the upper tube to ground serves acts to ground the grid for audio signals, while allowing the DC electrode voltages of the tube to be correctly set for linear operation. In some cases this capacitor is connected to the cathode of the bottom tube. Either connection gives similar performance. The resistor in series with the cathode of the upper tube serves to bias its grid negative to the cathode.

Unlike a common cathode amplifier stage, the input impedance of the common grid stage is quite low. The signal current through the load resistor RL also passes through the series connected triodes. The lower tube must supply all this current to drive the cathode of the upper tube. Compare this to the case of the common cathode amplifier stage, which has a high input impedance (at least at low frequencies) because the grid draws almost no signal current. This low input impedance means that the effective load resistance on the common cathode stage is low, so it normally provides little voltage gain. The common grid stage can have a substantial voltage gain, however, so that the complete cascode amplifier can have appreciably more gain than a simple common cathode amplifier.

The cascode is a two stage amplifier, and acts like one at high frequencies. This means that a complete amplifier consisting of a cascode stage, a common cathode stage, and a cathode follower may or may not be stable. Fortunately the low input impedance of the upper tube which lowers the voltage gain of the common cathode stage also extends this stage’s high frequency response. By careful design, a stable amplifier with enough gain for a moving coil cartridge can be achieved.

Fig. 17. Cascode amplifier stage. Note: location of capacitor

Vacuum tubes find other uses in preamplifiers and power amplifiers other than as amplifying devices. A triode (or less commonly a pentode) can also be used as a “constant current source. “ Such a circuit is illustrated in Fig. 18. The designation “constant current” is misleading because the tube does not supply a completely constant current to the circuitry of which it is part. What it does is to function as a very large value resistance for signal currents, so that when the voltage across the current source circuit is changed, the current through it varies only slightly. It is employed where the use of a comparably large value resistor would cause a prohibitively large DC voltage drop. Suppose an amplifier stage requires an effective load resistance of 100 k-Ohm, and the stage draws 10 mA of plate current. If an actual resistor were used, the voltage dropped across it would be (100,000 ohm ) (0.01 A) =1000 V. A very high voltage power supply would therefore be required, the resistor would dissipate large amounts of heat, and the circuit would be very wasteful of power. Alternatively, a tube current source could be used, and only about 200 V would have to be dropped across the entire current source circuit. Obviously this is a much more practical solution.

However, tubes are not perfectly linear devices, as was noted before, while resistors are nearly perfectly linear. A vacuum tube current source can itself be a source of amplifier distortion. The effective resistance RL’ of the tube current source for signal voltages (its dynamic resistance) depends on the amplification factor M and the plate resistance rp of the tube. While .i remains relatively constant independent of changes in voltage across and cur rent through the tube, this is not true of rp whose value can change significantly as the cur rent through the tube is varied. For a given output voltage, this current variation will be less as RL’ is made larger. This suggests that the value of Rk should be made as large as possible. When the value of Rk is large, the effect of changes in rp on RL’ is diminished, and the variation in rp is minimized. The battery B in Fig. 18 allows the use of a large value resistor for Rk while maintaining correct biasing for the tube. Sadly, a number of commercial preamplifiers use tube current sources without such a battery. This limits both the linearity and the voltage gain Qf the circuit. Finally, a tube current source will be noisier than an equivalent resistor, and this must be considered when current source loaded input stages for low level amplifiers are being designed.

All vacuum tubes are noise generators, but some tube types are quieter than others. There is a general relationship between the noise voltage produced by a tube and its transconductance gm. One way of quantifying this noise voltage is in terms of an equivalent noise resistance. Resistors are noise generators too, and there is a definite relationship between the noise voltage produced by an ideal resistor and its resistance. The noise resistance of a tube is defined as the value of an ideal resistor which would produce the same amount of noise as the vacuum tube. For most tubes, the value of noise resistance is approximately equal to 2. . This means that high transconductance tubes are generally quieter than low transconductance tubes. Tubes and resistors generate noise of all frequencies, so the noise voltage of a tube or resistor is usually specified over given range of frequencies (the bandwidth). In a given bandwidth, the total noise is proportional to the square root of the resistance: the noise doubles when the resistance is quadrupled. Therefore to halve the tube noise generated in an amplifier stage, the transconductance would have to be quadrupled.

The transconductance of a tube does vary slightly with changing plate current, increasing as the plate current is increased. Low noise stages will therefore tend to operate at comparatively high currents. Large decreases in tube noises cannot be obtained in this manner. When the transconductance of an individual tube is too low to provide sufficiently low noise operation, several tubes may be connected in parallel. Two identical triodes, with amplification factor u , plate resistance rp, and transconductance gm, when connected in parallel are equivalent to a single triode with amplification factor u’ = u, plate resistance rp’ = r and transconductance g 2 gm. Vacuum tube head amplifiers often make use of this fact, connecting two or four triode sections in parallel, for a noise reduction of about 3 to 6 dB respectively if the various triode sections are equally noisy. Even if one of the sections is moderately noisier than the others(s), there is a net reduction in generated noise. A noisy tube in parallel with a quiet one will always be equivalent to a single tube which is at least slightly quieter than the noise tube alone.

Power Supplies for Vacuum Tube Amplifiers

It is important to recognize that all of the circuit schematics presented thus far in the Figures have shown ideal battery sources (Ebb, etc.) as part of the vacuum tube amplifier stages. When such circuits are actually constructed, real world power supplies must be used. If these power supplies are not correctly designed and constructed, the amplifier may per form poorly or not at all. It is easy to overstate the importance of power supplies, just as the significance of any single factor in a complete amplifier design can be overemphasized. Power supplies can affect the sound of a preamplifier or power amplifier however, so a discussion of the principles of power supply design as they relate to vacuum tube amplifiers is in order. Vacuum tube amplifiers contain two principle classes of power supplies: heater sup plies, and plate (and sometimes grid) supplies. The heater supply will be discussed first.

Fig. 18. Vacuum tube constant current source and current source loaded common cathode amplifier stage.

The heater power supply provides the current required by the heater wire in each vacuum tube which heats the tube’s cathode, causing the emission of electrons. As was discussed earlier, the electron current which the cathode can provide depends on the cathode’s temperature, which in turn is determined by the current through the heater wire. This means that the characteristics of the vacuum tube, and therefore the performance of the amplifier stage, depends on the value of the heater current. If the power supply does not provide a suitably constant heater current, the amplifier may malfunction. One possible cause of heater current variations are changes in the AC line voltage. Your local power company does not keep the AC line voltage to your home constant. The line voltage changes on both a long term and short term basis as other power users switch electrical equipment on and off The AC line also usually contains very brief voltage spikes produced by lightning strikes, the turn-on and turn off transients of electrical motors, and the like. All these AC line voltage variations will be passed on to the heater power supply unless the power supply designer intervenes.

A properly designed voltage regulator can solve the problem of line voltage variations. A voltage regulator is a circuit which delivers a constant output voltage even though the input voltage to the circuit may be varying. Voltage regulators for heater supplies are very easy to design using IC’s, and can inexpensively deliver excellent, reliable performance. There is no good reason why the heaters of a vacuum tube preamplifier should not be regulated. Because the preamplifier is a high voltage gain circuit which is itself followed by additional gain stages (in the power amplifier), the effect of any heater current variations in the preamplifier will be magnified by the succeeding gain stages. Heater regulation is useful in any vacuum tube amplifier design, but it is vital for a stable preamplifier design.

Voltage regulation can also help to isolate the various stages making up a complete amplifier. A perfect voltage regulator also delivers a constant output voltage even though the current drawn from the regulator may be varying. In an unregulated power supply, if one heater draws an excessive amount of current it can lower the supply voltage, which in turn would decrease the current available to the other heaters sharing the same power supply. A good regulated power supply would maintain the correct supply voltage, ensuring that the current drawn by each heater is unaffected by the current drawn by the heaters of the other tubes.

These same benefits of voltage regulation are important for plate and grid power sup plies. Changes in the AC line voltage will be reflected in changes in the value of Ebb unless counteracted by a voltage regulator, and these voltage fluctuations can find their way into the audio signal being amplified. The effect of a voltage regulator in isolating individual amplifier stages is also important. If the power supply is not correctly designed, and it allows the various amplifier stages to interact, a signal in one amplifier stage can give rise to a spurious, distorted replica signal in another stage. This interaction between amplifier stages can lead to poor sound quality, and even oscillation. All these problems can be prevented by employing voltage regulation in the plate and grid power supplies. The same degree of isolation between amplifier stages can be obtained by using one or two very high quality voltage regulators to supply all the audio circuitry, or by using a number of simpler voltage regulators, each supplying only one or two stages. Either solution can yield excellent results, but the latter is usually easier to implement in an actual amplifier.

Amplifier stages can also interact with each other via the ground return wiring. As amplifier designs become more elaborate, using a larger number of higher current amplifier stages, grounding plays an increasingly important role in ensuring a stable, quiet, good sounding amplifier. Proper layout and grounding technique in a vacuum tube amplifier is just as important as good power supply regulation. One is of little use without the other.

Preamplifier Circuits

Before discussing the different types of preamplifier circuits, it is useful to describe the purpose and function of preamplifiers. Once the need for a preamplifier is understood, the merits of the different types of circuits can be assessed.

The purpose of the low level amplifier stage of a preamplifier is to amplify the (low) voltage produced by the phono cartridge as it plays a recording. The vast majority of phono cartridges are electromagnetic transducers of some type. They convert the mechanical waves cut into the record groove into a facsimile electrical wave: the cartridge’s output voltage signal. The audio signal (mechanical wave) cut into the record groove is small, and the phono cartridge is an inefficient transducer, so its output voltage is very low. If this were the only problem, the design of low level amplifiers would be fairly simple, mostly a matter of designing an appropriately quiet input stage.

Both the manner in which records are cut and the physical laws governing the behavior of a magnetic cartridge make matters more complicated, however. Magnetic phono cartridges are velocity sensitive transducers: the cartridge’s output voltage is proportional to the velocity of the stylus as it traces the mechanical wave cut into the record groove. In contrast, ceramic and strain gauge cartridges are amplitude sensitive transducers. Their output voltage is proportional to the physical size of the mechanical wave cut into the record groove.

These two classes of phono cartridges will behave differently when a record is played. Consider a 33 1/3 RPM record on which a 1 kHz sine wave (pure tone) has been recorded. Suppose that both types of cartridges produce the same voltage when playing this record. Now the record is replayed at 66 2/3 RPM, turning the 1 kHz sine wave into a 2 kHz sine wave (the turntable’s doubled speed makes the mechanical waves cut into the record groove moves the phono cartridge’s stylus back and forth twice as fast as before). The amplitude of these mechanical waves has not changed, so the amplitude sensitive transducer will pro duce the same output voltage as before. The doubled record speed has doubled the stylus velocity however, so the signal voltage generated by the velocity sensitive transducer will also double.

If records were cut so that the amplitude of the mechanical waves impressed on the record groove were proportional to the sound pressure level of the original musical event, and if all cartridges were amplitude sensitive transducers, there would be no need to equalize the signal generated by this phono cartridge. Records are not cut this way, however, and magnetic cartridges are velocity sensitive transducers. This is why equalization is necessary in the low level amplifier of a preamplifier.

The dominance of a magnetic phono cartridge has come about because of the technical advantages of such a design. Records are (supposed to be) cut according to a standard which minimizes the total amount of equalization which must be performed by the low level amplifier. Suppose that records were cut with a constant amplitude characteristic, so that the amplitude of the mechanical waves cut into the record groove was proportional to the sound pressure level of the original musical event. Then, for a fixed original sound pressure level, the output of a magnetic phono cartridge at 20 kHz would be 1000 times its output at 20 Hz. To produce a constant level voltage at the output of the low level amplifier, the amplifier’s voltage gain at 20 Hz would have to be 1000 times its gain at 20 kHz. This is a lot of equalization. Instead, parts of the frequency range of a record is cut with a constant velocity characteristic: the velocity of the mechanical wave cut into the record groove is now proportional to the sound pressure level of the original musical event. Over these frequency ranges, a magnetic cartridge requires no equalization. The gain of the low level amplifier need not decrease with increasing frequency over the constant velocity frequency ranges of the record.

The RIAA standard specifies that from 500 Hz to 2.1 kHz, and below 50 Hz, that records be cut with a constant velocity characteristic. From 50 Hz to 500 Hz, and above 2.1 kHz, records are to be cut with a constant amplitude characteristic. Actually, the transition from constant velocity to constant amplitude characteristic and vice versa is made smooth, and is specified in such a manner that the equalization necessary in both the cutting and playback parts of the reproduction chain can be achieved using simple circuitry. The manufacturers of magnetic phono cartridges, in turn, strive to produce cartridges which are perfect velocity sensitive transducers. These two facts imply a standard for the equalization which must occur in a preamplifiers’ low level amplifier. The gain must be flat from 500 Hz to 2.1 kHz and below 50 Hz. The gain must drop from 50 Hz to 500 Hz, and above 2.1 kHz.

There are two fundamental manners in which this equalization can be achieved. Negative feedback can be used to control the gain of the low level amplifier in a frequency selective manner. This is called active RIAA equalization. An actively RIAA equalized preamplifier circuit was illustrated in Fig. 16, in which R0, R1, R2, C1 and C2 formed a negative feed back network providing RIAA equalization. A second method is to use a simple resistor-capacitor filter network to passively equalize the audio signal. In this case, the amplifier stages in the low level amplifier are designed to have an overall constant gain. These stages may or may not have an overall negative feedback loop around them. A typical design is shown in Fig. 19.

These two different approaches to the RIAA equalization problem have different strengths and weaknesses. Vacuum tube feedback amplifiers tend to have rather low open loop (before feedback) voltage gains. This requires that the feedback component values be carefully selected based on a knowledge of the amplifier’s open loop gain. If this gain changes (caused by the aging of the tubes, for example), the equalization accuracy can suffer. The problem is far from insurmountable, but it does require careful thought during the design process. A passively RIAA equalized preamplifier can be designed to be much less sensitive to tube aging effects. The price paid for this is linearity. The input stage of a passively RIAA equalized pre-amplifier sees the full output voltage of the phono cartridge at all frequencies. As this voltage increases at mid to high frequencies (due to the velocity sensitive characteristic of the magnetic cartridge), the output voltage which the first stage tube must swing also increases. Because the linearity of an amplifier decreases as its output voltage increases, the linearity of the low level amplifier input stage suffers in a passively RIAA equalized design.

In contrast, the feedback network of an actively RIAA equalized amplifier acts to keep the effective input voltage to the input tube constant at all frequencies. The input tube does not need to swing greater output voltages at mid to high frequencies, so the first stage’s linearity is as good at high frequencies as at low. However, the output stage has to drive a highly capacitive load at high frequencies, taxing its output current capabilities and linearity. The high frequency stability of an actively RIAA equalized amplifier is also a matter of concern, and it may be difficult to prevent such an amplifier from exhibiting ringing or overshoot at high frequencies.

Fig. 19. Low level amplifier with passive RIAA equalization.

The perception of reproduced music is a subject which is both heatedly debated and little understood. It is difficult or impossible to predict whether a given actively equalized design will sound better or more accurate than a given passively equalized design. Both types of circuits are extensively used, with results both good and bad. Similarly the question concerning the different sound, if any, of tube and solid state amplifiers has been extensively discussed. Many theories explaining how and why tube amplifiers seem to sound different or more real have been put forth. Here too the results are inconclusive.

Vacuum tubes do have some advantages as amplifying devices over most transistors. For the most part vacuum tubes are more linear than their solid state counterparts. The distortion that they do produce tends to be primarily second and third harmonic, while transistors also generate significant amounts of harsher sounding, higher order harmonics. The greater inherent linearity of vacuum tubes means that less negative feedback is required to reduce the total distortion generated by an amplifier to an unobjectionable level. This means that simpler circuitry can be used, which also appears to be useful in achieving a good sound quality. The high voltages at which vacuum tube amplifier stages are commonly operated means that it is nearly impossible to cause voltage clipping in a vacuum tube preamplifier with any nor mal input signal. By using high current tube amplifier stages, current clipping can be made an equally unlikely event when the vacuum tube amplifier stage must drive a low input impedance solid state amplifier. Whatever the reason, and whether the perceived difference is real or illusory, many audiophiles prefer the sound of vacuum tube preamplifiers and power amplifiers.

Power Amplifiers

The task of the vacuum tube power amplifier is very different from that of the preamplifier. Rather than amplifying and equalizing a very low level signal, the power amplifier must pro duce the large voltages and currents needed to drive a loudspeaker. The loudspeaker represents not a simple, resistive load, but rather a highly complex, frequency dependent load. The design of the output stage of the power amplifier must reflect the difficult nature of the load.

Most vacuum tube power amplifiers employ an output transformer and one or more pairs of output tubes operated in push-pull. Such a circuit is illustrated in Fig. 20. The output transformer performs two vital functions. It adds the plate signal currents from the two halves of the output stage in such a way that all the even harmonic distortion of the tubes is cancelled or identical tubes and a perfectly balanced output transformer). It also transforms the low impedance loudspeaker load to a higher impedance load than the output tubes are able to drive.

Vacuum tubes, even the high power types used in the output stages of power amplifiers, are basically high voltage, low current devices. The characteristic curves of a common out put tube, the KT88, are shown in Fig. 21. The tube can only deliver a peak current of about 0.45 Amperes, corresponding to only 0.8 Watts into 8 Ohms. The output transformer transforms the low impedance loudspeaker load into a much higher impedance than the tube can drive with good linearity and efficiency. The output tube then swings a much larger voltage than is actually delivered to the loudspeaker, but the current it must swing is correspondingly reduced.

Of course, the perfect output transformer does not exist. An output transformer is a complicated device which is difficult and expensive to manufacture. At low frequencies the transformer becomes ineffective, and the output tubes are not properly loaded, causing in creased distortion and a drop in power delivered to the loudspeaker. A good low frequency transformer must be very large and heavy, because the size of the transformer’s iron core, and the quality of that iron, is directly related to how low in frequency it can perform correctly. At high frequencies, the effect of the various windings in the transformer on each other must be considered. The plate load windings for each half of the push-pull output stage must be segmented, and properly oriented with respect to the loudspeaker winding. If this is not done, the distortion cancelling benefits of push-pull operation will not be realized. A good high frequency transformer must be physically small, to allow a good coupling between the various windings at high frequencies. This conflicts with the requirements for good low frequency performance.

When the output transformer is placed within a negative feedback loop, which it usually will be, there are further complications. The transformer gives rise to roll-offs and phase shifts at the frequency extremes. This reduces the effectiveness of the negative feedback in lowering distortion, and can even lead to instability. These problems can be minimized by careful design, but never eliminated entirely. The best output transformer is no output transformer at all.

There is one practical tube amplifier design which does not require an output transformer. This is the OTL (output transformerless) amplifier devised by the late Julius Futterman. A simplified schematic for this amplifier is shown in Fig. 22. The output stage consists of four or six power tubes in a series connected push-pull arrangement. For simplicity, Fig. 22 only illustrates two output tubes, V and V In an actual Futterman OTL amplifier there would be two or three tubes in parallel in each of these locations. These tubes are not conventional power output tubes like the KT88 or EL34, but instead are special high current tubes originally designed for use in the horizontal deflection circuits of television sets. Each tube can deliver peak signal currents of about 1.5 Amperes, and by employing two or three tubes in parallel it becomes possible to construct an output transformerless vacuum tube power amplifier capable of delivering over 80 Watts of power into an 8 Ohm load.

The series connected push-pull output stage and its driver stage are also special, and con tribute to the success of the design. Vacuum tube V2 functions as a “phase splitter,” producing the necessary push-pull drive to the control grids of the upper and lower output tubes from a single-ended input voltage to its control grid. Many transformer coupled amplifiers also employ a phase splitter to perform this same task. In a conventional phase splitter, the top of the plate load resistor R5 would be connected to a fixed voltage power supply. Then, because the same signal current passes through both R4 and R5 (which have the same resistance value), the grid drive voltage for both the upper and lower output tubes is identical. If these tubes have identical characteristics, and the output transformer is balanced, perfect push-pull operation is achieved.

The Futterman OTL amplifiers use a modified phase splitter circuit. The top of R5 is connected not to a fixed voltage power supply, but rather to one which floats relative to ground. It maintains the voltage at the top of R at a fixed voltage relative to the amplifier’s output voltage. This forms a feedback loop which allows the series connected output tubes to operate in push-pull, eliminating all even harmonic distortion (if the output stage is perfectly balanced).

Fig. 20. Transformer coupled push-pull power output stage.

Fig. 21. KT88 characteristic curves.

This same floating power supply also acts as the screen grid power supply for the upper out put tubes. This allows them to function as pentodes, vastly increasing the efficiency of the amplifier.

The remainder of the power amplifier is conventional, employing a common cathode pentode amplifier input stage with overall negative feedback brought back to its cathode via resistors R and R A single-ended power supply is used, which necessitates the output coupling capacitor, but an output capacitorless design using a balanced power supply for the output stage is also feasible.

The output transformerless vacuum tube power amplifier is a special breed of power amplifier. There have been many other attempts at output transformerless amplifier design, but none match the theoretical and actual performance of the Futterman circuit. This is unlike the case of preamplifiers, where many designers and manufacturers have devised similar, competing circuits.

Fig. 22. Simplified Futterman OTL amplifier schematic. Note: Not Shown Input Coupling Capacitors and Biasing Networks for V1 And V2.

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This article is part of Understanding Tube Electronics (adapted from New York Audio Labs 1984 booklet, by Harvey Rosenberg)

ALSO SEE: The State of Audio Technology; Tubes Versus Transistors -- Is There an Audible Difference?

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Updated: Tuesday, 2015-04-28 19:36 PST