Vacuum tube theory
Edison Effect
Thermionic emission
Thermionic emission is the emission of electrons from the surface of a heated cathode or filament.
Type of Cathodes: directly heated, indirectly heated
Many Directly heated triodes (DHT) have been the sought-after tubes for audiophiles. Popular power DHTs are 10, 10Y, 45, 50, 71, 2A3, 6A3, 6B4G, 300B, 211, 805, 845.
Cathode materials
Material / Working temp., ℃ / featuresTungsten / 2200-2500 / 1. High temperature
2. Long life
3. High emission, high power
Thoriated tungsten / 1900 / 1. Thorium is a low radiative material. It emits mainly alpha particles.
2. Lower working temperature
3. Long life
4. High emission, high power (211, 805, 845).
Oxide coated / 800-1150 / 1. The most common coatings are of strontium and barium oxides.
2. Low working temperature.
3. Used for receiving tubes.
The diode
Space Charge: Electrons are emitted to form the cloud of electrons around the cathode, with each electron containing one negative charge, makes this area highly negative and thus gives it the name “space charge”. For any given cathode material at a certain given temperature, only so many electrons can be contained in the electron cloud. Other electrons will be prevented from entering the cloud from the cathode unless electrons in the cloud leave, as some do when the plate is made positive.
Plate dissipation
Diode circuit
- Half Wave
- Full Wave
Indirectly heated full wave rectification
Directly heated full wave rectification
The Triode
(a) Basic indirectly heated triode circuit (b) Basic directly heated triode circuit
Typical grid structures
The grid controls the amount of current flowing from cathode to plate. As the grid is more negative, the electrostatic force from the grid to repel the amount of current flowing from cathode to plate is larger. Thus the more negative the grid, the less the current flows from cathode to plate.
The triode tube is often called a valve, which is descriptive of the way that the grid controls the currents the current flow from cathode to plate.
Positive Grid Voltage
With the grid positive, some of the electrons will flow in the grid circuit to the grid battery. This current is called grid current.
In most applications the grid new goes positive. There are some cases, however, when the grid is made positive for a short period of time in each cycle. Some examples are in the horizontal amplifier in television sets and in radio transmitters and oscillators.
Static Grid-Voltage Curves (Plate Characteristics)
Plate current VS plate voltage for E88CC
Amplification Factor, μ(mu)
Where
is the change of anode voltage
is the change of grid voltage
When calculating from the equation, we will obtain a negative mu. This means there is a phase inverse between the grid voltage change and the anode voltage change.
Calculation of Amplification Factor
6DJ8: 33
12AU7:
Anode Resistance: ra (or Plate Resistance, rp)
Plate resistance is slightly different from point to point. It can be calculated by:
Where
is the change of anode current
Mutual Conductance (or transconductance): gm
The mutual conductance gm of a valve is the ratio of the change in anode current to the change in grid voltage , with anode voltage held constant.
The unit of gm is 1/Ohm (A/V), which is called mho. Instead of using mho, which may be too big, it is common to use μmho.
1 μmho = 10-6 mho1
Relationship between ra, gm and μ.
Ex. Using the following 6DJ8 Plate Characteristics diagram to find its mu, gm, ra.
6DJ8 Plate Characteristics diagram
Grounded Cathode Amplifier
1.Easily biased.
2. Small part count.
3. Miller Effect capacitance.
4. Gain never exceeds the mu of the tube in use.
5. The plate resistor can be replaced with a constantcurrent source, either tube or solid-state.
6. The maximum voltage occurs when (roughly): Rk = (ra + Rp) / μ.
7. If the cathode resistor is bypassed, both the gainand the distortion will increase, while the outputimpedance will decrease.
8. The cathode resistor could be replaced with adiode or LED or a precision voltage reference ICor even a rechargeable ni-cad battery.
1. Grid Bias (Fixed Bias)
Load Line
Plate characteristics for 12AX7 (ECC83)
Find mu and ra
voltage gain of the fixed bias amplifier
- Self Bias (Cathode Bias)
(2.1) Cathode decoupling (or bypass) capacitor
Capacitor Cin is the input coupling capacitor. It is used to isolate the grid circuit from the DC voltage at the output of the previous circuit.
Rg is the grid resistor, which is used to provide a reference voltage for the grid circuit (ground in this case). It is usually a high value but normally should not exceed 1 MΩ. This resistor controls the input impedance of the stage.
Rk is the cathode resistor, which is used to develop the cathode bias voltage.
Capacitor Ck is used to bypass the cathode resistance to ground for AC signals, which results in a higher gain. Without Ck, there is negative feedback, or degeneration, which reduces the gain of the stage and increases the output impedance.
Resistor Rp is the plate load resistor. The output signal voltage is developed across this resistor, by the action of the plate current flowing through it.
Capacitor Cout is the output coupling capacitor. It is used to isolate the plate DC voltage from the next stage it is driving.
Input Impedance
Output Impedance
voltage gain
Frequency response due to input circuit:
The low frequency response due to the input circuit is controlled by Cin and Rg. These components act as a high-pass filter with a -6dB/octave (-20dB/decade) slope and a lower -3dB point that can be calculated as follows:
The high frequency response due to the input circuit is controlled by the output resistance of the stage driving the common-cathode stage and the input capacitance of the stage. The input capacitance is governed primarily by the Miller capacitance of the stage, and can be calculated as follows:
Cin =Cgk + Cgp*(Av + 1)
where:
Cgk = the grid-to-cathode capacitance
Cgp = the grid-to-plate capacitance
Av = the stage voltage gain
Frequency response due to output circuit
The low frequency response due to the output circuit is controlled by Cout, and the output impedance of the stage. If the input impedance of the next stage is very high, then the low -3dB point that can be calculated as follows:
If the output impedance is low when comparing to Rout, the above equation can be approximated as follows:
Frequency response due to the cathode decoupling capacitor
Where R is the resistance that the cathode capacitor sees.
(2.2) unbypassed cathode bias
Input Impedance
Output Impedance
The internal plate resistance will increase if there is negative feedback due to an unbypassed cathode resistor, and the voltage gain of the stage will decrease as well.
ra'(unbypassed Rk) = ra + (μ+ 1)*Rk
Voltage Gain
Frequency response due to input circuit:
Frequency response due to output circuit
If the output impedance is low when comparing to Rout, the above equation can be approximated as follows:
Miller capacitance
CMiller = (A+1) Cag
Where Cag is the grid to plate interelectrode capacitance.
Maximum Rating
1. Maximum plate dissipation
Normally the maximum plate dissipation is not a problem for line amplifier or voltage amplifier. However it should be taken care of in the power output stage since we always want to get the maximum output from a tube.
2. Maximum plate voltage
This is the voltage between the cathode and the plate.
3. Maximum Grid Resistance, Rg
The input grid resistor should not normally exceed 1 megaohm with indirectly-heated valves. The output grid resistor may be the maximum recommended for the following stage by the valve manufacturers – usually 0.5 megaohm for power valves with cathode bias.
Ex. 2A3 directly heated triode
EX. 6DJ8
4. Peak heater-cathode voltage
Ex. 6DJ8
The Tetrode
Screen grid
Secondary Emission
The Pentode
Screen Grid and Suppressor or Suppress Grid
Using the EF86 small-signal pentode
gm = mu/ra = 5000/2500000 = 0.002 mho = 20,000 micromho
Gain= gm x Rp
= 20,000 x 10-6 x 47 x 103
= 94
The Beam Power Tetrode
6L6
Cathode Follower (CF)
The cathode follower has a voltage gain of slightly less than 1, a low output resistance, typically less than 1 kΩ, a high input resistance, and is non-inverting. The cathode follower is an excellent buffer stage for driving a tone stack, effects loop, power valve or any circuit which would otherwise present a heavy load to a "normal" stage. The cathode follower also produces a unique quality compression when DC coupled, which is to be found in most of the classic amp designs.
1. Fixed bias cathode follower
The cathode follower is simply a special case of the common cathode amplifier with 100% negative feedback.
A0 is the gain of the original grounded cathode amplifier.
output resistance
Where
2.Cathode bias cathode follower
For cathode bias cathode follower and DC direct-coupling cathode follower, their heater voltage may need to be elevated.
Design Example
76 and 6SN7 cathode follower line stage
The Shunt Regulated Push-Pull (SRPP) amplifier
output resistance
Grounded Grid Amplifier
1