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Semiconductor Electronics - Diode as a Rectifier

Grade 12CBSEPhysics

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Rectification: It is the process of converting alternating current (ACAC), which reverses its direction periodically, into direct current (DCDC), which flows in a single direction. A p−np-n junction diode is used for this purpose because it allows current to flow only when it is forward biased.

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Half-Wave Rectifier: Uses a single diode. It conducts only during the positive half-cycle of the ACAC input and blocks the negative half-cycle. The output is pulsating DCDC with a ripple frequency equal to the input frequency (fout=finf_{out} = f_{in}).

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Full-Wave Rectifier: Typically uses two diodes connected to a center-tapped transformer. One diode conducts during the positive half-cycle and the other during the negative half-cycle, ensuring current flows through the load in the same direction for both cycles. The ripple frequency is twice the input frequency (fout=2finf_{out} = 2f_{in}).

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Efficiency (η\eta): For a Half-Wave Rectifier, the maximum theoretical efficiency is 40.6%40.6\%, whereas for a Full-Wave Rectifier, it is 81.2%81.2\%.

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Filter Circuits: The output of a rectifier contains ACAC components called ripples. A capacitor connected in parallel to the load or an inductor in series is used to filter out these ripples to produce a steady DCDC voltage. A capacitor filters by bypassing ACAC components due to its low reactance XC=12πfCX_C = \frac{1}{2\pi f C} at high frequencies.

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Peak Inverse Voltage (PIV): The maximum reverse bias voltage a diode can withstand without breakdown. For a Half-Wave Rectifier, PIV=VmPIV = V_m; for a Center-Tapped Full-Wave Rectifier, PIV=2VmPIV = 2V_m.

📐Formulae

Idc=Imπ (Half-Wave Rectifier)I_{dc} = \frac{I_m}{\pi} \text{ (Half-Wave Rectifier)}

Idc=2Imπ (Full-Wave Rectifier)I_{dc} = \frac{2I_m}{\pi} \text{ (Full-Wave Rectifier)}

Vdc=Vmπ (Half-Wave Rectifier)V_{dc} = \frac{V_m}{\pi} \text{ (Half-Wave Rectifier)}

Vdc=2Vmπ (Full-Wave Rectifier)V_{dc} = \frac{2V_m}{\pi} \text{ (Full-Wave Rectifier)}

fripple(HWR)=finf_{ripple(HWR)} = f_{in}

ηmax(HWR)=0.406RLrd+RL≈40.6%\eta_{max(HWR)} = \frac{0.406 R_L}{r_d + R_L} \approx 40.6\%

ηmax(FWR)=0.812RLrd+RL≈81.2%\eta_{max(FWR)} = \frac{0.812 R_L}{r_d + R_L} \approx 81.2\%

fripple(FWR)=2finf_{ripple(FWR)} = 2f_{in}

💡Examples

Problem 1:

A Full-Wave Rectifier uses a center-tapped transformer. If the input ACAC supply frequency is 50 Hz50\text{ Hz}, calculate the ripple frequency of the output. If the peak voltage of the ACAC signal is 20 V20\text{ V}, what is the DCDC output voltage (neglecting diode resistance)?

Solution:

  1. Ripple frequency for a Full-Wave Rectifier is fout=2×finf_{out} = 2 \times f_{in}. Given fin=50 Hzf_{in} = 50\text{ Hz}, fout=2×50=100 Hzf_{out} = 2 \times 50 = 100\text{ Hz}.
  2. The DCDC output voltage VdcV_{dc} for a Full-Wave Rectifier is given by Vdc=2VmπV_{dc} = \frac{2V_m}{\pi}. Given Vm=20 VV_m = 20\text{ V}, Vdc=2×203.14≈12.74 VV_{dc} = \frac{2 \times 20}{3.14} \approx 12.74\text{ V}.

Explanation:

The ripple frequency is doubled in a full-wave rectifier because the output pulse occurs for every half-cycle of the input. The DCDC value is the average value of the rectified sine wave over a full cycle.

Problem 2:

Why is a capacitor used in a filter circuit of a rectifier? How does its value affect the 'ripple factor'?

Solution:

A capacitor is connected in parallel with the load resistance RLR_L. It stores charge during the rising part of the voltage cycle and discharges through the load when the rectified voltage falls. Its reactance is XC=12πfCX_C = \frac{1}{2\pi f C}. For a large capacitance CC, XCX_C is small for ACAC components, allowing them to pass through the capacitor, while DCDC is blocked and forced through RLR_L. A higher value of CC results in a smaller ripple factor and a smoother DCDC output.

Explanation:

The ripple factor is inversely proportional to the capacitance CC and the load resistance RLR_L. Increasing either reduces the fluctuations in the output voltage.

Diode as a Rectifier - Revision Notes & Key Formulas | CBSE Class 12 Physics