# Characteristic Curves of a Diode

## 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 m2;

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