Rectifiers, Zener Diodes and Light Devices: Quick Revision

A brief note on Rectifiers, Zener Diodes and Light Devices. Read it before a test. Try each question at the end before you open its answer.

Rectifiers

• Half-wave, ideal: $V_{dc} = \dfrac{V_m}{\pi}$, $V_{rms} = \dfrac{V_m}{2}$, $r = 1.21$, $\eta = 40.6\ \%$, ripple frequency $f$, PIV $= V_m$.
• Full-wave, ideal: $V_{dc} = \dfrac{2V_m}{\pi}$, $V_{rms} = \dfrac{V_m}{\sqrt{2}}$, $r = 0.48$, $\eta = 81.2\ \%$, ripple frequency $2f$.
• PIV: $V_m$ for the bridge, $2V_m$ for the centre-tap circuit, and about $2V_m$ for a half-wave circuit with a large capacitor.
• Diode drops: a silicon bridge loses $1.4$ V, a centre-tap rectifier loses $0.7$ V.
• Capacitor filter: $\Delta V = \dfrac{I}{f_r C}$, $V_{dc} \approx V_p - \dfrac{\Delta V}{2}$, $r = \dfrac{\Delta V}{2\sqrt{3}\, V_{dc}}$.

The Zener regulator

• Breakdown: a Zener diode works in reverse breakdown at a fixed $V_z$. The Zener effect is below about $5$ V and avalanche is above about $7$ V.
• Currents: $I_s = \dfrac{V_{in} - V_z}{R_s}$, $I_L = \dfrac{V_z}{R_L}$, $I_z = I_s - I_L$.
• Limits: $I_{z,min} \le I_z \le I_{z,max} = \dfrac{P}{V_z}$.
• Series resistor: $\dfrac{V_{in,max} - V_z}{I_{z,max} + I_{L,min}} \le R_s \le \dfrac{V_{in,min} - V_z}{I_{z,min} + I_{L,max}}$.

Light devices

• LED: forward biased, $\lambda = \dfrac{1240\ \text{eV nm}}{E_g}$, series resistor $R = \dfrac{V_s - V_f}{I}$.
• Photodiode: reverse biased, the photocurrent follows the intensity, $I = \eta\,\dfrac{P}{E}$.
• Solar cell: no bias, $P_{max} = FF \times V_{oc} I_{sc}$, efficiency $= \dfrac{P_{max}}{G A}$.

A worked example

A $6.8$ V Zener diode has $R_s = 100\ \Omega$ and a load of $1.0\ \text{k}\Omega$. The input is $12$ V. Find $I_z$.

1. The series current. $I_s = \dfrac{12\ \text{V} - 6.8\ \text{V}}{100\ \Omega} = 52$ mA.
2. The load current. $I_L = \dfrac{6.8\ \text{V}}{1000\ \Omega} = 6.8$ mA.
3. The Zener current. $I_z = 52\ \text{mA} - 6.8\ \text{mA} = 45.2$ mA.

Practise with new numbers

Check yourself

1. Why is the PIV of a half-wave circuit with a large capacitor about $2V_m$?

2. A regulator has no load. Where does the series current go?

3. Why does a photodiode work in reverse bias, and a solar cell with no bias?

Sources

• NCERT Physics Class 12, Semiconductor Electronics: Materials, Devices and Simple Circuits.
• Horowitz and Hill, The Art of Electronics, third edition.