Electronics Vaccum Tube Formulas

1. Work function

The minimum amount of energy to be given per electron to enable it to cross the potential barrier and come out of a metal surface is called work function.

2. Electronic emission

• Thermionic emission (by giving energy in the form of heat).
• Field emission (by applying a strong electric field)
• Photo-electric emission (by giving energy by light or radiations)

3. Thermionic emmission

According to Rechardson Dushman equation, current density
J = AT² e^-╬ª/kT (A/m²)
If ╬ª is in eV then J = AT² e^{-11600╬ª/T}
For a good emitter the work function must be low and the material should have the capacity to bear high temperatures (melting point must be high). Alkali-oxide coated indirectly heated emitters are good emitters.

4. Characteristics of diode

Diode have two electrodes called plate and cathode.

Characteristic curve is I_p – V_p curve. It has three parts:
(a) Space charge controlled region
I_p ∝ V_p^3/2 (Child’s law)
(b) Linear region: ΔI_p ∝ ΔV_p
(c) Saturation region (temperature controlled region) I_p is constant.

5. Dynamic or plate resistance of a diode

r_p = \(\left(\frac{\Delta V_{p}}{\Delta I_{p}}\right)\) ohm

6. Half wave rectifier

All factors are same as semiconductor diode rectification, accept using

7. Full wave rectifier

All factors are same as semiconductor diode rectification

8. Uses of diode

Diode are used in

• Rectifiers
• Detectors and
• Switches

9. Triode

It is a three electrode valve. Electrodes are

• Plate
• Detectors and
• Grid

Grid is mesh like structure which controls the space charge.

10. Chracteristics of triode

• Plate characteristics : Graph between I_p and V_p keeping V_g constant.
• Mutual characteristic : Graph between I_p and V_g keeping V_p constant.

11. Constants of triode

(a) Dynamic plate resistance r_p = \(\left(\frac{\Delta \mathrm{V}_{\mathrm{p}}}{\Delta \mathrm{I}_{\mathrm{p}}}\right)_{\mathrm{v}_{\mathrm{g}}}\) ohm

(b) Mutual conductance g_m = \(\left(\frac{\Delta \mathrm{I}_{\mathrm{p}}}{\Delta \mathrm{V}_{\mathrm{p}}}\right)_{\mathrm{V}_{\mathrm{p}}}\) mho

(c) Amplification factor ┬╡ = \(\left(\frac{\Delta \mathrm{V}_{\mathrm{p}}}{\Delta \mathrm{I}_{g}}\right)_{\mathrm{I}_{\mathrm{p}}}\)

(d) µ = g_m × r_p

(e) I_p = K \(\left[\mathrm{V}_{\mathrm{g}}+\frac{\mathrm{V}_{\mathrm{p}}}{\mu}\right]^{3 / 2}\)

12. Load line

The line representing the relation between plate current I_p and plate voltage E_b in the presence of load R_L. Equation is
I_p = \(\left(-\frac{1}{R_{1}}\right)\)E_b + \(\frac{E_{b b}}{R_{1}}\)
Slope = –\(\frac{1}{\mathrm{R}_{1}}\)
Point of intersection on E_b axis is (E_bb, 0) and on I_p axis (0, E_bb/R₁).

13. Triode amplifier

Voltage gain A = \(-\frac{\mu R_{1}}{r_{p}+R_{1}}\)
\(-\frac{\mu}{\left(1+r_{p} / R_{1}\right)}\)
The output and input voltages differ in phase by π.
|A_max| = ┬╡
For an input signal e_g –
Output signal current \(\mathrm{i}_{\mathrm{p}}=\frac{\mu \mathrm{e}_{\mathrm{g}}}{\mathrm{r}_{\mathrm{p}}+\mathrm{R}_{1}}\)
Output signal voltage \(v_{0}=\frac{\mu \mathrm{e}_{\mathrm{g}} \mathrm{R}_{\mathrm{L}}}{\mathrm{r}_{\mathrm{p}}+\mathrm{R}_{\mathrm{L}}}\)

14. Uses of triode

Tridoes are used in

• Amplifiers
• Oscillators
• Modulators

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