Chapter 4B.

In the next subsection you will see that small signal calculations are not accurate enough to be useful. However they can be used to correct the gain figures from the charts for an unbypassed cathode resistor.

Small Signal Calculations.

One note of caution. The transconductance of a pentode is very sensitive to screen grid voltage. For example, for the 6AU6 the lowest value for transconductance is given for a screen voltage of 100 volts. Yet the resistance coupled amplifier charts give values of E_g2 of around 40 volts. Obviously the value of Gm needs to be scaled down accordingly. The tube manual gives a graph of transconductance versus grid number 1 voltage for values of grid number 2 voltage of 50, 100, and 150 volts for the 6AU6. An example will illustrate.

Example 4B.1

A 6AU6 has a stated transconductance of 3900 micro mhos and a plate resistance of 0.5 meg ohms. Calculate the gain for a plate resistor of 270 k ohms and a following stage grid resistor of 470 k ohms.

Solution:

First calculating the value of R_bc

R_bc = 270 k x 470 k / (270 k + 470 k) = 171 k ohms.

A_v = G_m r_p R_bc / (r_p + R_bc)

A_v = 3900 micro mhos x 500 k x 171 k / (500 k + 171 k) = 497

E_bb = 250 volts.
R_b = 270 k ohms.
R_c2 = 680 k ohms.
R_cf = 470 k ohms.
R_k = 1,000 ohms.
I_c2 = 0.30 mA.
I_b = 0.74 mA.
E_c1 = -1.0 volt.
E_c2 = 40 volts.
E_b = 50 volts.
E_sig = 0.1 volt AC.
E_out = 25 volts AC.
Gain = 250.
% Dist = 1.1 %.
E_sig(1) = 0.22 volts AC.
E_out = 47.7 volts AC
Gain = 217.
% Dist = 2.6 %.
(1) Taken at the point of 1/8 microamp of grid current.

We do have curves for the 6AU6 of transconductance versus grid 1 voltage for three values of screen grid voltage including 50 volts. 50 volts is close to 40 volts and we are given the grid 1 voltage. Looking at the graph we find the value of transconductance of 2200 micro mhos. Using this value in equation 4B.2 gives a gain of 280. We would rather have calculations that do better than that. The error is likely caused by the 10 volt difference in the screen grid voltage. We can do it another way as seen below.

Gain for an Unbypassed Cathode.

Resistance coupled amplifier charts don't give gain values for an amplifier with no cathode bypass capacitor. If you want to design a low distortion pentode amplifier and need to know the gain for an unbypassed cathode here is the procedure.

1. Design a pentode amplifier from the resistance coupled amplifier charts in a tube manual.

2. Use the stated value of low distortion gain in equation 4B.5 to find the operating value of G_m.
   G_m = A_v (r_p + R_bc) / (r_p R_bc)  (4B.5)

3. Use this value of G_m in equation 4B.4 to calculate the true gain.

Example 4B.2

The plate resistance of the 6AU6 is given as 0.5 meg ohms. The data from the resistance coupled amplifier chart is given above.

This is a lot more information than we need to work the problem but The real world never gives only the information we need and no more.

Calculate (a) the operating transconductance of the tube, (b) the gain without a cathode bypass capacitor.

Solution:

First we must calculate R_bc = Rb Rcf / ( Rb + Rcf ) = 270 k x 470k / (270 k + 470 k) = 171 k ohms. Now we calculate the operating transconductance.

G_m = A_v (r_p + R_bc) / (r_p R_bc)

G_m = 250 (500 k + 171 k) / (500 k x 171 k) = 1962 micro mhos.

Now we calculate the gain without a cathode bypass capacitor as follows.

A_v = G_m r_p R_bc / [r_p + R_bc + R_k ( G_m r_p + 1)]

A_v = 1962 micro mhos x 500 k x 171 k / [500 k + 171 k + 1000 (1962 micro mhos x 500 k + 1)]

A_v = 101

If the screen grid bypass capacitor is returned to ground rather than to the cathode, as shown in Figure 4B.5, The gain is much lower, 73.5 to be exact. Distortion and gain figures are summarized in the table below.

As the name implies the heptode has 7 elements, one cathode, 5 grids, and 1 plate. This tube is often called a pentagrid converter. Pentagrid as in 5 grids. It has one application, to serve as a mixer in radio receivers. (I have breadboarded and tested an audio voltage controlled amplifier using one of these tubes, but that's another story).

The Principle of Heterodyning

There are some types of mixers in which the original signals are canceled out and ONLY the sum and difference frequencies appear in the output. These devices are called "doubly balanced mixers" or DBMs for short. We will get to them shortly. But for now we will be talking about mixers in which the original two signals appear in the output along with the sum and difference frequencies.

So What is a Mixer?

The Superhet Receiver

We can not offer a full course in radio receiver design theory in this book. The interested reader is referred to other texts on the subject.

The block diagram of a single conversion super heterodyne receiver with an RF amplifier is shown in Figure 4B.6.

The RF Amplifier has a tuned circuit in its input and another in its output. It increases the level of the wanted incoming signal, reduces the level of the ones that are not wanted and helps to prevent the local oscillator from being radiated by the antenna. Such radiation could interfere with reception of other radio stations or services. Automatic gain control can be, and is, applied to the amplifying device here.

The converter contains an oscillator which is a locally generated signal that combines with the received frequency to generate the difference signal. The converter also does the job of mixing the local oscillator with the incoming signal. The tuned circuit of the oscillator is tuned along with the two tuned circuits in the RF Amplifier as the operator turns the tuning knob. The difference between the oscillator frequency and the incoming signal frequency is a constant. Therefore the converter delivers a constant frequency signal to the Intermediate Frequency Amplifier. Some AGC (Automatic Gain Control) is also applied to the mixer part of the converter.

The IF (intermediate Frequency) amplifier follows the converter. Its frequency is lower than the frequencies of the stations being received but higher than audio frequencies. Thus, the reasoning went, it is between the station frequencies and audio frequencies so it is intermediate. Its operating frequency is fixed and cannot be changed by the operator, or even by a skilled technician. This is where most of the selectivity of the receiver is found. Selectivity is the ability of a receiver to bring in a single station and cut out the stations that are nearby in frequency. More AGC is applied to the amplifying device in the IF amplifier.

Following the IF amplifier is the detector. This is the combination of devices and circuitry that recovers the audio from the AM signal. The detector also recovers a negative DC voltage that is proportional to the strength of the incoming signal. This is the AGC (Automatic Gain Control) voltage that is applied to the IF and RF amplifiers and the converter.

If this is a stand alone radio or short wave receiver, the audio amplifier will deliver 1 or 2 watts of power to drive a speaker. If it is a high fidelity tuner The amplifier will deliver a line level signal at a moderate impedance level for driving the input circuitry of an amplifier.

Image Frequencies.

The Tube and the Circuit.

How the Converter Works.

The cathode and the first two grids work like a triode tube and are the local oscillator. The circuit is called a Hartley oscillator because it uses a tapped inductor. (See section 4B.5). The cathode goes to the tap and the first grid, called the oscillator grid, receives signal which is coupled from the top of the oscillator coil. The cathode current flows through a few turns at the ground, or low, end of the coil. The magnetic field induces voltage in the rest of the coil. The coil is tuned by one section of the variable capacitor and the alternating voltage which appears across the coil has the frequency to which the coil is tuned. The voltage which is applied to the grid is enough to drive the cathode current of the tube from saturation to cutoff. The pulses of cathode current flow through the lower turns of the coil and maintain the oscillation. When the alternating voltage at the top end of the coil swings positive the grid is driven slightly positive and begins to conduct current like a diode. (The grid is attracting electrons to its self and therefore acts like the plate of a diode.) The 220 pf capacitor charges up so the most positive voltage at the grid is just barely positive and most of the time the grid voltage is negative. A DC meter connected to the grid with proper isolation so it won't short out the AC, will indicate the average voltage which may be anywhere from -5 to -40 volts. So the cathode current is flowing in short pulses at the oscillator frequency. Since the cathode is the only source of electrons in the tube the plate current is also flowing in short pulses with little or no current in-between pulses.

Grid 2 is connected to B+ and acts like a plate but it is a leaky plate. Electrons pass on through it to go on and be effected by the remaining 3 grids. Grid 3 is called the mixer grid and is where the station's signal comes in from the antenna. Because the oscillator signal is over driving the tube it is a nonlinear device and the sum and difference frequencies appear. Grid 4 is connected to B+ and so accelerates the electrons on there way to the plate.

Sometimes the impact of electrons on the plate causes electrons already there to be knocked loose. This is called secondary emission. If grid 5, called the suppressor grid, were not present these secondary electrons would go to the screen grid, grid 4, and take away from the plate current as described above. There are times in the AC cycle when the plate voltage is actually less than the screen voltage. The suppressor grid, which may be grounded or tied to the cathode, is negative enough to cause the secondary electrons to go back to the plate because they have no where else to go. The wires of grid 5 are widely spaced so it has little effect on the high velocity electrons on their way to the plate.

The tuned circuit in the plate of the converter tube is tuned to 455 kHz and is the primary of the first IF transformer. Short wave receivers are likely to have a higher intermediate frequency.

Doubly Balanced Mixers.

Singly Balanced Mixer.

In the late 50s there were two tube types made that would function as a singly balanced mixer. One, the 7360, was made for the specific purpose of generating single sideband suppressed carrier signals in communications equipment. The other, the 6AR8, was made to demodulate the chroma signal in color TV receivers. Both are shown schematically in Figure 4B.11.

Neither type is being manufactured today but because of supply and demand the 7360 is selling for about 10 times the price of the 6AR8.

In operation the electrons come out in a beam and if there is no potential difference between the two deflectors, the beam will strike both plates equally. An AC voltage applied to the control grid will cause an AC voltage to appear at the plates which is out of phase with the grid voltage but the voltage at the two plates will be in phase with each other.

For ease of understanding we will assume that both deflectors are driven with opposite phase voltages. This causes the electron beam to swing back and forth between the two plates. When the electron beam is on one plate that plate current will be high and the current on the other plate will be low. As the electron beam swings back the other way the current on the high current plate decreases and that on the low current plate increases. Thus the signals on the two plates are 180 degrees out of phase with each other.

To review then, the control grid causes in-phase voltages at the two plates, and the deflectors cause out of phase voltages at the two plates.

If there are two signals of different frequency applied to the control grid and deflectors the sum and difference frequencies will appear as for each plate the two signals are multiplied.

If the two plates were connected in parallel, the deflector voltage would be canceled while the control grid voltage would not. I have never seen a circuit like this. I suspect it produces quite a bit of distortion in this mode of operation.

Circuits I have seen connect the plates to the ends of a center-tapped transformer with B plus going to the center-tap. If you apply in-phase signals to the ends of a center-tapped transformer, there is no net magnetic field and no, or very little, voltage is induced in the secondary. This means that the voltage applied to the control grid will be canceled in the output. This is a singly balanced mixer.

If you apply a radio frequency of say 455 kHz to the control grid and audio to one of the deflectors, as shown in Figure 4B.12, the RF signal will be canceled in the transformer. The audio will not be canceled but the output transformer is a tuned circuit at 455 kHz and the audio signal won't come through. Because this device is a mixer the sum and difference frequencies will be created. These are the sidebands of an AM signal but the carrier is suppressed. We are generating a double-sideband suppressed-carrier signal on 455 kHz. It could be heterodyned to any desired frequency.

The Magic Eye Tube.

As the grid voltage is made negative, the plate voltage increases and the eye moves toward being closed as shown on the right above. The plate of the right hand triode is called the target and is the anode which is coated with the phosphor material as seen in the top picture above. The phosphor glows green when bombarded by electrons.

The grid of the right hand triode is called the "Shadow Control Grid" in Figure 4B.15 below. It is connected internally to the amplifier plate. The voltage on the "Shadow Grid" varies from a low of 25 volts to approximately 60 % of B+.

These tubes were used frequently as tuning indicators in deluxe radios from about 1935 into the 1950s. Most people could tune a radio by ear so their functionality was questionable.

The writer has heard a story, maybe true, maybe not, that some unscrupulous salesmen were telling people that if you looked into the eye and tuned in the station absolutely perfectly you could see what was going on in the radio studio. Nobody could ever achieve the level of perfection necessary to see Jack Benny, Bob Hope, et al.

Fraudulent claims not withstanding, the magic eye was used as a record level indicator on real to real tape recorders, (there weren't any other kind back then). It also turned up on a 2 meter transceiver as a modulation and power output indicator, as well as on an SSB exciter. Magic eye tubes have been used by radio hams and audio hobbyist in many applications for years.

The cathode ray tube.

If you told a service technician or maintenance engineer that he had to travel a great distance and work on an unknown piece of equipment, and he could only take one item of test gear, 999 out of 1,000 would take an oscilloscope. That 1,000th one would find himself up the proverbial creek without a paddle. An oscilloscope as it stands can measure voltage, time interval, and frequency. By the clever use of some resistors it can be used to measure current, resistance, capacitance and even transistor beta. Although there are digital multimeters that will measure all of these things the scope can still do something that no other test instrument can. That is show the shape of the wave. There are times when nothing will substitute for this.

The reader is referred to section 2.12 of this book for a detailed discussion of the cathode ray oscilloscope and its tube. There does not seem to be any point in repeating the information here.

TGTP (tuned plate tuned grid) oscillators are never used because changing the frequency requires turning the variable capacitors in two tuned circuits. If you want to play with one it usually helps to supplement the plate to grid capacitance with an external capacitor of 10 pf or so. If you use a pentode, the external capacitor is an absolute must.

Colpits and Hartley Oscillators.

In the Hartley oscillator the inductor is tapped and the tap may or may not be connected to AC ground. It also may or may not be connected to DC ground.

Figure 4B.16a shows a parallel fed Colpits oscillator. It is parallel fed because the DC plate current does not flow through the inductor. R₃ may be replaced by an RF choke if desired. C₃ keeps B+ from appearing across the variable capacitor which is generally a no no. If R₁ were not present, C₃ might not charge up and there would be B+ on the variable capacitor anyway. R₁ makes sure that the inductor and the outer plates of the variable capacitor are held at DC ground potential. The tuning capacitor is sometimes known as a split stator but is actually the familiar dual ganged capacitor. The rotor and drive shaft are at both AC and DC ground potential.

The capacitor is, in effect, center tapped. This will place the center of the coil at AC ground potential. The effect of this is to cause the AC voltage at one end of the tuned circuit to be 180 degrees out of phase with the AC voltage at the other end. Since the plate voltage is 180 degrees out of phase with the grid voltage, the voltage fed back to the grid has the proper phase to reinforce and sustain oscillation.

The two halves of the variable capacitor need to be the same size or in a constant ratio to one another. If the oscillator is to be tuned over a narrow range, the capacitor on the plate side may be fixed and the variable capacitor on the grid side would have a fixed capacitor in parallel with it to limit its tuning range.

The AC voltage supplied to the grid is considerable. On the positive peak it drives the grid positive and C₂ will be charged. When the grid is forced positive it begins to attract electrons to itself and current will flow. The grid acts like the anode of a diode. This current causes the capacitor to charge with the end of the capacitor which is toward the grid being negative. The grid never goes very far positive because the capacitor charges up and holds the charge. A small amount of charge leaks off through R₂ but gets replenished on the next positive half cycle. A substantial average DC voltage, as much as -50 volts, is developed at the grid and this voltage makes the oscillator self adjusting. The negative bias lowers the gain of the tube and it will set itself to exactly what is needed to sustain oscillation. When the grid voltage goes negative, in most oscillators this will drive the tube into cutoff. This will cause the plate current to flow in short pulses but the tuned circuit rings like a bell and the waveform at the grid is a very good sine wave. The wave at the plate may not be as good.

This is still a series fed circuit because the cathode current flows through the coil. You will note that the tap has been moved from the center to near one end and that end of the coil has been grounded. This removes B+ from the capacitor and permits the drive shaft to be at ground potential.

The reason for moving the tap has to do with gain around the loop. A center tapped inductor gives phase inversion and unity gain. With the tuned circuit connected from plate to grid the tube provides gain enough to ensure the oscillator will start and keep going. In figure 4B.17b the tube is now a cathode follower which has a little less than unity gain. The coil acts as an auto transformer and steps up the voltage applied to the tap. The top to tap ratio is typically 10 to 1. The cathode follower does not invert the phase and neither does the coil since both connections are on the same side of the ground point.

The cathode coupled series fed Hartley oscillator has become the most popular oscillator circuit among receiver design engineers. In addition to the ubiquitous All American 5 it is found in short wave, and ham receivers from about 1940 on.

Figure 4B.18a shows a parallel tuned Colpits Oscillator. The inductor labeled RFC is an RF choke. It is used in place of a resistor to provide a high impedance to the oscillator and at the same time a low DC resistance. The tuned circuit requires a high parallel impedance. If a resistor were used it would have to be of such a high value as to reduce the plate current of the tube to a very low value. If it were lowered to get the plate current up it would adversely effect the Q of the tuned circuit.

Remember that a series tuned circuit has minimum impedance at resonance. Just a little off resonance, on the high side, it is still a low impedance but appears inductive. A low inductive reactance means a small apparent inductance. It may seem as if the Q is low but the basic LC circuit has a high Q which will make the oscillator very stable.

Oscillator Stability.

As the last sentence of the previous paragraph indicates, the drift of an oscillator can't be eliminated, just minimized. Let's first examine the causes of drift and then see how they can be minimized.

The main cause of frequency drift is a change in temperature. In vacuum tube equipment the heat generated by the tubes is unavoidably transferred to the elements of the tuned circuit.

As the inductor warms up the wire making up the coil gets longer. The form on which the coil is wound gets larger in diameter, and all that translates into a larger inductance.

In an air capacitor such as a variable, The plates get bigger and farther apart. Those two effects may seem to cancel each other and they do to some extent. In ceramic and mica capacitors the dielectric, (insulator), usually has a temperature coefficient all its own. This can be adjusted by the manufacturer to give a capacitor a positive, zero, or negative temperature coefficient.

The coil is sitting there with its big positive temperature coefficient so if we can incorporate a negative coefficient into the resonating capacitor this will go a long way toward making the oscillator stable.

Another source of instability is the change in tube capacitance. This change occurs much faster than those caused by warming up of the coil and capacitor. An attempt to compensate for changes in tube capacitance could result in an oscillator that would drift down in frequency until the tube reaches its operating temperature and then up as the coil and capacitor start to feel the heat from the tubes.

The trick here is to make the fixed capacitors in the circuit so large that the tube capacitances will be a small part of the total. In any of the circuits the capacitor can be made larger and the inductor smaller. This can only be carried so far. This will result in a lower Q because a coil which is too small for the frequency will have more resistance in relation to its inductance.

The parallel tuned Colpits goes somewhat in this direction. The ARRL Radio Amateurs Handbook recommends for an oscillator to tune from 3.5 to 4 MHz, that C₃ be 680 pf and C₄ be 0.0022 uf. For the Clap oscillator they recommend that C₃ and C₄ both be 0.001 uf. Although the writer once owned a VFO, (Variable Frequency Oscillator), made by E. F. Johnson that used 0.005 uf capacitors for C₃ and C₄.

Electron Coupled Oscillator, (ECO).

Notice that the screen voltage needs to be regulated and it doesn't hurt to regulate the plate voltage as well. The tuned circuit in the plate serves to clean up the waveform which is not a good sine wave if a resistor is used. R₂ lowers the Q of L₂ and C₆ so it does not have to be tuned along with C₁ and L₁.

This oscillator can be plugged into the crystal socket on a 50 or 75 watt transmitter. If used as part of a transmitter it should be followed by a class A pentode stage before going into the class C stages. If used in a receiver or transceiver the output could probably be fed straight to the mixer.

Crystal Oscillators.

The crystal is cut into thin rectangular plates along a particular axis of the crystal. The subject of quarts crystals can fill a book all its own. No attempt will be made here to delve into the various orientations in which a crystal can be cut.

Every physical object has a mechanical resonant frequency. Some are low enough to hear such as a common drinking glass filled, or partly filled, with water. Early TV remote controls used aluminum rods about 3/8 inch in diameter and about 2 inches long. When one of these rods was struck on the end it would ring at a frequency above the range of human hearing. A specially designed microphone in the TV set would pick up the ultrasonic frequencies and after amplification a set of tuned circuits allowed the particular rod being struck to initiate the corresponding function. The tiny plates of quarts have mechanical resonant frequencies that are in the radio frequency range. When this mechanical resonance is translated into electrical resonance by the piezoelectric effect, the crystal exhibits the resonance of the circuit of Figure 4B.20a.

Figure 4B.20b is the circuit of a Colpits oscillator. It operates the crystal in its parallel resonant mode. There are many crystal oscillator circuits but this is by far the best one for almost all crystals. Typical values for the capacitors are 33 pf for grid to cathode and 100 to 220 pf for cathode to ground.

The output may be taken off the cathode or if a cleaner waveform is desired a pentode may be used with a tuned circuit in its plate circuit as shown in figure 4B.19 above.

There is only one way to change the frequency of a crystal oscillator. Order a new crystal and when it comes in the mail, plug it into the socket. That's the price to be paid for a high degree of stability. In Chapter 9 of this book we will study the frequency synthesizer which gives both the agility of a tunable oscillator and the stability of a crystal oscillator. It would not be practical to construct one of these devices with vacuum tubes.

1. The plate resistance of the pentode section of a 6U8 is 0.4 Meg ohms. The RC amplifier data for it is as follows.

   E_bb = 250 volts.
   R_b = 270 k ohms.
   R_cf = 1.0 Meg ohms.
   R_c2 = 820 k ohms.
   R_k = 1200 ohms.
   V_in = 0.1 v.
   V_out = 22.0 v.
   Gain = 220.
   % Dist = 0.82 %.
   

   Calculate (a) the transconductance of the pentode under the above conditions, and (b) the gain of the amplifier if the cathode bypass capacitor is removed and the screen is bypassed to the cathode.

2. A ham band receiver has a first IF of 2250 kHz, and the local oscillator operates above the incoming frequency. If the receiver is tuning the 3.5 to 4.0 MHz band what is the frequency range of the image?

3. A doubly balanced mixer has the following input frequencies, 3.5 MHz, and 60 kHz. What frequencies will be present in its output?

4. A singly balanced mixer has the following input frequencies, 1.5 MHz to the balanced input, and 2.5 MHz to the unbalanced input. What frequencies will be present in its output?

5. The AGC voltage of a radio receiver is about -1 volt between stations and changes to -10 volts when a particular station is tuned in. A tuning eye (magic eye tube) in this radio will be,

   (a) closed when between stations and open when a station is tuned in.

   (b) open when between stations and closed when a station is tuned in.

6. A wave on an oscilloscope is 3.4 cm from the lowest to the highest point and 2 complete cycles cover 8.7 cm. The controls on the scope are set as follows. Vertical to 50 milli volts/cm and time-base to 20 nsec/cm. A times 10 probe is in use. What is the RMS voltage of this wave?

7. A wave on an oscilloscope is 3.4 cm from the lowest to the highest point and 2 complete cycles cover 8.7 cm. The controls on the scope are set as follows. Vertical to 50 milli volts/cm and time-base to 20 nsec/cm. A times 10 probe is in use. What is the frequency of this wave?

8. An oscillator with a tapped coil is a;

   (a) Hartley.

   (b) Colpits.

   (c)Clap.

9. An oscillator with the inductor and variable capacitor in series is a;

   (a) Hartley.

   (b) Colpits.

   (c)Clap.

10. In an oscillator employing a tapped coil, When the coil is connected to the plate and grid the tap is;

    (a) at the center of the coil.

    (b) near one end.

11. In an oscillator employing a tapped coil, When the coil is connected to the cathode and grid the tap is;

    (a) at the center of the coil.

    (b) near one end.

12. In any of the oscillator circuits employing a triode tube the best waveform is found at;

    (a) the cathode.

    (b) the grid.

    (c) the plate.

13. In an ECO the signal is coupled from the oscillator to the output by;

    (a) capacitive coupling.

    (b) magnetic inductive coupling.

    (c) the electrons inside the tube.

1. (a) 1,585 micro mhos, (b) 98.0.

2. 8.0 MHz to 8.5 MHz.

3. 3440 kHz and 3560 kHz.

4. 1.0 MHz, 2.5 MHz, and 4.0 MHz.

5. (b)

6. 1.7 volts.

7. 11.5 MHz.

8. (a)

9. (c)

10. (a)

11. (b)

12. (b)

13. (c)