The diode and its applications

Explain what it means to rectify an alternating current and how half-wave and full-wave rectification differ: how many input half-cycles are used in each case, what the output voltage waveform looks like for each, and which of the two delivers more energy to the load.

A sinusoidal voltage of $12\ \text{V}$ RMS is half-wave rectified using a silicon diode (threshold of $0{,}7\ \text{V}$). a) Calculate the peak value of the input voltage. b) Calculate the peak voltage reached across the load. c) Calculate the average value of the output, given that for half-wave $V_{med} = \frac{V_{max}}{\pi}$, and comment on the result.

In a diode bridge, two diodes always conduct simultaneously, so the output loses two threshold voltage drops. If the sinusoidal input has a peak value of $18\ \text{V}$, calculate the peak value of the rectified output and explain, following the current path, why in each half-cycle it passes through two different diodes in the bridge.

A capacitor is connected in parallel with the load after a bridge rectifier. Explain how this smoothing capacitor works: when it charges, when it discharges into the load, what the ripple voltage is, and what happens to the ripple if the equipment draws more current.

In a power supply with a bridge rectifier and smoothing capacitor, explain qualitatively how the ripple changes when: (a) the capacitance of the capacitor is doubled; (b) the current drawn by the load is doubled; (c) it is changed from half-wave to full-wave while keeping everything else the same. Reason each answer using the charging and discharging times of the capacitor between peaks.

An installer claims that to power a purely resistive load of $150\ \Omega$ from a sinusoidal voltage of $12\ \text{V}$ peak and $50\ \text{Hz}$, it makes no difference whether a half-wave rectifier or a full-wave bridge rectifier is used, arguing that by connecting a sufficiently large filter capacitor "both options deliver the same average voltage with identical ripple". Assuming ideal diodes, refute their claim by solving:

1. a) Determine the ripple frequency and the time during which the capacitor must sustain the load current between successive recharge peaks for each of the two topologies.
2. b) Analytically calculate the capacitance $C$ required in each case so that the peak-to-peak ripple voltage does not exceed $5\,\%$ of the maximum value ($V_{\text{ripple}} \le 0{,}6\ \text{V}$).
3. c) Compare the resulting average voltage and the peak inverse voltage ($PIV$) that each diode must withstand in both configurations, and write a technical conclusion explaining why half-wave rectification is ruled out in power supplies of any significant power rating.

The Zener diode operates deliberately in the breakdown region. Explain which bias orientation it is connected in within a regulator circuit, what voltage it maintains across its terminals while regulating, and what happens if it is connected the other way round (forward-biased). What is this property used for?

An unregulated power supply delivers $15\ \text{V}$ and a circuit needs to be powered at $5{,}1\ \text{V}$ using a Zener diode. The load draws $30\ \text{mA}$ and the Zener requires at least $5\ \text{mA}$ to regulate properly. a) Calculate the current that must flow through the series resistor. b) Calculate its value using $R = \frac{V_{ent} - V_Z}{I}$ and select the nearest commercial value.

The figure shows a Zener diode regulator. a) Calculate the series resistance $R$, marked with the question mark, so that with the load connected there is at least the indicated Zener current of $5\ \text{mA}$. b) Calculate the current flowing through the Zener if the load is disconnected and reason why this is its worst-case scenario. c) Calculate the power dissipated by the Zener in this case and comment on whether a $0{,}5\ \text{W}$ Zener is suitable.

A Zener regulator powers a load that varies between $10\ \text{mA}$ and $40\ \text{mA}$. The power supply delivers $12\ \text{V}$ and the Zener is rated at $5{,}1\ \text{V}$ and $1\ \text{W}$, requiring a minimum of $5\ \text{mA}$ to regulate. a) Calculate the series resistor that guarantees regulation in the worst-case scenario (maximum load). b) Check that with the minimum load the Zener does not exceed its maximum power. c) Explain what happens if the load exceeds the maximum design value.

An LED is a diode that emits light when forward-conducting. Explain the voltage drop across it when conducting according to its colour (typical values: about $1{,}8\ \text{V}$ for red and about $3{,}4\ \text{V}$ for blue or white) and reason why an LED should never be connected to a power supply without a series resistor.

A red LED ($2\ \text{V}$, $15\ \text{mA}$) is to be connected to a $9\ \text{V}$ battery. a) Calculate the protective resistance using $R = \frac{V_{cc} - V_{LED}}{I}$. b) Choose the next highest standard preferred value, calculate the actual current that will flow, and comment on whether the LED is well protected.

A blue LED rated at $3{,}2\ \text{V}$ is powered from $5\ \text{V}$ with a resistor of $150\ \Omega$. a) Calculate the current in the circuit. b) Calculate the power dissipated in the resistor and in the LED. c) Explain what happens if it is replaced by a red LED rated at $1{,}9\ \text{V}$ keeping the same resistor.

For signaling in a piece of equipment connected to $12\ \text{V}$, two indicators are available: a green LED ($V_{D1} = 2{,}1\ \text{V}$, recommended nominal current $10\ \text{mA}$) and a red LED ($V_{D2} = 1{,}9\ \text{V}$, recommended nominal current $20\ \text{mA}$). A technician proposes saving space by connecting both LEDs in parallel and using a single series limiting resistor calculated for the combined current of $30\ \text{mA}$.

1. a) Analytically refute the technician's proposal using the diode threshold model: explain what voltage will be set across the parallel junction, which diode will take virtually all the current, and why the other will remain off.
2. b) Design the correct circuit using independent branches from the $12\ \text{V}$ supply: calculate the theoretical resistance for each diode, select the most suitable commercial value from the E12 series ($\pm 5\,\%$), and calculate the actual current that will flow through each LED with that commercial value.
3. c) Determine the power dissipated by each resistor during continuous operation and select for each one the standardized commercial power rating ($1/8\ \text{W}$, $1/4\ \text{W}$, $1/2\ \text{W}$, or $1\ \text{W}$) that ensures operation with a safety factor of at least $50\,\%$.