Block 12 — Diode Applications

Learning objectives

90-minute plan

• Warm-up (10 min):
  • What happens if an LED is connected directly to \(24~{\rm V}\)?
  • Recall from Block 11: diode polarity, forward voltage, reverse blocking.
  • Recall from switching transients: inductor current cannot jump.

• Core concepts (55 min):
  • LED operation with a series resistor.
  • Z-diode voltage limitation and stabilization.
  • Freewheeling diode for inductive loads.
  • Clamp diodes for sensitive inputs.
  • Diode rectifiers: M1, M2, B2.
  • Capacitor smoothing and ripple.

• Practice (20 min):
  • Calculate an LED series resistor.
  • Check Z-diode current limits.
  • Estimate switching overvoltages in an inductive load.
  • Calculate average rectifier voltages and smoothing capacitors.

• Wrap-up (5 min):
  • Which diode application belongs to which engineering problem?
  • Preview: bipolar transistors as controlled switches and amplifiers.

Conceptual overview

Core content

LED with series resistor

An LED is operated in forward direction. It converts part of the electrical energy into light.

For a supply voltage \(U_{\rm E}\), an LED forward voltage \(U_{\rm F}\), and a desired LED current \(I_{\rm F}\), the series resistor is

\[ \begin{align*} \boxed{ R_{\rm V} = \frac{U_{\rm E}-U_{\rm F}}{I_{\rm F}} } \end{align*} \]

The resistor power is

\[ \begin{align*} P_R = (U_{\rm E}-U_{\rm F})I_{\rm F} = R_{\rm V}I_{\rm F}^2. \end{align*} \]

The LED power is approximately

\[ \begin{align*} P_{\rm LED} = U_{\rm F}I_{\rm F}. \end{align*} \]

<tabcaption tab_led_values|Typical LED values for first estimates>

LED operation with AC voltage

LEDs tolerate only small reverse voltages. Therefore, operation directly at AC voltage needs protection.

A second diode can be placed antiparallel to the LED. Then, during the reverse half-wave, the normal diode conducts and limits the reverse voltage across the LED.

Z-diode voltage limitation and stabilization

A Z-diode is operated in reverse breakdown. In its working range, the voltage is approximately constant:

\[ \begin{align*} u_{\rm Z}\approx U_{\rm Z}. \end{align*} \]

The input current through the series resistor is

\[ \begin{align*} I_{\rm V} = \frac{U_{\rm E}-U_{\rm Z}}{R_{\rm V}}. \end{align*} \]

The load current is

\[ \begin{align*} I_{\rm L} = \frac{U_{\rm Z}}{R_{\rm L}}. \end{align*} \]

The Z-diode current is

\[ \begin{align*} \boxed{ I_{\rm Z} = I_{\rm V}-I_{\rm L} } \end{align*} \]

and must stay in the allowed operating range:

\[ \begin{align*} I_{\rm Z,min} \leq I_{\rm Z} \leq I_{\rm Z,max}. \end{align*} \]

The power limit is

\[ \begin{align*} P_{\rm Z} = U_{\rm Z}I_{\rm Z} \leq P_{\rm tot}. \end{align*} \]

Freewheeling diode for inductive loads

Inductors resist a sudden change of current:

\[ \begin{align*} u_L=L\frac{{\rm d}i_L}{{\rm d}t}. \end{align*} \]

If a relay coil, solenoid, or small motor is switched off, the current tries to continue flowing. Without a safe current path, the voltage can become very large.

When the switch is opened, the freewheeling diode becomes forward-biased. The inductor current circulates through the diode and the coil.

The magnetic energy stored in the inductance is

\[ \begin{align*} W_L = \frac{1}{2}LI_0^2. \end{align*} \]

With a freewheeling diode, the switch voltage is limited to a safe value. The disadvantage is that the current decays more slowly, so a relay or solenoid may release more slowly.

Clamp diodes for sensitive inputs

Microcontroller and sensor inputs tolerate only a limited voltage range. Clamp diodes can conduct disturbances away from the sensitive input.

For a \(5~{\rm V}\) input, the input node is often clamped approximately to

\[ \begin{align*} -0.7~{\rm V} \lesssim u_{\rm in} \lesssim 5.7~{\rm V}. \end{align*} \]

The resistor \(R_{\rm V}\) limits the clamp current:

\[ \begin{align*} I_{\rm clamp} \approx \frac{U_{\rm disturb}-U_{\rm clamp}}{R_{\rm V}}. \end{align*} \]

Half-wave rectifier M1

A rectifier converts an AC voltage into a unidirectional voltage.

Assumptions for the basic formulas:

• sinusoidal input voltage,
• RMS value \(U_\sim\),
• ohmic load,
• ideal diode.

For a half-wave rectifier:

\[ \begin{align*} \boxed{ U_{\rm di} = \frac{\sqrt{2}}{\pi}U_\sim } \end{align*} \]

The ripple frequency is

\[ \begin{align*} f_\sigma=f. \end{align*} \]

The ripple factor for the ideal M1 circuit is

\[ \begin{align*} w_U = \frac{U_\sigma}{U_{\rm di}} \approx 1.21. \end{align*} \]

Center-tap rectifier M2 and bridge rectifier B2

A full-wave rectifier uses both half-waves.

For the center-tap rectifier M2:

\[ \begin{align*} U_{\rm di} = \frac{2\sqrt{2}}{\pi}U_{1{\rm N}} = \frac{\sqrt{2}}{\pi}U_{\rm S}. \end{align*} \]

Here \(U_{1{\rm N}}\) is the RMS voltage of one half of the secondary winding and \(U_{\rm S}\) is the RMS voltage of the full secondary winding.

For the bridge rectifier B2:

\[ \begin{align*} \boxed{ U_{\rm di} = \frac{2\sqrt{2}}{\pi}U_\sim } \end{align*} \]

The ripple frequency is

\[ \begin{align*} f_\sigma=2f. \end{align*} \]

The ideal ripple factor is

\[ \begin{align*} w_U\approx 0.48. \end{align*} \]

<tabcaption tab_rectifier_summary|Comparison of simple rectifier circuits>

Capacitor smoothing

A rectifier output is not constant. A smoothing capacitor stores charge near the voltage maximum and supplies the load between maxima.

For a bridge rectifier with a sufficiently large smoothing capacitor, the DC voltage is approximately

\[ \begin{align*} U_{\rm di} \approx \sqrt{2}U_\sim \end{align*} \]

for ideal diodes and small ripple.

With real silicon diodes in a bridge rectifier:

\[ \begin{align*} U_{\rm di} \approx \sqrt{2}U_\sim - 2U_{\rm TO} - \frac{\Delta U}{2}. \end{align*} \]

Here \(\Delta U\) is the approximate peak-to-peak ripple voltage.

A simple estimate for the smoothing capacitor is

\[ \begin{align*} \boxed{ C \approx \frac{I_{\rm d}}{f_\sigma\Delta U} } \end{align*} \]

with

• \(I_{\rm d}\): load current,
• \(f_\sigma\): ripple frequency,
• \(\Delta U\): allowed peak-to-peak ripple voltage.

Application overview

<tabcaption tab_diode_applications|Typical diode applications in mechatronics and robotics>

Exercises

Common pitfalls

• Connecting LEDs without current limitation: The LED current can become destructive.
• Forgetting resistor power: In \(24~{\rm V}\) control cabinets, LED resistors can dissipate noticeable heat.
• Using a Z-diode without load-current check: The Z-current must remain between \(I_{\rm Z,min}\) and \(I_{\rm Z,max}\).
• Using clamp diodes without a series resistor: The clamp current must be limited.
• Thinking the freewheeling diode removes energy instantly: It gives the current a safe path, but turn-off may become slower.
• Ignoring diode drops in bridge rectifiers: Two diodes conduct at the same time.
• Confusing RMS and peak values: A \(12~{\rm V}\) RMS sine has a peak value of about \(17~{\rm V}\).
• Assuming a smoothing capacitor creates perfect DC: The output still has ripple and charging-current pulses.
• Using capacitor formulas without checking ratings: Check voltage rating, ripple current, polarity, and inrush current.

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