Exercises: The diode and its applications

A silicon diode can be in three situations: (a) forward-biased above its threshold voltage, (b) forward-biased below the threshold, (c) reverse-biased. Match each situation with its behaviour — it conducts a significant current with a drop of about $0{,}7\ \text{V}$ across it; it hardly conducts even though the anode is more positive than the cathode; it does not conduct except for a negligible leakage current — and justify each match using the characteristic curve.

State whether these statements about a silicon diode are true or false, justifying each answer: (a) in forward bias it conducts no matter how small the applied voltage is; (b) in reverse bias it can withstand any voltage without damage; (c) once conducting, the voltage across its terminals remains approximately constant; (d) an ideal diode does not allow current to pass in either direction.

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 transformer feeds a resistive load through a single series diode. Draw the input sine wave and, underneath and on the same time scale, the waveform that appears across the load, explaining what happens in each half-cycle and why.

You can do it on paper and send a photo with your answer.

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.

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 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.

Match each component with its typical application and justify your choice: (a) 1N4007 rectifier diode, (b) Zener diode, (c) LED, (d) photodiode; with these applications: converting AC to DC, maintaining a constant voltage, light signalling on a display panel, and detecting the ambient light level.

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.

In a full-wave bridge rectifier, the alternating current source is connected to the top and bottom vertices of the bridge, and the load between the right vertex (positive terminal) and left vertex (negative terminal). The diodes are correctly oriented in the four branches: $D_1$ (upper left), $D_2$ (upper right), $D_3$ (lower right), and $D_4$ (lower left). a) State which two diodes conduct during the positive half-cycle of the input and which ones during the negative half-cycle. b) Calculate the peak value of the output if the input is $12\ \text{V}$ RMS and each conducting diode drops $0{,}7\ \text{V}$. c) Explain why the frequency of the output waveform is twice that of the input.

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 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.

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.

You need to power a sensor that requires a stabilized DC voltage of $9\ \text{V}$ from the Spanish electrical grid ($230\ \text{V}_{\text{eff}}$, $50\ \text{Hz}$). In the workshop, you have three step-down transformers with secondary voltages of $6\ \text{V}_{\text{eff}}$, $12\ \text{V}_{\text{eff}}$, and $24\ \text{V}_{\text{eff}}$, silicon bridge rectifiers ($V_D = 0{,}7\ \text{V}$ per diode), electrolytic capacitors, and $9\ \text{V}$ Zener diodes.

1. a) Draw the complete electrical schematic of the power supply identifying its four stages and justify the technical function of each one to obtain DC from the AC mains.
2. b) Analytically justify which of the three transformers is suitable to ensure that at least $13\ \text{V}$ DC is available at the Zener input prior to regulation (taking into account the actual drop across the bridge and the peak charge of the filter), ruling out the other two due to voltage deficiency or due to overheating and excessive thermal dissipation.
3. c) Calculate the peak inverse voltage ($PIV$) that each diode of the bridge must withstand with the selected transformer.

In a diode bridge, one of the four diodes blows and becomes an open circuit. Analyse the consequences: which half-cycles now reach the load, what shape the output voltage waveform has, by approximately how much its average value is reduced compared to normal operation, and why the ripple worsens even though the smoothing capacitor remains the same.

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.

Design a complete Zener regulator: a supply of $18\ \text{V}$ is available to power a $12\ \text{V}$ circuit that draws between $5\ \text{mA}$ and $25\ \text{mA}$. Choose the Zener voltage, set its minimum current to $10\ \text{mA}$, calculate the series resistor, choose an E12 preferred value, and check the maximum power dissipated by both the Zener (with minimum load) and the resistor.

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 figure shows a symmetrical wave-shaping and clipping circuit consisting of a series resistor $R$ and two identical back-to-back Zener diodes ($V_Z = 3{,}3\ \text{V}$ and $V_D = 0{,}7\ \text{V}$ in forward conduction), along with the oscillograms of the input sinusoidal voltage $v_e(t)$ and the output voltage $v_s(t)$.

1. a) Reasonably analyze the operating state (forward conduction, cutoff, or Zener breakdown) of each of the two diodes during the positive half-cycle and during the negative half-cycle of the input signal.
2. b) Quantitatively determine the symmetrical saturation levels marked with a question mark "?" in the oscillogram.
3. c) Justify the essential role played by resistor $R$ and predict what immediate consequences the diodes and the source would suffer if it were removed and replaced by a short circuit.
4. d) Predict how the waveform of the output voltage $v_s(t)$ would change if, due to a fault or an assembly error, the bottom Zener were replaced by a standard silicon rectifier diode ($V_D = 0{,}7\ \text{V}$).

On the test bench, you are inspecting four $12\ \text{V}$ linear power supplies (with an input fuse, step-down transformer, silicon bridge rectifier, electrolytic capacitor, and integrated regulator) that have shown anomalies during testing under nominal load:

1. In supply A, the output voltage is $12\ \text{V}$, but the oscilloscope shows an abnormally high $100\ \text{Hz}$ ripple (several volts peak-to-peak) across the capacitor terminals that causes the regulator to drop out of stabilization at the troughs of the wave.

2. In supply B, there is no output voltage and the mains fuse blows immediately every time the main switch is turned on.

3. In supply C, the average voltage before the regulator has dropped to approximately half its design value and the oscilloscope detects that the fundamental ripple frequency is $50\ \text{Hz}$ instead of the expected $100\ \text{Hz}$.

4. In supply D, the regulated $12\ \text{V}$ voltage and the ripple are correct, but the output indicator LED remains off.

For each of the four power supplies:

1. a) Deduce and identify the damaged component and the most likely failure mode (short circuit, open circuit, or degradation).
2. b) Justify the physical and circuit mechanism that produces the measured symptoms.
3. c) Describe the verification procedure using a multimeter (quantity, scale, and circuit powered on/off conditions) to conclusively confirm each diagnosis.

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 $50\,\%$.