Diode Formulas & Equations – Zenner, Shockley & Rectifier

Electrical Technology

Shockley, Zenner & Diode Rectifier Formulas and Equations

Table of Contents

Diode Equation for I-V Curve

The I-V curve (diode characteristic curve) can be find by the following no linear equations. This equation is also known as Ideal Equation of Diode or Diode Law.

i = I_S ( e^qv/kT – 1 )

Where:

i = Current flowing through the diode
I_s = Reverse or dark saturation current (Typical value for silicon is 10^-12 Amperes)
e = Base of the neutral logarithm (2.71828)
q = Charge on electron (1.602 x 10^-19) in coulombs (Absolute Value of electron charge).
v = Applied voltage across the diode
k = Boltzmann’s constant (1.380 x 10^-23 jouals/Kelvin)
T = Absolute Temperature in Kelvin (Typical Room Temp is 300 Kelvin)

Shockley Diode Equation:

Where

I_D= current through the diode
V_D= diode voltage
I_s = leakage or reverse saturation current
n = emission coefficient or ideality factor, for germanium n=1, for silicon it ranges in 1.1-1.8.
V_T= thermal voltage which is

Where

q = charge of electron = 1.6022 x 10^-19 coulomb
T = absolute temperature in Kelvin (K = 273 + °C)
k = Boltzmann’s constant = 1.3806 x 10²³J/K

Zenner Diode Formulas & Equations

You may check the Zener diode based regulator calculator in the previous post.

Series Current

I_S= V_IN – V_Z/R_S ….. (Ohm’s Law)

Zener Current

I_Z = I_S – I_L

Load Current

I_L = V_L/R_L

Load Voltage

V_L= V_Z

Change in Load Voltage

∆V_L = I_Z R_Z

Output (Regulated) Voltage

V_Out = V_IN – I R
V_Out = V_IN – (I_Z + I_L)/R_S
V_Out = (V_IN – I_S)/R_S

Series Resistance

R_S = (V_L– V_out) / (I_Z + I_L) = (V_L– V_out)/(I_S)

Max Series Resistance

R_{S (MAX)} = R_{L (MIN)}x [(V_IN _(MIN) / V_Z) -1]

R_{S (MAX)} = R_{L (MIN)}x [(V_IN _(MIN) – V_Z)/I_L(MAX)]

Value of Resistor

R = [(V_IN _(MIN) – V_OUT)/(I_L + 10)]

Power of Resistor

R_P = (V_IN _(Max) – V_out)² / R

Power of Zener Diode

Z_P = (V_IN(MIN) – V_OUT) / R) x V_OUT

Output Ripple

V_R _(OUT) ≈ V_R _(IN) x (R_Z/R_S)

Diode Rectifier Equations:

A rectifier’s output contains DC as well as AC components, So;

Output DC Power:

P_dc= V_dc I_dc

Where

V_dcis the average output voltage
I_dcis the average output current

Output AC Power:

P_ac= V_rms I_rms

Where

V_rmsIs the rms of output voltage
I_rmsis the rms of output current

Rectifier Efficiency:

The efficiency of the rectifier denote by η is given by:

Where

P_dcis the output DC power
P_acis the output AC power

Output AC Voltage:

The rms of AC component of the output voltage is:

Form Factor:

The ratio of RMS voltage to the average dc voltage,

Ripple Factor:

It’s the ratio between the AC and DC component of the rectifier. It shows the purity of the DC output.