**Characteristic
Curves of a Diode**

A graph represents the variation of \({{i}_{p}}\) with \({{V}_{p}}\) at a given filament current \(\left( {{i}_{f}} \right)\) is known as characteristic curve.

The curve is not linear hence diode valve is a non – ohmic device.

**1) Space charge limited region (SCLR):
**In this region
current is space charge limited current. Also, \({{i}_{p}}\propto
V{}_{p}^{3/2}\)\(\Rightarrow {{i}_{p}}=kV_{p}^{3/2}\) ; where \(k\) is a constant
depending on metal as well as on the shape and area of the cathode. This is
called child’s law.

**2) Linear region (LR):** In this region \({{i}_{p}}\propto
{{V}_{p}}\)

**3) Saturated region (SR) or
Temperature limited region (TLR):**
In this part, the current is independent of potential difference applied
between the cathode and anode.

\({{i}_{p}}\ne f\left( {{V}_{p}} \right)\) , \({{i}_{p}}=f\left( Temperature \right)\)

The saturation current follows Richardson Dushman equation i.e. \(i=AS{{T}^{2}}{{e}^{-{{\phi }_{0}}/kT}}\)

Where,

\(A=\) Emission constant =\(\frac{4\pi me{{k}^{2}}}{{{h}^{3}}}amp/{{m}^{2}}-{{k}^{2}}\);

S = Area of emitter in m^{2};

T = Absolute temperature in K;

\({{\phi }_{0}}\) = Work function of metal in Joule;

\(k=\) Boltzmann constant

The small increase in \({{i}_{p}}\) after saturation stage due to field emission is known as Shot-key effect.

**4) Diode Resistance: **

i) Static plate resistance (or) dc place resistance, \({{R}_{p}}=\frac{{{V}_{p}}}{{{i}_{p}}}\)

ii) Dynamic (or) ac plate resistance: If at constant filament current, a small change \(\Delta {{V}_{p}}\) in the plate potential produces a small change \(\Delta {{i}_{p}}\) in the plate current, then the ratio \(\Delta {{V}_{p}}/\Delta {{i}_{p}}\) is called the dynamic resistance (or) the plate resistance of the diode, \({{r}_{p}}=\frac{\Delta {{V}_{p}}}{\Delta {{i}_{p}}}\)

iii) In SCLR: \({{r}_{p}}<{{R}_{p}}\) ; In TLR: \({{R}_{p}}<{{r}_{p}}\) and \({{r}_{p}}=\infty \)

**5) Uses of Diode valve: **i) As a rectifier ii) As a detector iii) As a
transmitter iv) As a modulator