53Diode and Triode valves

📚
DIODE AND TRIODE VALVES
▢ Thermionic Emission:
❖ Definition: Emission of electrons from metal surface when heated suitably
❖ Also Called: Edison effect
❖ Discovered By: Edison
❖ Emitted Electrons: Thermions / thermal electrons

Table 1: Thermionic Emission Formulae

Quantity
Formula / Meaning
Richardson-Dushman equation
\(I=A_0ST^2e^{-W_0/kT}\)
Current density
\(J=\frac{I}{S}=A_0T^2e^{-W_0/kT}\)
Temperature relation
\(J\propto T^2\)
Work function relation
Lower \(W_0\) → more electron emission
❖ Symbols:
  • •
    \(I\) = thermionic current
  • •
    \(S\) = surface area of metal
  • •
    \(T\) = absolute temperature in Kelvin
  • •
    \(k\) = Boltzmann constant \((1.38\times10^{-23}J/K)\)
  • •
    \(A_0\) = emission constant
  • •
    \(W_0\) = work function
❖ Electron Emitter Requirements:
  • •
    High melting point
  • •
    Low work function
  • •
    Good conductor of heat and electricity
❖ Important Points:
  • •
    Thermionic emission occurs at different temperatures for different materials
  • •
    Thermions may have different kinetic energies and velocities
  • •
    Thermionic process does not depend on melting point alone
▢ Types of Electron Emitters:

Table 1: Directly vs Indirectly Heated Emitter

Feature
Directly heated emitter
Indirectly heated emitter
Structure
Tungsten filament coated with barium oxide acts as cathode
Metal cathode sleeve surrounds filament; sleeve coated with barium oxide
Heating
Current passes directly through cathode filament
Filament heats cathode indirectly
Thermionic current
Less
More
Life
Small
More
Energy consumption
Small
More
Noise
Noise may be produced in thin emitter
Noise not created
▢ Diode Valve:
❖ Definition: Simplest thermionic tube containing two electrodes
❖ Invented By: Sir Fleming
❖ Based On:
  • •
    Thermionic emission
  • •
    Edison effect

Table 1: Diode Valve Parts

Part
Function / Material
Cathode
Emits electrons
Plate / Anode
Hollow metallic structure surrounding cathode; collects electrons
Anode material
Nickel / molybdenum / tungsten
Envelope
Highly evacuated glass tube
❖ Working:
  1. Current from low tension battery heats filament/cathode
  2. Cathode emits electrons by thermionic emission
  3. Number of emitted electrons per second is controlled by filament current
  4. If plate is positive w.r.t. cathode, electrons reach plate and plate current flows
  5. If plate is negative w.r.t. cathode, electrons do not reach plate and plate current becomes zero
  6. If plate potential is zero, plate current is generally zero/very weak
❖ Current Direction:
  • •
    Conventional current in diode battery: plate → cathode
  • •
    Electron current: cathode → plate/anode
❖ Uses:
  • •
    Rectifier
  • •
    Modulator
  • •
    Detector
▢ Space Charge:
❖ Definition: Negative electron cloud formed near cathode when plate potential is insufficient to attract all emitted electrons
❖ Effect: Space charge repels electrons emitted from cathode
❖ Condition: Occurs at low plate potential
▢ Diode Characteristic Curve:
❖ Definition: Graph between plate current \((I_p)\) and plate potential \((V_p)\) for constant filament current

Table 1: Regions of Diode Characteristic Curve

Region
Name
Main Feature
Law / Formula
OA
Space-charge limited region
Effect of filament current negligible; \(I_p\) changes with \(V_p\)
\(I_p=KV_p^{3/2}\)
A→B / A→C / A→D
Temperature-limited region
Effect of plate potential negligible; \(I_p\) changes with filament current
Richardson equation applicable
Saturation region
Plate current becomes constant
\(r_p=\infty\)
❖ Important Points:
  • •
    Diode valve is non-linear / non-ohmic device
  • •
    Before saturation, diode follows Child's three-half power law
  • •
    After saturation, plate current can be increased only by increasing filament current
  • •
    On increasing plate voltage, plate current first increases and then becomes constant
▢ Child's Three-Half Power Law:
❖ Statement: In space-charge limited region, plate current varies as three-half power of plate voltage
❖ Formula: \(I_p\propto V_p^{3/2}\)
❖ Also: \(I_p=KV_p^{3/2}\)
▢ Triode Valve:
❖ Discovered By: Lee De Forest
❖ Definition: Thermionic valve having three electrodes: cathode, grid and plate

Table 1: Triode Parts

Electrode
Symbol
Function
Cathode
\(K\)
Emits electrons
Grid
\(G\)
Controls electron flow from cathode to plate
Plate / Anode
\(P\)
Collects electrons
❖ Grid:
  • •
    Third electrode placed between plate and cathode
  • •
    Thin conducting cylindrical mesh surrounding cathode
  • •
    Placed nearer to cathode than anode
  • •
    Usually kept slightly negative w.r.t. cathode
  • •
    If grid is positive, electrons may hit grid instead of plate
❖ Plate: Always kept positive w.r.t. cathode
❖ Important Points:
  • •
    If grid is at zero potential, triode behaves like diode
  • •
    Current in plate circuit is controlled by grid
  • •
    Plate current direction is plate → cathode
  • •
    Triode can be used as amplifier, oscillator and modulator
▢ Triode Characteristic Curves:

Table 1: Static Characteristics

Type
Graph
Condition
Plate characteristics
\(I_p\) vs \(V_p\)
\(V_g\) constant, no load
Mutual characteristics
\(I_p\) vs \(V_g\)
\(V_p\) constant, no load

Table 2: Dynamic Characteristics

Type
Graph
Condition
Plate characteristics
\(I_p\) vs \(V_p\)
\(V_g\) constant, with load
Mutual characteristics
\(I_p\) vs \(V_g\)
\(V_p\) constant, with load
❖ Important Point: While using triode as amplifier, grid is not made positive because mutual characteristic is not straight
▢ Triode Constants:

Table 1: Amplification Factor, Plate Resistance and Mutual Conductance

Constant
Symbol
Definition
Formula
Amplification factor
\(\mu\)
Ratio of change in plate potential to change in grid potential for same change in plate current
\(\mu=\left(\frac{\Delta V_p}{\Delta V_g}\right)*{I_p}\)
Plate resistance
\(r_p\)
Ratio of change in plate potential to change in plate current at constant grid voltage
\(r_p=\left(\frac{\Delta V_p}{\Delta I_p}\right)*{V_g}\)
Mutual conductance
\(g_m\)
Ratio of change in plate current to change in grid voltage at constant plate potential
\(g_m=\left(\frac{\Delta I_p}{\Delta V_g}\right)*{V_p}\)
❖ Relation: \(\mu=r_pg_m\)
❖ Amplification Factor:
  • •
    \(\mu>1\)
  • •
    \(\mu\) is unitless and dimensionless
  • •
    \(\mu\) increases when distance between grid and cathode decreases
  • •
    At constant plate potential, if grid is moved closer to plate, amplification factor decreases
❖ Plate Resistance:
  • •
    Depends on plate voltage
  • •
    Depends on grid voltage
  • •
    Depends on relative separation and size of plate, grid and cathode
  • •
    In cut-off bias or saturation state, \(r_p=\infty\)
❖ Mutual Conductance:
  • •
    Equal to slope of mutual characteristic curve
  • •
    Depends on separation between grid and cathode
  • •
    Smaller separation → larger \(g_m\)
  • •
    In saturation state, \(\Delta I_p=0\), so \(g_m=0\)
▢ Triode as Amplifier:
❖ Use: Converts small input signal into large output signal

Table 1: Amplifier Points

Fact
Answer
Voltage gain in triode
Depends on plate resistance
Cascaded amplifier gain
\(A_v=A_1\times A_2\times A_3\times...\times A_n\)
Positive grid avoided
Mutual characteristic is not straight
Grid function
Controls plate current
▢ Filter Circuit:

Table 1: Filter Components

Component
Function
Inductance
Smooths current
Capacitor
Smooths voltage
▢ Getter:
❖ Definition: Gas-absorbing material used in triode/valve
❖ Function: Maintains high vacuum by absorbing residual gases
▢ Read and Digest:

Table 1: Important Points

Fact
Answer
Thermionic emission
Emission of electrons from heated metal surface
Thermionic emission discovered by
Thomas Edison
Thermions
Thermal electrons
Richardson-Dushman equation
\(I=A_0ST^2e^{-W_0/kT}\)
Good emitter
High melting point, low work function, good conductor
Diode valve
Two-electrode thermionic tube
Diode invented by
Sir Fleming
Diode use
Rectifier, modulator, detector
Space charge
Electron cloud near cathode
Child's law
\(I_p\propto V_p^{3/2}\)
Diode characteristic
Non-linear / non-ohmic
Temperature-limited region
\(r_p=\infty\)
Triode discovered by
Lee De Forest
Triode electrodes
Cathode, grid, plate
Triode grid
Controls plate current
Triode plate
Positive w.r.t. cathode
If grid voltage is zero
Triode behaves like diode
Plate current direction
Plate to cathode
Amplification factor
\(\mu=\left(\frac{\Delta V_p}{\Delta V_g}\right)*{I_p}\)
Plate resistance
\(r_p=\left(\frac{\Delta V_p}{\Delta I_p}\right)*{V_g}\)
Mutual conductance
\(g_m=\left(\frac{\Delta I_p}{\Delta V_g}\right)*{V_p}\)
Triode constant relation
\(\mu=r_pg_m\)
Cascaded amplifier gain
\(A_v=A_1A_2...A_n\)
▢ Objective Answer Key:

Table 1: Diode and Triode Valves MCQ Answers

Q
Ans
1
a
2
a
3
b
4
b
5
c
6
b
7
b
8
c
9
d
10
c
▢ High-Yield Recall:

Table 1: Diode and Triode One-Liners

Fact
Answer
Thermionic emission
Electron emission from heated metal
Edison effect
Thermionic emission
Thermions
Thermally emitted electrons
Richardson-Dushman
\(I=A_0ST^2e^{-W_0/kT}\)
Current density
\(J=A_0T^2e^{-W_0/kT}\)
Emitter requirement
High melting point, low work function
Diode valve
Cathode + plate
Diode inventor
Sir Fleming
Plate positive
Current flows
Plate negative
No plate current
Space charge
Electron cloud near cathode
Child law
\(I_p\propto V_p^{3/2}\)
Diode nature
Non-ohmic
Diode use
Rectifier
Triode inventor
Lee De Forest
Triode electrodes
Cathode, grid, plate
Grid
Controls plate current
Plate
Always positive w.r.t. cathode
Amplification factor
\(\mu=\frac{\Delta V_p}{\Delta V_g}\)
Plate resistance
\(r_p=\frac{\Delta V_p}{\Delta I_p}\)
Mutual conductance
\(g_m=\frac{\Delta I_p}{\Delta V_g}\)
Triode relation
\(\mu=r_pg_m\)
Triode uses
Amplifier, oscillator, modulator
Getter
Gas absorber
Filter inductor
Smooths current
Filter capacitor
Smooths voltage
Q1.
Child's law relation is
📅BP 2011
Q2.
At constant plate potential, if the grid is moved closer to the plate, amplification factor of triode is
📅IE
Q3.
The dynamic resistance of a vacuum tube diode in saturation region will be
Q4.
Before saturation state of a diode, at plate voltages 400 V and 200 V respectively, the currents are I1 and I2. The ratio I1/I2 will be
Q5.
The plate resistance of a triode is 3 × 10^3 Ω and its mutual conductance is 1.5 × 10^-3 mho. The amplification factor will be
Q6.
A triode has mutual conductance 2 × 10^-3 mho and amplification factor 50. The anode is connected through resistance 25 kΩ to 250 V supply. The voltage gain of this amplifier is
Q7.
The amplification factor of a triode is 20. If grid voltage is reduced by 1 V, how much should plate voltage be increased so that plate current remains constant?
Q8.
In a triode valve, current in the plate circuit is controlled by
Q9.
In a triode, the grid is at -2 V with respect to cathode. An electron is ejected with initial kinetic energy 5 eV. The energy of electron when it reaches the grid is
Q10.
In a diode valve, a change in anode voltage from 200 V to 240 V at constant grid voltage produces increase of anode current from 5 mA to 9.6 mA. The AC anode resistance is